![(a) Example of typical THz traces acquired at different positions across the sample in Fig. 3(a). (b) Amplitude of the electric field at t 0 = 27.6 ps : E x , y ( t 0 ) . (c) Normalized amplitude of the main peak: max ( | E x , y ( t ) | ) / max ( | E ref ( t ) | ) . (d) Delay of the main peak relative to a reference peak: t { max [ | E x , y ( t ) | ] } − t { max [ | E ref ( t ) | ] } .](https://www.researchgate.net/profile/Hichem-Guerboukha/publication/328966527/figure/fig4/AS:11431281253558419@1718920462348/aExample-of-typical-THz-traces-acquired-at-different-positions-across-the-sample-in_Q320.jpg)
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Toward real-time terahertz
imaging
HICHEM GUERBOUKHA,
1,2
KATHIRVEL NALLAPPAN,
1
AND MAKSIM SKOROBOGATIY
1,*
1Engineering Physics, Polytechnique de Montréal, C. P. 6079, succ. Centre-ville, Montréal,
Quebec H3C 3A7, Canada
2e-mail: hichem.guerboukha@polymtl.ca
*Corresponding author: maksim.skorobogatiy@polymtl.ca
Received May 2, 2018; revised August 31, 2018; accepted September 21, 2018; published
November 15, 2018 (Doc. ID 330724)
Terahertz (THz) science and technology have greatly progressed over the past two decades
to a point where the THz region of the electromagnetic spectrum is now a mature research
area with many fundamental and practical applications. Furthermore, THz imaging is posi-
tioned to play a key role in many industrial applications, as THz technology is steadily
shifting from university-grade instrumentation to commercial systems. In this context, the
objective of this review is to discuss recent advances in THz imaging with an emphasis on
the modalities that could enable real-time high-resolution imaging. To this end, we first
discuss several key imaging modalities developed over the years: THz transmission, re-
flection, and conductivity imaging; THz pulsed imaging; THz computed tomography; and
THz near-field imaging. Then, we discuss several enabling technologies for real-time THz
imaging within the time-domain spectroscopy paradigm: fast optical delay lines, photo-
conductive antenna arrays, and electro-optic sampling with cameras. Next, we discuss the
advances in THz cameras, particularly THz thermal cameras and THz field-effect transis-
tor cameras. Finally, we overview the most recent techniques that enable fast THz imaging
with single-pixel detectors: mechanical beam-steering, compressive sensing, spectral en-
coding, and fast Fourier optics. We believe that this critical and comprehensive review of
enabling hardware, instrumentation, algorithms, and potential applications in real-time
high-resolution THz imaging can serve a diverse community of fundamental and applied
scientists. © 2018 Optical Society of America
https://doi.org/10.1364/AOP.10.000843
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845
2. Terahertz Imaging: Methods and Applications. . . . . . . . . . . . . . . . . . . . 848
2.1. Imaging with a THz Time-Domain Spectroscopy System . . . . . . . . . 848
2.2. THz Transmission, Reflection, and Conductivity Imaging. . . . . . . . . 851
2.2a. Transmission Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 852
2.2b. Reflection Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 854
2.2c. Conductivity Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854
2.3. THz Pulsed Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857
2.4. THz Computed Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859
2.5. THz Near-Field Imaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 843
2.5a. THz Aperture Near-Field Optical Microscopy . . . . . . . . . . . . . 865
2.5b. THz Scattering Near-Field Optical Microscopy . . . . . . . . . . . . 866
3. Enabling Real-Time THz-TDS Imaging . . . . . . . . . . . . . . . . . . . . . . . . 867
3.1. Coherent THz Generation and Detection THz-TDS . . . . . . . . . . . . . 868
3.1a. Photoconductive Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . 868
3.1b. Optical Rectification and Electro-Optic Sampling . . . . . . . . . . 869
3.2. Fast Optical Delay Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871
3.2a. Rotary Reflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872
3.2b. Rotary Prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873
3.2c. Non-Mechanical Time-Domain Sampling . . . . . . . . . . . . . . . . 875
3.3. Photoconductive Antenna Arrays . . . . . . . . . . . . . . . . . . . . . . . . . 878
3.4. EOS with Visible/Infrared Cameras . . . . . . . . . . . . . . . . . . . . . . . 879
3.4a. Dynamic Subtraction and Balanced Electro-Optic Detection in a
Camera....................................... 879
3.4b. Real-Time Near-Field EOS Imaging . . . . . . . . . . . . . . . . . . . 879
3.4c. Temporal Encoding in the Camera . . . . . . . . . . . . . . . . . . . . 882
3.5. Section Summary and Future Directions . . . . . . . . . . . . . . . . . . . . 882
4. THz Cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885
4.1. THz Thermal Cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885
4.2. THz Field-Effect Transistor-Based Cameras . . . . . . . . . . . . . . . . . . 888
4.3. Section Summary and Future Directions . . . . . . . . . . . . . . . . . . . . 892
5. THz Imaging with Single-Pixel Detectors. . . . . . . . . . . . . . . . . . . . . . . 893
5.1. Mechanical Beam Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893
5.1a. Oscillating Mirror with an f-Theta Scanning Lens . . . . . . . . . . 893
5.1b. Gregorian Reflector System . . . . . . . . . . . . . . . . . . . . . . . . . 895
5.2. Single-Pixel Imaging and Compressive Sensing . . . . . . . . . . . . . . . 896
5.2a. THz Imaging with Compressive Sensing . . . . . . . . . . . . . . . . 898
5.2b. Optical Spatial Light Modulation and Near-Field Imaging . . . . 900
5.2c. Metamaterial-Based SLM and Multiplexed Mask Encoding. . . . 902
5.3. Spectral/Temporal Encoding and Fourier Optics . . . . . . . . . . . . . . . 904
5.3a. Spectral and Temporal Encoding. . . . . . . . . . . . . . . . . . . . . . 904
5.3b. Fourier Optics and k-Space/Frequency Duality . . . . . . . . . . . . 906
5.4. Section Summary and Future Directions . . . . . . . . . . . . . . . . . . . . 912
6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 913
Funding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915
844 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
Toward real-time terahertz
imaging
HICHEM GUERBOUKHA,KATHIRVEL NALLAPPAN,
AND MAKSIM SKOROBOGATIY
1. INTRODUCTION
Science and technology behind modern day imaging have come a long way since the
invention of the photography in the 1800s. In the same century, many great minds
devoted their energy to comprehend the nature of light, culminating in the famous
theory of electromagnetism summarized in Maxwell’s equations. Today, it is taken
for granted that light is an electromagnetic wave, and that visible light constitutes
only a very small portion of the electromagnetic spectrum. In the 20th century, im-
aging moved far beyond the visible spectral range, resulting in the development of
many novel imaging techniques, from x-ray radiography that uses waves of subatomic
size to radars that employ waves as large as several meters.
Currently, many parts of the electromagnetic spectrum are being widely used for
countless applications. This review is dedicated to only a small part of the electro-
magnetic spectrum in rapid development—the terahertz (THz) range. While there
is no unique definition of the THz band, it is generally considered to cover the range
of frequencies from 0.1 to 10 THz, having respective wavelengths from 3 mm down to
30 μm (Fig. 1). Today, research in application of THz waves constitutes a very
dynamic and multidisciplinary field in rapid development, with many fundamental
discoveries being made and practical applications identified [1,2]. At the junction be-
tween microwaves and infrared, the THz range shares many of their properties and
potential applications. For example, as a natural extension of microwaves, it is seen by
many as the next frontier in wireless communications, promising higher data
transmission rates to answer the ever-increasing demand for information transfer
capacity [3–7].
In the field of sensing and imaging, THz radiation offers unique means to interrogate
matter [8]. Like microwaves, THz is capable of penetrating most dielectric materials,
revealing inner structures with meaningful contrast. However, different from micro-
waves, the THz wavelength is sufficiently small to also provide much higher image
resolution. Furthermore, many molecular species have unique spectral fingerprints in
the THz range. Already, these advantages have been used in multiple fields: industrial
environments [9,10]; the pharmaceutical [11,12] and biomedical [13–16] sectors; the
agri-food industry [17–19]; defense and security [20,21]; art conservation [22,23]; etc.
We start our review by summarizing in Table 1some of the most promising commer-
cial sources of THz radiation. For real-time imaging, an intense THz source is clearly
beneficial when active illumination of the sample is required. The wavelength of the
source is also an important factor as image spatial resolution is directly related to the
wavelength of light used in illumination.
Similarly, there are many choices today for detection of THz radiation. Such detectors
range widely in their physical operation principles and sensitivities, ranging from ther-
mal bolometers to solid-state transistors. At the same time, with few exceptions, most
commercially available detectors, particularly those offering coherent detection,
currently come as single-pixel devices. Furthermore, some achieve exceptional sen-
sitivities, at the cost of cryogenic cooling. In the context of THz imaging, important
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 845
research effort is currently concentrated toward the development of sensitive multi-
pixel THz cameras operating at room temperatures (see Table 2for a list of uncooled
detectors). While coherent detection is probably too much to hope for in the short
term, we nevertheless foresee considerable improvement of the sensitivities and
the frame rates of THz cameras, taking advantage of existing microfabrication tech-
nology to enable scalability and lower fabrication costs. For more detailed reviews of
THz detectors, we suggest several recent publications on this subject [71–73].
As surprising as it may seem, the lack of THz cameras did not impede the develop-
ment of many ingenious relatively fast and high-resolution THz imaging modalities.
In fact, many such imaging techniques cannot be realized using existing THz cameras
as they rely on frequency-/time-resolved and field-resolved measurements. The most
obvious example is imaging using a THz time-domain spectroscopy system
Table 1. Typical THz Sources for Off-the-Shelf Imaging Applications
Source and Emission Principle Mode Frequency Power References
Diode-based frequency multiplier
Frequency multiplication of microwave source
(e.g., Gunn/IMPATT diodes) with Schottky diode
CW tunable <2 THz ++ [24]
Backward wave oscillator
Backward acceleration of an electron beam in a
corrugated traveling wave-tube under vacuum
CW tunable <1 THz +++ [25–27]
Quantum cascade laser
Cascade of electrons in intersubband transitions
by engineered quantum well heterostructures
CW pulsed ∼1−10 THz ++ [28–31]
Photomixer
Frequency difference through beating of two
optical frequencies in a semiconductor
CW tunable <3 THz +[32–34]
Difference frequency generation
Nonlinear polarization at the difference frequency
of two optical pump beams in a nonlinear crystal
CW tunable <4 THz +++ [35]
Parametric amplification and injection seeding
Second-order nonlinear conversion of a pump pulse into
two photons of lower energies (signal and idler)
CW tunable <3 THz +++ [36–39]
Photoconductive antenna (THz-TDS)
Ultrafast photoexcitation of charge carriers in a
biased semiconductor gap
Pulsed <3 THz ++ [40–46]
Optical rectification (THz-TDS)
Time-varying polarization proportional to the
picosecond envelope of a pumping ultrafast
optical pulse in a nonlinear crystal
Pulsed <6 THz ++ [47–51]
Figure 1
MicrowavesRadio waves Terahertz Infrared Visible Ultraviolet X-rays Gamma
(Hz) 10
8
10
9
10
10
10
11
10
12
10
13
10
14
10
15
10
16
10
17
10
18
10
19
10
20
3 m
300 mm
30 mm
3 mm
300 µm
30 µm
3 µm
300 nm
30 nm
3 nm
300 pm
30 pm
3 pm
Terahertz range in the electromagnetic spectrum.
846 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
(THz-TDS) that measures directly the electric field of a short THz pulse in time do-
main. In fact, historically, the first THz image was obtained using THz-TDS [74]. The
principal strength of this method comes from the fact that it provides a broadband
spectral image with both amplitude and phase information (Fig. 2). The principal
Table 2. Typical THz Detectors/Cameras Operating at Room Temperature
Detector Detection Principle NEPa
(pW∕ffiffiffiffiffiffi
Hz
p)
Array References
Thermal
Microbolometer Resistive change by thermal excitation ∼10–100 Possible
(Section 4.1)
[52–54]
Pyroelectric detector Polarization change by thermal
excitation of a pyroelectric crystal
∼10–1000 Possible
(Section 4.1)
[55–57]
Golay cell Pressure change by thermal
excitation of an encapsulated gas
∼100–1000 Single-pixel [58]
Mixer
Schottky-barrier diode High-frequency detection enabled
by fast switching speeds in
metal/semiconductor junction
∼10–100 Possible [59,60]
Plasmonic detector
Field-effect transistor Plasmonic excitation of electronic
charge densities in transistor channels
∼10–100 Possible
(Section 4.2)
[61–63]
Optically triggered (THz-TDS)
Photoconductive antenna Ultrafast photoexcitation of charge
carriers in a semiconductor gap
—Possible
(Section 3.3)
[40–46]
Electro-optic sampling Birefringence-induced by THz pulse
in nonlinear media
—Possible
(Section 3.4)
[64–68]
Air-biased-coherent-
detection (ABCD)
THz field-induced second harmonic
(TFISH) in plasma gas
—Single-pixel [69,70]
aThe noise-equivalent power (NEP) is defined as the input power that gives a signal-to-noise ratio of
1 with a 1 Hz output bandwidth. It is a measure of the minimum detectable power, and a lower NEP
indicates a more sensitive detector.
Figure 2
0 5 10 15 20 25 30
Time (ps)
-1
-0.5
0
0.5
1
1.5
Electric field (a.u.)
01234
Frequency (THz)
10-2
10-1
100
Amplitude (a.u.)
(a)
(b) (c)
01234
Frequency (THz)
-600
-400
-200
0
Phase (rad)
THz-TDS measurement. (a) A THz pulse in the time domain. (b) The corresponding
Fourier transform amplitude and (c) phase. The dips in the spectrum correspond to
absorption in water vapor.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 847
disadvantage of a classic THz-TDS approach is the necessity of a lengthy two-
dimensional (2D) raster scanning in order to obtain an image. This is in clear contrast
with THz cameras, which are fast, but limited to the measurement of some spectrally
averaged power distribution.
This review is dedicated to the means of achieving real-time THz imaging. The paper
is structured as follows. In Section 2, we first review many important THz imaging
modalities developed so far: THz transmission, reflection, and conductivity imaging;
THz pulsed imaging; THz computed tomography; and THz near-field imaging. In
addition to the presentation of those modalities, we also discuss their specific chal-
lenges toward real-time image acquisition. Then, in the following sections, we detail
various practical realizations of real-time THz imaging systems. In Section 3,we
begin by reviewing the fundamentals of THz-TDS and discuss several enabling tech-
nologies for real-time imaging: fast optical delay lines, photoconductive antennas
arrays, and electro-optic sampling with cameras. In Section 4, we review two major
candidates for real-time high-resolution imaging THz cameras. Particularly we review
recent progress in THz thermal cameras and THz field-effect transistor (FET)-based
cameras. Finally, in Section 5, we overview several promising techniques that enable
fast THz imaging with single-pixel detectors: mechanical beam-steering, compressive
sensing, spectral encoding, and fast Fourier optics. We believe that this critical and
comprehensive review of enabling hardware, instrumentation, mathematical algo-
rithms, and potential applications in real-time high-resolution THz imaging can serve
a diverse community of fundamental and applied scientists.
2. TERAHERTZ IMAGING: METHODS AND APPLICATIONS
In this section, we review several classical THz imaging techniques developed over
the past two decades. These techniques serve as a benchmark to the novel THz im-
aging methods that we will detail in the following chapters. Particularly, we discuss
the following THz imaging modalities: (1) Imaging with a THz-TDS; (2) THz trans-
mission, reflection, and conductivity imaging; (3) THz pulsed imaging; (4) THz com-
puted tomography; and (5) THz near-field imaging. In the context of this review, our
objective is to explain the relevant principles of image reconstruction and identify
various potential applications of THz imaging. We will also discuss their specific
challenges to achieve real-time image acquisition. Since each of the abovementioned
techniques has already been a subject of in-depth reviews in the past, we also refer the
reader to these publications.
2.1. Imaging with a THz Time-Domain Spectroscopy System
Historically, the THz time-domain spectroscopy system (THz-TDS) was one of the
first ways to measure THz radiation. In THz-TDS, broadband THz pulses are gen-
erated and detected using photoconductive antenna or nonlinear optical methods.
The generation and detection of THz pulses is detailed in Section 3.1. The strength
of the THz-TDS technique is in its ability to measure the amplitude and the phase of
the THz electric field in time domain.
We first discuss a classic way of obtaining an image using THz-TDS. As an example,
we use a THz-TDS in transmission mode and image a triangle made of high-density
polyethylene (HDPE), a star made of paper, and a metallic washer [Fig. 3(a)]. The
three samples are placed on top of a paper sheet surrounded by a metallic aperture
made of aluminum foil.
To obtain a 2D image, the sample is raster-scanned and individual traces are recorded
point by point in the focal plane of a pair of lenses or parabolic mirror that focuses a
pre-collimated THz beam [Fig. 3(b)]. The result is a three-dimensional (3D) data cube
848 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
with the third dimension being time. A Fourier transform is performed on the third
dimension to obtain a hyperspectral image, i.e., an image per THz frequency. To ex-
tract useful information and to create an image, a certain normalization must be used
to convert the raw one-dimensional (1D) time or frequency data into physically sig-
nificant values [75–77]. The normalization is chosen to enhance the image contrast
and is generally application dependent. It can also involve a reference measurement,
for example, a measurement through an empty system or an uncovered substrate.
Different examples of normalizations are presented in Fig. 4(time domain) and
Fig. 5(frequency domain).
Figure 3
(a)
THz
x
y
Air
Metal
Star (paper)
Triangle (HDPE)
Paper
(b)
(a) Photograph of the sample. (b) The sample was mechanically moved in the x,y
focal plane of a pair of lenses.
Figure 4
250
200
150
100
50
x (mm)
y (mm)
(b)
(c) (d)
1.5
1
0.5
0
-0.5
(a) Time (ps)
52035302
300
200
100
0
-100
Electric field (a.u.)
40
Triangle (HDPE)
Metal
Star (paper)
Paper
Air
t0
Amplitude at t0
Normalized peak amplitude Delay (ps) of the main peak
(a) Example of typical THz traces acquired at different positions across the sample in
Fig. 3(a). (b) Amplitude of the electric field at t027.6ps:Ex,yt0. (c) Normalized
amplitude of the main peak: maxjEx,ytj∕maxjEref tj. (d) Delay of the main peak
relative to a reference peak: tfmaxjEx,ytjg −tfmaxjEref tjg.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 849
In Fig. 4(a), typical THz pulses are shown for different positions in the sample. When
interacting with the sample, the THz pulse can be attenuated, delayed, or broadened.
In Visualization 1, we present an example of a 3D cube image as a function of time,
while in Fig. 4(b), we present a slice of this cube at t027.6ps. Visualizing the
electric field as a function of time reveals the irradiation dynamics at the picosecond
scale. A second common way of creating a THz image is to look at the maximum peak
in time domain, normalized by the maximum peak of a reference function [Fig. 4(c)].
Here, the reference is taken as the THz pulse measured in air. The result is an image
that provides information about the absorption, reflection, or scattering losses in the
material. For example, scattering losses are clearly observable at the borders of the
HDPE triangle. A third image can be obtained by mapping the time delay of the main
peak with respect to the reference measurement [Fig. 4(d)]. This allows us to map the
optical path change Δx,ynx,ydx,yacross the sample, which can then provide
material/thickness contrast. The temporal cross correlation of the two THz waveforms
(with and without the sample) can also be used to visualize the optical path
change [78].
By applying a Fourier transform on the third dimension of the data cube, one gets the
amplitude [Fig. 5(a)] and the phase [Fig. 5(b)] of the spectrum. The amplitude gives a
general indication of the losses, which, in general, increase with the frequency. The
phase is related to the optical path (the refractive index/thickness). When necessary, it
must be carefully unwrapped in regions of adequate signal-to-noise ratios (SNRs) to
avoid numerical artifacts. In Visualization 2, we present an example of a 3D data cube
as a function of frequency. In particular, the spatial resolution increases with the THz
frequency. In Fig. 5(c), we plot the amplitude at 0.475 THz, while the phase (wrapped
into a −πto πinterval) is shown in Fig. 5(d). The amplitude image shows the losses in
Figure 5
(c) (d)
Amplitude at 0Phase at 0
500
400
300
200
100
3
2
1
0
-1
-2
-3
Triangle (HDPE)
Metal
Star (paper)
Paper
Air
101
102
103
Amplitude (a.u.)
Frequency (THz)
0 0.2 0.4 0.6 0.8 1 1.2
Frequency (THz)
0 0.2 0.4 0.6 0.8 1 1.2
0
-50
-100
-150
-200
Unwrapped phase (rad)
(a) (b)
00
(a) Amplitude and (b) unwrapped phase of the spectrum at different positions across
the sample in Fig. 3(a). (c) Amplitude and (d) phase images at ν00.475 THz.
850 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
the material, which are maximal for the propagation through the metallic washer.
Again, scattering losses are observable at the borders of the HDPE triangle. Inside
the star paper and the HDPE triangle, the phase image offers more contrast than
the amplitude image. This is because, although the losses are similar in those materi-
als, the refractive index is sufficiently different to provide a meaningful contrast. In
general, phase imaging inherently possesses a 2πambiguity that can be removed using
a multiwavelength approach [79] or an interferometric scheme [80]. In Section 2.2,we
show how to further analyze the THz-TDS measurement to extract the complex
refractive index of a material.
Regarding the real-time operation of THz-TDS imaging systems, there are two major
problems when using classical THz-TDS setups (see Section 3for more technical
details). The first problem is the need to use an optical delay line to obtain the
temporal/spectral dimension. Common to many pump–probe optical experiments,
the optical delay line usually comes in the form of a pair of mirrors mounted on
a micropositioning stage. The linear mechanical movement of the delay line becomes
a hurdle for real-time operation. In Section 3.2, we present alternative solutions for
fast optical delay lines that can provide acquisition time in the millisecond scale. The
second problem is that one typically employs single-pixel THz detectors due to their
wide commercial availability. This means that to obtain an image, one needs to
mechanically scan the sample point by point. As an alternative to this slow imaging
technique, in Section 3.3, we detail the technical realization of 2D THz-TDS photo-
conductive antenna arrays, while in Section 3.3, we discuss 2D electro-optic sampling
(EOS) in the context of THz-TDS imaging.
2.2. THz Transmission, Reflection, and Conductivity Imaging
In THz-TDS measurements, both the amplitude and the phase of a THz waveform can
be extracted. With appropriate numerical treatment, one can then obtain the complex
refractive index using the Fresnel coefficients expressed in terms of the relevant
material refractive indices. Consider, for example, an interface between media 1
and 2, each media characterized with its own complex refractive index
˜
n1,2n1,2−ik1,2. Assuming that a THz parallel beam is transiting from media 1 into
media 2, then the corresponding transmission and reflection coefficients can be
written as
Transmission coefficient t12 2˜
n1
˜
n1˜
n2
,
Reflection coefficient r12
˜
n1−
˜
n2
˜
n1˜
n2
:(1)
By fitting experimentally measured transmission and refraction coefficients with the
corresponding analytical expressions [Eqs. (1)], one can extract the material complex
refractive indices, thus opening a way for direct imaging of the material refractive
index distribution across the sample. In this example, we assume a collimated
THz beam, while classical imaging is normally done via point-by-point raster
scanning with a THz beam focused at the plane of a sample. In that case, one can
still use the method described above; however, expressions for the Fresnel coefficients
have to be somewhat modified to account for the non-planar wavefront of the probing
beam [81,82].
In the following subsections, we detail several common imaging modalities that allow
imaging complex refractive index distribution at the interface between dissimilar
media: THz transmission, reflection, and conductivity imaging.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 851
2.2a. Transmission Spectroscopy
First, we present a more in-depth review on interpreting complex transmission data to
extract the sample complex refractive index. In what follows, we suppose a collimated
THz beam, while, as mentioned earlier, the same algorithm with minor modifications
can also be used in the case of focused THz beams for point-by-point imaging.
Following [83], consider a sample in the form of a plate of thickness L(media 2)
and complex refractive index ˜
n2, located between two media, media 1 and 3, having
complex refractive indices ˜
n1and ˜
n3, respectively. In what follows we assume normal
incidence of the probing THz wave [Fig. 6(a)]. To obtain the normalized transmission
function Stωfor a collimated THz beam, one performs two measurements: one is
THz transmission through the sample Esω, while another (reference measurement)
is THz transmission through an empty system (sample removed and replaced with
media 1) Eref ω. Then, the normalized transmission function at the angular frequency
ωcan be written as
Stω Esω
Eref ωt12t23 expi˜
n2ωL
c
t13 expi˜
n1ωL
c·FPL,ω 2˜
n2˜
n1˜
n3
˜
n1˜
n2˜
n2˜
n3
·exp i˜
n2−
˜
n1ωL
c·FPL,ω,(2)
where
FPL,ωX
∞
k0r23r21 expi2˜
n2ωL
ck
1
1−˜n2−˜n1
˜
n2˜
n1˜n2−˜n3
˜
n2˜
n3·exp i2˜
n2ωL
c(3)
is the Fabry–Perot term that accounts for multiple reflections inside the sample. This
term becomes important when characterizing thin films [84], but it can be neglected
(FPL,ω1) if the sample under consideration is optically thick. In a THz-TDS
measurement, a sample can be considered optically thick if the echoes (multiple re-
flections) are well separated in time, and only the directly transmitted wave (k0
term in the sum of Eq. (3) is sampled during the time-domain measurement) [83].
Alternatively, a sample can be considered optically thick when the sample material
loss is high enough, 2·Im˜
n2ωL∕c≫1, so that multiple reflected waves in Eqs. (3)
are so small in amplitude that they can be disregarded. A generalization of Eq. (2) for
non-normal incidence is provided in Ref. [85].
Several methods can be used to solve Eq. (2)[83,85,86–90]. For example, if the
sample ˜
n2˜
nn−ikis in air (˜
n1˜
n3˜
nair 1) and if the Fabry–Perot term
is neglected (FPL,ω1), Eq. (2) becomes
Figure 6
Media 2
(sample)
Media 1
(air)
Media 3
(air)
L
(a) (b)
Media 2
(window)
Media 1
(air)
Media 3
(sample)
L
(a) Schematic of the transmission and (b) reflection setups for the experimental
measurement of the transmission and reflection coefficients.
852 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
Stω 4˜
n
˜
n12·exp −kωL
cexp in−1ωL
c(4)
and can be rearranged to
nω c
ωLarg ˜
n12
4˜
nStω1,(5)
kω−
c
ωLln
˜
n12
4˜
nStω
,(6)
where argzis the phase of the complex number z. A fixed-point algorithm can be
used to get nωand kω[86,88,90]. In this algorithm, initial values of n0ωand
k0ωare injected into Eqs. (5) and (6) to give new values of nωand kω.By
repeating this process iteratively, a fixed point is found, for which the values of
nωand kωconverge. As an initial guess for n0ωand k0ω, one can assume
that 4˜
n∕˜
n121[88]. Then,
n0ω c
ωLfargSωg 1,(7)
k0ω−
c
ωLlnjSωj:(8)
This approximation becomes almost exact if the material losses are small, i.e., k≪
n[91].
For optically thick samples, the cut-back method can also be used to measure the
sample complex refractive index. This is an adaptation of the waveguide characteri-
zation technique detailed in Refs. [92–96], and it can also be applied to planar uniform
samples. Within this method, transmission measurements are performed for two
sample lengths, L1and L2. The main advantage of this technique is that the complex
refractive index can be analytically obtained without resorting to iterative algorithms.
Indeed, assuming that Fabry–Perot terms do not contribute FPL1,ω
FPL2,ω1, the relative transmission function does not include any Fresnel
coefficients:
StωE2ω
E1ωt12t23 expi˜
nωL2
c
t12t23 expi˜
nωL1
cexp i
˜
nω
cL2−L1
exp −
kω
cL2−L1exp inω
cL2−L1:(9)
From this, the complex refractive index ˜
nnik can be computed analytically:
nω c
ωL2−L1argStω,(10)
kω−
c
ωL2−L1lnjStωj:(11)
This method can be used to rapidly retrieve the complex refractive index without
relying on iterative algorithms.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 853
2.2b. Reflection Spectroscopy
Complementary to the transmission spectroscopy covered in the previous subsection,
one can also interrogate materials in the reflection mode. In this subsection, we review
interpretation of the complex reflection data to extract the sample complex refractive
index. Thus, using analytical expressions for the generalized Fresnel coefficients
[Eq. (1)], equations can be derived for the normalized reflection function, which
depends on both the collimated THz beam polarization and incidence angle (see
Ref. [97] for a comprehensive formulation).
A common experimental setup for reflection spectroscopy is depicted in Fig. 6(b).The
sample under study (media 3) is placed behind a window of thickness L(media 2),
which, in turn, is placed in air (media 1). As an example, we assume normal incidence
of the THz beam, and we also assume that both THz emitter and detector are on the same
side (transceiver configuration). This configuration, for example, was used to character-
ize liquids inside plastic bottles [97–101]. If the window is sufficiently thick, so that one
could separate in time domain the traces coming from the air/window reflection Eref ω
and the window/sample reflection Esω, and if we can disregard the Fabry–Perot effect
in the window, then the normalized reflection function can be written as
Srω Esω
Erefωt12 r23t21
r12
exp −
i˜
n2ωL
c4˜
n1
˜
n2
˜
n2
1
−
˜
n2
2
exp −
i˜
n2ωL
c˜
n2−
˜
n3
˜
n2˜
n3
:
(12)
If we assume that media 1 is air (˜
n11) and media 2 is a window of a known
refractive index (˜
n2˜
nw), Eq. (12) can be written as
CEsω
Erefω
1−
˜
n2
w
4˜
nw
expi˜
nwωL
c
˜
nw−
˜
n3
˜
nw˜
n3
:(13)
Then, ˜
n3ωcan be found analytically as
˜
n3ω1−C
1C˜
nwω:(14)
When the sample is strongly absorbing, reflection geometry is clearly superior to the
transmission spectroscopy as it does not rely on transmission through absorbing
samples. Indeed, transmission spectroscopy is limited by the maximal dynamic range
of the THz-TDS system, defined as the frequency-dependent maximal signal amplitude
relative to the noise floor. When a sample is strongly absorbing, the noise floor is quickly
reached for a short length of the sample. On the other hand, reflection spectroscopy does
not rely on transmission through the sample, but rather on the amplitude and phase ac-
curacy of the reflected signal. Therefore, the maximal absorbing coefficient depends on
the SNR, defined as the average signal divided by its standard deviation [100,102]. For
example, since liquid water is strongly absorbing in the THz spectral range, many bio-
medical applications of THz waves are performed in reflection geometry [14,103].
2.2c. Conductivity Imaging
In this subsection, we detail how to extract the electrical properties of a material from
the complex refractive index. In many important physics problems, one needs to ac-
curately determine the complex permittivity to electrically characterize a material.
THz-TDS gives an almost direct experimental contactless measurement of the
complex permittivity without resorting to the Kramers–Kronig relations, as is often
done in Fourier-transform infrared spectroscopy (FTIR), for example. Indeed, from
the refractive index calculated using the methods described in Sections 2.2a and 2.2b,
the complex permittivity ˜
εωcan be obtained with [104,105]
854 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
˜
εωε1ωiε2ω1i
˜σ
ε0ω,
ε1ωnω2−kω2,
ε2ω2nωkω:(15)
The complex permittivity is also related to the complex conductivity ˜σωthrough
˜
εω1i˜σω∕ε0ω, with ε0the vacuum permittivity. Therefore,
˜σωσ1ωiσ2ω,
σ1ωε0ε2ωω,
σ2ω−ε1ω−1ε0ω:(16)
Insights about the nature of the conductivity can be obtained by fitting the frequency-
dependent conductivity with a conductivity model. For example, in the Drude model,
the conductivity can be fitted to
˜σω σDC
1−iωτ ,σDC neμne2τ
mε0ω2
pτ,(17)
where nis the charge-carrier density, ethe elementary charge, μthe mobility, mthe
mass of the carrier, τthe Drude scattering time, and ωpthe plasma frequency.
Furthermore, the THz pulse can provide insights into the charge-carrier dynamics at the
picosecond time scale. Time-resolved THz spectroscopy (TRTS), also known as
optical-pump–THz-probe spectroscopy, is a technique derived from THz-TDS in which
an optical pump is used to photoexcite the charge carrier in a material under study. By
using an optical delay line, the transient conductivity is then probed with the THz pulse.
This method is often used to study conductive materials [104–108]. In Section 2.5b,we
will see an application of this method in the context of THz near-field imaging.
As an example of THz conductivity imaging, we now discuss contactless mapping of
the electrical properties of graphene using THz-TDS. Graphene is a unique bidimen-
sional material with many extraordinary properties that has attracted significant
attention due to its potential applications in many fundamental and applied fields
[109–111]. With the upcoming integration of graphene into a variety of commercial
products comes the need for a rapid, non-destructive, and accurate electrical charac-
terization of this material on an industrial scale [112]. In this context, THz-TDS offers
a contactless solution to such a need [113–116].
In Ref. [112], Bøggild et al. presented a comparative analysis of three techniques for
large-area mapping of the graphene electrical properties. The dry laser lithography
first transforms a graphene wafer into multiple electrode devices in 1–2 h before using
an automated probe station to extract the relevant parameters using the field-effect or
Hall-effect measurement (minutes per measurement point). The need to pattern
individual electrode devices makes this method destructive by nature. The micro
four-point probes (M4PP) use metal-coated silicon microcantilevers to scan across
the graphene sheet and obtain the electrical properties using the field-effect measure-
ment (∼1minper measurement point). This technique is non-destructive since it re-
quires no sample preparation. However, contamination can occur because the tips and
the graphene sheet are in contact. In comparison, THz-TDS imaging is non-contact
and non-destructive. Furthermore, the acquisition time for a measurement point is
limited by the mechanical scanning speed of the detector and the need to use an optical
delay line to sample the temporal dimension (∼millisecond per measurement point).
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 855
In Ref. [117], Buron et al. demonstrated the conductance mapping of graphene
with THz-TDS. Large-area graphene thin films were first grown using the
chemical vapor deposition technique, before being transferred onto silicon substrates
[Fig. 7(a)]. Then, the prepared samples were scanned in transmission geometry using
a focused THz beam. By using the Fresnel coefficient in transmission geometry, the
complex conductance could be determined in the thin film limit. The conductance was
found to be virtually constant across the whole THz range, with an imaginary part
close to zero and a real part near its DC value [Fig. 7(b)]. The real part of the con-
ductance was 0.768 0.077mS comparable to 0.64 0.13mS measured with a
contact-based M4PP. Next, to demonstrate nonuniform imaging, a damaged graphene
sample [photograph in Fig. 7(c)] was imaged using THz-TDS [see Fig. 7(d)]. Again,
the sheet conductance results agree with the M4PP measurement in Fig. 7(e).In
Ref. [118], the same group used a gate voltage on the graphene sheet to map the carrier
mobility, while in Ref. [119] the carrier mobility, carrier density and carrier scattering
time were obtained by fitting the Drude model to the conductance spectra.
In general, the challenges of real-time THz spectroscopy and conductivity imaging
are similar to those of the THz-TDS imaging system. To speed up image acquisition,
the spectrum needs to be rapidly obtained using a fast optical delay line (see
Section 3.2) and the detector needs to be a 2D array (see Sections 3.3 and 3.4).
Furthermore, to determine the complex refractive index, one may need to use iterative
algorithms, which can be problematic for real-time operation. However, in some
cases, analytical solutions can be found. For example, in transmission spectroscopy,
if the material losses are small (i.e., k≪n), Eqs. (7) and (8) can be directly used,
while the cut-back method provides an analytical solution [Eqs. (10) and (11)].
As for conductivity imaging, similar iterative algorithms must be used to obtain
acceptable fits of the frequency-dependent permittivity with conductivity models.
Ideally, the calculation times could be improved by using graphical processing units
(GPUs).
Figure 7
(a) Photograph of the graphene sheet and (b) corresponding sheet conductance map
obtained using THz-TDS. (c) Damaged graphene sheet and (d) corresponding con-
ductance mapped using THz-TDS and (e) M4PP. Reprinted with permission from
Buron et al., Nano Lett. 12, 5074–5081 (2012) [117]. Copyright 2012 American
Chemical Society.
856 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
2.3. THz Pulsed Imaging
THz pulsed imaging (TPI) also known as THz time-of-flight imaging (TOF) refers to
mapping the arrival times of the THz pulses to the detector. The measurement is
performed in reflection geometry using a THz-TDS configuration. The temporal delay
between the reflected pulses reveals the internal structure of the sample.
Already in the early days of THz imaging, TPI was demonstrated by imaging the
internal structure of a 3.5 inch floppy disk [120]. In a TOF measurement, the optical
path travelled by the pulse is directly related to the pulse temporal delay Δt. Assuming
a constant refractive index nover the relevant THz frequency range (associated with
the pulse Fourier transform), one can use the time delay between the pulse reflected
by the sample surface and the pulse reflected by the sample internal interface to mea-
sure the distance dfrom the sample surface to such internal interface:
dcΔt
2n:(18)
One of the practical applications of the TPI technique was demonstrated in the phar-
maceutical industry [12,121–123]. There, an important problem is quality control of
medicinal tablet coatings during their fabrication. Unlike in the visible/infrared re-
gions of the spectrum, the majority of dry tablets are semi-transparent to THz radi-
ation, thus enabling non-destructive imaging at high penetration depth [124,125]. In
[126], for example, May et al. developed an inline sensor to monitor the tablet coating
thickness in real time. The THz radiation was focused on a commercial perforated
tablet coater [Figs. 8(a)–8(c)]. With a prior knowledge of the coating refractive index,
Eq. (18) was used to measure the tablet coating thickness during the coating process
[Fig. 8(d)]. The general concept behind TPI was also used to assess the hardness,
Figure 8
(a) Schematic of the tablet coating monitoring using THz-TDS in reflection geometry.
(b) Time-domain measurement of the coating thickness and (c) reference measure-
ment. (d) TPI of a tablet during the coating process and corresponding thickness evalu-
ation. Reprinted from J. Pharm. Sci. 100,Mayet al.,“Terahertz in-line sensor for
direct coating thickness measurement of individual tablets during film coating in
real-time,”1535–1544 (2011) [126]. Copyright 2011, with permission from Elsevier.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 857
density, [127] and porosity [128] of the pharmaceutical tablets, as well as thickness
uniformity of automobile exterior coatings [129].
Moreover, in the field of art conservation, TPI was used as a non-destructive method to
study the paint layers of ancient masterpieces [23,130–133]. Thus, in Ref. [134], by
using TPI in reflection mode, a hidden portrait has been revealed in an 18th century
easel painting by the Danish painter Nicolai Abildgaard. While the visible image
portrays an old woman [Fig. 9(a)], the x-ray image revealed a portrait of a man under-
neath the top paint layer [Fig. 9(b)]. However, x-ray radiation, due to its ionizing
property, can be hazardous to paint and it can compromise radiometric dating.
Moreover, while x-ray essentially probes the losses in the paint, TPI can provide
supplementary information, such as the paint thickness.
To create a THz image, the authors first deconvoluted the reflected THz signal using a
plane metal surface placed at the position of the paint as a reference. Various paint
layers were then identified by looking for the distinct reflected pulses in the time-
domain data [Fig. 9(c)]. Additionally, the authors used spectral integration over certain
frequency ranges to reveal various details of the internal painting:
MZν2
ν1jFFTEt1<t<t0jdν,(19)
where the time intervals t0and t1correspond to the beginning and the end (in time
domain) of a particular reflected pulse. For example, by integrating over the whole
frequency range for the reflected pulse that defines the second paint layer, they ob-
served the hidden portrait [Fig. 9(d)], while by integrating over the 0.55–0.62 THz
Figure 9
(a) (b) (c)
(d) (e) (f)
Complete frequency range
Visible X-ray
0.55-062 THz Composite image
(a) Visible image of the painting. (b) X-ray image reveals the hidden paint. (c) Time-
domain data shows several distinct layers of paint. (d) THz image obtained by inte-
grating over the full frequency range of the reflected pulse that defines the second
paint layer. (e) THz image as in (d) but with spectral data integrated over the
0.55–0.62 THz range. It reveals sharper details around the mouth and the nose.
(f) THz false color image obtained by superimposing various frequency-averaged im-
ages (blue, 0.22–0.36 THz; red, 0.36–048 THz; and green, 0.48–055 THz). It reveals
that several distinct pigments have been used in the painting. Adapted with permission
from [134].
858 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
range, finer details were observed around the nose and the mouth of the subject
[Fig. 9(e)]. In Fig. 9(f), a false color image was realized by superimposing various
frequency-averaged THz images obtained using different frequency integration inter-
vals. The color differences in the composite image can be interpreted by noting that
different paint pigments have distinct spectral optical properties.
In Ref. [135], TPI imaging was combined with computational imaging techniques to
extract, in a fully automated manner, information about the sample layered structure.
In particular, by using a THz-TDS setup in reflection geometry [Fig. 10(a)], Redo-
Sanchez et al. demonstrated an automatized reading of the roman characters written
on pages pressed together to mimic a closed book [Figs. 10(b) and 10(c)]. First, using
a -probabilistic pulse extraction (PPEX) algorithm developed by the authors, they
identified the presence of different pages by recognizing (numbering) the temporal
intervals containing distinct reflected THz pulses [Fig. 10(d)]. Next, they performed
Fourier transforms of the individual reflected pulses in order to obtain spectrally
resolved images of distinct pages. To select the frequency image with the highest con-
trast, they analyzed the kurtosis of the pixel intensity histograms, assuming that kur-
tosis is higher for higher image contrasts [Figs. 10(e) and 10(f)]. In those selected
images, the characters can then be easily recognized in the first paper layers, but
the character recognition becomes challenging as the depth increases due to decreased
contrast and the presence of phantom images from other layers. To address this issue,
the authors used a convex cardinal shape composition (CCSC) optimization algorithm
[136] to automatically recognize the letters. The CCSC algorithm works essentially by
comparing the regions of high intensity to a set of letters at different positions and
orientations.
As for real-time imaging using the TPI technique, the optical delay line is a crucial
component (see Section 3.2) in such systems, since the method relies on the detection
of the reflected echoes obtained in the temporal data of the THz-TDS system.
Furthermore, to speed acquisition, 2D arrays can be used to avoid mechanical
movement of the sample (Sections 3.3 and 3.4). Alternatively, single-pixel detection
combined with compressive sensing techniques can be employed (see Ref. [137] and
Section 4.2a). Moreover, TPI measurements usually involve multiple reflections for a
sample with multiple layers. Therefore, manual intervention is necessary to identify
the temporal intervals corresponding to the distinct reflected echoes. To avoid human
involvement in the data acquisition process and to speed up the image construction,
artificial intelligence or other algorithms can be developed to automatically distin-
guish the temporal intervals (see, for example, the PPEX algorithm detailed in
Ref. [135]).
2.4. THz Computed Tomography
Since many materials are relatively transparent to THz radiation, developing 3D THz
imaging modalities that can reveal the material’s internal structure constitutes an
active research field. Extensive reviews of various reconstruction methods for 3D im-
aging are provided in [77,138,139]. As an example, here we detail the THz computed
tomography (THz-CT) technique. First demonstrated in the THz spectral range in
Refs. [140,141], the technique derives from the x-ray CT commonly used in the
biomedical field.
A typical setup for THz-CT is presented in Fig. 11(a). A parallel THz beam is incident
onto a sample having, for example, local optical losses distributed according to αx,y.
Here, we define an auxiliary function fx,y−αx,y, where x,yare the coor-
dinates in the local coordinate system associated with the sample. A sample is then
placed onto a rotational stage with an instant position characterized by the rotation
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 859
angle θ. The sample is then rotated, while the detector (or the sample) is moved along
a fixed line by distance tto construct the sinogram Pθ,t[Fig. 11(b)]. In this par-
ticular example, the auxiliary function Pθ,tis defined as the natural logarithm of the
measured THz intensity distribution Pθ,tlnIθ,t. Therefore, in this example,
Figure 10
(a) (b)
(c) (d)
(e)
(g)
image intensity values
normalized histogram
normalized histogram
image intensity values (f)
(a) Experimental setup featuring a THz-TDS setup in reflection mode. (b) Images of
different pages in the visible spectral range and (c) schematic of the book pages.
(d) Page number identification using the PPEX algorithm. (e) Pixel intensity
histogram for a THz frequency image with a low kurtosis and (f) a high kurtosis.
(g) Automatic character recognition by using the CCSC optimization algorithm.
Adapted from [135] under the terms of the Creative Commons Attribution 4.0
License. With copyright permission.
860 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
the sinogram physically corresponds to some measure of the cumulative optical loss
due to transmission through the sample along a certain straight line Lθ,tdefined by
the stage rotation angle and the detector position [142]:
Pθ,tZLθ,t
fx,ydl:(20)
The mathematical operation in Eq. (20) is known as the Radon transform. It corre-
sponds to the line integral over Lθ,t. The detector or sample is moved laterally
(variable t) and rotated (variable θ) and the sinogram Pθ,tis measured.
Therefore, to reconstruct the original object fx,y(for example the optical loss
distribution), the inverse Radon transform is computed through the filtered back-
projection (FBP) algorithm [143] or using iterative algorithms, such as the
simultaneous algebraic reconstruction technique (SART) and the ordered subsets
expectations maximization (OSEM) [144].
In Ref. [142], Brahm et al. used the broadband information provided by THz-TDS to
identify chemical contents. A sample made of glucose and lactose in a polystyrene
holder [Fig. 11(c)] was measured at different angles. To create the sinogram, the mea-
surements were normalized by reference measurements of lactose and glucose. In the
resulting sinogram, the amplitude values varied between −1and 1to indicate the
presence of lactose and glucose, respectively [Fig. 11(d)]. Then, the FPB algorithm
was used to reconstruct the slice of the object [Fig. 11(e)]. In [145], the identification
and localization were refined by using a wavelet-based method.
THz-CT measures a slice of the object. To obtain the information about the third
dimension, instead of measuring along a unidimensional line [axis tis Fig. 11(a)],
Figure 11
Angle
Position t
t
Radon transform
(c) (d) (e)
THz
(a) (b)
(a) THz-CT in the transmission geometry. (b) A typical sinogram from THz-CT.
(c) Photograph of the sample with glucose and lactose, (d) corresponding sinogram,
and (e) reconstructed material’s distribution of the slice in (c). Reprinted with permis-
sion from Brahm et al., Appl. Phys. B 100, 151–158 (2010) [142]. Copyright 2010
AIP Publishing LLC.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 861
a 2D image per angle θmust be acquired. In Ref. [146], Bessou et al. performed THz-
CT on dried human bones. In Figs. 12(a)–12(c), a photograph, an x-ray radiograph,
and a THz transmission image of a right human coxal bone are presented. As can be
seen from Fig. 12(b), the wing of the ilium is transparent to the x rays, while the
inferior part is opaque. The THz image [Fig. 12(c)] presents similar characteristics
despite a lower spatial resolution. In Fig. 12(d), angular slices of the reconstructed
bone are presented, while the 3D reconstruction is shown in Fig. 12(e).
In x-ray CT, since the relative size of the wavelength (∼nanometers) is much smaller
than that of the object (∼millimeters), one can ignore the illuminating beam self-
diffraction and consider it strictly parallel. On the other hand, in THz-CT, the beam
size is limited by the size of the focusing optics, which is typically no larger than
∼10 cm in diameter, while the wavelength of THz light can be as large as several
millimeters. Thus, in the THz regime, parallel beam approximation might not be ad-
equate and should be replaced by a Gaussian beam approximation. To obtain better
reconstructions, the Gaussian beam intensity profile was introduced into the propa-
gation model in Ref. [147]. In Ref. [148], a statistical reconstruction method called
maximum likelihood for transmission (ML-TR) initially developed for x-ray CT was
modified to include the Gaussian beam propagation. Alternatively, a nondiffractive
Figure 12
(a) Photograph, (b) x-ray, and (c) THz transmission image of a dried right human
coxal bone. (d) THz-CT for four different orientations of the bone. (e) 3D
reconstruction and (f) internal structure revealed by THz-CT. Reprinted with permis-
sion from [146]. Copyright 2012 Optical Society of America.
862 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
Bessel THz beam was shown to improve the quality of the reconstruction in
Ref. [149].
Furthermore, while in x-ray CT, only the absorption losses are measured, in THz-CT,
reflection and refraction losses become important for non-uniform samples with large
refractive index. In Ref. [150], Abraham et al. used a multipeak averaging procedure
coupled to the algorithm to reduce the effect of the refraction losses on image quality,
while in Refs. [151,152], the Fresnel reflection and refraction losses were evaluated
and eliminated using a ray-tracing method. Among successful applications of THz-
CT, we note in particular, a study of the internal content of a 18th Dynasty Egyptian
sealed pottery reported in Refs. [153–155]. In Ref. [156], polymer additive manufac-
turing objects from the aerospace and medical industries were successfully imaged in
3D using THz-CT.
Real-time THz-CT is particularly challenging since a third dimension (the angular
rotation of the sample) must be measured. However, THz-CT does not require the
time-domain/spectral information to reconstruct an object’s internal structure. In fact,
schemes involving only the transmitted amplitude/intensity THz radiation can be
used. For example, in Ref. [157], silicon-based CMOS emitter and detector were used
at a frequency of 490 GHz. Other CW THz-CT works involved the use of a double-
heterojunction bipolar transistor at 350 and 650 GHz [158], a gas laser at 2.52 THz
[159], a superconducting intrinsic Josephson junction oscillator at 440 GHz [160], and
injection-seeded parametric emitter and detector [161]. This opens the possibility of
using THz cameras (Section 4) to simultaneously obtain two spatial dimensions. For
example, in Ref. [162], a pyroelectric camera was used to obtain a 3D image of a
straw. Furthermore, if one uses THz-TDS for THz-CT, in addition to the need of array
detectors (Section 3.3 and 3.4), one also needs to use fast optical delay lines
(Section 3.2). In particular, in Section 3.4b, we review the work of Jewariya et al.
[163] who demonstrated THz-CT acquisition in only 6 min using EOS and a
CCD camera. Finally, if one wants to avoid the use of array detectors, a single-pixel
detector can also be used for THz-CT, either with fast beam-steering optics [164]or
with compressive sensing [165] (Sections 5.1a and 5.2a).
2.5. THz Near-Field Imaging
The imaging systems that we have discussed so far operate in the far-field regime, and,
thus, feature resolutions that are limited by diffraction of the THz beam on the
elements of the optical system. For example, light from a point source positioned near
the microscope objective focal plane and passing through a circular lens produces a
diffraction pattern in the shape of concentric rings (Airy disk). The spatial resolution
in the object plane is generally defined using the Rayleigh criterion [166], where the
minimal resolvable feature δxis defined as the minimal distance between a point
source central maximum and the second point source first minimum. This can be
written as
δx1.22 λF
D,(21)
where Fand Dare the focal length and diameter of the lens, respectively. This cor-
responds to the size, in the object plane, of the smallest object that the lens can resolve
and also the radius of the smallest spot to which a collimated beam of light can be
focused. Therefore, according to Eq. (21), the smallest resolvable feature is normally
comparable to or larger than the wavelength of the THz light.
To resolve the object’s subwavelength features, one needs to detect the evanescent
fields, which exist only at short distances from the object (near-field region). This
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 863
type of imaging is known as THz near-field imaging. Prior reviews of this topic are
found in Refs. [167–170]. Several techniques have been explored to enable subwave-
length THz imaging. In the following, we first briefly overview some recent subwave-
length imaging techniques, before focusing on two major types of techniques that
have attracted the most attention in the literature, namely, aperture-based and
scattering-based near-field imaging.
The confocal THz near-field imaging technique, as its name suggests, derives from the
confocal microscopy at optical wavelengths. It consists of using a pair of apertures
(pinholes) that act as spatial filters to block THz radiation propagating outside the
cone of light, thus resulting in increased lateral and depth resolution [171–174].
For example, in Ref. [173], using a quantum cascade laser at 2.9 THz, the authors
demonstrated lateral and axial resolutions of 70 μm(λ∕1.4) and 400 μm. In
Ref. [174], medieval manuscripts were imaged with confocal THz imaging at
0.3 THz with a lateral resolution of 0.5 mm (λ∕2). In confocal microscopy, the lateral
resolution is improved by reducing the pinhole diameter. However, the diameter
cannot be reduced below a certain threshold for which no signal is collected at
all, therefore requiring powerful sources.
In comparison, the solid-lens immersion approach allows for more throughput light
intensities. The idea here is to use a specially designed lens that generates a spot size
smaller than the diffraction limit in the evanescent field region following the lens. For
example, the lens can be a cube [175,176] or a sphere [177]. In Ref. [178], a combi-
nation of an aspheric lens and a truncated sphere was used to achieve a resolution of
λ∕3.1(at 0.5 THz), better than the resolution of an aspheric lens alone (λ∕1.2). In this
case, however, the spatial resolution (although subwavelength) is fundamentally lim-
ited by the material properties of the immersion lens (specifically its refractive index).
In Ref. [179], a similar setup was used to image soft biological tissues with a
resolution of λ∕6.7at 0.6 THz.
In the direct-contact method, the sample is placed in direct contact with a subwavelength
detector. This approach is generally employed with EOS using THz-TDS (Section 3.1a).
In this case, the detector is a femtosecond optical beam (the size of which is smaller than
the THz wavelength) that probes the polarization change in a nonlinear crystal. The
sample is then in direct contact with the crystal, leading to a direct measurement of
the THz electric field in the near-field region. For example, in Ref. [180], Adam et al.
demonstrated a 20 μm resolution by imaging various metal structures deposited onto an
electro-optic GaP crystal. In Ref. [181], Seo et al. measured the 2D time-domain THz
electric field behind the slit arrays, from which the magnetic and Poynting fields were
reconstructed. Because of the possibility of using cameras operating in the visible/
infrared range, the direct-contact EOS technique is a serious candidate for real-time
near-field THz imaging. This will be reviewed in Section 3.4b. Very recently, an addi-
tional approach using SiGe heterojunction bipolar transistor technology has emerged for
direct-contact near-field imaging [182]. Fabricated with 130 nm BiCMOS process tech-
nology, the sensor operating at 0.55 THz both generated and detected THz radiation.
The close on-chip proximity of the emitter and the detector allowed the demonstration
of a lateral resolution of 10–12 μm(λ∕55).
Among other THz near-field imaging techniques, we note the deconvolution from the
image of the point-spread function, mathematically modeled using the Gaussian beam
theory and variables such as the beam divergence, depth of focus, and absorption
coefficient of the object [183,184].
Realizing real-time near-field imaging is not trivial since most of the techniques rely
on the mechanical scanning of subwavelength apertures/tips. Therefore, the parallel
864 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
acquisition of multiple images becomes difficult. In that context, the direct-contact
THz near-field imaging technique distinguishes itself as it allows acquiring 2D
images. Furthermore, spectroscopic features being rich at the subwavelength scale,
there is great interest in combining THz-TDS with near-field THz imaging. This
combination is realized in EOS with crystals and it is the subject of Section 3.4b.
2.5a. THz Aperture Near-Field Optical Microscopy
The most direct way of enabling a near-field imaging system is to use a subwave-
length-size aperture in the near field. In the visible/infrared this approach is also
known as scanning near-field optical microscopy (SNOM). The resolution of this
method scales with the size of the aperture, however, the sensitivity of the method
decreases rapidly (superlinearly) with smaller aperture sizes [185]. The aperture
can also be a tapered metal cone tip [186], a dynamically moving aperture produced
by optically pumping a semiconductor wafer [187]. We mention that, in principle,
apertureless subwavelength dielectric probes can be designed using a solid immersion
lens approach, which can provide much higher throughput light intensities than
aperture-based methods [178]. In this case, however, the spatial resolution (although
subwavelength) is fundamentally limited by the material properties of the immersion
lens, which is not the case for aperture-based near-field imaging.
In more detail, in Ref. [185], the detector (a photoconductive antenna) was placed at a
subwavelength distance from a near-field rectangular aperture probe to detect the
exponentially decaying evanescent THz field [188]. In this arrangement, the spatial
resolution is determined by the aperture size [189]; however, following Bethe’s study
of diffraction by a circular hole [190,191], the transmitted electric field decreases with
the third power of the aperture size, thus rendering the transmission through deeply
subwavelength apertures extremely small. To increase the optical transmission
through subwavelength apertures, in Ref. [192], Ishihara et al. inscribed concentric
periodic grooves onto a metallic substrate around the aperture. In this bull’s-eye struc-
ture, the incident THz wave excites surface waves that increase the electric field values
in the subwavelength aperture 20-fold. In Ref. [193], the circular aperture was re-
placed by a bow-tie aperture to increase the transmission by 3 and enable a resolution
of 12 μm(λ∕17 at 1.45 THz).
Recently, the near-field probe and the THz photoconductive antenna were integrated
on a single-chip. In Ref. [194], Macfaden et al. placed the aperture probe at a 1 μm
distance from the THz antenna, which resulted in a sub-1-μm thickness of
the GaAs semiconductor active layer, which is a key enabling element of the antenna.
The problem with such a small thickness of the GaAs layer is that it is much smaller
than the characteristic optical absorption length (1.4 μm) at the wavelength (800 nm)
used for photoexcitation (infrared pump beam) of the antenna. This means that few
charge carriers are generated by the pump beam within the GaAs layer of the PCA
and, consequently, sensitivity of the THz detection is reduced. To increase the detec-
tion efficiency, the authors introduced a distributed Bragg reflector between the semi-
conductor layer and the subwavelength aperture [Fig. 13(a)]. The purpose of this
reflector was twofold. First, it behaved as a resonator that enhanced the optical field
of the pumping infrared beam at the position of the antenna gap. Second, it provided
optical isolation of the sample under study from the pumping optical pulse, which is
important when imaging light-sensitive materials such as semiconductors. As a result,
with the integrated chip, a spatial resolution of 3 μm(λ∕100 at 1 THz) was demon-
strated. In Ref. 195], to increase the sensitivity of the antenna even further, a gold
nanoantenna array was added in the vicinity of the active layer of the antenna
[Fig. 13(b)]. The array was designed to have a plasmonic resonance at 800 nm
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 865
and the experimental spectra showed that 80% of the pump light was absorbed. With
this structure, a spatial resolution of 2 μm was demonstrated (λ∕150 at 1 THz).
2.5b. THz Scattering Near-Field Optical Microscopy
A second class of THz near-field systems is known as THz scattering near-field optical
microscopy. In those systems, the THz radiation is focused on a metallic tip that con-
fines strongly the THz radiation in a small region. When brought close to a sample, the
tip scatters in the far field the THz radiation that has interacted with the sample in the
near field. To distinguish the scattered field from the background noise, the tip is
mechanically modulated at a certain fixed frequency that enables THz detection with
a lock-in amplifier.
In the early demonstrations of the scattering-type THz near-field imaging, spatial res-
olutions of 18 μm(λ∕110 at 0.15 THz) [196] and 150 nm (λ∕1000 at 2 THz) [197]
were achieved. Those resolutions were essentially determined by the size of the tip
apex. One of the main advantages of the scattering-type THz near-field imaging is that
the THz system can be coupled with existing imaging techniques that use vibrating
probing tips. For example, in Ref. [198], THz illumination and detection were com-
bined with the vibrating cantilever of an atomic force microscope (AFM) to map the
charge-carrier concentration of a transistor at the nanometer scale with 40 nm
resolution (λ∕3000 at 2.54 THz).
Laser THz emission microscopy (LTEM) is a near-field imaging technique initially
proposed for non-destructive inspection of electrical failures in circuits [199]. Within
this method, upon femtosecond illumination of a sample, charge carriers are accel-
erated, and THz pulses are emitted. In LTEM, the spatial resolution is determined by
the femtosecond pulse spot size, leading to a spatial resolution of 3 μm(λ∕2000 at
0.05 THz) in Ref. [199]. Very recently, nanoscale LTEM was proposed by focusing
Figure 13
(a) Integrated subwavelength aperture/THz-PCA in a single chip separated by a dis-
tributed Bragg reflector. Adapted from Macfaden et al., Appl. Phys. Lett. 104, 01110
(2014) [194]. Copyright 2014 AIP Publishing LLC. (b) Integrated chip enhanced with
a plasmonic nanoarray. Adapted with permission from Mitrofanov et al., ACS Photon
2, 1763–1768 (2015) [195]. Copyright 2015 American Chemical Society.
866 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
the infrared femtosecond pulse on a commercial AFM metal tip and a semiconductor
substrate [200]. Dipole oscillations of the charges are the source of THz pulses in the
region of the tip apex. Nanoscale imaging can then be performed by detecting the THz
pulses that have interacted with a sample brought close to the metal tip. In [200], a tip-
size-limited spatial resolution of 20 nm was achieved and allowed the THz imaging of
a single gold nanorod.
In Ref. [201], THz-TDS was coupled to a scanning tunneling microscope (STM) to
combine the nanometer spatial resolution of the STM with the subpicosecond time
resolution of the THz-TDS. Without modifying the STM design, the THz pulse was
focused onto the probe tip to produce a subpicosecond voltage transient that drove
electrons across the junction [Fig. 14(a)]. Since the measured current is localized in
the tunnel junction, the spatial resolution is defined by the size of the tip apex, which
was measured to be 2 nm (λ∕150000 at 1 THz) in Ref. [201]. To demonstrate the
potential of the THz-STM in measuring ultrafast carrier dynamics, Cocker et al.
[201] optically pumped a sample of InAs nanodots grown on GaAs. Then, they mea-
sured both the STM topography and the THz-STM images. By varying the time delay
between the optical pulse and the THz pulse, clear contrast in the THz-STM images
was observed [Fig. 14(b)]. In Ref. [202], by using THz-STM, the authors imaged the
dynamics of the orbital structure of a pentacene molecule.
3. ENABLING REAL-TIME THZ-TDS IMAGING
Many of the imaging techniques we reviewed in Section 2use the THz-TDS setup. In
this section, we have a closer look at THz-TDS, as well as at various techniques that
can speed up acquisition of the THz pulses and enable real-time imaging.
Figure 14
THz-STMSTM
Before excitationAfter excitation
(b)
(a)
(a) Schematic of the THz-STM. (b) STM image, THz-STM image and schematic be-
fore and after optical excitation. Reprinted by permission from Macmillan Publishers
Ltd.: Cocker et al., Nat. Photonics 7, 620–625 (2013) [201]. Copyright 2013.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 867
Figure 15 depicts two classical experimental setups for THz-TDS in transmission and
reflection modalities. An ultrafast laser beam is divided and sent along two optical
paths. THz pulses are generated in the emission arm and then they travel to a sample
placed at the focal plane of the focusing optics. After interacting with the sample, the
THz pulses are coherently detected in the detection line arm, using an optical delay
line to induce a temporal difference between the optical pump and the probe pulses.
There are two main methods to generate and detect THz pulses: (1) using photocon-
ductive antennas (PCA) and (2) using optical rectification and EOS in nonlinear crys-
tals. In this section, we begin by detailing the emission and detection principles using
the abovementioned technologies (Section 3.1). For real-time imaging, the predomi-
nance of the relatively slow optical delay lines presents one of the main challenges.
Therefore, in Section 3.2, we review several novel optical delay line designs that speed
up pulse acquisition. Typically, both PCA and EOS are single-pixel detectors, which
complicates the acquisition of high-resolution THz images. Therefore, in Section 3.3,
we overview some of the recent works aimed at fabricating PCA arrays, while in
Section 3.4, we detail the use of cameras to perform EOS.
3.1. Coherent THz Generation and Detection THz-TDS
3.1a. Photoconductive Antenna
A photoconductive antenna (PCA) can be used to generate and detect THz pulses
[40–46]. The PCA is made of two metal electrodes deposited onto a semiconductor
substrate. Photoexcited carriers are created in the gap between the electrodes by
optical excitation (typically using ultrafast infrared pump laser beams). The PCA
is essentially a photoswitch, where, for THz generation and detection, both the
switch-on and switch-off times must be subpicosecond [203]. The switch-on is de-
termined by the pump pulse duration of the optical excitation (typically <100 fs),
while the switch-off time is dictated mainly by the carrier lifetime.
To generate THz, the antenna gap is voltage-biased and illuminated with a femtosec-
ond laser pulse [Fig. 16(a)]. Excited photocarriers are then accelerated on a subpico-
second time scale. This rapid rise and fall of the transient photocurrent is the source of
a THz electromagnetic field irradiated away from the antenna. The process of transient
photocurrent switching can generate broadband THz pulses with bandwidths up to
15 THz [204], the limitation being the carrier lifetime. Recently, average THz power
levels as high as 3.8 mW (with 240 mW optical pumping) were achieved, by using a
large-area PCA with embedded plasmonic contact electrode gratings [205,206], while
Figure 15
Emission path
Detection path
Ultrafast laser
THz
Detection
THz
Emission
Transmission
x
y
Sample
(a)
Reflection
Sample
(b) Optical delay line
x
y
Schematic of a THz time-domain spectroscopy system in (a) transmission and
(b) reflection geometries. The emission and detection hardware are described in
Section 3.1.
868 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
most THz-TDS systems operate with THz pulses of ∼1–100 μWaverage power. To
improve the SNR, the emitter antenna is typically biased with an alternating voltage
and lock-in amplification is used.
For THz detection, no bias voltage is applied between the electrodes [Fig. 16(b)],
while the excited photocarriers are accelerated by the incoming THz radiation.
This results in a time-varying photocurrent Jωbetween the antenna electrodes,
which is proportional to the field amplitude of the THz radiation ETHzω:
Jω∝IωRωETHzω,(22)
where Iωis the spectrum of the optical source, and Rωis the Fourier transform of
the time response of the semiconductor photocarriers, which includes the trapping and
recombination times [207,208]. The term IωRω is the spectral sensitivity of the
PCA, and it can be seen as a low-pass filter function applied to the incident THz pulse
ETHzω. Consequently, the detected THz bandwidth can be improved by pumping the
PCA detector with temporarily shorter optical pulses (larger bandwidth) or by tuning
the charge-carrier lifetimes. In Refs. [209,210], significant improvement in the THz
detection sensitivity was reported by using nanostructured plasmonic contact elec-
trodes that effectively reduce the average transport path length of the photocarriers.
Consequently, an increased number of carriers reached the contact electrodes, leading
to higher photocurrent and increased sensitivities.
Finally, we note that the classic PCA is a single-pixel detector, which is problematic
for real-time high-resolution THz imaging due to the necessity of slow raster scanning
of the sample. Recently, there were several reports of designing arrays of PCA
detectors, which can be beneficial for imaging applications. We detail these advance-
ments in Section 3.3.
3.1b. Optical Rectification and Electro-Optic Sampling
Optical rectification is a second-order nonlinear process commonly used to generate
pulsed THz radiation [47–49] [Fig. 17(a)]. An ultrafast optical pulse Eωpropagating
inside a nonlinear electro-optic crystal is the source of a time-varying second-order
polarization term that can be expressed as [203]
P2
i0X
j,k
ε0χ2
ijk 0,ω,−ωEjωE
kω,(23)
where the indices i,j, and kcorrespond to the Cartesian components of the field, and
χ2
ijk is the second-order susceptibility tensor element for the crystal. Equation (23)
indicates that, when the optical electric field Eωis correctly oriented relative to
the crystal axis, the induced second-order polarization is roughly proportional to
Figure 16
THz
DC bias
Semiconductor
Optical
pulse THz
Photocurrent
Semiconductor Optical
pulse
A
(a) (b)
Schematic of the photoconductive antenna operation to (a) generate and (b) detect
THz pulses.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 869
its square j~
P2j∝jEωj2. For THz generation, the optical field is a time-dependent
femtosecond pulse, for example, a Gaussian distribution with a width related
to a[211]:
Et∝E0e−at2eiωt:(24)
Therefore, the induced polarization is also time dependent and proportional to the
envelope of the optical pulse:
jP2j∝E0e−2at2:(25)
Furthermore, this induced polarization is the source of a THz electric field ~
ETHzω
through the wave equation
∇2~
ETHz −
nTHz
c2
∂2~
ETHz
∂t21
ε0c2
∂2~
P2
∂t2,(26)
where nTHz is the crystal’s refractive index at THz frequencies. Thus, in principle, the
THz pulse spectral bandwidth can be increased by reducing the optical pump pulse
duration. In practice, the phase-matching condition, which includes the crystal
dispersion at optical and THz frequencies [212], bounds the interaction length
(walk-off length) and limits the efficiency of the THz generation. ZnTe is the most
commonly used crystal for THz generation. A second popular choice is the LiNbO3
crystal, which has a larger nonlinear coefficient, but that requires a tilted-pulse-front
excitation for efficient generation [213–215]. With this method, single-cycle THz
pulses with amplitudes exceeding 1 MV/cm can be generated [216]. Recently, non-
linear organic crystals have also been successfully used to generate THz pulses
through optical rectification [50]. In Ref. [51], Vicario et al. used a Cr:forsterite laser
at 1.25 μm to pump organic crystals DAST, OH1, and DSTMS, generating THz pulses
with peak electric fields of 6.2, 9.9, and 18 MV/cm, respectively. We also mention the
generation of THz pulses with tight focus of ultrafast optical pulses to generate gas
plasma (for example, in air) and THz radiation through a four-wave mixing process
involving third-order nonlinear susceptibility [69]. The reciprocal nonlinear process
can also be used to coherently measure the THz pulse from the THz field-induced
second harmonic (TFISH). This technique is known as the THz air-biased coherent
detection technique (THz-ABCD). Compared to the generation/detection with optical
rectification in a crystal, THz-ABCD provides a very large spectral bandwidth (from
0.2 THz to >30 THz), limited primarily by the optical pulse duration [70].
Using nonlinear crystals, the detection is based on electro-optic sampling (EOS),
which is conceptually the opposite of optical rectification [64–68,212]. Under the
Pockels effect, the THz electric field modulates the birefringence of a χ2crystal.
Therefore, by probing the birefringence with a femtosecond optical beam, the
THz electric field can be coherently measured. Figure 17(b) shows a typical exper-
imental setup for detecting THz pulses using EOS. The optical probe beam and the
THz pulse interact inside the crystal. The linearly polarized optical beam will have a
slightly elliptical polarization at the output of the crystal. Then, a polarization control
system is used to extract from the elliptical polarization its two orthogonal linear com-
ponents for balanced detection. For example, a quarter-wave plate can be used to con-
vert the optical probe beam polarization into an almost-circular polarization. Then, a
Wollaston prism can be used to divide the almost-circular polarization into two
orthogonal components. Finally, a balanced photodetector measures the intensity
difference between the two orthogonal components, which is proportional to the
applied THz electric field.
870 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
Since EOS measures the state of polarization of a probing optical beam, conventional
visible/infrared cameras can be used to provide real-time THz images (see Section 3.4
for details). We mention that the nonlinear parametric upconversion process
[39,217,218] has also been used to demonstrate CW THz imaging with infrared
cameras [161,219,220].
3.2. Fast Optical Delay Line
In THz-TDS, an optical delay line is used to scan and measure the THz pulse in time
domain. The pulse spectrum is then retrieved using Fourier transform. In a classic
THz-TDS setup, a linear reflective optical delay line positioned either in the emission
or detection side is used. Such delay lines are realized by mounting a retroreflective
prism onto a linear mechanical micropositioning stage. Thus, when the delay line
travels a distance Δz, the time delay between the probe and pump pulses is modified
to Δt2Δz∕c. In this expression, the factor 2 expresses the fact that the optical beam
travels twice the distance (back and forth) in the delay line. As a typical THz pulse has
∼1ps duration, one normally uses δt0.01 ps sampling resolution to correctly
resolve the THz pulse. This, in turn, imposes restriction on the precision of the micro-
positioning stage δzcδt∕2∼1.5μm, which is readily achievable with high-quality
commercial micro-positioning mechanical stages.
The THz spectrum is obtained by taking the Fourier transform of the temporal pulse.
From the properties of the Fourier transform, it follows that the pulse maximal
frequency νmax and the frequency resolution δν are given by
νmax 1
2δtc
4δz,(27)
δν 1
Δtmax c
2Δzmax
,(28)
where δtand Δtmax are the temporal sampling resolution and the total temporal delay
used in the pulse acquisition, respectively, while δzand Δzmax are the positional
increment and the total movement of the delay line, respectively. For example, a
Figure 17
Optical pulse THz pulse
Induced polarization
Nonlinear medium
Electro-optic
crystal
/4
waveplate
Wollaston
prism
Balanced
photodetector
Optical pulse
THz pulse
(a)
(b)
(a) THz generation using optical rectification and (b) THz detection using EOS.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 871
δz30 μmpositioning step size and a total delay line displacement of Δzmax
30 mm gives a spectrum with a maximal frequency of 2.5 THz and a resolution
of 5 GHz.
For real-time imaging applications, the raster scanning of a sample is too time-
consuming mostly due to the limited scanning speed of the optical delay lines, which
typically do not exceed 1 Hz, thus resulting in ∼1sper pixel acquisition rates. The
limited speed of traditional optical delay lines that use mechanical micropositioning
stages is essentially due to their interrupted back-and-forth linear displacement. From
a mechanical point of view, rotary movements enable uninterrupted displacements
with higher speeds, which prompted significant research into the development of
rotary delay lines. In the following, we begin by reviewing two major types of
mechanical rotary delay lines that are based on rotary reflectors (Section 3.2a)
or rotary prisms (Section 3.2b). Finally, in Section 3.2c we focus our attention on
non-mechanical delay lines.
Here, it is important to note that even if infinitely fast optical delay lines would
become available in the future, one still has to be aware of the fundamental signal
acquisition delay per pixel, which is related to the averaging time constant of the
lock-in amplifier used to increase the SNR of the detected signal. As more powerful
THz emitters become available in the future, the averaging times could become
shorter. A typical lock-in averaging time used in the current low-power THz-TDS
systems is larger than δtav 1ms. Ideally, lock-in averaging has to be done for every
position of the delay line, thus resulting in a total acquisition time for a single THz
pulse (single pixel) of δtavΔtmax ∕δtδtavΔzmax∕δz∼1sin the case of δtav 1ms,
Δzmax 30 mm, and δz30 μmdiscussed above, which is a an example of a typical
high-resolution THz scan.
3.2a. Rotary Reflectors
Rotary delay lines can feature planar or curvilinear mirrors that are mounted directly
or otherwise actuated by a rotating motor shaft. Rotary reflector lines were typically
placed in the path of an optical pump beam, but they could be placed in the THz
beam path.
Rotary optical delay lines were originally developed for optical coherence tomogra-
phy (OCT) (notably multiple-pass cavity delay lines [221,222]), and they generally
feature a combination of rotating curved and planar mirrors [223,224], which can even
include turbines in place of motors for faster rotation speeds. Although optical delay
lines for OCT enable very high scanning rates of up to several tens of kilohertz, such
delay lines show small optical delays (∼20 ps) that are insufficient for THz-TDS
applications.
To increase the maximal optimal delay, retroreflectors coupled to a galvanometer were
proposed for ultrafast optical measurements [225]. Such a system achieved an optical
delay of 300 ps with a scanning rate of 30 Hz. However, since the linear movement of
the mirror induced by the rotating galvanometer was sinusoidal in time, an additional
calibration step was needed to recover the instant value of the linear optical delay as a
function of time.
Curvilinear reflective surfaces designed to provide linear optical delay as a function of
the reflector rotation angle were first reported in Refs. [226–230]. In Ref. [228], Kim
et al. mounted six reflectors onto a servo motor and demonstrated acquisition of the
THz pulses with a net scanning rate of 400 Hz and a maximal optical delay of 70 ps.
However, in their design, the incident beam and the reflected beam were collinear.
Therefore, a beam splitter was needed to separate the incident and reflected beams,
thus leading to a significant loss of optical power. The importance of this design is in
872 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
its linear dependence on the reflector rotation angle. Thus, by using a motor with a
fixed and stable angular rotation frequency, a linear optical delay as a function of time
is assured, and no additional calibration steps are needed.
In Ref. [229], Skorobogatiy developed a comprehensive mathematical theory for the
design of rotary delay lines that feature up to three rotating and stationary curvilinear
reflectors. Analytical and semi-analytical expressions for the reflector shapes were
given for four classes of rotary delay lines that included linear dependence of the
optical delay on the reflector rotation angle. Thus, the work analyzed (1) a single
rotating reflector, (2) a single rotating reflector and a single stationary reflector,
(3) two rotating reflectors, and (4) two rotating reflectors and a single stationary re-
flector. In the case of two rotating reflectors, the author showed that it is possible to
separate the incoming and outgoing beams, while still keeping a linear relationship
between the delay and the rotation angle.
In the follow-up work [230], a linear rotary delay line featuring two rotating reflectors
was realized experimentally and employed in a THz-TDS setup designed for spec-
troscopy of dynamic processes. Particularly, four pairs of curvilinear reflectors were
fabricated using computer numerical control (CNC) machining on the same rotary
disk [Fig. 18(a)]. The acquisition of THz pulses was demonstrated with a speed
of up to 48 Hz per blade (192 Hz with four blades), with a maximal optical delay
of ∼80 ps [Fig. 18(b)]. The input and output beams were physically separated in
space, thus avoiding the use of a beam splitter. To record THz traces with such high
acquisition rates, the authors replaced the lock-in amplifier with a low-noise transi-
mpedance amplifier. They showed that the bandwidth of the detected signal decreased
as the rotation speed increased, and they related this to the acquisition electronics
[Fig. 18(c)]. As for practical applications of such a system, the authors monitored
the time dynamics of a spray painting process by observing the amplitude and tem-
poral position evolution of the main THz peak during paint deposition and drying
[Figs. 18(d) and 18(e)]. They also demonstrated detection of thickness of free-falling
polyethylene samples (moving speeds of up to 1 m/s) by monitoring in real time the
optical delay of the THz pulse [Figs. 18(f) and 18(g)] with and without a sample. The
results were shown to be on par with manual micrometer measurements of the sample
thickness.
However, the curvilinear reflectors developed in Refs. [226–230] were essentially
designed with ray optics, assuming infinitely thin laser beams. Therefore, distortion
of the wavefront was important and, consequently, the parallel incident beam was
distorted after reflection. This results in a less efficient generation or detection of
THz radiation.
3.2b. Rotary Prisms
Rotary delay lines can also feature rotating prisms. In such systems, the variable op-
tical delay is generated by rotating a prism in the path of the optical pump or the THz
beams. In Ref. [231], Ballif et al. used a rapidly rotating BK7 glass cube (n1.5at
850 nm) to realize such a delay line. They showed that the optical delay as a function
of the angle had 20% deviation from a linear curve. In Ref. [232], they demonstrated a
high repetition rate of 28.6 kHz with a maximal optical delay of 6.67 ps. However, this
delay is too small to be useful for applications in THz-TDS. By increasing the size of
the cube, the total optical delay can be increased. Thus, with a cube size of 50 mm, the
same authors demonstrated a total optical delay of up to 215 ps [231]. However, with
large cubes, when placed in the path of a pump beam, group velocity dispersion
(GVD) becomes important, which leads to broadening of the femtosecond pulse,
lower THz generation efficiency, and reduced THz pulse bandwidth.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 873
Figure 18
20 30 40 50 60 70
−2.5
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Linear
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III IVV
III
(a) (c)
(b)
(d)
(f)
(e)
(g)
Time (s) Time (ps)
Time (ps)
(a) Experimental realization of a linear rotary delay line featuring four pairs of the
curvilinear reflectors. (b) Time-domain THz pulses and (c) corresponding spectra
for different angular rotation speeds. (d) Real-time monitoring of the spray-painting
process. Amplitude (blue top) and temporal position (red bottom) of the THz peak that
passes through a sprayed-on layer of paint. (e) Time-domain THz pulses during spray-
ing action (region I) and during paint layer drying (region II). (f) Thickness evaluation
of free-falling polyethylene samples. Induced time delay due to passing of polyethyl-
ene samples of different thicknesses. Inset: passing of a 14.72 mm sample and (g) cor-
responding time traces. © 2015 IEEE. Reprinted, with permission, from Guerboukha
et al., IEEE Trans. Terahertz Sci. Technol. 5, 564–572 (2015) [230].
874 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
The abovementioned rotary delay line was designed for an infrared pump of nano-
meter-size wavelength. Therefore, complex alignment and precise manufacturing
was required, with prism surface roughness smaller than λ∕10. To circumvent these
complexities, in Ref. [233], Probst et al. used an 80 mm cube of high-density
polyethylene (n1.53) in the path of a THz beam to generate the optical delay
[Fig. 19(a)]. This cost-effective method was relatively simple to implement.
However, it provided a highly nonlinear dependence of the time delay on the rotation
angle [Figs. 19(b) and 19(c)], thus requiring an additional calibration step. A complete
rotation of the cube generated eight THz pulses with maximal optical delay of 40 ps
each. The authors demonstrated acquisition rates of up to 800 Hz, the main limitations
being the acquisition electronics, the induced air turbulence at high rotation speeds,
relatively small time delay, and THz signal attenuation due to absorption in the
prism material [Figs. 19(d) and 19(e)]. Furthermore, the authors used their delay line
to image a floppy disk (100 mm ×100 mm) in less than 3 min, limited by the raster
scanning of the sample and the acquisition electronics [Figs. 19(f) and 19(g)].
3.2c. Non-Mechanical Time-Domain Sampling
To avoid mechanical sampling of the time delay, methods based on modifying the
laser repetition rate of the femtosecond laser can be used. Asynchronous optical
Figure 19
(a) Rotary optical delay line featuring a rotating HDPE cubic prism. (b) Nonlinear
time delay as a function of the angle of rotation. (c) Raw THz traces for different
rotation speeds of a prism. (d) Calibrated time traces and (e) corresponding spectra
for different rotation speeds. (f) Photograph and (g) THz transmission image of a 3.5
inch floppy disk. Reprinted with permission from [233]. Copyright 2014 Optical
Society of America.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 875
sampling (ASOPS) was introduced in the pump–probe scheme to detect molecular
species concentrations in flames [234,235]. It was first implemented in the THz-
TDS configuration in Refs. [236,237]. In this technique, scanning of the time delay
is obtained by using two femtosecond lasers (one laser is placed in the emission line,
another in the detection line) featuring two slightly different pulse repetition rates
f1,f2. Consequently, the relative time delay between the two pulse trains will mimic
a linear ramp from 0 to Δt1∕f1(assuming f2>f1), while the scan rate will be
determined by the beat frequency between the two lasers Δff2−f1[Fig. 20(a)].
In Ref. [238], Bartels et al. used two mode-locked Ti:sapphire femtosecond lasers
with repetition rates close to 1 GHz and an offset frequency of Δf10 kHz.As
a result, a temporal 1000 ps scan was performed with a scan rate of 10 kHz (acquis-
ition time per single THz pulse trace of 100 μs). By reducing the temporal window,
one can furthermore increase the scan rate. For example, in Ref. [239], 100 ps total
delay has been demonstrated at a repetition rate of 100 kHz. However, to obtain such
performance, unconventional lasers with 10 GHz repetition rate were used.
As ASOPS constantly scans the entire time interval between two consecutive pulses,
this might be wasteful if the size of the scanned temporal window (say ∼1000 ps)
exceeds greatly the time duration of a typical broadened THz pulse (10–100 ps).
Figure 20
Acquisition time
Time delay
Δt
1/Δf
Pump (f1
( eborP)f2)
Acquisition time
Time delay
Δt
1/Δf
Pump (f1
( eborP )
f2)
(a)
(b)
ASOPSECOPS
Schematic description of the (a) ASOPS and (b) ECOPS technique. In ASOPS, the
pump and probe pulses have slightly different repetition rates, leading to a continuous
scan of the time delay between consecutive pulses. In ECOPS, the repetition rate of
the pump is modulated to avoid wasting the temporal window between consecutive
pulses.
876 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
To reduce the size of the scanned temporal window, electronically controlled optical
sampling (ECOPS) has been developed as an alternative to ASOPS [240–242]. In
ECOPS, the repetition rate of one of the lasers is precisely controlled by electronically
modulating the cavity length of one of the lasers. Consequently, the scan range can be
correctly adjusted to the time of the THz pulse [Fig. 20(b)]. As a result, in Ref. [241],
a 77 ps time delay window is scanned at a scan rate of 1 kHz, an improvement of 50
times compared to the conventional ASOPS, using the same parameters. In Ref. [243],
for versatility, both the ASOPS and ECOPS techniques were implemented in the same
fiber-based laser system.
ASOPS and ECOPS techniques have many benefits. The absence of moving parts
allows for faster scanning rates, eliminates the positional instabilities of the laser
beam, and removes the electronic noise caused by motor movement. However, its
main disadvantage is the need to use two ultrafast lasers, which essentially doubles
the cost of the THz-TDS system.
The optical sampling by laser cavity tuning (OSCAT) technique simplifies the system
by using a single femtosecond laser [244–246]. Instead of having balanced optical
paths in the emitter and detector sides, OSCAT uses the pulse iand the successive
pulse iain the same pulse train. Consider a laser emitting a train of optical pulses
with a repetition rate of fthat can be tuned by Δf(Fig. 21). The pulse iand the pulse
iahave unbalanced optical paths, where the pulse iahas travelled the
additional optical path length:
laac
nf ,(29)
with cthe speed of light and nthe refractive index of the propagation medium for the
pulse ia, for example, an optical fiber. With such unbalanced optical paths, the
optical delay between the pulse iand the pulse iais a function of the laser
repetition rate fand its tuning Δfthrough the following relation:
δta1
f
−
1
fΔf:(30)
Therefore, by dynamically changing the tuning Δf, the temporal window between two
optical pulses can be scanned.
OSCAT was first introduced and demonstrated in cross-correlation measurements in
Refs. [244,245]. In Ref. [246], the OSCAT technique was implemented for THz-TDS,
with a 1550 nm fiber-coupled laser with a repetition rate of f250 MHz that
could be tuned over Δf2.5 MHz using a precise intracavity stepper motor in
the laser cavity. Therefore, to use the maximal delay between two adjacent pulses
Figure 21
1234
3
4
i
i+a
δ
tla
Laser
f and Δf
Schematic description of the OSCAT technique.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 877
(Δt1∕f4ns), a101st consecutive pulse must be used. This results in an ad-
ditional optical path of la121 m in free space for the pulse ia. Since this dis-
tance is impractical for compact THz-TDS systems, a combination of a standard
single-mode fiber and a telecom dispersion fiber of a total length of 80 m was used.
The same system was also operated in a rapid scan regime using a 3.5 kHz piezoac-
tuator in the laser cavity to demonstrate over 5 ps optical delay at a scan rate of 100 Hz.
Today, using the OSCAT technology, commercial systems achieve up to 40 ps total
delay at scanning rates of 200 Hz.
3.3. Photoconductive Antenna Arrays
Integration of several PCAs into imaging arrays is an interesting proposition for
real-time THz-TDS imaging. In this section, we overview some attempts to fabricate
arrays of PCAs. In Ref. [247], Pradarutti et al. fabricated an array of 15 antennas with
an inter-antenna distance of 1 mm packaged into a single photoconductive chip. Each
antenna featured a gap of 30 μmby5μm. By using a telescope system and cylindrical
lenses, they focused a 350 mW optical beam into an array of 15 PCA detectors
[Fig. 22(a)]. A multichannel lock-in amplifier was used to improve the SNR
[248]. The measured THz traces [Fig. 22(b)] demonstrate a lateral variation of the
amplitude that was related to the incident THz nonuniform profile. Then, they imaged
a metallic Siemens star of 60 mm ×50 mm [Fig. 22(c)] by moving the PCA array. The
image was acquired in ∼10% of the time required to measure it with a single-pixel
PCA. However, the area covered by the optical beam on the multiarray PCA
(10,000 μm×10,000 μm) was significantly larger than the effective gap area of
the PCA (75 μm×75 μm). Consequently, only about 2.6 mW illuminated each
gap, while the remaining increased the overall noise level. In Ref. [249], a microlens
array was used to focus the optical beam into the gaps. In Ref. [250], the authors
proposed and experimentally explored a concept of dynamically reconfigurable
THz-PCA arrays. Such arrays feature several wide-gap THz antennas placed in
parallel to each other that were dynamically interrogated by steering a multifocused
Figure 22
(a) Schematic and geometry of the linear array of PCA with 15 detectors used in
Ref. [247]. (b) Simultaneously recorded THz pulses. (c) Photograph and (d) imaging
of a metallic Siemens star. Reprinted with permission from [247]. Copyright 2014
Optical Society of America.
878 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
optical pump beam along the antenna gaps. The pump beam was formed and steered
using a spatial light modulator.
Designing and using PCA arrays, although very attractive, presents many challenges.
Considering that the efficiency of a single PCA is relatively low, simultaneous inter-
rogation of multiple PCAs requires powerful probe beams. For example, a 10 ×10
array using 10 mW per channel would require a 1 W femtosecond laser. Additionally,
the focusing optics are complicated to manufacture, and dense integration on multiple
antennas on the same chip is problematic due to crosstalk or interference between
them. These practical difficulties currently confine almost exclusively the use of
PCAs as coherent single-pixel detectors for imaging (see Section 5).
3.4. EOS with Visible/Infrared Cameras
3.4a. Dynamic Subtraction and Balanced Electro-Optic Detection in a Camera
Within the EOS modality, since it is an optical beam in the visible/infrared region that
is detected, conventional charge-coupled device (CCD) or complementary metal-
oxide semiconductor (CMOS) visible/infrared cameras can be used to obtain a 2D
THz image. However, unlike single-pixel detection schemes, the use of unfocused
beams decreases the local amplitude of the detected signal, approaching it to the noise
level. Furthermore, the SNR of an EOS-based THz imager suffers from the limited
ability of directly using lock-in detection with the CCD and CMOS devices. In the
following, we highlight some techniques developed in the literature to increase the
SNR when using CCD/CMOS cameras with EOS.
Already in 1996, Wu et al. demonstrated EOS imaging with a ZnTe crystal and a
thermoelectrically cooled CCD camera [67]. However, unlike in the case of
single-pixel EOS, the THz beam is spread over a larger surface and no lock-in am-
plifier can be directly used with the CCD. This resulted in a poor SNR that required
the use of a thermoelectrically cooled camera. The dynamic subtraction technique was
introduced in Refs. [251–253] to improve the sensitivity. The technique essentially
consists of subtracting a reference frame (without THz) from a signal frame (with
THz) to dynamically remove the background noise.
To increase the sensitivity even further, in Ref. [254], Pradarutti et al. demonstrated
balanced electro-optic detection using a linear array consisting of eight pairs of
InGaAs photodiodes in conjunction with a Wollaston prism. Although their approach
combined lock-in amplification to enable high SNR, raster scanning was still neces-
sary to scan along the second dimension. In Ref. [255], both dynamic subtraction and
balanced electro-optic signals were used to increase the SNR. A Wollaston prism
divided the optical probe beam into two mutually orthogonal polarizations that were
detected simultaneously by a CCD [Fig. 23(a)]. As expected [256], the two measured
polarizations had opposite values such that their difference increased the signal by a
factor of 2 [Figs. 23(b) and 23(c)]. An algorithm was designed to perform the sub-
traction of the two images and reduce the misalignment errors. Furthermore, dynamic
subtraction was performed by subtracting one frame (with THz signal) from a refer-
ence frame (without THz). An example of a THz image is given in Figs. 23(d) and
23(e). In Ref. [257], the authors added a half-wave plate in the probe beam to
perform real-time THz polarization imaging.
3.4b. Real-Time Near-Field EOS Imaging
Real-time near-field imaging using EOS is possible by placing the sample in direct
contact with the nonlinear EOS crystal. In Ref. [258], Blanchard et al. imaged an area
of 370 μm×420 μmat 35 frames per second with a spatial resolution of 14 μm(λ∕30
at the center frequency of 0.7 THz). To achieve such performance, the authors
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 879
generated a THz pulse with a peak electric field of 200 kV/cm by optical rectification
in LiNbO3using a tilted-pulse-front excitation. For detection, the THz pulse was
focused on a LiNbO3crystal with a thickness of 20 μm [Fig. 24(a)]. On the opposite
side, the 800 nm probe light interacted with the crystal and was reflected into a
balanced imaging setup using a CCD camera. As in Ref. [255], corresponding pixels
of the orthogonal polarizations were subtracted to increase the SNR. To obtain high
spatial resolution, a very thin electro-optic crystal has to be used. At the same time, a
powerful THz source was necessary to compensate for the small interaction length
between the THz and the optical probe. To demonstrate the ability of their THz micro-
scope in imaging near-field structures, a metallic dipole antenna of subwavelength
dimensions was directly deposited on top of the LiNbO3crystal [Fig. 24(b)]. By
displacing the delay line, the reemitted THz radiation from the dipole could then
be imaged at the picosecond scale [Fig. 24(c)].
In Ref. [260], to demonstrate biomolecule probing, free induction decay of a tyrosine
crystal was observed in the near field, while in Ref. [261], resonant modes of a split
ring resonator were imaged. Since then, many methods have been considered to
Figure 23
(a) Experimental setup for EOS with a CCD camera. (b) Both polarizations measured
spatially by the CCD and (c) as a function of time with the delay line. (d) Photograph
of the letter T engraved in wood and (e) reconstructed THz image by subtracting cor-
responding pixels in the CCD. Reprinted from Opt. Commun. 283, Wang et al.,
“Terahertz real-time imaging with balanced electro-optic detection,”4626–4632
[255]. Copyright 2010, with permission from Elsevier.
880 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
further increase the spatial resolution [170,259,262]. In Ref. [259], spatial resolution
up to λ∕600 at 100 GHz has been demonstrated. To achieve such performance, the
LiNbO3crystal thickness has been reduced to 1 μm, the optical probe was spectrally
Figure 24
(a) Experimental setup of the EOS THz microscope with a CCD camera. (b), (c) Near-
field imaging of a metallic antenna in the process of re-irradiating the incident THz
pulse. Reprinted with permission [258]. Copyright 2011 Optical Society of America.
(d) Demonstration of improved spatial resolution by imaging a Sierpinski fractal
(e) without spectral filtering and a 10 μm crystal (top), with spectral filtering and
a10μm crystal (middle), and with spectral filtering and a 1 μm crystal (bottom).
Reprinted with permission from [259]. Copyright 2016 Optical Society of America.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 881
filtered, and a 10× objective lens was used. A 100 nm thick gold Sierpinski fractal was
patterned on top of 10 μm and 1 μm crystals [Fig. 24(d)] and imaged in Fig. 24(e).By
reducing the crystal thickness and by using spectral filtering, the spatial resolution was
increased. To enable real-time near-field EOS imaging, a detailed description of the
needed components is reviewed in Ref. [170].
3.4c. Temporal Encoding in the Camera
To record the complete THz temporal waveform, an optical delay line is still
necessary. In principle, one could use the methods described in Section 3.2.
However, for EOS sampling, one of the spatial dimensions of the camera can be used
to encode the temporal dimension of the waveform. This idea was first demonstrated
in Refs. [263–265] by using a chirped optical probe beam. Since distinct wavelengths
travel with different speeds inside the EOS crystal, their polarizations are differently
affected by the THz radiation through the Pockels effect. This essentially encodes
temporal information about the THz waveform into the spectrum of the optical probe.
Therefore, by using a grating to disperse the optical spectrum into a linear detector
array, the THz temporal waveform can be sampled without the use of an optical
delay line.
In Ref. [266], Shan et al. demonstrated single shot measurement of the temporal
waveform by introducing an angle between the optical probe beam and the THz pulse.
Thus, different points in the transverse spatial profile of the optical probe beam ex-
perienced different temporal positions of the THz electric field. Again, a linear array
of detectors was used to resolve the THz waveform in a single shot. In Ref. [267],
Yasuda et al. used a similar non-collinear geometry with a CCD camera [Fig. 25(a)].
One dimension was used to encode the temporal THz waveform, while the second
was used to image one spatial dimension [Fig. 25(b)]. In [163], 3D imaging using
THz-CT (Section 2.4) was demonstrated by imaging a pharmaceutical tablet in only
6 min [Fig. 25(c)]. To obtain a 2D image, the sample can be moved in the second
dimension [268]. This approach is attractive for many industrial applications where
a conveyer belt is used. This was demonstrated for biomedical applications in
Ref. [269]. There, pharmaceutical tablets moving on a conveyer belt were imaged.
Furthermore, spectroscopic identification of the crystallinity of dental tissue was
demonstrated, along with observation of the drying process of wet hair.
3.5. Section Summary and Future Directions
Even though THz cameras are in rapid development (see Section 4), the development
of THz-TDS-based imaging systems is still of great importance, since they can pro-
vide additional/complementary spectroscopic information to reconstruct an image
(Section 2.1). Furthermore, they feature outstanding SNR due to the lock-in tech-
nique. The ability of THz-TDS to measure both the amplitude and the phase of
the THz pulse electric field allows for unique imaging modalities that simply cannot
be achieved with conventional intensity-based THz cameras. For example, THz-TDS
imaging can be used to map the complex refractive index and the conductivity of a
sample, even at a subwavelength scale (near-field imaging).
As we saw in this section, the technical challenges to enable real-time THz-TDS im-
aging are intrinsically related to the THz-TDS setup. First, the mechanical linear op-
tical delay line must be replaced to enable the acquisition of multiple THz pulses per
second. Rotary optical delay lines in the form of curved mirrors in the optical path or
prisms in the THz path are simple and cost-effective solutions. Ultimately, their speed
is still limited by the motor or turbine rotation speeds and air turbulence, as well as by
the need for costly high-speed electronics for signal processing. At the same time,
non-mechanical solutions such as ASOPS, ECOPS, and OSCAT are attractive since
882 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
they can provide acquisition rates in the kilohertz range. Some of them are already
commercially available, but ASOPS and ECOPS require the use of two synchronized
femtosecond lasers, which essentially doubles the cost of the THz-TDS systems. In
comparison, the OSCAT technique needs only one laser, at the expense of using
dispersive fibers to generate the optical path differential.
The second problem that impedes real-time imaging is the fact that classical THz-TDS
systems are built with single-pixel detectors. There are two major technologies to
detect THz pulses: photoconductive antennas and EOS. For now, it seems that photo-
conductive antennas, while having a very high SNR, do not constitute the preferred
approach for real-time THz imaging due to the necessity of slow raster scanning. So
far, dense integration of multiple antennas on a single chip has proven to be
problematic due to the electromagnetic crosstalk between them and the necessity
of using multichannel lock-in systems (one lock-in per pixel). Additionally, interrog-
ating multiple antennas at the same time also requires a powerful probe laser and
intricate micro-optics for laser focusing. While several works demonstrated the
fabrication of arrays of photoconductive antennas, we believe that the main applica-
tion of photoconductive antennas will remain in the context of single-pixel imaging
(Section 5) using beam-steering optics (Section 5.1), compressive sensing
(Section 5.2), spectral encoding methods (Section 5.3), or other computational
imaging techniques.
Figure 25
(c)(b)
(a)
I
II
I
II
5 mm 5 mm
(a) EOS imaging setup using a non-collinear geometry and a CCD camera. (b) One
dimension of a CCD camera records the temporal waveform, while the second one
measures spatial information along one dimension. Reprinted from Opt. Commun.
267, Yasuda et al.,“Real-time two-dimensional terahertz tomography of moving ob-
jects,”128–136 [267]. Copyright 2006, with permission from Elsevier. (c) 3D imaging
of a pharmaceutical tablet acquired in 6 min using a THz-CT. Reprinted with permis-
sion from [163]. Copyright 2013 Optical Society of America.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 883
In comparison, EOS has recently attracted much attention in the context of 2D real-
time THz-TDS imaging. The fact that the technique records visible/infrared light
means that conventional visible/infrared CMOS/CCD cameras can be used. EOS-
based imaging still lacks in SNR compared to a photoconductive antenna detector
with a lock-in amplifier, so further noise management within this technique is re-
quired. Moreover, there is a real interest in near-field EOS imaging since the crystals
used to generate the EOS signal can also be used as sample substrates (contact-based
near-field imaging). This interest is certainly driven by the recent development of ef-
ficient generation techniques with optical rectification and tilted-pulse excitation that
allow reduction of crystal thickness, and, therefore, increase spatial resolution. In this
context, EOS THz-TDS microscopes are within reach.
Finally, we would like to discuss two research directions that have emerged recently
that may have important impact on THz-TDS systems in general, and THz-TDS
imaging in particular. These are (1) THz quasi-time-domain spectroscopy systems
(THz-QTDSs) and (2) CMOS-based electronic generation and detection of THz
pulses. The THz-QTDS aims at replacing an expensive ultrafast laser by less expen-
sive multimode laser diodes [270–272]. In short, a multimode laser beam comprising
equally spaced spectral lines is focused onto a photoconductive antenna. In time do-
main, the result is a THz pulse train with a repetition rate that is determined by the
mode spectral spacing [273]. In Ref. [274], imaging with a THz-QTDS system was
demonstrated by using a 100 mW multimode laser diode at 662 nm, with mode spac-
ing of 25 GHz and spectral emission bandwidths of 3 nm. In Ref. [275], a compact and
cost-effective THz-QTDS system was proposed by mounting the laser diode directly
onto a mechanical delay line extracted from a DVD drive. This prototype was fully
controlled by a Raspberry Pi single-board computer with a sound card that fed the
emitter antenna with a reference voltage, detected the current for digital software
lock-in amplification, and controlled the stepper motor. In Ref. [276], a fiber-coupled
THz-QTDS system was demonstrated using conventional telecom technology at
1550 nm. All these prototypes may pave the way for extremely affordable THz spec-
troscopy systems. However, the challenges for imaging applications using THz-QTDS
are similar to those based on THz photoconductive antenna technology, namely, those
related to the single-pixel nature of the detection device.
A second emerging idea for THz spectroscopy is the electronic generation and
detection of THz pulses. Here, the main advantage is to completely avoid the use
of lasers for THz pulse generation. These recent developments are based on
CMOS processing technology, which may be beneficial toward mass fabrication
of THz spectroscopy systems at lower costs. Two avenues are being considered
for electronic generation of THz pulses. The first idea uses a technique similar to
mode-locking in femtosecond lasers to dynamically shape pulses [277]. Using oscil-
latory CW sources on silicon, picosecond pulses are emitted by carefully controlling
the amplitude and phase of the fundamental frequency and the multiple harmonics.
The second idea is inspired by the spark gap transmitter, where an electromagnetic
pulse is emitted by an antenna following a fast-rising/falling current switching [278].
Initially, an antenna stores a DC current in the form of magnetic energy, and, when the
current is turned OFF, the antenna converts the energy into a radiated picosecond
pulse. Similarly, an impulse is emitted following an ON switch. For now, the detection
of these picosecond pulses has been demonstrated using a conventional THz-TDS
system or using horn antenna detectors. Interestingly, in Ref. [279], an on-chip
THz spectral detector is realized by measuring the scattered current density on a multi-
port antenna. The general concept is that different scattering modes are excited on the
antenna depending on the excitation frequency. Therefore, the spectrum can be recon-
stituted by measuring the spatial current density and by using a one-time calibration
884 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
procedure. For now, these ideas of emission and detection of THz pulses using
electronic means are limited to the sub-THz region.
4. THZ CAMERAS
Over the past decade, intensive research has been conducted to develop THz cameras
similar to those available in the visible region of the spectrum. THz cameras must
satisfy a number of requirements before deployment in industrial applications.
First, they must operate at room temperatures while still retaining high sensitivity,
thus forgoing the complexity associated with cumbersome and expensive cryogenic
cooling systems. Second, to reduce the cost, the fabrication process of the THz cam-
eras should be compatible with modern fabrication techniques, such as the CMOS
process technology, which also allows scaling into high-resolution imaging arrays.
Third, the size and weight of a THz camera along with its total power consumption
should be small enough to facilitate the integration into industrial imaging systems.
Finally, a THz camera should be sensitive enough to allow recording of THz videos at
a high frame rate. This is especially important since powerful THz sources (particu-
larly broadband sources) are still sparse. Ideally, the detector should be sensitive
enough to record a THz image in passive imaging, i.e., without an active THz source.
Ideally, THz cameras should be able to detect complex electric fields, while, for now,
most THz cameras can detect only intensity. This, and the fact that cheap, high-power
THz sources are still lacking, drive the competition between imaging using single
point detection versus imaging using multipixel arrays.
In general, the performance of THz detectors can be characterized with two important
figures of merit: the responsivity and the noise-equivalent power (NEP). The respon-
sivity is the direct detector response (either in volts or amperes) to the incident THz
power (in watts). It can be expressed in V/W or A/W, with the majority of THz im-
aging arrays employing voltage to characterize the THz signal. To measure the re-
sponsivity, one typically measures the total incident power using an etalon
technique. In the case of THz cameras, assuming that the imaging array captures
all the incident THz power, the responsivity per pixel can be assessed by summing
the voltages of all the pixels and then dividing it by the total incident power. In general,
higher responsivity is an indication of a better performing detector.
The NEP is a measure of the minimum detectable power. It is defined as the input
power that results in a signal equal to the noise (SNR 1) with a 1 Hz bandwidth
output. It is measured in W
ffiffiffiffi
Hz
p, and a lower NEP indicates a more sensitive detector.
However, due to specific data acquisition conditions when using a camera, the mini-
mum detectable power (in W) is often a better quantity to characterize the video mode
operation. It corresponds to the lowest power that can be measured by a single pixel in
a single frame. Clearly, this parameter depends on the frame rate, and a reduced frame
rate can generally detect lower THz powers.
In this section, we review the two main classes of THz cameras that have been
reported in the modern literature: THz thermal cameras and THz FET cameras.
4.1. THz Thermal Cameras
THz thermal cameras detect the heat generated by incident THz radiation. Depending
on the detection principle of the heat, one usually distinguishes three types of thermal
detectors of THz radiation: 1) Golay cells, 2) pyroelectric sensors, and 3) bolometers.
In an imaging setup, they are commonly used with a modulated source, which is pro-
duced using an optical chopper, for example. While this allows reducing the ambient
noise, it reduces the overall maximum frame rate that can be obtained at room
temperature. The main advantage of thermal detectors is that they have very broad
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 885
spectral range of operation, something that is typically not obtainable with photon
detectors.
In Golay cells, the generated heat is transferred to an expanding gas cell. The increased
pressure is then optically measured by moving mirrors [58]. Since they rely on the
mechanical movement of a membrane, Golay cells are slow detectors. Nevertheless,
due to their simple operating principle, they are widely used to measure THz power.
However, they are difficult to integrate into dense arrays of detectors. Consequently,
THz imaging with Golay cells is often done in a single-pixel detection scheme [280].
Values for the NEP in Golay cells range between 0.1 and 10 nW∕ffiffiffiffiffiffi
Hz
p.
Pyroelectric sensors detect changes in the electrical polarizability of certain crystals
caused by increase in the temperature. When an absorbing layer transfers the heat to
the crystal, a temporary voltage is generated. Common pyroelectric crystals are tri-
glycine sulfate (TGS), deuterated triglycine sulfate (DTGS), lithium tantalate
(LiTaO3), and barium titanate (BaTiO3). Among these, TGS and DTGS have the high-
est sensitivities at THz frequencies [281], with typical responsivity and NEP of
∼1kV∕Wand 1nW∕ffiffiffiffiffiffi
Hz
p, respectively, at a modulation frequency of ∼10 Hz.
Unlike Golay cells, pyroelectric detectors are commercially available as array
cameras. For example, in Ref. [282], Yang et al. used a 124 ×124 pixel pyroelectric
commercial camera to demonstrate THz imaging with a gas laser source at 1.89 THz
(70 mW average power). Sensitivity of the pyroelectric detectors can be improved by
reducing the crystal thickness and by increasing THz absorption in the crystal coating
layer. Typical minimum detectable power for commercial pyroelectric cameras is in
the range of 50–100 nW.
Another type of THz camera uses thermal bolometers as individual pixels. Because of
the relatively high sensitivity and established fabrication technology, bolometer im-
aging arrays are currently considered prime candidates for real-time THz imaging.
The bolometer pixel operates by measuring changes in a temperature-dependent re-
sistance. In Fig. 26(a), we have summarized the main constituents of a bolometer as
described by Richards [283]. The radiation power PTHZ from the THz beam is incident
onto an absorbing element (heat capacity CA) connected via a thermal link (conduct-
ance GL) to a heat sink (reservoir at temperature TS). The temperature of the absorbing
element TArises at a rate dTA∕dt PTHz∕CAto the limiting value TATSPTHz
GL,
with the thermal time constant τCA∕GL. When the illumination is turned off, the
temperature TArelaxes back to Tswith the same time constant [Fig. 26(b)]. This
Figure 26
Thermal link (GL)
Resistive
thermometer
Absorber (CA)
Heat sink (Ts)
THz (PTHz)
Temperature
Time
THz ON THz OFF THz ON
Ts
Ts + PTHz/GL
(a) (b)
(a) Schematic representing the main components of the bolometer. (b) Rise and fall of
the temperature in the absorber as a function of time.
886 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
temperature change is measured with a resistive thermometer (typically amorphous
silicon or vanadium oxide) connected to the absorbing element.
Microbolometers are arrays of bolometers mounted onto readout integrated circuits
(fabricated with CMOS process technology) for focal-plane camera operation. As the
operation principle of microbolometers is not wavelength specific, commercial micro-
bolometers designed for infrared radiation were first used for real-time THz imaging
[284–287]. For example, in Ref. [285], Lee et al. used a commercial 320 ×240 pixel
uncooled vanadium oxide (VOx) microbolometer focal-plane array camera designed
for 7.5–14 μm wavelengths. They used a quantum cascade laser at 4.3 THz (50 mW
peak power) as a source to image the contents of a closed envelope. Since the camera
was sensitive to both THz and infrared background radiation, three frames were nec-
essary to obtain a THz image. The third frame (infrared signal only) was subtracted
from the first frame (both infrared and THz signals), while the second frame was used
as a buffer for the temperature to decay in the bolometer. This resulted in an overall
frame rate of 20 frames per second (fps). In their following work, the authors also
demonstrated stand-off real-time THz imaging at a distance of 25 m [288].
In more recent years, microbolometers were specifically designed to operate in the
THz range. When cooled at cryogenic temperatures to remove background thermal
noise, they can achieve remarkable NEP in the range of 10−16 W∕ffiffiffiffiffiffi
Hz
p[71].
However, with proper design modifications, even at room temperatures, microbolom-
eters can demonstrate high enough sensitivities to be suitable for a variety of industrial
imaging applications. In Refs. [52,289], the authors at NEC corporation proposed to
use a cavity structure to increase the sensitivity of a microbolometer THz camera of
320 ×240 pixels. Their device is schematically presented in Fig. 27(a) [290]. A thin
metallic layer of TiAlV absorbed the THz radiation and induced changes in the re-
sistance of the thermometer (VOxfilm). Under the THz absorber layer, a thick metallic
layer was placed, which reflects the unabsorbed THz radiation back into the bolom-
eter. This geometry represents a resonating Fabry–Perot cavity between the bolometer
and the reflector. A SiNxlayer was added to ensure the mechanical stability of the
device and to match the effective cavity length with the THz wavelength. This addition
led to an increase in the sensitivity in the sub-THz region, where the microbolometers
are generally underperforming. They reported a minimum detectable power of
100 pW at 1 THz. Using optical rectification with tilted-pulse-front excitation in
LiNbO3, they demonstrated THz imaging of a dry leaf [Fig. 27(b)]. In Ref. [291],
they used the microbolometer in conjunction with a diffraction grating to develop
a real-time spectrometer that could operate at 15 fps.
In Refs. [54,292,293], the authors, affiliated with CEA-LETI, used an antenna to in-
crease coupling of THz radiation to the amorphous silicon-based transducer in a
bolometer [Fig. 27(c)]. Crossed bow-tie antennas were placed on top of a microbridge
bolometer membrane. Both THz radiation polarizations were coupled through the dis-
sipative currents in the load resistances located in the center of a bolometer. The an-
tenna-coupled bolometer membrane was suspended on an 11 μm thick SiO2layer
deposited over a metallic reflector to create a resonant cavity. In principle, the dimen-
sions of the antenna and the cavity length can be tailored to any THz frequency. They
achieved a minimum detectable power of 30 pW at 2.5 THz [quantum cascade laser
(QCL) source]. Hidden objects under a shirt were imaged, and the field of view was
increased with fast scanning optics [Fig. 27(d)].
Metamaterials have been investigated to increase the absorption of THz radiation
[294–297]. In Ref. [298], Carranza et al. fabricated a 64 ×64 focal-plane array with
metamaterial absorbers using a 180 nm CMOS process. Their main motivation was to
exploit as much of the CMOS process technology as possible, thereby avoiding costly
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 887
postprocessing fabrication techniques. Thus, they integrated the readout electronics
and the metamaterial absorber in the CMOS process. The metamaterial was designed
to provide a broadband response centered around 2.5 THz. As for the sensor, they
investigated two types of resistive thermometer. First, they patterned a VOxsensor
using postprocessing techniques, and they achieved a minimum NEP of
108 pW∕ffiffiffiffiffiffi
Hz
pand a responsivity of 59 kV/W. Their second prototype used a silicon
p−ndiode as the sensor. Although the diode is less sensitive to temperature changes,
it can be patterned directly with the CMOS process. They obtained NEP of
10.4nW∕ffiffiffiffiffiffi
Hz
pand a responsivity of 274 V/W.
4.2. THz Field-Effect Transistor-Based Cameras
Rectification in the field-effect transistor (FET) is the second technological trend in
THz cameras. Previous reviews on the topic can be found in Refs. [62,299,300,301].
The general idea is to use plasma wave excitations to enable response at frequencies
considerably higher than the maximal transistor operation frequency (cut-off fre-
quency). In the 1990s, using a direct analogy between the electron transport equation
in 2D gated material and the hydrodynamic equations in shallow water, Dyakonov and
Shur theoretically demonstrated that plasma waves in the FET channel could be used
for THz detection [302]. Figure 28(a) schematically represents their proposed FET for
THz detection. A DC voltage U0is applied between the gate and the source, while the
incident THz radiation causes an alternating voltage Ua. Because of the asymmetry of
the boundary conditions and due to the nonlinear properties of the plasma waves, a
constant drain-to-source voltage ΔU∝U2
ais generated.
Figure 27
(a) Schematic representation of the cavity microbolometer developed in Ref. [290]
(inset: micrograph). (b) Raw images without (top) and with (bottom) the dry leaf.
(c) Corrected image for the non-uniform THz beam profile. © 2016 IEEE.
Reprinted, with permission, from Nemoto et al., IEEE Trans. Terahertz Sci.
Technol. 6, 175–182 (2016) [290]. (d) Schematic representation of the antenna-
coupled bolometer developed in Ref. [54]. (e) Photograph of objects under a shirt
that were (f) imaged with THz. Reprinted with permission from Simoens et al.,J.
Infrared Millim. Terahertz Waves 36, 961–985 (2015) [54]. Copyright 2015 Springer.
888 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
They predicted resonant (frequency-specific) and non-resonant (broadband) detection
mechanisms, depending on the electron momentum relaxation time τthat defines the
conductivity in the channel σne2τ∕m(n,e, and mare the electron density, charge,
and mass, respectively). Given an incident THz radiation at frequency ω, the resonant
case occurs when ωτ >1, that is to say, when the channel conductivity is large. In this
case, provided that the channel length Lis sufficiently small, the plasma waves reach
the drain side of the channel, are reflected back, and create a standing wave. A wave-
length-specific DC voltage is then developed between the drain and the source [302]:
ΔUReτ2
L2mU2
a
4ω−mω02τ21,(31)
where m1,3,5,7,…. Experimental evidence of THz detection in the resonant re-
gime was demonstrated with a III–V high-electron mobility transistor in Ref. [303].
In the non-resonant regime (when ωτ <1), the plasma waves are overdamped and
cannot fully reach the other side of the transistor channel. In this case, a DC photo-
response between the drain and the source still exists in the form of an exponential
decay [300]:
ΔUNR U2
a
4U01−exp−2x∕lc,(32)
where xis the distance from the source and lcis the characteristic decay length
(typically a few tens of nanometers [304]). This type of broadband detection occurs
in silicon FETs.
The seminal work by Dyakonov and Shur sparked a series of experimental demon-
strations of THz detection in FETs, first with III–V semiconductors [305–309], then,
more recently, with InAs nanowire [310], graphene [311], and black phosphorus
[312]. However, in the short term, the work on silicon-based FETs will probably have
more impact on development of THz cameras thanks to the compatibility of silicon
material with the standard CMOS-foundry process, thus enabling large scale array
fabrication at lower costs.
THz detection with silicon FETs was first experimentally demonstrated in
Refs. [313,314]. Their behavior was explained by using the non-resonant broadband
detection mechanism of Dyakonov and Shur. In Ref. [61], it was shown that the NEP
of silicon FETs (100 pW∕ffiffiffiffiffiffi
Hz
p) was comparable to conventional THz detectors op-
erating at room temperature (such as thermal detectors). In Ref. [315], using circuit
theory, the authors described the non-resonant FET detection mechanism with the
distributed resistive self-mixing concept, where the channel was modeled as a
Figure 28
Gate
Source Drain
ΔU
U0
Ua
Schematic representation of the field-effect transistor used for THz detection. A DC
voltage U0is applied between the gate and the source, while the incident THz
radiation causes an alternating voltage Ua.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 889
nonlinear resistance–capacitance (RC) transmission line [316]. This theoretical frame-
work helped them to design an efficient 3×5 pixel array of FET detectors using
250 nm CMOS process technology [Fig. 29(a)]. Each pixel consisted of a patch an-
tenna designed for 0.65 THz coupled to a FET detector and a voltage amplifier,
achieving a minimal NEP value of 300 pW∕ffiffiffiffiffiffi
Hz
p. Using lock-in amplification, they
imaged the inside of an envelope [Fig. 29(b)]. In Ref. [317], the same group dem-
onstrated improvement in the image contrast by using a heterodyne detection scheme
in transmission mode [Fig. 29(c)]. A reference THz source (local oscillator) was
combined to the transmitted THz beam to image details of the inside of a tablet
[Fig. 29(d)]. In Ref. [318], a similar heterodyne scheme was used in both transmission
and reflection modalities with an antenna-coupled FET fabricated on 150 nm CMOS
process technology [319].
In Ref. [304], Schuster et al. studied the performance of several THz FET detectors
fabricated using 130 nm Si CMOS, with embedded bow-tie antennas of different
geometries and configurations. They obtained record NEP (<10 pW∕ffiffiffiffiffiffi
Hz
p) and
responsivity (>5kV∕W, without amplification) at 0.3 THz by reducing the size
of a silicon substrate (to reduce absorption losses), by using a shorter channel length
and by connecting the antenna to the gate and source (to avoid parasitic THz collection
on the drain side). They also demonstrated imaging up to a frequency of 1.05 THz. In
Ref. [320], multispectral THz imaging was demonstrated with silicon FETs fabricated
Figure 29
(a) Micrograph of the 3×5array of FET developed in Ref. [315]. (b) THz radiation
revealing the inside of an envelope. © 2009 IEEE. Reprinted, with permission,
from Ojefors et al., IEEE J. Solid-State Circuits 44, 1968–1976 (2009) [315].
(c) Heterodyne detection scheme using a second source as a local oscillator [317].
(d) Image of a dextrose tablet wrapped in polyethylene foils. When compared to
the direct detection mode, the heterodyne mode provides more contrast. Reprinted
with permission from Glaab et al., Appl. Phys. Lett. 96, 042106 (2010) [317].
Copyright 2010 AIP Publishing LLC.
890 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
using a commercial 90 nm CMOS process. A record high frequency of 4.25 THz with
a NEP of 110 pW∕ffiffiffiffiffiffi
Hz
pwas measured.
In the works reviewed above, the THz images were still obtained by mechanically
scanning the sample, limiting the image acquisition time. However, the main
advantage of using silicon FET is its compatibility with mainstream CMOS process-
ing, which also enables on-chip integration with read-out electronics for mass fabri-
cation of imaging arrays. Thus, in Refs. [63,321], Al Hadi and co-workers fabricated
an array of 32 ×32 pixels using 65 nm CMOS process technology [Fig. 30(a)]. In
addition to the ring antenna and the FET detector, each pixel included a reset circuit to
clear the accumulated charges, an integration capacitor, and a differential amplifier.
Each row was biased one at a time and the columns were consecutively selected
with an external programmable logic device located inside the camera. The THz
camera was packaged in a metal box with an integrated silicon lens for compact
handheld applications [Fig. 30(b)]. The authors demonstrated 0.65 THz video
recording using a focal-plane array configuration [Fig. 30(c)]. A digital still taken
from the 24 fps video recording is presented in Fig. 30(e). The authors measured
a minimum detectable power of 20 nW. Recently, Zdanevičius et al. were able to
measure a minimal power of 1.4 nW at 30 fps [322]. The noise was reduced by
using a parallel read-out architecture to simultaneously interrogate 48 pixels of their
24 ×24 pixel array.
Figure 30
(a) Micrograph of the 32 ×32 focal-plane array developed in Ref. [63].
(b) Photograph of the THz camera device. (c) Transmission mode imaging setup
in a focal-plane array configuration. (d) Photograph of a 6 mm wrench and
(e) THz still image obtained from a 25 fps video stream at 650 GHz. © 2012
IEEE. Reprinted, with permission, from Hadi et al., IEEE J. Solid-State Circuits
47, 2999–3012 (2012) [63].
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 891
4.3. Section Summary and Future Directions
As we saw in this section, several requirements are necessary to enable mass deploy-
ment of THz cameras in various applications. They must operate at room temperature
without the need of cryogenic cooling. Their fabrication must be compatible with
modern standard process technologies, such as the CMOS process technology.
Their size, their weight, and their power consumption should be relatively small
for easy integration into optical systems. Finally, they should be sensitive enough
to allow recording of a THz signal at high frame rate, eventually without any active
THz source. In the past decade, two major types of THz cameras have attracted
attention: THz thermal cameras and THz FET-based cameras.
The first demonstrated THz cameras recorded an image based on the heat generated by
THz radiation. There are three types of thermal detectors. The Golay cell measures the
pressure change induced by the thermal expansion of a gas. Because of their simple
operating principle, they are routinely used to measure THz powers. However, they are
difficult to integrate into dense arrays of detectors and do not constitute a valid choice
for THz cameras. Pyroelectric sensors detect the generated electrical polarizability of
certain crystals when they are heated. Unlike Golay cells, pyroelectric cameras are
commercially available. However, their low sensitivity makes them less attractive
for THz imaging.
Bolometers detect the change in a temperature-dependent resistance. The main com-
ponents of a bolometer are the absorber that generates the heat, the resistive thermom-
eter that outputs the voltage, and the thermal link that dissipates the heat to the heat
sink. Microbolometers are arrays of bolometers mounted onto a read-out integrated
circuit for focal-plane camera operation. Microbolometers can reach impressive sen-
sitivities when cryogenically cooled due to the suppression of background thermal
noise. However, room temperature operation with remarkable sensitivities (minimum
detectable power of 100 pW) has been achieved thanks to recent advances in the
design, such as the inclusion of a Fabry–Perot cavity, antennas, and metamaterials
to increase the absorbed THz radiation.
THz FET-based cameras measure a rectified voltage after interaction of the THz ra-
diation with a plasma wave in a transistor channel. The theoretical work predicted
resonant (frequency-specific) and nonresonant (broadband) detection mechanisms.
There were numerous demonstrations of THz FET-based detectors, using a variety
of materials ranging from III–V semiconductors to graphene layers. However, in
the short term, silicon-based FETs will probably have more impact on the develop-
ment of THz cameras thanks to the compatibility of silicon material with the standard
CMOS-foundry process. This key advantage could enable large-scale array fabrica-
tion at reduced costs. The behavior of silicon FET can be explained using the non-
resonant broadband detection mechanism, as well as the distributed self-mixing
concept where the channel is modeled as an RC transmission line. Record NEP in
the range of pW∕Hz1∕2was obtained by using a bow-tie antenna to couple the incident
THz radiation at 0.3 THz, while broadband detection was used to measure frequencies
up to 4.25 THz with an NEP of 100 pW∕Hz1∕2. As for camera operation, minimal
detectable power in the range of 1–20 nW has been reported with up to 1024 pixels.
In addition to silicon-based FET cameras, future research directions include the de-
velopment of a THz emitter on a silicon platform. This would enable all-silicon THz
imaging systems attractive toward imager implementation at reduced costs. Several
silicon-based THz sources have already been demonstrated in the literature: 0.19 mW
at 0.28 THz [323], 0.81 mW at 0.34 THz [324], 1 mW at 0.53 THz [325], and 2 mW at
0.32 THz [326]. We expect increase in the power outputs and operation at higher THz
frequencies. For THz imaging, there are several important advantages of using such
892 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
sources. These types of sources can be used as local oscillators in heterodyne detection
schemes for coherent imaging [326], therefore increasing the image contrast. They
could also allow fabrication of on-chip transceivers, where the close proximity of
the emitter and detector allows subwavelength imaging in the near-field region
[182]. Finally, distributed arrays of silicon emitters could allow dynamic electronic
THz beam steering to increase the field of view of an imaging system [323].
We would like now to discuss on the potential of THz cameras and compare it with
THz-TDS imaging systems. Although the development of THz cameras is crucial for
many applications, we believe that it is not directly competing with THz-TDS imaging
systems. While THz cameras provide non-discriminatory intensity-based imaging, we
expect that amplitude-based THz-TDS imaging systems will develop into niche
sectors, where the application will drive the system design. Indeed, as we saw in
Section 2, the ability of THz-TDS to provide spectroscopic information in addition
to THz imaging proves to be useful in various applications, for example, in quality
control of large-area graphene or pharmaceutical applications.
5. THZ IMAGING WITH SINGLE-PIXEL DETECTORS
Historically, due to high cost and difficulty of manufacturing multipixel THz cameras/
arrays, many techniques have been proposed to enable real-time THz imaging using
single-pixel detectors. Such techniques are mature and can be used to build cost-
effective industrial imaging systems. Additionally, they have a large modernization
potential, as they could be greatly improved when substituting a single-pixel detector
with 1D or 2D THz pixel arrays (when they would become commercially available).
Finally, single-pixel imaging is often phase sensitive, allowing measurement of both
amplitude and phase information of the electric field with very high SNR, which is
one of its key advantages over intensity-only imaging using multipixel THz arrays.
Therefore, even with an advent of multipixel THz arrays, further development of
single-pixel techniques remains highly pertinent. In this section, we review the three
most prominent single-pixel imaging techniques: 1) mechanical beam steering, 2)
single-pixel imaging and compressive sensing, and 3) spectral/temporal encoding
and Fourier optics.
5.1. Mechanical Beam Steering
In a conventional THz imaging system, the sample is positioned at the focal point of
focusing optics. Then, using a single-pixel detector, the THz image is constructed by
physically moving the sample in the focal plane (see Fig. 15). However, in many
situations, sample displacement is not desirable or even possible. Instead of moving
the sample, one can steer the THz beam over the sample. In principle, one could use
spatial light modulation [327–330], special THz generation techniques [331–333], or
a distributed array of THz emitters [323,334] to accomplish this task. However, most
of the demonstrated applications for real-time THz imaging use mechanical beam
steering. In the following, we review two main types of mechanical devices:
(1) the oscillating mirror with an f-theta scanning lens and (2) the Gregorian reflector
system.
5.1a. Oscillating Mirror with an f-Theta Scanning Lens
The f-theta lens is a specially designed lens that provides a flat image plane for a range
of input angles [335–338]. Also known as a scanning lens, the f-theta lens is often
used along with galvanometers to convert an incident angle into a linear position in the
focal plane [Fig. 31(a)]. In Ref. [336], Katletz et al. combined flat mirrors mounted on
a two-axis galvanometer and a rotationally symmetric f-theta scanning lens to steer
the THz beam in two dimensions. A maximal scanning area of 100 mm ×100 mm
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 893
was collected in 1–2 min at the rate of 1 line/s, mainly limited by the speed of the
galvanometer. However, since the system was based on THz-TDS, the movement of
the delay line was still necessary. In Ref. [337], Yee et al. used similar beam steering
with ECOPS to obtain the temporal dimension (see Section 3.2c). A time delay win-
dow of 52 ps was acquired in 1 ms, which led to the acquisition of 100 mm ×100 mm
in 40 s. The authors also demonstrated 3D THz TOF imaging.
To avoid the need for a delay line, in Refs. [335,338], Ok et al. used a 210 GHz source
with an output power of 75 mW to demonstrate applications in food quality inspec-
tion. In Ref. [335], a combination of a single-axis galvanometer and an f-theta lens
were used to get the first spatial dimension, while the second was obtained with a
linear translation stage (conveyer belt configuration). A 100 mm ×150 mm image
was acquired in 15 s, limited again by the galvanometer speed. To further increase
the acquisition rate, in Ref. [338], a polygonal mirror was designed and fabricated to
replace the galvanometer [Fig. 31(b)]. With its four faces, one line can be acquired at
80 Hz, 4 times the rotor speed. To demonstrate food inspection, the authors buried
crickets in noodle flour [Fig. 31(c)]. A transmission image of 288 mm ×207 mm was
acquired in only 3.13 s [Fig. 31(d)] and compared with a conventional raster-scan
image obtained in 42 min [Fig. 31(e)].
In Refs. [164,339], a fast two-axis scanning mirror was used to steer a 2.5 THz beam
emitted from a THz QCL. The mirror could tilt in two directions and was placed at a
focal length from a high-density polyethylene lens. The THz beam was scanned over a
40 mm diameter region by spiral scanning of the mirror. An image with 0.5 mm res-
olution was acquired in 1.1 s. THz computed tomography was demonstrated in 87 s by
rotating the object by 180 deg in steps of 3 deg.
Figure 31
(a) f-theta scanning lens used in Ref. [335]. The colored lines correspond to an input
angle and are focused on a single point in the focal plane. Adapted with permission
from [335]. (b) Polygonal mirror used in Ref. [338] to replace the galvanometer.
(c) Photographs of the crickets. Inset shows the crickets buried under the noodle flour.
(d) Transmission image obtained in 3.13 s with the f-theta lens and the polygonal
mirror and (e) obtained in 42 min with a conventional raster-scan. Adapted with
permission from [338].
894 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
5.1b. Gregorian Reflector System
Security and defense are potential applications of THz imaging that has attracted
much of attention recently. Since many textiles are transparent to THz, concealed ob-
jects can be detected without exposure to ionizing radiation. In the f-theta lens that we
previously described, the field of view and the distance between the imaging optics
and the sample were limited to a few centimeters, which is not sufficient for stand-off
security applications. In this subsection, we review the Gregorian reflector system that
addresses this problem.
Llombart and co-workers proposed in Refs. [340–342] to use a confocal ellipsoidal
reflector system in reflection geometry to mechanically scan a sample with a THz
beam. Their transceiver system was based on a previously developed frequency-
modulated continuous wave (FMCW) radar at 675 GHz [343,344]. The scanning op-
tics included two paraboloid reflectors sharing a common focal point, similar to a
Gregorian telescope. Between the two reflectors, a planar mirror with a diameter
of 13 cm was rotated by 2.5 deg in elevation and azimuth direction [Fig. 32(a)].
The mirror rotation allowed scanning of the sample on a 50 cm ×50 cm area. The
paraboloid reflectors’characteristics were chosen to provide a 25 m stand-off distance
for which the beam spot size was 1 cm. Imaging at 1 fps is enabled by a rotary mirror
oscillating at 31.25 Hz. Imaging of hidden PVC pipes behind a subject’s jacket was
demonstrated [Figs. 32(b)–32(d)]. In Ref. [345], a bifocal Gregorian reflector system
was proposed to increase the field of view without impacting the beam quality or
imaging speed. Geometrical optics calculations were used to substitute the ellipsoidal
reflectors by specially designed shaped surfaces, which were able to increase the field
Figure 32
(a) Gregorian reflector system with a rotating mirror to scan the subject positioned at
25 m. (b), (c) Photograph of the hidden PVC pipes inside the subject’s jacket. (d) THz
image obtained in 1 s with the FMCW radar at 675 GHz. © 2011 IEEE. Reprinted,
with permission, from Cooper et al., IEEE Trans. Terahertz Sci. Technol. 1, 169–182
(2011) [342].
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 895
of view by 50%. Finally, most recently, similar opto-mechanical devices are combined
with THz cameras to provide meter-scale field of view at 25 fps [346,347].
5.2. Single-Pixel Imaging and Compressive Sensing
In the past, computational imaging techniques have been developed to enable imaging
with single-pixel detectors. One such technique is compressive sensing. There, instead
of directly imaging a sample, the detector performs a series of measurements of
the transmitted intensity through a sample covered with different pixelated masks
[Fig. 33(a)]. The measured data set can be mathematically described by using
matrix–vector multiplication [348]:
¯
yΦ¯
x,(33)
where ¯
xis the vectorized version of a sample (local sample transmission), ¯
yis the
corresponding vector of measured intensities by a detector, and the matrix Φcontains
the information about the concatenated collection of the vectorized masks.
For example, to mimic a raster-scan, an aperture can be moved in the object plane.
Every position of the aperture can be described by a mask. In Fig. 33(b), we present 16
masks for a sample of 4×4 pixels. For each mask, a vectorized version of the aperture
(¯
ϕRS) is constructed with values of 0 and 1 corresponding to opaque or transparent
regions of the mask, respectively. The matrix ΦRS is then constructed by stacking the
vectors ¯
ϕRS. For the raster-scan, the measurement matrix is simply an identity matrix
[Fig. 33(c)]. However, the identity matrix corresponds to a very poor choice of Φsince
the aperture blocks most of the light, and therefore the useful signal is buried in noise.
In fact, there are more judicious choices for the matrix Φ. One of the most commonly
used sets of masks is derived from the Hadamard basis, which was shown to provide
the best SNR [349]. In Fig. 33(d), we present the 16 Hadamard masks, while the
corresponding Hadamard matrix is shown in Fig. 33(e). Other possible choices
of Φinclude the Fourier or wavelet basis.
In the measurement process within single-pixel imaging, Φis predetermined and ¯
yis
measured. The sample image ¯
xcan then be recovered by performing the matrix inverse
¯
xΦ−1¯
y. Mathematically, the matrix inversion requires that the number of masks
must be equal to the number of pixels in the object.
The compressive sensing theory proposes to use a number of masks smaller than the
number of pixels, while employing a pseudo-inversion in place of a true matrix
inversion. In general, images are compressible (sparse) under certain representations.
In fact, this compression property is commonly used to reduce the size of images in
computers. For example, JPEG compression uses the discrete cosine transform, which
takes advantage of the difficulty of the human visual perception system to distinguish
features with high spatial frequency components [350]. In JPEG compression, those
frequencies are equated to zero in postprocessing after the image is taken with a digital
camera.
In compressive sensing, the image is compressed directly during the measurement
step [351,352], and it essentially allows reconstruction of an image with a number
of measurements that is smaller than the number of pixels [353], which at first glance
seems to defy the Nyquist requirement. In compressive sensing imaging, while
Eq. (33) becomes under-determined and an infinite number of solutions is possible,
the pseudo-inverse can still be defined, for example, in the least square sense so as to
minimize the norm of the difference between the right and left parts of Eq. (33)[354].
In more detail, compressive sensing theory indicates that it is possible to recover an
approximation of ¯
xfrom a number of measurements smaller than the image size, given
896 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
that the signal ¯
xis sparse under a certain representation [348]. To ensure robust signal
recovery even when noise is introduced in the measurements, the sensing matrix Φ
must respect the restricted isometry property [355]. This property ensures that column
vectors taken from arbitrary subsets of a representation basis are almost orthogonal.
For example, the measurement matrix Φcan take the form of random subsets of the
Fourier, Hadamard, or wavelet basis. Remarkably, even random binary apertures
derived from a Bernoulli distribution give satisfactory reconstruction results in most
cases [351]. Furthermore, if Φrespects the restricted isometry property, then the object
¯
xcan be reconstructed with high probability using just M≥OKlogN∕K random
measurements, where Kis the number of nonzero coefficients.
Then, if the measurement ¯
yoriginates from a highly sparse object ¯
x, the compressive
sensing problem can be formulated as searching for the sparsest signal ¯
xthat produces
¯
y. This leads to a minimization formulation with the l0-norm:
Figure 33
(a) Experimental setup for imaging with a single pixel using a mask aperture.
(b) Raster-scan basis and set of 16 masks (φi
RS) for a 4×4sample. (c) Measurement
matrix ΦRS constructed by concatenating the vectorized versions of the masks φi
RS.
(c) Hadamard basis and set of 16 masks φi
Hand (e) corresponding measurement
matrix ΦH.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 897
minimize k¯
xk0subject to ¯
yΦ¯
x,(34)
where k¯
xk0is the l0-norm, i.e., the number of non-zeros in ¯
x. However, such a min-
imization problem is NP-hard in general and, therefore, is computationally prohibitive
[356]. A common alternative is to use the l1-norm, for which tractable programming is
possible:
minimize k¯
xk1subject to ¯
yΦ¯
x:(35)
It can be shown that, if Φsatisfies the restricted isometry property, then Eq. (35)
(l1-norm) shares similar solutions with Eq. (34)(l0-norm). This type of minimization
is known as the basis pursuit [351,352,357]. Among the other types of optimization
algorithms, we note the basis pursuit with inequality constraints, where a bound is
added in the constraint to include additive noise:
minimize k¯
xk1subject to k¯
y−Φ¯
xk2<ε:(36)
The greedy algorithms are alternatives to the optimization-based algorithms [358]. In
these methods, the solution ¯
xis constructed iteratively by selecting columns of Φ
depending on their correlation with the measurements ¯
y. For example, in the orthogo-
nal matching pursuit [359], the solution is found by selecting the column of Φthat is
most correlated to a residual, defined by subtracting a partial estimate to the measure-
ments ¯
y. The CoSamp algorithm is also a commonly used greedy algorithm [360]. We
note that many other types of algorithms can be used to solve the compressive sensing
problem. Readers may find excellent reviews on this topic in Refs. [355,358,361].
In the following, we review compressive sensing in the context of THz imaging. Apart
from assuming sparsity of the imaged object, the compressive sensing theory does not
specify the nature of the measurement. The measured data can be amplitude, phase,
intensity, and so on. Therefore, compressive sensing can also be used with incoherent
measurements as is commonly done in the visible range. In the following, some works
used incoherent measurements in the THz range (for example [362–364]). Others used
the broadband amplitude and phase measurement obtained from a THz-TDS system to
reconstruct an image per THz frequency (hyperspectral imaging) or used the complex
spectral information to improve image quality.
5.2a. THz Imaging with Compressive Sensing
Chan et al. were the firsts to propose using compressive sensing theory for THz
imaging [365,366]. In their first implementation [367], the measurements were per-
formed in the Fourier plane, and the image was reconstructed using a 2D spatial in-
verse Fourier transform. The object mask was placed in the front focal plane of a lens
and the detector was scanned in the back focal plane [Fig. 34(a)]. Using THz-TDS,
both amplitude and phase at 0.2 THz were measured over an area of 64 ×64 mm,at
1 mm intervals (4096 pixels). Then, assuming sparsity of the image, they used the
compressive sensing theory to select random points in the Fourier plane, therefore
using a random subset of the Fourier basis function. Using the spectrally projected
gradient algorithm [357], they demonstrated successful image reconstruction that used
only 12% (500 pixels) of the original data points [Figs. 34(b) and 34(c)].
In the first experimental approach, it was still necessary to mechanically move a sin-
gle-pixel detector in the Fourier plane. In their second experiment [366], the authors
used a set of random binary metal masks in the object plane and a fixed single-pixel
detector at the center of the Fourier plane [Fig. 34(d)]. The binary masks formed a
basis from which a 1024 pixel image was reconstructed using as little as 300 (29%)
measurements at a frequency of 0.1 THz. Thanks to the ability of THz-TDS to
898 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
measure both the amplitude and the phase of the THz electric field [368], the authors
also demonstrated phase contrast imaging of a rectangular hole half-covered with
transparent plastic tape. While the amplitude of the reconstructed image shows no
difference between the plastic and the air regions [Fig. 34(e)], the phase image clearly
demonstrates contrast between the two regions [Fig. 34(f)].
The prospect of reducing the number of measurements by using only a single-pixel
detection scheme resulted in a spurt of activity in compressive sensing applied to THz
imaging. In Ref. [369], instead of random binary metal masks, Shen et al. used a set of
optimized masks calculated to approximate the Karhunen–Loeve transform [370].
They showed that, using the same number of masks, the optimized masks gave better
images than random masks. Also, using a broadband THz spectrum, they demon-
strated spectroscopic contrast of lactose monohydrate power and polyethylene, owing
to the fact that lactose has absorption peaks at 0.54 and 1.38 THz.
In Ref. [371], the authors used additional constraints in the optimization algorithm to
obtain images of better quality. Thus, they used the assumption that the phase is gen-
erally a piecewise slow-varying function in the object plane and that the object is
piecewise homogeneous with a uniform thickness. Additionally, using the information
across all the THz frequencies, they showed improvement in the quality of the
reconstructed image.
In the abovementioned works, the metallic masks were manually placed in the object
plane. In Ref. [372], Shen et al. used a spinning metallic disk with holes as a mask set
[Figs. 35(a) and 35(b)]. They used a THz-TDS setup and they fixed the delay line to
the position of the main peak in time domain. They showed reconstruction of a THz
Figure 34
(a) Experimental setup for the Fourier transform compressive sensing reconstruction.
(b) Reconstruction using 4096 measurements (100%) and (c) 500 measurements
(12%) using compressive sensing. Reprinted with permission from [365].
Copyright 2008 Optical Society of America. (d) Experimental setup for the random
binary masks compressive sensing reconstruction. Complex reconstruction of a 1024
pixels objects using 400 measurements (39%): (e) amplitude and (f) phase. Reprinted
with permission from Chan et al., Appl. Phys. Lett. 93, 121105 (2008) [366].
Copyright 2008 AIP Publishing LLC.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 899
image in 80 s by continuously rotating the mask at a speed of 5 deg/s [Figs. 35(c) and
35(d)]. They noted that the limitation in the acquisition speed was the SNR.
Three-dimensional imaging is also possible using single-pixel imaging. In Ref. [373],
Jin et al. demonstrate pulse-echo reflectance tomography using compressive sensing
applied to the scattering equation derived from the scalar wave equation [138]. In
Ref. [165], THz-CT was performed using compressive sensing and the SART algo-
rithm with Hadamard masks. In Ref. [137], Cho et al. demonstrated TPI using block-
based compressed sensing. The general idea of the block-based approach, developed
in Ref. [374], is to divide the original object into several regions and to simultaneously
apply the same binary operator in each region. This results in a reduction of the com-
putational burden associated with the conventional compressive sensing, which allows
computation of the image directly during the acquisition.
5.2b. Optical Spatial Light Modulation and Near-Field Imaging
To forgo completely the use of mechanically moving parts, the current trend in THz
imaging within compressive sensing modality is to use spatial light modulation
(SLM). There are many methods to spatially modulate the THz beam, and intensive
research on this subject is still ongoing (see, for example, reviews on THz modulation
in Refs. [375–378]). The general idea is to modulate the amplitude/phase of the trans-
mitted or reflected THz beam, thus simulating the action of a mask.
Optically based modulation for compressive sensing THz imaging has been reported
in Ref. [328]. There, the THz beam was spatially modulated with an optically con-
trolled SLM made of a computer controlled digital light processing (DLP) projector
that redirected light from an incoherent 8 W mercury arc lamp onto a photosensitive
semiconductor material. In particular, apertures were optically inscribed onto a high-
resistive silicon wafer with a thickness of 500 μm. Within the silicon, the free carriers
induced by the absorbed photons increase the conductivity and, hence, the absorption
coefficient [379]. In Ref. [328], the reconstruction was made by raster-scanning a
single aperture, which is not the efficient type of mask for compressive sensing
imaging. In Refs. [380–382], the authors optically pumped Hadamard masks in
the silicon wafer, while in Ref. [383], random masks were used on a germanium wafer.
Figure 35
Real-time THz compressive sensing with a spinning disk. (a) Schematic of the
spinning disk and (b) experimental setup. (c) Photograph of the sample and
(d) reconstruction of a 32 ×32 pixel image using 160 measurements. Reprinted with
permission from [372]. Copyright 2012 Optical Society of America.
900 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
In Ref. [364], using only intensity measurements, phase-sensitive imaging at 690 GHz
was demonstrated with the PhaseLift algorithm presented in Ref. [384].
In Ref. [385], Stantchev et al. performed single-pixel near-field imaging using opti-
cally based modulation. They used an 800 nm, 100 fs optical pump onto a highly
resistive 115 μm thick silicon wafer. The binary patterns were generated by reflecting
the pump beam onto a digital micromirror device (DMD) [Fig. 36(a)]. Since the dis-
tance travelled by the THz beam in the silicon wafer was smaller than the wavelength,
they were able to record an image before far-field Fraunhofer diffraction occurred.
They demonstrated a resolution of 103 μm(∼λ∕4), significantly smaller than the
375 μm peak wavelength of the THz pulse [Figs. 36(b) and 36(c)]. Finally, by imaging
a circuit board [Fig. 36(d)], they showed that the polarization of the THz pulse affected
the resolution. They observed that the subwavelength conducting wires were more
clearly observed when the THz radiation was parallel to the wires [Figs. 36(e)
and 36(f)]. In Ref. [386], they used a similar THz near-field imaging system to
map the photoconductivity of a graphene sheet.
In Ref. [387], the same group demonstrated that the thickness of the silicon plate plays
a crucial role in determining the resolution of the reconstructed image. They exper-
imentally demonstrated resolutions of 154, 100, and 9 μm(λ∕45 at 0.75 THz) for
thicknesses of 400, 110, and 6 μm, respectively [Figs. 37(a)–37(c)]. Then, they used
adaptive sampling to further reduce the number of required measurements. Using the
Haar wavelet decomposition [388], they performed a coarse edge identification to
Figure 36
(a) Experimental setup using a silicon wafer and a digital micromirror device to gen-
erate the binary patterns. (b) Optical image of a metallic star and (c) reconstruction
using Hadamard masks. (d) Schematic of a circuit board design. (e) Hadamard
reconstruction of the region in (b) using vertical and (f) horizontal polarizations.
Reproduced from [385] under the terms of the Creative Commons Attribution 4.0
License. With copyright permission.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 901
determine where to sample with higher resolution. In Figs. 37(d)–37(f), comparison of
their adaptive sampling algorithm with standard compressive sensing revealed that,
with the same number of measurements, adaptive sampling outperforms compressive
sensing by increasing the SNR.
5.2c. Metamaterial-Based SLM and Multiplexed Mask Encoding
Direct electronic SLM is desirable to reduce the complexity associated when adding a
dedicated optical source to optically pump the semiconductor wafer [389]. In
Ref. [390], instead of using an optically based SLM, Watts et al. introduced an active
metamaterial SLM [Figs. 38(a) and 38(b)] originally reported in Refs. [391,392]. The
metamaterial SLM was electrically controlled to allow phase-sensitive mask encod-
ing. By measuring the phase of a detected signal with a lock-in amplifier, instead of
simply measuring a binary mask, the authors were able to measure and symbolically
represent negative and positive values with the in-phase and out-of-phase electrical
signals. This allowed reducing the overall noise when using Hadamard masks.
Furthermore, the metamaterial SLM allowed rapid changes of the binary masks.
By displaying 45 masks for 22.4 ms each, they were able to demonstrate video
recording at 1 fps [Figs. 38(c)–38(f)].
The possibility of using phase information in mask encoding and signal led to the idea
of multiplexed mask encoding. The concept is summarized by the constellation
Figure 37
Adaptive sampling
Compressive sensing
75% 50 % 25%
(a) (b) (c)
(d) (e) (f)
400 µm110 µm 6 µm
Improvement of the resolution by using thinner silicon wafer: (a) 400 μm, (b) 110 μm,
and (c) 6 μm thick wafers. Comparison of reconstruction using adaptive sampling and
compressive sensing, with (d) 75%, (e) 50%, and (f) 35% of the measurements
required by the Nyquist theorem. Adapted with permission from [387].
902 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
diagrams in Figs. 39(a) and 39(b). Thus, in Ref. [390], Watts et al. used in-phase and
out-of-phase electrical signals to encode symbolically f1gand f−1gvalues in the
mask [2-phase-shift keying in Fig. 39(a)]. As in any communications system, the idea
can be extended by using electrical signals with different phase values to symbolically
represent more states. Consequently, multiple masks can be encoded simultaneously to
further reduce the acquisition time. In Ref. [363], Nadell et al. demonstrated the encod-
ing of two masks in parallel using quadrature amplitude modulation [Fig. 39(b)].
In practice, they used square waves with phases: fπ∕4; 3π∕4; −3π∕4; −π∕4gto
represent four possible combinations of symbols: f1,1g,f−1,1g,f−1,−1g,and
f1,−1g, where the first index corresponds to the value of the first mask and the second
index the value of the second mask. Then, by coherently measuring the phase of the
signal, the authors could acquire two elements of ¯
yin the time that only one element can
be acquired using conventional mask change. By comparing the obtained image of their
quadrature amplitude modulation [Fig. 39(c)] to a conventional 2-phase-shift keying
[Fig. 39(d)], they measured less than 5% difference in the averaged l2-norm.
In Ref. [362], the same group demonstrated frequency-division multiplexing with
metamaterials. The idea was to encode simultaneously different masks using square
waves of different frequencies [Fig. 39(e)]. To avoid crosstalk, the frequencies were
selected such that they were all mutually orthogonal:
Zτ
0
gmtgntdt0 for m≠n,(37)
Figure 38
(a) Metamaterial SLM and (b) experimental setup. (c) Reconstructed object at 0.7 fps
and (d) 1 fps of (e) a metallic cross. (f) Five frames of a 1 fps movie reconstructed with
45 masks displayed for 22.4 ms on the SLM. Reprinted by permission from
Macmillan Publishers Ltd.: Watts et al., Nat. Photonics 8, 605–609 (2014) [390].
Copyright 2014.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 903
where τis the integration time of a lock-in amplifier and gtis the square waveform.
In Ref. [362], up to four frequencies were selected for the image reconstruction
[Fig. 39(f)]. As the number of frequencies nfincreased, the total acquisition time
decreased as 1∕nf[Fig. 39(g)].
In principle, both frequency and phase multiplexing can be used at the same time to
increase the number of channels and reduce the overall acquisition time. Eventually,
when the number of channels equals the total number of pixels, the image can be
acquired in a one-shot process. In practice, as in any communications system, the
total number of channels is limited by the noise floor. Consequently, as the acquisition
time decreases, so does the overall SNR.
5.3. Spectral/Temporal Encoding and Fourier Optics
In this section, we review spectral/temporal encoding techniques, in which the infor-
mation about the image structure is encoded into the spectrum/temporal waveform.
These methods rely on the Fourier transform relationships, linking the time/frequency
domains to the space/k-space domains (Fig. 40).
5.3a. Spectral and Temporal Encoding
A classic implementation of the space-to-time image transformation in the infrared/
visible range is the serial time-encoded amplified (STEAM) system [393,394]. In the
STEAM system developed in Ref. [393], spatial dispersers were used to encode spa-
tial information into a broadband spectrum. Then, using a dispersion compensating
fiber and Raman amplification, the spectrum of an optical pulse was mapped in time
domain. A single-pixel photodetector was then used to reconstruct the 2D image at a
laser repetition rate of 6.1 MHz, allowing for the real-time video acquisition of fast
dynamic phenomena.
Figure 39
Frequency (hz)
204 Hz 208 Hz 213 Hz 216 Hz
Time
216 Hz
213 Hz
208 Hz
204 Hz
2-PSK QAM
Q
I
y
xx
y
-1 +1
Number of carrier modulation frequencies
Time of image reconstruction
(e) (f) (g)
(a) (b) (c) (d)
(a) Constellation diagram for the phase-shift key modulation with 2 states (2-PSK) and
(b) 4 states (QAM). (c) Reconstruction of an inverted metallic cross using 2-PSK and
(d) QAM. Adapted with permission from [390]. (e) Constellation diagram for fre-
quency multiplexing. (f) The spectrum (top) and the square waveforms in the time
domain (bottom) of the selected modulation frequencies. (g) Reduction of the time
to reconstruct an image using an increasing number of carrier modulation frequencies
and corresponding images. Adapted with permission from [362].
904 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
Similar to the spatial disperser used in the STEAM system [395], blazed diffraction
gratings have been introduced in the THz range to map the spectrum in 1D space. In
Ref. [396], Schuman et al. fabricated an aluminum blazed diffraction grating with a
groove depth and period chosen to achieve an angular dispersion of 15 deg per
100 GHz. The authors selected the first diffractive order between 300 and
600 GHz since it achieved a high diffraction efficiency of 85%. The grating was then
used in combination with an f-theta lens to ensure that the focal points of the indi-
vidual frequencies were in the same plane, either in transmission [Fig. 41(a)]orin
reflection geometry [Fig. 41(b)]. To calibrate the measurement, the THz detector
was linearly scanned in the focal line, and a third-order polynomial was used to cor-
relate the THz frequency with the spatial position [Fig. 41(c)]. Thus, by directly meas-
uring the spectrum, a complete 1D line in the image can be acquired. In Fig. 41(d),
metal letters attached to a sheet of paper were imaged in transmission and in reflection
(inset) using blazed gratings. There, the horizontal axis has been acquired from the
spectrum while the vertical axis was imaged by linearly scanning the object. It can be
observed that the right side of the image exhibits better resolution than the left side,
which can be directly attributed to the nonlinear frequency-to-space relationship mea-
sured in Fig. 41(c). A second grating perpendicular to the first one can be added to
map the frequencies in 2D spatial coordinates [397,398]. In Ref. [399], the authors
mapped a 60 cm ×60 cm area using 401 frequency points between 75 and 110 GHz.
In Ref. [400], Lee et al. demonstrated near-field imaging using spectral encoding with
a metasurface. Gold cross-type mesh filters were fabricated via photolithography on a
polyimide substrate [Fig. 42(a)]. These filters act as transmission bandpass filters in
the frequency domain. By spatially patterning the meshes with varying geometrical
dimensions, the authors designed a metasurface able to map the spatial positions in the
THz spectrum. Then, they demonstrated two reconstruction techniques using either an
angular scan of the object [Figs. 42(c)–42(e)] or a translation scan of a metallic slit
[Figs. 42(f)–42(h)]. In the angular scan, the reconstruction was made with an inverse
Radon transform, while in the translation scan, a collection of measurements repre-
sented the image directly in the spectrum. Using numerical simulations, they found
that both reconstructions are sensitive to the Qfactor of the mesh filter. For a uniform
mesh distribution, the Qfactor is defined as the ratio of the central wavelength to the
bandwidth of the bandpass filter. Therefore, a larger Qfactor characterizes a narrower
bandpass filter. With the angular scan, due to the nature of the reconstruction, a lower
Qfactor caused a blur in the entire image. In the translation scan, the Qfactor affected
the yaxis resolution, while the xresolution was determined by the width of the slit.
Figure 40
Spatial frequencies (kx,ky)
(k-space)
Space (x,y)
Frequency ( )
(spectrum)
Temporal Fourier transform
Spatial Fourier transform
[396-400]
[401, 403] [402-404]
Time (t)
Schematic description of the spectral/temporal encoding. The references of
Section 5.3 are indicated at the relative positions in the schematic.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 905
An example of a space-to-time conversion imaging is demonstrated in Ref. [401].
With a THz-TDS system, Stübling et al. made a multipixel emitter unit by dividing
a single THz pulse into multiple pulses using a set of polymer beam splitters
[Fig. 43(a)]. On the detector side, specially designed mirrors were placed to redirect
the individual pulses into a single-pixel THz photoconductive antenna. Then, a series
of THz pulses appear in the time-domain measurement by scanning over a sufficiently
large temporal window [Fig. 43(b)]. These pulses correspond to different spatial po-
sitions, as confirmed by the raster-scan above the emitter head [Fig. 43(c)]. Therefore,
they can be used to reconstruct an image. As this configuration relies on scanning
the optical delay line, the methods that we have described in Section 3.2 can be ap-
plied to reduce the acquisition time. Here, the authors used ASOPS in their system
implementation.
5.3b. Fourier Optics and k-Space/Frequency Duality
By using Fourier optics relationships, the spatial frequencies can be encoded into the
spectrum [402–404]. The concept here is to use a diffractive element to retrieve a
linear relationship between the k-vector and the frequency. The simplest implemen-
tation uses a lens to do the encoding [Fig. 44(a)]. The Fourier optics theory states that a
given field profile Sx,y,νat the front focal plane (object plane) of a convex lens is
Fourier transformed at the back focal plane (Fourier plane) according to [166]
Uξ,η,ν ν
jcF ZZ dxdySx,y,νexp −
j2πν
cF xξyη,(38)
where Fis the lens focal length, cis the speed of light, and νis the frequency. The
coordinates x,yand ξ,ηare the spatial positions in the object plane and the Fourier
plane, respectively. The original field distribution Sx,y,νcan then be reconstructed
by using the inverse Fourier transform:
Figure 41
(a) Transmission and (b) reflection geometry with a blazed diffraction grating and an
f-theta lens system. (c) Calibration measurement of the frequency as a function of the
spatial position (d) Demonstration of THz imaging in transmission geometry. Inset:
reflection geometry. Reprinted with permission from [396]. Copyright 2012 Optical
Society of America.
906 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
Sx,y,νjν
cF ZZ dξdηUξ,η,νexp j2πν
cF xξyη:(39)
The spatial frequencies, also known as components of the k-space, are related to the
ξ,ηcoordinates through
kξξν
cF kηην
cF :(40)
Since the spatial frequencies are proportional to the frequency ν, one can use the THz
spectrum to scan along a line in the k-space. In other words, by fixing the detector in
the Fourier plane at ξ0,η0and using a broadband source such as ν∈νmin ,νmax,
Eq. (40) can be combined to give
kηη0
ξ0
kξ:(41)
By changing the ratio η0∕ξ0, the whole k-space can be sampled. The simplest way to
change this ratio is to measure points along a circle of radius ρ0in the Fourier plane.
Therefore, the 2D raster-scan [Fig. 44(b)] that provides a hyperspectral cube in the
Figure 42
(a) Cross-type mesh-based metasurface with varying geometrical parameters.
(b) Photograph of the sample. (c) Angular scan geometry, (d) THz spectrum as a func-
tion of the angle, and (e) reconstructed image with the radon transform.
(f) Translational scan geometry, (g) THz spectrum as a function of the position of
the slit, and (h) reconstructed image. Adapted from [400] under the terms of the
Creative Commons Attribution 4.0 License. With copyright permission.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 907
k-space [Fig. 44(c)] can be substituted by a 1D linear scan [Fig. 44(d)] along a circle,
and the measured spectrum can be mapped into the radial dimension of the k-space
[Fig. 44(e)].
This idea was demonstrated in the THz range by Lee et al. in Ref. [402]. In their
implementation, they used a parabolic mirror as the diffractive element. An aperture
of 5 mm diameter at 15 mm away from the optical axis was placed at the Fourier plane,
while a second parabolic mirror focused the THz beam into a fixed single-pixel
detector. Then, using a THz-TDS setup, they measured several spectra for different
angular positions of the mask. They demonstrated reconstruction of a metallic object
using 10–30 THz-TDS traces.
Figure 43
(a) The beam is divided into multiple spatial positions using beam splitters. (b) Time-
domain measurement of the 10 pulses corresponding to the spatial positions in (d).
Reprinted with permission from [401]. Copyright 2016 Optical Society of America.
908 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
In Ref. [403], the same group demonstrated similar spectral encoding using a slanted
phase retarder made of Teflon at the position of the object. However, as in Ref. [402],
mechanical rotation of the mask was necessary. Therefore, they also proposed to com-
bine their approach with temporal encoding in k-space. For that purpose, they placed a
mask in the Fourier plane that contained an angular pattern of holes, each containing
additional phase retardation elements (Teflon disks of different thicknesses). The
resultant long-time scan contained multiple THz pulses separated in time, each
corresponding to a unique angular position in the k-space, which was then used to
reconstruct the image.
In Ref. [404], Guerboukha et al. presented the rigorous mathematical theory behind
the image reconstruction process reported in Refs. [402,403], as well as several novel
imaging modes, which included amplitude- and phase-based modalities. They started
by expressing the Fourier integral 39 in polar coordinates:
S~
r,νjν
cF ZZ dθρdρU~
ρ,νexpj2πν
cF ~
r·~
ρ:(42)
In fact, the idea of spectral encoding implies that the integral over the radial coordinate
dρshould somehow become an integral over the spectrum dνin Eq. (42). Therefore,
instead of the classic backward Fourier transform given Eq. (39), the authors rhoosed a
new form of the reconstruction integral:
˜
S~
rZZ dθνdνjρ2
0
cFν
U~
ρ0,ν
Uref νexp j2πν
cF ~
r·~
ρ0:(43)
Recognizing that the reconstruction ˜
S~
ris different from the original object S~
r,ν,
the authors used in Eq. (43) a certain reference measurement Uref νthat allows attrib-
uting a physical meaning to the reconstruction ˜
S~
r. For example, in the case of
Figure 44
(a) (d) (e)
(b) (c)
(a) General setup for k-space encoding using a lens. (b) Conventional raster-scan and
(c) hyperspectral cube, and (d) circular scan and (e) k-space reconstruction using spec-
tral encoding. Reprinted with permission from [404]. Copyright 2018 Optical Society
of America.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 909
amplitude imaging with binary metal masks (cut-outs in metal), the following
reference was used:
Uref νjcF
νU0,ν,(44)
where U0,νis a measurement in the middle of the Fourier plane with the metal mask
in place. Then, they mathematically showed that the reconstructed image according
to the definition given by Eq. (43) is simply the original object normalized by the
total area:
˜
Sr,ϕ Sr,ϕ
RR Sr,ϕdϕrdr:(45)
Figures 45(a)–45(f) present the experimental results when reconstructing a cut-out
in the metal sheet in the form of a maple leaf (amplitude mask). The amplitude
[Fig. 45(d)] and the phase [Fig. 45(e)] of the k-space reconstructed with the spectral
encoding are comparable to those acquired with a raster scan [Figs. 45(a) and 45(b)].
However, the reconstructed object with the spectral encoding [Fig. 45(f)] required
sampling of only 45 spatial positions, compared to the raster-scan with 4624 spatial
positions [Fig. 45(c)].
Using the mathematical theory described above, the authors extended the idea to phase
masks. As an example, they imaged a polymer plate (refractive index nm) with a
shallow 100 μm engraving. Interestingly, to enable imaging of phase masks, only
the reference has to be modified in Eq. (43)as
Uref νjcFU 0,ν,(46)
where U0,νis a measurement in the center of the Fourier plane using a polymer
plate without the engraving. Then, the authors showed that the imaginary part of the
reconstructed object using Eq. (43) is proportional to the optical path Δ~
rnm−1
h~
rdue to the engraving:
Imf
˜
S~
rg −
2π
c
S~
r
RR S~
rd~
rΔ~
r:(47)
Therefore, by measuring a plate with [Fig. 45(g)] and without the engraving
[Fig. 45(h)], they were able to directly map the height of the engraving [Fig. 45(i)].
Contrary to the spectral encoding techniques described in Section 5.3b, encoding an
image into k-space requires no complex optical devices. Thus, a simple lens was used
in Ref. [404] and the detector was simply positioned off-axis. In fact, instead of using
a circular lens, one could use a cylindrical lens to perform 1D Fourier transform. Then,
by simply scanning the object in the other dimension, every measured spectrum would
provide a 1D line of the object. This type of configuration could be used in a conveyer
belt system to obtain a 2D THz image.
The spatial resolution when using spectral encoding of the k-space can be directly
derived from the Nyquist theorem that states that the minimal achievable resolution
is δx0.5∕kmax, where kmax is the maximal spatial frequency sampled in k-space.
Therefore, the resolution of the image can be improved by measuring the larger
k-space components located at the periphery of the limiting aperture (field of view)
in the Fourier plane. When using spectral encoding of the k-space, Eq. (40) shows that
kmax νmaxρ∕cF , with νmax being the maximal THz frequency, ρthe radial position
910 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
of the detector (in the Fourier plane), and Fthe focal length. Therefore, the resolution
becomes δx0.5cF∕νmaxρand can be increased by using a lens with a shorter focal
lens, by positioning the detector at a larger radial position and by using spectrally
broader THz source.
Finally, we would like to discuss the impact of the THz spectral encoding and Fourier
optics on the broadband spectral information. One must recognize that fast
reconstruction algorithms as presented above [see Eq. (43)] use spectral information
to sample the k-space. Therefore, the reconstructed image is different from a hyper-
spectral image obtained, for example, using THz-TDS. Moreover, uneven power
distribution in the pulse spectrum should be mitigated by acquisition of a reference
spectrum of an empty system or a substrate (see, for example, the calibration step in
Ref. [396] or the normalizations in Ref. [404]), which somewhat complicates the im-
aging procedure. Additionally, in the case of samples exhibiting significant frequency-
dependent loss variations, image resolution might suffer due to effective loss of
information at frequencies characterized by strong absorption. For example, for many
dielectrics, one expects reduction of the maximal useful frequency value due to
stronger sample absorption at higher frequencies. Inversely, if the sample has piece-
wise weakly dependent losses, then we expect excellent reconstruction results. For
example, spectral encoding in Fourier space can be used together with a fast
Figure 45
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(a) General setup for k-space encoding using a lens. (b) Conventional raster-scan and
(c) hyperspectral cube and (d) Circular scan and (e) k-space reconstruction using spec-
tral encoding. Reprinted with permission from [404]. Copyright 2018 Optical Society
of America.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 911
Fourier transform algorithm to efficiently reconstruct amplitude variations at the edges
between distinct materials. This case is already important for defense and mail
screening applications.
5.4. Section Summary and Future Directions
In this section, we have reviewed three main techniques to enable THz imaging with
single-pixel detectors: (1) mechanical beam steering, (2) single-pixel imaging and
compressive sensing, and (3) spectral/temporal encoding and Fourier optics.
Historically, these techniques have been developed to mitigate the high cost and dif-
ficulty of manufacturing multipixel THz cameras. Today, these techniques are mature
enough to be an integral part of the cost-effective imaging systems. Furthermore, the
single-pixel detectors used in such systems are often phase sensitive and can measure
both amplitude and phase of the electric field with very high SNR. This is a key ad-
vantage when compared to THz cameras that commonly detect only the signal inten-
sity. Therefore, even with the advent of THz cameras, we believe that development of
the single-pixel imaging techniques will remain highly pertinent.
The first single-pixel imaging technique that we have reviewed is mechanical beam-
steering. Historically, to obtain a THz image, the sample was positioned at the focal
point of focusing optics and physically moved pixel by pixel. In many situations,
sample displacement is not desirable or even possible. Instead of moving the sample,
one can mechanically steer the THz beam over the sample. A combination of oscil-
lating mirrors and an f-theta lens can provide a simple and cost-effective solution for
short-range applications, for example, in industrial environments using conveyer belts.
In comparison, the Gregorian reflector system is seen as a desirable candidate for large
stand-off distances, for example, in the security and defense sector. Eventually, the
future development of non-mechanical beam-steering technology would allow stable
and rapid dynamic scans. This has already been explored using electrically controlled
liquid crystal devices [327], optically pumped semiconductor wafers [328,330], spe-
cial THz generation techniques [331–333], or distributed arrays of emitters [323,334].
In particular, in Ref. [323], Sengupta and Hajimiri fabricated a distributed array of
active radiators in CMOS to generate a 0.28 THz beam. By tuning the relative phase
of the 4×4emitter array, the THz beam could be steered in two dimensions, over 80°
in azimuth and elevation. Finally, we mention that the beam-steering technique is not
strictly limited to single-pixel detectors. In fact, they could be used with THz cameras
to increase the field of view.
In parallel, single-pixel imaging using compressive sensing has seen important devel-
opment in the context of THz imaging. Within this method, the image is reconstructed
by successive single-pixel measurements of a spatially modulated THz beam over the
sample (aperture functions). Then, assuming that the object is naturally sparse, the
compressive sensing theory can be used to reconstruct the image with a number
of measurements smaller than the total number of pixels. As for real-time imaging,
recent schemes involve the use of SLM. Spatial patterns can be optically encoded in a
semiconductor wafer, which can also act as a substrate for near-field compressive
sensing imaging. At the same time, electronic modulation allows for more complex
pattern modulation. Notably, the simultaneous modulation of multiple masks can lead
to major improvements in terms of acquisition rates. There, the different masks are
encoded using sine waves of different phases and frequencies, to enable fast image
acquisition through channel multiplexing and detection with a lock-in amplifier.
Eventually, when the number of channels equals the total number of desired masks,
the image can be acquired in a one-shot process. In practice, as in any communications
system, the total number of channels is limited by the noise floor. Consequently, as the
acquisition time decreases, so does the overall SNR. Finally, the developments in this
912 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
field are intimately related to the development of efficient SLM devices with
near-unity modulation factor and low transmission/reflection losses, to reduce the
overall integration time of the detector and enable even faster acquisition rates.
Finally, spectral encoding techniques take advantage of the relationships between time
and space to encode the spatial information of a sample in the spectrum, the temporal
waveform, or in the Fourier space. The idea here is to use a broadband pulse along
with frequency-dependent diffraction devices to spread the frequencies over the sam-
ple. Then, the transmitted/reflected spectrum can be recorded using a single-pixel de-
tector, for example, using a THz-TDS system. The diffraction device can be a
diffraction grating, a specially designed metasurface, a series of polymer retarders,
or just a common lens. If THz-TDS is used, one must be aware that the spatial
dimensions are often traded for a 1D spectral dimension that is obtained by measuring
the temporal waveform with an optical delay line. In this case, the spatial line acquis-
ition rate is often determined by the speed of the optical delay line (see Section 3.2). In
principle, as it is done in the visible range, one could also use THz cameras (Section 4)
to directly measure the spectrum and therefore avoid the use of the optical delay line.
In fact, in Section 3.4c, we saw demonstration of such a device, using temporal
encoding, a camera, and EOS.
6. CONCLUSION
In conclusion, THz imaging uses the properties of THz waves to interrogate matter in
unique ways. In the past 20 years, important technological developments have taken
place to enable real-time high-resolution imaging. Today, research in THz imaging is
steadily shifting from laboratory-based instrumentation to commercial products. In
this context, we have reviewed THz imaging with an emphasis on the imaging modal-
ities and tools that could enable high-resolution real-time imaging and its fundamental
and industrial applications.
We started this review by detailing recent advances in some of the most promising
THz imaging modalities. Particularly, in THz transmission and reflection spectros-
copy, the complex refractive index of a material can be obtained using Fresnel co-
efficients, which leads to the determination of the complex permittivity and
conductivity. In THz pulsed imaging, the temporal delay between several reflected
THz pulses is used to image through layered structures. THz-CT exploits the ability
of THz waves to penetrate matter to reconstruct a volumetric image of an object. In
THz near-field imaging, apertures and scattering tips are used to enable subwave-
length resolution, thus beating the diffraction limit.
We then focused our attention on three major research directions to enable real-time
THz imaging: THz-TDS real-time imaging, THz cameras, and THz single-pixel
imaging.
Many of the developed imaging techniques rely on THz-TDS systems that allow
coherent measurement of the amplitude and phase of the pulsed THz electric field
at the picosecond time scale. However, imaging with a THz-TDS system requires
using relatively slow instrumentation that impedes real-time imaging. To speed up
acquisition time of the THz signal, many modifications to the THz-TDS system sub-
components were proposed. Thus, to forgo the linear movement of the optical delay
line, reflective or prism-based rotary delay lines have been developed. Alternatively,
one can use asynchronous optical sampling, electronically controlled optical
sampling, and optical sampling by cavity tuning, which are various techniques that
can be used to avoid altogether the mechanical movement of a delay line.
Additionally, we have mentioned that photoconductive antennas and EOS are
currently the two key methods for coherent detection of THz pulses. While in their
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 913
simplest form both techniques offer single-pixel coherent detection, recently there
was significant progress in realizing arrays of THz photoconductive antennas, as well
as using infrared/visible cameras with EOS, thus greatly speeding up image
acquisition times.
In parallel, intensive research has been conducted to develop THz cameras similar to
those available in the visible region of the spectrum. Among their technical require-
ments for mass deployment, they should operate at room temperature, be compatible
with standard fabrication technologies (such as CMOS process), have little weight,
small size, and low power consumption, and offer high sensitivities (for high frame
rate THz imaging even without an active THz source). Two major technological trends
are being pursued to realize THz cameras that would respond to those criteria: THz
thermal cameras and THz FET-based cameras. On one hand, THz thermal cameras
measure the heat generated by the absorption of the THz radiation. Pyroelectric cam-
eras and microbolometers have been used for THz imaging. In particular, microbol-
ometers have achieved remarkable sensitivities at room temperature thanks to the
inclusion of a Fabry–Perot cavity, coupling antennas, and metamaterial absorbers
to increase the absorbed THz radiation. On the other hand, the THz FET-based cam-
eras measure a rectified voltage after interaction of the THz radiation with a plasma
wave in the transistor channel. Theoretical works predicted both frequency-specific
(resonant) and broadband (non-resonant) detection mechanisms, which have been
used to describe the behavior of THz-FET detectors of a variety of materials, ranging
from III–V semiconductors to graphene layers. The silicon FET is an attractive
candidate for THz cameras, since it is compatible with CMOS process technology,
therefore enabling scaling into high-resolution arrays at reduced costs.
At the same time, we have emphasized that single-pixel detectors can be efficiently
used for fast acquisition of THz images within the framework of fast mechanical steer-
ing and computational imaging. Mechanical beam-steering with oscillating mirrors
and f-theta lenses allow rapid image acquisition using a conveyer belt arrangement,
while a Gregorian reflector system can be used to construct an image at stand-off
distances for security applications. Furthermore, in recent years, there were substantial
developments in computational imaging, leading to a plethora of single-pixel imaging
techniques that allow image reconstruction from a series of judicially designed single-
pixel spectroscopic measurements. Thus, one can reconstruct an image by performing
a series of single-pixel measurements with a series of aperture masks that partially
conceal the image. By using the sparsity property of natural images, compressive
sensing can reduce the number of measurements well below the limit imposed by
the Nyquist theorem, resulting in reduced time acquisitions. By using SLM and ad-
vanced mask encoding methods, real-time THz single-pixel imaging is within reach,
even in the near-field imaging context. Finally, taking advantage of the relationships
between time and space, the spatial information about an object can be encoded in the
spectrum or in the temporal waveform, using blazed diffraction gratings, specially
designed metasurfaces of beam-splitting devices. Finally, by using the principles
of Fourier optics with broadband pulses, the spatial frequency information about
the imaged object can be efficiently reconstructed from the spectral data recorded
in the k-space, thus leading to fast Fourier optics image modalities.
We would like to note that the three major research directions that we have reviewed in
this work are not necessarily in direct competition with one another, nor are they mu-
tually exclusive. In fact, they can profit from each other via development of hybrid
systems. For example, intensity-sensitive THz cameras are important for various
applications where object differentiation via simple absorption is prevalent. At the
same time, phase-sensitive THz-TDS imaging is of great importance for material
914 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
characterization and finer measurements of local changes in material physical proper-
ties. At the same time, the hardware and computational techniques developed within
the single-pixel imaging modality can be considerably enhanced or sped up by
substituting single-pixel detectors with THz detector arrays.
To summarize, in this work, we presented a critical and comprehensive review of
enabling hardware, instrumentation, algorithms, and potential applications in real-
time high-resolution THz imaging. We believe that this review can serve a diverse
community of fundamental and applied scientists as it covers extensively both
practical aspects of imaging system designs, as well as fundamental physical and
mathematical principles on which such designs are based. Finally, many practical
applications of the imaging systems were presented, making this review of interest
to a wider audience.
FUNDING
Canada Research Chairs I of Prof. Skorobogatiy in Ubiquitous THz photonics;
Canada Foundation for Innovation (CFI); Natural Sciences and Engineering
Research Council of Canada (NSERC); Fonds de Recherche du Québec—Nature
et Technologies (FRQNT).
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Hichem Guerboukha received a B.Sc. degree in Engineering
Physics and a M.Sc. degree in Applied Science from the
Polytechnique Montréal, Montréal, Quebec, Canada, in 2014
and 2015, respectively. He is currently working toward a Ph.D.
degree in THz computational imaging. His research interests in-
clude THz instrumentation and waveguides, THz communica-
tions, and THz computational imaging. He was the recipient of
the Etoile Student-Researcher from Fonds de Recherche–Nature
et Technologies in 2015 and the Best M.S. Thesis Prize from the Polytechnique
Montréal in 2015.
Review Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics 937
Kathirvel Nallappan received a B.E. degree in Electronics and
Communication Engineering and a M.Tech degree in Laser and
Electro-optical Engineering during 2010 and 2013, respectively,
from Anna University, Tamilnadu, India. After working as a
Senior Project Fellow in the Structural Engineering Research
Center (CSIR), India for a period of one year, he joined as a re-
search intern in the research group of Prof. Maksim Skorobogatiy
at Polytechnique Montréal, Canada. He is currently working to-
ward the Ph.D. degree in Terahertz Communications at Polytechnique Montréal.
His research interest includes terahertz and infrared free space communications,
THz waveguides, spectroscopy, and imaging.
Maksim Skorobogatiy has been a Professor of Engineering
Physics at Polytechnique Montréal since 2003. He graduated in
2001 from MIT with a Ph.D. in Physics and an M.Sc. in Electrical
Engineering and Computer Science. He then worked at the MIT
spin-off Omniguide Inc. on the development of hollow-core fibers
for guidance of high-power mid-IR laser beams. He was awarded
a Tier 2 Canada Research Chair (CRC) in Micro and Nano
Photonics and then a Tier 1 CRC in Ubiquitous THz Photonics
in 2016. Thanks to the support of the CRC program, he could pursue many high-risk
exploratory projects in guided optics, and recently THz photonics, which have
resulted in significant contributions in these two booming research fields. In 2012
he was awarded the rank of Professional Engineer by the Order of Engineers of
Québec, Canada. In 2017, he was promoted to Fellow of The Optical Society
(OSA) for his pioneering contributions to the development of microstructured and
photonic crystal multimaterial fibers and their applications to light delivery, sensing,
smart textiles, and arts. Additionally, in 2017 he was promoted to Senior Member of
the IEEE for his contributions in engineering and applied research.
938 Vol. 10, No. 4 / December 2018 / Advances in Optics and Photonics Review
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