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Abstract— We report an elliptical beam design for aberration
mitigation in high-resolution optical coherence tomography
(OCT). We polished a large angle on the fiber terminal facet in the
sample arm to make a non-rotational symmetric beam with
different numerical apertures (NA) for the two axes vertical to the
optical axis. By sacrificing the resolution in the out-of-plane
transverse direction, the elliptical beam mitigated the aberration
introduced by the focusing optics in the OCT system. The elliptical
beam with a doubled NA in the in-plane transverse direction
promoted the axial field-of-view (FOV) by about 50% and
increased the signal back-coupling efficiency by about 25%. We
verified the feasibility of the design by imaging the USAF 1951
resolution chart, swine cornea ex vivo, and human skin in vivo.
Results show that the proposed method relieves aberration-related
problems in high-resolution OCT.
Index Terms— Interferometry; Optical coherence tomography;
Spectroscopy.
I. INTRODUCTION
PTICAL coherence tomography (OCT) is a noninvasive
imaging technique, which has become one of the leading
diagnostic tools in modern ophthalmology [1-3]. Like most of
the traditional optical systems, OCT images suffer from optical
aberrations while the methods to manage aberration are very
limited. For OCT applications, such as ophthalmology OCT,
hardware-based adaptive optics (HAO) is still the only choice
for restoring both the signal intensity and the imaging
resolution. However, for an HAO correction, a set of correction
parameters is valid only over a sufficiently small volume and
over a sufficiently short period of time during which the
sample-induced aberrations are constant. Consequently, it is
time-consuming to image large tissue areas [4-7]. From a
practical point of view, the high complexity and cost of the
system also impede its applications. In OCT, the optical
aberrations are recorded as the interferometric wavefront
distortions that are optoelectronically detected, which opens up
the possibility to restore the detection resolution digitally.
Wide-field computational techniques, such as sub-aperture
This work was supported in part by China Railway Siyuan Survey and
Design Group Co., Ltd. (2020K183), National Medical Research Council
(MOH-OFIRG19may-0009), and Ministry of Education Singapore (MOE-
T2EP30120-0001).
Jinhan Li is with Beijing Jiaotong University, Beijing, China and China
Railway Siyuan Survey and Design Group Co., Ltd., Wuhan, China (e-mail:
jli036@e.ntu.edu.sg).
correlation [8], computational adaptive optics [9-11], and
model-based methods [12-14] have been developed to
overcome the above-mentioned issues with HAO.
Nevertheless, these computational techniques can only digitally
correct the wavefront distortion and are not capable of storing
the signal intensity. In addition, most of these algorithms are
highly demanding of phase stability over the full field
acquisitions, making the required acquisition speed much
higher than that of the prevailing commercial OCT devices.
Like most of the flying-spot imaging optics, OCT
conventionally operates with quasi-rotational symmetric optics,
which give rise to aberrations in all the radial directions.
Nevertheless, in the routine B-mode scanning, the transverse
resolution along the out-of-plane direction may not necessarily
be as high as that along the in-plane transverse direction. [15]
Under certain conditions, if the B-scan sectioning thickness
requirement was relieved, the resolution along the out-of-plane
direction becomes less important. Such conditions may exist
when the microstructural features of tissues are invariant along
the out-of-plane direction over the relieved sectioning
thickness, such as layered tissues like the retina, or when the
relieved sectioning thickness is about one cell size following
the convention of routine histology. In these scenarios, a non-
rotational symmetric beam such as the elliptical beam is
advantageous over the corresponding circular beam in
aberration management.
In this paper, we report an elliptical beam design for
aberration mitigation in high-resolution optical coherence
tomography (OCT). We evaluated the focusing performances
of the elliptical beam under defocus and primary spherical
aberration conditions using scalar diffraction theory and
Zernike polynomial representations. We numerically simulated
that the elliptical beam design offers around 50% larger axial
field of view (FOV) and 25% higher signal back-coupling
efficiency than those of the circular beam given the same
transverse resolution along the in-plane transverse direction.
Experiments were conducted by imaging the USAF 1951
resolution chart, swine cornea ex vivo, and human skin in vivo.
Jun Xie is with Nanyang Technological University, Singapore 639798. (e-
mail: jun.xie@ntu.edu.sg).
Linbo Liu is with Nanyang Technological University, Singapore 639798. (e-
mail: liulinbo@ntu.edu.sg).
Aberration Mitigation in High-resolution
Optical Coherence Tomography Implementing
Elliptical Beam Design
Jinhan Li, Jun Xie, and Linbo Liu
O
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The experimental results were in agreement with the simulation
results.
II. METHODOLOGY
A. Elliptical beam generation
To generate the elliptical beam, the incident fiber in the
sample arm was polished a large angle at the terminal facet.
Since the effective fiber NA along the X-axis of the incident
beam increases as the polishing angle increases, the polishing
angle should be maximized. However, the reflectivity of the
fiber facet also increases as the polishing angle increases.
Therefore, we set a criterion for the application that the 1%
maximum intensity should not be total internal reflected.
Considering the fiber implemented is the single mode fiber
(780-HP, Thorlabs Inc., USA), the fiber is NA = 0.13 (1%
maximum intensity), and the core refractive index is n=1.493.
The schematic of the angled terminal is shown in Fig. 1. The
maximal half-angle of the cone of light that can exit the fiber α
can be calculated by NA=n sinα and α=5.1°. The maximal
polishing angle βmax was calculated using (1) - (3).
1
sin( ) sinn
(1)
2
sin( ) sinn
(2)
12
sin( )
x
NA
(3)
θ1 and θ2 are the refractive angles of the 1% intensity edge.
The maximum polishing angle βmax was obtained when sinθ1=0,
and it was calculated to be 38.02°, which corresponds to an
effective NA along the X-axis NAx=0.32.
In order to compare the performances of the circular beam and
the elliptical beam, we make the two transverse resolutions
equal before comparing the axial FOVs and back-coupling
efficiencies. In this paper, the polishing angle β was set to 37.5°
to generate the elliptical beam with an output NAx twice as large
as that of the circular beam, which was equal to 0.26 measured
at the 1% intensity level. Aberration corrected objective lenses
(Mitutoyo M Plan Apo NIR 10× and 20×) were implemented to
make the two beams sharing the same in-plane transverse
resolution.
B. Elliptical beam OCT system
The system schematics are demonstrated in Fig. 2a. A
superluminescent diode (M-T-850-HP, Superlum, Ireland) was
used as the power source to provide a spectral input centered at
850 nm wavelength. We used a 50:50 fiber coupler
(TW850R5F2, Thorlabs, USA) to direct the illumination beam
to the reference arm and sample arm. For the elliptical beam
system, the collimators (L1 and L2) were 20× objective lenses
(M Plan Apo NIR 20×, Mitutoyo, Japan), and the focusing
lenses (FL1 and FL2) were 10× objective lenses (M Plan Apo
NIR 10×, Mitutoyo, Japan). The backscattered interference
signal was guided back to the spectrometer, which was
composed of a 30mm achromatic lens collimator (AC127-030-
B-ML, Thorlabs, USA), a 1200 lines/mm grating (Wasatch
Photonics 840nm, Munich, Germany), a camera lens (AF
Nikkor 85mm f:1.8D, Nikon, Japan), and a CCD camera
(AViiVA EM4, E2V, UK).
The fiber terminal at the sample arm was embedded in a fiber
ferrule and the facet was polished an angle of 37.5° with respect
to the flat facet to generate the elliptical beam. Fig. 2b shows
the angled terminal. Fig. 2c depicts the image of the
illumination collimated elliptical beam obtained by a laser
beam profiler (LBP2-HR-VIS2, Newport, USA), which shows
that the illumination beam was stretched by two folds over the
X-axis to perform the elliptical beam.
α
β
θ1
θ2
Fig. 1. Schematics of angled fiber facet.
Fiber Coupler
L2
L3
Camera
Spectromete r GCL
L1
Light
Source
RM
Ferrule
Galvo
Sample
FL1
(a)
(b) (c)
37.5°
37.5°
Angle
FL2
X
YZ
PC1
PC2
1.39mm
0.73mm
Fiber Coupler
L2
L3
Camera
Spectrometer
G
CL
L1
Light
Source
RM
FL2
Galvo
Sample
FL1
PC
(d)
Fig. 2. (a) Schematic of the elliptical beam OCT system. PC1-PC2:
polarization controller; L1-L3: achromatic lenses; FL1-FL2: focusing lens;
RM: reflective mirror; G: grating; CL: camera lens. (b) A photograph of the
fiber termination. (c) Cross-sectional intensity profile at the pupil plane of the
focusing lens. (d) Schematics of the benchmark conventional OCT system.
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C. Benchmark circular beam OCT system
A conventional circular beam OCT system was set as the
benchmark system for performance comparison. The schematic
of the benchmark system is demonstrated in Fig. 2(d). To make
a fair comparison between the circular beam and the elliptical
beam systems, the illumination power and in-plane transverse
resolutions were set to be equal between the two systems.
Because the in-plane NA of the 37.5°angled fiber was twice as
large as that of the flat fiber, this difference in fiber NA was
balanced by the magnification of the objective lens.
Specifically, the magnification of the objective lens in the
circular beam setup was two times larger than that in the
elliptical beam setup so that the in-plane transverse resolutions
were the same between the two setups. In the circular beam
setup, the collimators and focusing lens of the benchmark
circular beam system were all 20× objective lenses (M Plan
Apo NIR 20×, Mitutoyo, Japan), with other optical components
the same with the elliptical beam OCT system.
III. SIMULATIONS
For theoretical modeling of the detected signal, we
considered the flying-spot imaging optics of an OCT system as
in Fig. 3. The optics in OCT is described by the Fraunhofer
diffraction equations. The exit pupil of the focusing lens is in
the x’y’ plane. Assuming the system is illuminated by a
monochromatic wave with its wavelength λ and complex
amplitude A(x’, y’). The complex amplitude U(x, y) of the
diffracted wave is given by the Fraunhofer diffraction equation
as (4):
2
( , ) ( ', ')exp( ( ' ' )) ' '
Aperture
U x y A x y i x x y y dx dy
z
(4)
where z is the distance between the exit pupil and the object
plane. Considering that the focusing optics in OCT systems
consists of a collimator and a focusing lens, the lateral electric
field distribution before the exit pupil is the Fourier transform
of that on the front-focal plane.
22
22 0
' / , ' /
22
0
( ' ' )
( ', ') [exp( )] exp[ ]
()
co co
x f y f co
xy
u x y F f
(5)
where F is the Fourier transform function, ξ and η denote the
position in the front-focal-plane, ω0 is a constant defined by the
Gaussian field radius at 1/e2 maximum intensity of the incident
beam, fco is the focal length of the collimator.
Table I lists the Zernike terms for defocus and primary
spherical aberration [16, 17]. The listed aberrations were the
major factors we were concerned about in the later simulation
process.
For Zernike polynomials, the calculations are usually in polar
coordinates. However, since the elliptical beam introduces a
non-rotationally symmetric wavefront, the simulation should be
transferred into the Cartesian coordinate system. Therefore, we
converted the Zernike polynomials into Cartesian coordinate
with . Equation (6) gives the complex amplitude
at the exit pupil including the aberrations
( ', ') ( ', ')exp( ( ', '))
m
sn
A x y u x y iz Z x y
(6)
where
is the Zernike polynomials representing the
wavefront deviation (aberration), is the Zernike expansion
coefficient meaning the amplitude of the wavefront deviation.
The field distribution before the exit pupil is given by (7) for
circular beam and (8) for elliptical beam
22
02
()
( , ) ( , )exp[ ]
()
circular co
xy
u x y p x y f
(7)
22
02
[( / 2) ( ) ]
( , ) 2 ( , )exp{ }
()
elliptical co
xy
u x y p x y f
(8)
where p(x, y) is the aperture of the collimator. Assume the X-
axis is in the in-plane direction. Practically, the NAx of the
elliptical beam is twice as large as that of the circular beam The
incident circular beam radius ω0 was set to be 2.5 µm (1/e2)
according to the specifications of the single mode fiber HP-780.
To make an equitable comparison between the two situations,
was set to obtain a similar in-plane
transverse resolution for the two beams. The aperture size was
set to be 4.5mm in diameter. The elliptical beam distribution
had an amplitude of to match the incident power of the two
beams. The simulation results are demonstrated in Fig. 4.
The back-coupling efficiency was evaluated using the
encircled energy, which was defined by the 1/e2 maximum
intensity radius of the aberration-free beam spot. Specifically,
the encircled area for the circular beam was a 2.5um radius
circle, and that for the elliptical beam was a corresponding
elliptical area.
Fig. 4a is the aberration-free transverse PSF along the X-axis,
and the width of the 1/e2 maximum intensity in the X-axis is 2.5
µm for both elliptical and circular beam systems. Fig. 4b and 4c
are the aberration-free 2D PSF of the circular beam and
elliptical beam spot on the focal plane, respectively. The
elliptical beam spot on the focal plane expands on Y-axis. The
two beams showed equal encircled energy, indicating similar
performance when there is no optical aberration.
TABLE I
LOW-ORDER ON-AXIS OPTICAL ABERRATIONS WITH THEIR CORRESPONDING
ZERNIKE POLYNOMIALS
Aberration
Zernike
polynomials
Zernike expansion
coefficient
Defocus
0
2
Z
2
3(2 1)
Primary
Spherical
0
4
Z
42
5(6 6 1)
Object Plane
Exit pupil
Front-focal-plane
Collimator
Focusing
Lens
(ξ,η)(x’,y’)(x,y)
fco z
Fig. 3. Schematic diagram of the OCT focal optics.
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The influence of defocus was simulated in Fig. 4d, 4e, and
4f. Fig. 4d is the image of the Zernike polynomials with n=2,
m=0. A Zernike coefficient of 1.42 was set in both elliptical and
circular illumination beams to simulate the same level of
defocus aberration. The Zernike coefficient was chosen because
such a wavefront deviation led to a Strehl ratio of 0.5 for
circular beam (-3dB maximum intensity). Fig. 4e and 4f depict
the corresponding defocused beam spots, respectively. The
encircled energy was simulated to be 63.34% for circular beam
and 73.46% for elliptical beam, respectively.
The influence of the primary spherical aberration was also
investigated. The simulation results are shown in Fig. 4g, 4h,
and 4i. Fig. 4g is the image of the Zernike polynomials with
n=4, m=0, meaning that the wavefront deviation was
considered caused by primary spherical aberration. The Zernike
coefficient was 4 for both elliptical and circular beams for the
same reason that such spherical aberration makes the Strehl
ratio in the circular beam 0.5. Fig. 4h and 4i are the
corresponding beam spot. The performances were also
evaluated by the encircled energy and an improvement of
21.3% was observed (59.2% for circular beam and 71.8% for
elliptical beam).
The simulation results show that implementing the elliptical
beam helps to mitigate defocus and primary spherical
aberrations.
IV. EXPERIMENTAL RESULTS
A. Intensity profile and resolution
In order to investigate the ability of the elliptical beam to
mitigate aberration and extend axial FOV, both real-world
example simulations and experiments were conducted.
The simulation was performed using Zemax software. The
incident spectrum band was set ranging from 750nm to 950nm
wavelength. A widely-used achromatic lens (AC050-010-B-
ML, Thorlabs, USA) was implemented to simulate the
objective lens in both systems. The collimated beam size on
both axes was 1.3mm at the 1% intensity level for the circular
beam, while the collimated beam size for the elliptical beam
was 1.3mm on X-axis and 0.65mm on Y-axis.
The on-axis PSF distributions for the two systems are
demonstrated in Fig. 5a and 5b. Fig. 5c demonstrates the
simulated axial FOV. The simulation was conducted by
analyzing the Zemax simulation results. The intensity profile
was established by obtaining the on-axis intensity at different
depths and plotted by the Matlab software. Fig 5c depicts that
when the two systems matched the comparable transverse
resolution (simulated 3 µm), the axial FOV were simulated
106.1 µm (circular) and 156.3 µm (elliptical), respectively. This
result indicated that a theoretical 47.3% axial FOV extension
was achieved by implementing the elliptical beam.
The simulation result was verified in the experiment. The
experimental intensity profiles were acquired by measuring the
back-coupling power from the sample arm while moving the
reflection mirror along different axial or depth locations. The
effect caused by the chromatic focal shift was minimized by
implementing the apochromatic lenses and limiting the
illumination bandwidth. The illumination bandwidth was
limited to around 60nm centered at 840nm (channel 2 of the
SLD). In Fig. 5d, the solid line and the dashed line were for the
intensity profiles of the elliptical beam system and the
benchmark circular beam system, respectively. The -6dB
-1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1-1
-0.5
0
0.5
1
x/m
y/m
-10 -5 0 5 10
-10
-5
0
5
10 0
0.1
0.2
0.3
0.4
0.5
0.6
x/m
y/m
-10 -5 0 5 10
-10
-5
0
5
10 0
0.1
0.2
0.3
0.4
0.5
0.6
-1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1-1
-0.5
0
0.5
1
x/m
y/m
-10 -5 0 5 10
-10
-5
0
5
10 0
0.1
0.2
0.3
0.4
0.5
0.6
x/m
y/m
-10 -5 0 5 10
-10
-5
0
5
10 0
0.1
0.2
0.3
0.4
0.5
0.6
-5 0 5
0
0.2
0.4
0.6
0.8
1
x/m
Intensity
Elliptical
Circular
x/m
y/m
-10 -5 0 5 10
-10
-5
0
5
10 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x/m
y/m
-10 -5 0 5 10
-10
-5
0
5
10 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(a) (b) (c)
(d) (e) (f)
Defocus
Primary Spherical
x
y
x
y
Defocused Circular PSF Defocused Elliptical PSF
Spherical aberrant Circular PSF Spherical aberrant Elliptical PSF
(g) (h) (i)
Circular PSF Elliptical PSF Transverse PSF
2.5 µm
Fig. 4. Simulation results of the defocus and the primary spherical aberration.
(a) Aberration-free transverse PSFs along the X-axis. (b) Aberration-free
circular PSF on focal plane. (c) Aberration-free elliptical PSF on focal plane.
(d) Image of the Zernike polynomials with n=2, m=0 (defocus). (e) Image of
the defocused beam spot of circular beam. (f) Image of the defocused beam
spot of elliptical beam. (g) Image of the Zernike polynomials with n=4, m=0
(primary spherical aberration). (h) Image of the beam spot of circular beam
with primary spherical aberration. (i) Image of the beam spot of elliptical beam
with primary spherical aberration.
-80 -60 -40 -20 0 20 40 60 80
0
0.2
0.4
0.6
0.8
1
x/m
Intensity
Experimental Intensity Profile
Elliptical
Circular
-80 -60 -40 -20 0 20 40 60 80
0
0.2
0.4
0.6
0.8
1
z/m
Intensity
Simulated Intensity Profile
Elliptical
Circular
(a) (b)
(c)
(d)
112 µm 179 µm
106 µm 156 µm
Fig. 5. Simulated and experimental results of axial FOV. (a) Elliptical beam
illumination PSF. (b) circular beam illumination PSF. (c) Simulated axial
intensity profile comparison. Axial FOV comparison: 106.1 µm (circular) and
156.3 µm (Elliptical) (d) Experimental axial intensity profile comparison.
Axial FOV comparison: 112 µm (circular) and 179 µm (elliptical).
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maximum intensity full widths of the two profiles were
measured to be 179 µm (elliptical beam) and 112 µm (circular
beam), indicating a 60% axial FOV extension. The
experimental results were in agreement with the simulation
results.
To verify that the two systems shared comparable in-plane
transverse resolution, the resolutions for the two systems were
tested by the USAF 1951 resolution chart. Fig. 6a and 6b
demonstrate the resolution chart images with the reference arms
blocked.
Fig. 6a depicts that the elliptical beam OCT system reached
a high resolution in the vertical direction (X-axis) that can
resolve the last element of group 7 on the resolution chart.
However, due to the non-rotational symmetric beam
illumination, the image in the vertical direction (6th element of
group 7) performs far better than horizontal orientation (2nd
element of group 7) in resolution. As for the circular beam
system, Fig. 6b shows that the 6th element of group 7 was
resolved in both orientations. The transverse resolution along
the X-axis was derived from the intensity profile of the symbol
edge images. Fig. 6c and 6d illustrate the system transverse
resolutions acquired by scanning the edges of the symbols on
the resolution chart. Considering the FWHM image can be
obtained by 1.39 times the 10% - 90% edge width, the in-plane
transverse resolutions for the two focal systems were measured
3.2 µm and 3.1 µm, respectively, which are comparable. The
simulation and the experimental results are compared in Table
Ⅱ, indicating that an axial FOV extension of around 50%
(47.3% for simulation, 60% for experiment) was achieved by
the elliptical beam OCT.
B. Swine cornea imaging
To demonstrate the axial FOV extension in biological
samples using the elliptical beam, a specimen of swine cornea
was utilized to conduct OCT imaging ex vivo. The cross-
sectional images of the specimens are present in Fig. 7.
In the experiment, the illumination power on the tissue for
both the systems was set 2.45mW and both focal planes were
set 100 µm axially deep into the stroma layer to provide a fair
comparison between the circular-beam OCT and the elliptical-
beam OCT systems to image the depth information. In Fig. 7a
and 7b, the epithelium, the endothelium, and the Bowman’s
layer were resolved in both figures. However, the in-depth
information such as Descemet’s membrane, which was
hyporeflective in OCT images with a high scattering interface
with the stroma, was resolved in elliptical beam images. While
the circular beam system can only obtain a blurred image of it.
Fig. 7c depicts the intensity profile comparison in the place
of the Descemet’s membrane and the endothelium for the two
obtained images. The profile was obtained by averaging 512
adjacent A-lines. The profile verifies that the image intensity of
the Descemet’s membrane obtained by elliptical beam system
is 2dB superior over the circular beam system obtained image.
The swine cornea tissue experiment results verified that the
axial FOV was extended by the elliptical beam system.
C. Spherical aberration and signal intensity
The spherical aberrations degrade the encircled energy,
TABLE Ⅱ
COMPARISON ON THE FOCUSING PERFORMANCES
Transverse resolution
along X axis
Axial FOV
Simulation
Experiment
Simulation
Experiment
Circular
beam
3.024 m
3.1 m
106.1m
112 m
Elliptical
beam
3.03 m
3.2 m
156.3 m
179 m
10%
90%
2.29µm
FWHM: 3.2µm FWHM: 3.1µm
10%
90%
2.22µm
(a)
(c)
(b)
(d)
Edge Profile (Circular)
Edge Profile (Elliptical)
Fig. 6 System resolution examinations. (a) Images of the USAF 1951
resolution chart (groups 6 and 7) acquired by elliptical beam system. (b)
Images of the USAF 1951 resolution chart (groups 6 and 7) acquired by
circular beam system. Scan directions: vertical (X) and horizontal (Y). (c)
Edge scan profile of elliptical beam system. (d) Edge scan profile of circular
beam system. The edge scan profiles were used to calculate the transverse
resolution along the X-axis.
EP
BM
S
DM
ED
(a) (b)
50 µm
(c)
EP
BM
S
DM
ED
50 µm
dB dB
DM
ED
Fig. 7 Ex vivo swine cornea imaging covering a cross-sectional area of 250 µm
× 400 µm (X ×Z). (a) Image obtained with elliptical beam system. (b) Image
obtained with circular beam system. (c) Intensity profile of the Descemet’s
membrane and the endothelium. Ep: epithelium; BM: Bowman’s layer; S:
stroma; DM: Descemet’s membrane; Ed: endothelium; FP: focal plane
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which mainly has influences on the back-coupling efficiency of
the sample arm optics and affects the system sensitivity. To
investigate how elliptical beam could mitigate spherical
aberrations in terms of the sample arm back-coupling
efficiency, we used a 20mm focal length plano-convex lens
(LA4647, Thorlabs, USA) as the collimator and a 10× objective
lens (M Plan Apo NIR 10×, Mitutoyo, Japan) as the focusing
lens for the elliptical beam implemented sample arm. The
benchmark circular beam system used the same collimator and
a different focusing lens with 20× magnification (M Plan Apo
NIR 20×, Mitutoyo, Japan) to maintain the same transverse
resolution. This real-world example was simulated by the
Zemax software. The above-mentioned LA4647 plano-convex
lens was implemented to simulate the objective lens in both
systems. The collimated beam size on both axes was 1.3mm at
the 1% intensity level for the circular beam, while the
collimated beam size for the elliptical beam was 1.3mm on X-
axis and 0.65mm on Y-axis. The simulated PSFs are
demonstrated in Fig. 8.
The Zernike coefficient for primary spherical at different
interfaces in the ZEMAX model is present in Table Ⅲ. The
collimated beam before the plano-convex lens was assumed
perfect Gaussian beam with no aberration. When the beam
reached the plano-convex lens, the aberration was added to the
illumination beam. For the same plano-convex lens, the
elliptical beam mitigates the primary spherical aberration and
the Zernike coefficient was simulated to be 0.283 which is
superior to the circular beam. Then the beam will propagate to
the image plane, the Zernike coefficient for the primary
spherical aberration was increased to 0.355 for elliptical beam
and 0.779 for circular beam, respectively. The simulation
results show that the spherical aberration does get decreased
after the plano-convex lens by the elliptical beam design.
The back-coupling efficiency was calculated with the
overlapping rate between the mode field of the incident fiber
and the back-reflected field distribution [18]. The overlapping
integral equation is given by (9)
2
*
**
( , ) ( , )
( , ) ( , ) ( , ) ( , )
fd fiber
fd fd fiber fiber
U x y U x y dxdy
U x y U x y dxdy U x y U x y dxdy
(9)
where Ufd is the amplitude of the back-reflected field
distribution and Ufiber is the fiber mode field. The simulation
results are compared in Table Ⅳ. The simulated back-coupling
efficiency were 0.481 for the elliptical and 0.398 for the circular
beam, respectively.
To verify the simulation result, the back-coupling power
from a perfect reflector (reflective mirror) was measured at the
fiber terminal at the spectrometer using a power meter
(PM100D, Thorlabs Inc.) with a power sensor (S122C,
Thorlabs Inc.). Considering the 3.9dB insertion loss of the
50:50 fiber coupler and a 10% intensity loss at the galvo
scanning system, the resulted back-coupling efficiency was
listed in Table Ⅳ. The results show that the back-coupling
efficiency was improved by the elliptical beam by 24.8%
(simulated 23.4%).
The experimental results are in agreement with the
simulation results, showing that the spherical aberration was
mitigated by the elliptical beam and the back-coupling
efficiency was improved.
To ensure that the spatial resolution was achieved as
designed, we acquired reflectance images of the 1951 USAF
resolution chart with reference arm blocked. The experimental
results are illustrated in Fig. 9. Fig. 9a and 9b depict the
resolution chart images acquired by the elliptical beam and
circular beam system, respectively. The image contains the
elements from group 6th and group 7th on the resolution chart.
Both systems are capable of resolving the last element of group
7th, indicating a leveled transverse resolution for the two
systems. The intensity obtained by the two systems is compared
x/m
y/m
Elliptical
-10 -5 0 5 10
-10
-5
0
5
10 0.1
0.2
0.3
0.4
0.5
0.6
x/m
y/m
Circular
-10 -5 0 5 10
-10
-5
0
5
10 0.1
0.2
0.3
0.4
0.5
0.6
(a) (b)
Fig. 8 Real-world example simulation of the spherically aberrated PSFs
focused by plano-convex lens. (a) Elliptical beam result. (b) Circular beam
result.
TABLE Ⅲ
THE ZERNIKE COEFFICIENT FOR PRIMARY SPHERICAL ABERRATION
AT DIFFERENT INTERFACES IN THE ZEMAX MODEL
Collimated
Beam
Plano-convex
Lens
Image plane
Circular Beam
0
0.627
0.779
Elliptical Beam
0
0.283
0.355
TABLE Ⅳ
COMPARISON BETWEEN THE SIMULATED COUPLING EFFICIENCY AND
THE EXPERIMENTAL BACK-COUPLING EFFICIENCY
Elliptical
beam
Circular
beam
Improvement
Simulated Coupling
Efficiency
0.481
0.398
23.4%
Back-coupling
Efficiency
0.332
0.266
24.8%
010 20 30 40
0
2000
4000
6000
8000
10000
12000
14000
x/m
Intensity/a.u.
Elliptical
Circular
0 5 10 15 20
0
1000
2000
3000
4000
5000
Intensity/a.u.
x/m
Elliptical
Circular
(a)
(c)
(b)
(d)
Fig. 9 Image of the 1951 USAF resolution chart. (a) Image obtained with
elliptical beam system. (b) Image obtained with benchmark circular beam
system. (c) Intensity profile comparison of the square element. (d) Intensity
profile comparison of the 6th element in the 7th group. The intensity is in
arbitrary unit (AU).
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in Fig. 9c and 9d in arbitrary units (AU). The results show that
the elliptical beam improved the intensity of the square element
by 27.51% (13869 AU for elliptical beam and 10877 AU for
circular beam), which is in agreement with the previous results.
However, the intensity of the transverse element (element 6th
in group 7th) was improved by 54.22% (4838AU for elliptical
beam and 3137AU for circular beam). The reason was that the
elliptical beam experienced the transverse anisotropic back-
scattering process which result in different back-scattered
intensities when the illuminating elements are in different
orientations.
D. Human skin image in vivo
To verify the aberration mitigation and the back-coupling
efficiency enhancement of the elliptical beam in cellular level
images, the human skin was tested in vivo. The imaging was
conducted on the human finger with ultrasound transmission
gel (Aquasonic 100, Parker Laboratories, Inc., USA) at the
surface to minimize the surface reflectivity. The image result is
demonstrated in Fig. 10a and 10b, respectively. The two images
were adjusted to the same noise level for image comparison.
The cell nuclei in the epidermis, as the arrows point, were
resolved in both images, indicating that both the two OCT
systems were cellular level µOCT. The elliptical beam obtained
an extended in-depth image in the reticular dermis and the
intensity on the focal plane was observed higher with respect to
the circular beam obtained image. The intensity profiles of the
two images were compared in Fig. 10c. The result shows that
the elliptical beam obtained a 25% higher image contrast, which
is in agreement with the previous results, verifying that the
elliptical beam mitigated the aberration and enhanced the signal
back-coupling efficiency.
V. DISCUSSION
A. Angled terminal and transmission efficiency
Theoretically, if we consider merely the elliptical beam itself,
the increased NA ratio between the X-axis and the Y-axis will
further increase the aberration mitigation performance, which
will promote the back-coupling efficiency. However, the
polishing terminal angle will also have influences on the fiber
terminal back-reflection. The elliptical beam was generated by
a large angled fiber terminal in the proposed OCT system.
However, implementing such a large angle increased the
Fresnel reflection at the fiber facet, which adds to the system
sensitivity loss. The Brewster’s angle of the terminal facet is
34.4° for normal SMF, and the most optimized polishing angle
should be around Brewster’s angle so that the fiber terminal
back-reflection can be minimized.
The facet angle proposed in this paper was close to
Brewster’s angle. Controlling the polarization state of the
incident beam suppresses the surface reflectance. According to
Fresnel equations (10) and (11), the curve of reflectance for
different polarization states with respect to emergence angle for
780-HP single mode fiber is demonstrated in Fig 11. When the
emergence terminal was polished at a 37.5° angle facet, the
reflectance of the s-state polarization is 19.1% and that of the
p-state polarization is only 0.77%. Therefore, we implement a
polarization controller at the sample arm, as Fig 2a shows. Most
p-state polarized beam at the fiber terminal facet was
transmitted, which solves the sensitivity loss problem caused by
the facet reflectance.
2
12
12
cos cos
cos cos
it
sit
nn
Rnn
(10)
2
12
12
cos cos
cos cos
ti
pti
nn
Rnn
(11)
B. Tissue induced aberration mitigation
There are usually tissue-induced aberrations due to the
refractive index mismatch between the superficial tissue
structure and the coupling medium. The tissue-induced
aberrations cause signal intensity modulations along the optical
010 20 30 40 50
0
0.2
0.4
0.6
0.8
1
Emergence Angle / degree
Reflectance
P State
S State
θi=37.5°
Fig. 11 The curve of reflectance for different polarization states with respect
to emergence angle for 780-HP single mode fiber.
(a) (b)
EP
SC
PD
RD
50 µm 50 µm
(c)
Fig. 10 Cross-sectional images of human skin in vivo. Cross-sectional area:
250µm×400µm (X × Z). (a) A representative image obtained using the
elliptical beam system showing nuclei of keratinocytes (arrows). (b) A
representative image obtained using the circular beam system. SC: Stratum
Corneum; EP: Epidermis; PD: Papillary Dermis; RD: Reticular Dermis. (c)
Intensity profile comparison in linear scale.
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axis, which is one of the major imaging artifacts in cross-
sectional images.
Such refractive index mismatch can be regarded as phase
masks with continuous random phase variation. Reduction of
beam size along the out-of-plane direction should help to
mitigate this problem. To provide an example of tissue-induced
aberration mitigated by the elliptical beam, images of human
skin on the back of the hand were obtained in vivo. As there is
a refractive index gap between the hair shaft and the
surrounding skin tissue, there were strong image artifacts below
the hair shaft, forming either enhancement in the intensity or
the shadowing. The images with hair shaft obtained with
elliptical beam and circular beam systems were demonstrated
in Fig. 12a and 12b. By comparing the two images, it is resolved
that the modulation caused by the hair shaft was much severe
in circular beam obtained images than that in elliptical beam
obtained images, indicating that the modulation was lightened
by the elliptical beam. Assuming that the tissue microstructures
are randomly distributed along the transverse directions, the
intensity modulation caused by tissue structures can be largely
canceled by averaging 100 cross-sectional frames along Y-axis.
The remaining intensity variations along X-axis are mainly
caused by the intensity modulation by aberrations. By
performing discrete Fourier transform on the averaged cross-
sectional image along X-axis, we can evaluate the tissue
induced intensity artifact in the frequency domain (Fig. 3.12c).
The result shows that the elliptical beam system suffered less
from tissue-induced aberrations.
VI. CONCLUSION
In conclusion, we have established an elliptical beam OCT to
overcome aberration-related problems in high-resolution OCT.
The proposed method provides extended axial FOV and
enhanced image contrast for high-resolution OCT cross-
sectional imaging. The proposed method is superior to the
existing axial FOV extension technologies in three aspects.
Firstly, it adds no system complexity to the conventional OCT
system to achieve aberration mitigation, therefore, it can be
readily used for various applications. Secondly, it is a flexible
method to implement in small-size OCT optical probes. Finally,
our method can be used in combination with other technologies,
such as wavefront engineering techniques and digital
refocusing, to further improve the performances. This novel
design is promising to be widely implemented in many kinds of
OCT systems.
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(a) (b)
(c)
Hair Shaft
Modulation
Hair Shaft
Modulation
50 µm 50 µm
Fig. 12 in vivo images of human skin on the back of the hand. (a) Elliptical
beam system obtained images, the modulation signal is caused by the hair
shaft. (b) Circular beam system obtained images. (c) Artifact intensity
comparison in Fourier domain.
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1982.
Jinhan Li was born in Wuhan, Hubei,
China in 1992. He received the B.Eng.
degree in optoelectronic engineering from
the Huazhong University of Science and
Technology, China in 2014, and the M.Sc
degree in communication engineering from
the Nanyang Technological University,
Singapore in 2015, and Ph.D. degree in
electrical and electronic engineering from the Nanyang
Technological University, Singapore, in 2020.
Since 2021, he has been a research fellow with the Beijing
Jiaotong University, Beijing, China and China Railway Siyuan
Survey and Design Group Co., Ltd., Wuhan, China. His
research interest includes optical coherence tomography,
wireless communication technologies, and geographic 3D
imaging technologies.
Jun Xie was born in Fujian, China in 1993.
He received the B.Eng. degree in
biomedical engineering from Tsinghua
University, China, in 2015, and the Ph.D.
degree in electrical and electronic
engineering from Nanyang Technological
University, Singapore, in 2020.
Since 2020, he has been a Research
Fellow in School of Computer Science and Engineering,
Nanyang Technological University, Singapore. His research
interests include optical coherence tomography, deep learning,
and medical image processing.
Linbo Liu was born in Yulin, Sha’anxi,
China, in 1978. He received the B.Eng.
degree in measurement and control
technology and instrumentation, and
M.Eng. degree in optical engineering from
Tianjing University, China, in 2004, and
the Ph.D. degree in bioengineering from
National University of Singapore in 2009.
From 2009 to 2012, he was a Research Fellow and Instructor
with the Wellman Center for Photomedicine, Massachusetts
General Hospital and Harvard Medical School. Since 2012, he
has been an Assistant Professor and Associate Professor with
the School of Electrical & Electronic Engineering and School
of Chemical & Biomedical Engineering, Nanyang
Technological University, Singapore. His research interests
include development and validation of noninvasive optical
diagnostic tools.
