Single-pixel three-dimensional imaging with time-based depth resolution

Abstract

Time-of-flight three-dimensional imaging is an important tool for applications such as object recognition and remote sensing. Conventional time-of-flight three-dimensional imaging systems frequently use a raster scanned laser to measure the range of each pixel in the scene sequentially. Here we show a modified time-of-flight three-dimensional imaging system, which can use compressed sensing techniques to reduce acquisition times, whilst distributing the optical illumination over the full field of view. Our system is based on a single-pixel camera using short-pulsed structured illumination and a high-speed photodiode, and is capable of reconstructing 128 × 128-pixel resolution three-dimensional scenes to an accuracy of ~3 mm at a range of ~5 m. Furthermore, by using a compressive sampling strategy, we demonstrate continuous real-time three-dimensional video with a frame-rate up to 12 Hz. The simplicity of the system hardware could enable low-cost three-dimensional imaging devices for precision ranging at wavelengths beyond the visible spectrum.

Full text

ARTICLE
Received 30 Sep 2015 |Accepted 20 May 2016 |Published 5 Jul 2016
Single-pixel three-dimensional imaging with
time-based depth resolution
Ming-Jie Sun1,2, Matthew P. Edgar2, Graham M. Gibson2, Baoqing Sun2, Neal Radwell2, Robert Lamb3
& Miles J. Padgett2
Time-of-flight three-dimensional imaging is an important tool for applications such as object
recognition and remote sensing. Conventional time-of-flight three-dimensional imaging
systems frequently use a raster scanned laser to measure the range of each pixel in the scene
sequentially. Here we show a modified time-of-flight three-dimensional imaging system,
which can use compressed sensing techniques to reduce acquisition times, whilst distributing
the optical illumination over the full field of view. Our system is based on a single-pixel
camera using short-pulsed structured illumination and a high-speed photodiode, and is
capable of reconstructing 128 128-pixel resolution three-dimensional scenes to an accuracy
of B3 mm at a range of B5 m. Furthermore, by using a compressive sampling strategy, we
demonstrate continuous real-time three-dimensional video with a frame-rate up to 12 Hz.
The simplicity of the system hardware could enable low-cost three-dimensional imaging
devices for precision ranging at wavelengths beyond the visible spectrum.
DOI: 10.1038/ncomms12010 OPEN
1Department of Opto-electronic Engineering, Beihang University, Beijing 100191, China. 2SUPA, School of Physics and Astronomy, University of Glasgow,
Glasgow G12 8QQ, UK. 3Selex ES, Edinburgh EH5 2XS UK. Correspondence and requests for materials should be addressed to M.-J.S. (email:
mingjie.sun@buaa.edu.cn) or M.J.P. (email: miles.padgett@glasgow.ac.uk).
NATURE COMMUNICATIONS | 7:12010 | DOI: 10.1038/ncomms12010 | www.nature.com/naturecommunications 1

Whilst a variety of three-dimensional (3D) imaging
technologies are suited for different applications,
time-of-flight (TOF) systems have set the benchmark
for performance with regards to a combination of accuracy and
operating range. TOF imaging is performed by illuminating a
scene with a pulsed light source and observing the back-scattered
light. Correlating the detection time of the back-scattered light
with the time of the illumination pulse allows the distance dto
objects within the scene to be estimated by d¼tc/2, where tis the
TOF and cis the propagation speed of light.
The transverse spatial resolution of the image obtained is
retrieved either by using a pixelated array or by using a
single-pixel detector with a scanning approach1–8. In both
cases, the inherent speed of light demands the use of detectors
with a fast response time and high-speed electronic read-out to
obtain high precision depth resolution. Advances in sensor
development have enabled the first TOF single-photon avalanche
detector array cameras to enter the commercial market, having a
resolution of 32 32 pixels. However, such devices are still in
their infancy9–11. On the contrary, there are mature single-pixel
detectors on the market, which provide stable time-resolved
measurements, and by using compressed sensing principles
for image reconstruction, which takes advantage of the sparsity
in natural scenes, the acquisition times of the scanning approach
is largely reduced12–16.
Recently there have been some interesting developments in 3D
imaging utilizing single-pixel detectors. One technique utilizes
structured illumination and spatially separated photodiodes to
obtain multiple images with different shading properties from
which 3D images can be reconstructed via photometric stereo17.
Another scheme scans a scene, pixel by pixel, using a pulsed
illumination source and measures the reflected light using an
avalanche photodiode, whereon the first detected photon is
used to recover depth and reflectivity via TOF18. An alternative
method for scanning a scene and recovering depth and
reflectivity via TOF has also been demonstrated utilizing
structured pulsed illumination19–22.
Among the mentioned demonstrations, many5,18,20–22 used
photon-counting detection (that is, Geiger mode), which is well
suited for low-light-level imaging. However, one limitation of
photon-counting detectors is the inherent electronic dead time
between successive measurements, often 10s of nanoseconds,
which prohibits the retrieval of short-range timing information
from a single illumination pulse. Instead, an accurate temporal
response from a 3D scene requires summing the data over many
back-scattered photons and hence many illumination pulses
(usually several hundreds or thousands21,22). In contrast, as
first demonstrated by Kirmani et al.19, a high-speed photodiode
can retrieve the temporal response from a single illumination
pulse, which can be advantageous in certain circumstances, for
instance when the reflected light intensity is comparatively large.
Incidentally, photon counting cannot operate under such
conditions since the detection will always be triggered by back-
scattered photons from the nearest, or most reflective, object,
rendering more distant objects invisible (Supplementary Note 1).
In this paper, we present a single-pixel 3D imaging system using
pulsed structured illumination and a high-speed (short response
time) photodiode for sampling the time-varying intensity of the
back-scattered light from a scene. We show that by using an
analogue photodiode to record the full temporal form of the back-
scattered light, along with our original 3D reconstruction
algorithm, it is possible to recover surface profiles of objects with
an accuracy much better than that implied by the finite temporal
bandwidth of the detector and digitization electronics. At distances
of B5 m we demonstrate a range profile accuracy of B3mmwith
image resolutions of 128 128 pixels, whilst simultaneously
recovering reflectivity information of the object. This accuracy is
achieved despite a detection bandwidth and a digitization interval
corresponding to distances of 150 and 60 mm, respectively. We
further demonstrate that by using a compressive sampling scheme,
the system is capable of performing continuous real-time 3D video
with a frame-rate up to 12 Hz.
Results
Experimental set-up. The single-pixel 3D imaging system,
illustrated in Fig. 1, consists of a pulsed laser and a digital
micromirror device (DMD) to provide time-varying structured
illumination. A high-speed photodiode is used in conjunction
with a fresnel lens condenser system to measure the back-
scattered intensity resulting from each pattern. The analogue
photodiode output is passed through a low-noise amplifier and
sampled using a high-speed digitizer. In our work we chose to use
the Hadamard matrices23 for providing structured illumination.
To remove sources of noise, such as fluctuations in ambient light
levels, we obtain differential signals by displaying each Hadamard
pattern, followed by its inverse pattern, and taking the difference
in the measured intensities24,25. Detailed information about
experimental set-up is provided in the Methods section.
Pulsed
laser
Beam
expander
DMD
Projection
lens
Scene
Collecting
lens
Single-pixel
photodiode
Laser
pulse
Broadened
signal
Ball
Head
Screen
v
v
t
t
Figure 1 | Single-pixel 3D imaging system. A pulsed laser uniformly illuminates a DMD, used to provide structured illumination onto a scene, and the
back-scattered light is collected onto a photodiode. The measured light intensities are used in a 3D reconstruction algorithm to reconstruct both depth and
reflectivity images.
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12010
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A 3D image of the scene is reconstructed utilizing the time-
varying back-scattered intensities (measured for each output pulse
of the laser) and the associated set of Npatterns used to provide
the structured illumination. An overview of the reconstruction
algorithm is shown in Fig. 2 (the result in this diagram represents a
scene of three objects B0.5 m apart in depth). An incident laser
pulse (Fig. 2a) is back-scattered from a scene. The high-speed
digitizer converts the amplified analogue signals (Fig. 2b) into
discrete data points (Fig. 2c), which are subsequently processed by
the computer algorithm. Whereas typical single-pixel imaging
schemes use the integrated signal for each illumination pattern to
reconstruct a two-dimensional image, our algorithm utilizes M
discretely sampled intensity points from the time-varying signal to
reconstruct Mtwo-dimensional images, resulting in an x,y,z
image cube (Fig. 2d). In the image cube, each transverse pixel (x,y)
has an intensity distribution (Fig. 2e) along the longitudinal axis
(z), which is related to the temporal shape of the pulse, the detector
response, the read-out digitization and the pixel depth and
reflectivity information.
To enhance the range precision beyond the limits imposed by
the sampling rate of the system, methods such as parametric
deconvolution19,21 and curve fitting can be used. However, often
these methods can be computationally intensive, which makes
them unsuitable for real-time applications. Instead we choose to
apply cubic spline interpolation to the reconstructed temporal
signal at each pixel location, which introduces minimal
computational overhead. The depth map of the scene (Fig. 2f)
is subsequently determined by finding the maximum in these
interpolated signals. In addition, the scene reflectivity (Fig. 2g)
can be calculated by averaging the image cube along the
longitudinal axis. Utilizing both the depth and reflectivity
information, a 3D image of the scene is then reconstructed.
It is worth mentioning that, with the assumption that there is
only one surface at each transverse pixel location, our depth
estimation (see detail in Methods) works well for scenes that
have smooth features, such as the mannequin head and ball, since
the reconstructed temporal signals should be slowly varying
between sample points. We note that the depth accuracy
is limited by the amplitude noise of the data points, over-
interpolation only increases the depth precision, but not
necessarily the accuracy. In addition, more interpolation adds
more processing time, therefore, in our experiments we chose to
interpolate by a factor of five times when investigating the
static scenes with 20 pulses per pattern (Figs 3–5), and four
times when investigating scenes with motion (Fig. 6), balancing
the computational overhead and 3D image quality.
High-resolution imaging. In one experiment, a scene containing
a 140-mm diameter polystyrene soccer ball, a life-size skin-tone
mannequin head and a screen was located at a distance of B5.5 m
from the imaging system (Fig. 3a). The objects were closely
separated in distance such that the total depth of the scene was
B360 mm. A complete Hadamard set of 16,384 patterns, and
their inverse, was used as the structured illumination, and the
back-scattered intensities (Fig. 3b) measured for reconstructing
128 128-pixel resolution depth map, reflectivity and 3D image
(Fig. 3c-3e). The illumination time of each pattern was 2.66 ms,
corresponding to 20 laser pulses. The total time for acquisition,
ab c
Objects
reflection
Digitizer
sampling
Image
computation
de
Image cube
510
555
610
Greyscale
255
0
Greyscale
255
0
Greyscale
255
0
Depth (cm)
Depth (cm)
Depth (cm)
450
450
450
750
750
750
Processing
Laser pulse
V
Time (ns)
010
Broadened signal
V
Time (ns)
30 50
V
Time-discretized signal
Time (ns)
30 50
Intensity distribution of depth for
different transverse pixels
Reflectivity
estimation
Depth
estimation
Depth map Reflectivity
fg
.... .... .... ....
Distance (m)
6.30
5.10
z
y
x
Figure 2 | Overview of the reconstruction algorithm. The incident laser pulses (a) back-scattered from a 3D scene are temporally broadened (b) and
discretely sampled using a high-speed digitizer (c). An image cube (d) is obtained using a reconstruction algorithm, having an intensity distribution along
the longitudinal axis (e), from which the depth map (f) and the reflectivity (g) of the scene can be estimated.
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V
Time (ns)32 52
b
c
Distance (m)
6.00
5.50
ea
0.36 m
0.25 m
Scene Temporal signal
Depth map Reflectivity
3D image
x
y
z
d
Figure 3 | 3D image of a scene. (a) Illustration of the scene containing multiple objects in close proximity. (b) Reflected intensity measured for
uniform illumination, indicating temporally indistinguishable objects. (c) The estimated depth map of the scene. (d) The reconstructed scene reflectivity.
(e) A textured 3D image of the scene.
Distance (m)
5.70
5.50
0
9
Depth map
Reflectivity
3D image
Error (mm)
Side view
Front view
Error map
x
y
z
50 mm
b
ca
e
fd
Figure 4 | Quantitative analysis of 3D reconstruction. The depth estimation (a) reflectivity (b) and 3D reconstruction (c) of a white polystyrene
mannequin head at a range of B5.5 m. Superposed depth reconstruction and photograph of the mannequin head, viewed from the front (d) and side
(e). For a chosen region of interest an error map (f) showing the absolute differences between our depth result and that obtained using a
stereophotogrammetric camera system.
0.5 m
Netting
Head
Line of sight
Scene Conventional photo
Time-gated reflectivity
3D image
Distance (m)
Depth map
3.67
3.50
x
y
z
c
bea
d
Figure 5 | 3D imaging through obscuring material. (a) Illustration of scene containing a mannequin head with black netting material obscuring the
line-of-sight. (b) A photograph of the scene taken from the perspective of the 3D imaging system. The scene depth (c) and reflectivity (d) reconstructed
by time-gating the measured intensity data. (e) 3D reconstruction of the mannequin head.
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data transfer from the digitizer buffer to the computer and image
processing was B130 s. The 3D reconstruction shown in Fig. 3e
exhibits distinguishable features, such as the profile of the head
and the ball.
To quantitatively determine the accuracy of our 3D imaging
system, the scene was modified to contain only a polystyrene
mannequin head (180 270 250 mm), for which we had
reference 3D data obtained via a high-accuracy stereophotogram-
metric camera system17,26. The mannequin head was located at a
distance of 5.5 m from the imaging system. To further
demonstrate the system capability for retrieving reflectivity in
addition to the depth, two grey stripes were placed on the head.
Performing the same acquisition and imaging processing used in
Fig. 3, we obtained the results shown in Fig. 4a–c. Figure 4d,e
show the front and side view comparisons between our 3D
reconstruction (green) and photographs of the head (white),
respectively. After lateral and angular registration and subsequent
depth scaling, an error map representing the absolute differences
for a chosen region of interest was obtained (shown in Fig. 4f).
From this comparison we find our single-pixel 3D imaging system
has a root mean squared error of 2.62 mm. More detailed analysis
is provided in Supplementary Fig. 1 and Supplementary Note 2.
Time-gated imaging. One advantage of time-resolved imaging is
the ability to distinguish objects at different depths, by artificially
time-gating the measured intensity. In certain cases this enables
obscuring objects to be isolated from objects of interest. Similar to
previous demonstrations20, we constructed a 3D scene containing
a polystyrene mannequin head (located at a distance of B3.5 m)
and black-coloured netting used to obstruct the line of sight
(located at a distance of B3 m), as illustrated in Fig. 5a. An
image of the scene taken using a conventional camera is shown in
Fig. 5b, where the head is obscured by the black netting.
Performing the same acquisition and imaging processing used in
Figs 3 and 4, along with an artificial gating on the photodiode
data to ensure no reflected signals from the black netting are
included in the 3D reconstruction, we obtained the results shown
in Fig. 5c–e. As before, we note the characteristic features of the
mannequin head can be resolved.
Real-time compressed video. In addition to obtaining
high-quality 3D images of static scenes, many applications
demand video frame-rates for motion tracking in dynamic scenes.
A key merit of single-pixel imaging is the ability to take advantage
of the sparsity of the scene and use compressive sensing to reduce
the acquisition time. Most compressive-sensing schemes are
performed by minimizing a certain measure of the sparsity,
such as L
1
-norm, to find the sparsest image as the optimal
reconstruction of the scene. However, for resolutions greater than
32 32 pixels, the time taken by the construction algorithm often
prohibits real-time application22,27.
In this work we use an alternative scheme, known as
evolutionary compressive sensing6,7, which aims to reconstruct
the image with significant less time than conventional compressive
sensing by performing a linear iteration (Supplementary Figs 2 and
3 and Supplementary Note 3). In short, the evolutionary
compressive sensing scheme chooses a subset of the Hadamard
basis to display, by selecting the patterns with the most significant
intensities measured in the previous frame, in addition to a fraction
of randomly selected patterns that were not displayed. In this
experiment, a scene consisting of a static polystyrene mannequin
head and a polystyrene white ball (140mm diameter) swinging
along the line of sight with a period of B3 s (Fig. 6a). The scene
was located at a distance of B4 m from the imaging system. Two
laser pulses were used per illumination pattern. With the approach
described above we obtained continuous real-time 3D video with a
frame-rate of 5Hz using 600 patterns (including their inverse)
from the available 6464 Hadamard set, equivalent to a
t= 11.4 s t= 11.6 s t= 11.8 s
t= 12 s t= 12.2 s t=12.4 s t=12.6 s
Distance (m)
4.3
3.7
Reflectivity
255
0
0.6 m
Scene
a
Distance (m)
4.3
3.7
Reflectivity
255
0
bc d
efgh
Figure 6 | Real-time 3D video. (a) Illustration of the scene containing a static mannequin head and a swinging ball. (b–h) Sample of consecutive depth and
reflectivity frames reconstructed at B5 Hz frame-rate in real-time for a transverse resolution of 64 64 pixels. The experiments of Figs 3–6 were
replicated more than 10 times.
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compression ratio of C7% (Supplementary Movie 1). The
experimental parameters for this result were chosen to balance
the inherent trade-off between frame-rate and image quality
(Supplementary Note 3). Figure 6b–h show a sample of
consecutive frames from the 3D video. The result shows an
identifiable 3D image of the mannequin head and ball, in addition
to the real-time motion of the ball. Importantly, however, 3D
reconstruction can be performed using fewer patterns to achieve
higher frame-rates if required, for instance using 256 patterns
provides 12 Hz video (Supplementary Movie 2).
Discussion
We have demonstrated that our single-pixel 3D imaging system is
capable of reconstructing a scene with millimetric ranging
accuracy using modest hardware. In addition, we obtained real-
time video rates by taking advantage of a modified compressive
sensing scheme that does not rely on lengthy post-processing.
The performance of the system in this work was mainly limited
by the repetition rate of the laser used, 7.4 kHz. Using a laser with
a repetition rate greater than or equal to the DMD modulation
rate, could enable faster 3D video rates by a factor of three and/or
increase reconstruction accuracy by increased averaging.
Furthermore, the broad operational spectrum (400–2,500 nm)
of the DMD could enable the system to be extended to the
non-visible wavelength, such as the infrared, using modified
source and detection optics. The use of DMDs in the infrared has
already been demonstrated in microscopy6and real-time video
cameras7. The potential application of 3D imaging in the infrared
could provide enhanced visibility at long-range, due to reduced
atmospheric scattering28.
Methods
Hardware specifications.The following components were used in the
experimental set-up (Fig. 1): a pulsed laser (Teem Photonics SNG-03E-100,
532 nm); a DMD (Texas Instruments Discovery 4100 DMD); a projection lens
(Nikon ED, f¼180 mm); a collection lens (customized fresnel condenser lens,
f¼20 mm); a Si biased photodiode (Thorlabs DET10A); and a high-speed USB
digitizer (PicoScope 6407, 2.5 GS s 1for two-channel acquisition).
Operating configurations.There are several important points worth mentioning.
(a) The modulation rate of the DMD can reach up to 22.7kHz, however, in this
experiment the DMD is operated in slave-mode, meaning the modulation rate is
determined by the repetition rate of the laser at 7.4 kHz. (b) The active area of the
photodiode is 0.8 mm2, used in conjuction with a 20-mm focal length fresnel lens
system, giving a 2.6°field of view, which matches that of the projection system. The
depth estimation includes Gaussian smoothing, intensity calibration, cubic spline
interpolation and depth determination. More experiment methods and details are
provided in Supplementary Methods.
Data availability.The data used to generate all of the figures in this study can be
found at http://dx.doi.org/10.5525/gla.researchdata.317.
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Acknowledgements
We thank Prof. Adrian Bowman and Dr Liberty Vittert for providing the
stereophotogrammetric 3D data of the polystyrene mannequin head. M.S. acknowledges
the support from National Natural Foundation of China (Grant No. 61307021) and
China Scholarship Council (Grant No. 201306025016). M.J.P. acknowledges financial
support from UK Quantum Technology Hub in Quantum Enhanced Imaging (Grant No.
EP/M01326X/1), the Wolfson foundation and the Royal Society.
Author contributions
M.-J.S., R.L. and M.J.P. conceived the concept of the experiment; M.-J.S., M.P.E. and
G.M.G. designed and performed the experiments; M.-J.S., M.P.E. and M.J.P. designed the
reconstruction algorithm; N.R. developed the evolutionary compressed sensing
algorithm; M.-J.S., M.P.E., B.S. and M.J.P. analysed the results; M.-J.S., M.P.E. and M.J.P.
wrote the manuscript and other authors provided editorial input.
Additional Information
Supplementary Information accompanies this paper at http://www.nature.com/
naturecommunications
Competing financial interests: The authors declare no competing financial interests.
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How to cite this article: Sun, M.-J. et al. Single-pixel three-dimensional imaging with
time-based depth resolution. Nat. Commun. 7:12010 doi: 10.1038/ncomms12010 (2016).
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