A time-resolved optical tomography, optical coherence computed tomography, is proposed to bridge the gap between diffuse optical tomography and optical coherence tomography. Both ballistic and multiple-scattered photons are measured at multiple source-detection positions by low-coherence interferometry providing a temporal resolution smaller than 100fs. A light-tissue interaction model was established using the time-resolved Monte Carlo method. The optical properties were then reconstructed by solving the inverse transient radiative transport problem under the first Born approximation. Absorbing inclusions of 100μm diameter were imaged through a 2.6-mm-thick (∼30 scattering mean-free-paths) scattering medium

Li, Li

Wang, Lihong V.

Caltech Authors - Main

Optical coherence computed tomography
Li Li and Lihong V. Wang 
 
Citation: Applied Physics Letters 91, 141107 (2007); doi: 10.1063/1.2793625 
View online: http://dx.doi.org/10.1063/1.2793625 
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/91/14?ver=pdfcov 
Published by the AIP Publishing 
 
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Optical coherence computed tomography
Li Li and Lihong V. Wanga
Optical Imaging Laboratory, Department of Biomedical Engineering, Washington University in St. Louis,
St. Louis, Missouri 63130, USA
Received 16 July 2007; accepted 11 September 2007; published online 2 October 2007
A time-resolved optical tomography, optical coherence computed tomography, is proposed to bridge
the gap between diffuse optical tomography and optical coherence tomography. Both ballistic and
multiple-scattered photons are measured at multiple source-detection positions by low-coherence
interferometry providing a temporal resolution smaller than 100 fs. A light-tissue interaction model
was established using the time-resolved Monte Carlo method. The optical properties were then
reconstructed by solving the inverse transient radiative transport problem under the first Born
approximation. Absorbing inclusions of 100 m diameter were imaged through a 2.6-mm-thick
30 scattering mean-free-paths scattering medium. © 2007 American Institute of Physics.
DOI: 10.1063/1.2793625
The last decade has witnessed the revolutionary devel-
opment of optical imaging techniques for biomedical appli-
cations. Among them, time-resolved techniques are known to
provide the richest information on tissues’ optical properties.
We present a time-resolved optical imaging modality re-
ferred to as optical coherence computed tomography OCCT
or optical CCT. OCCT marries the concepts of the two most
popular optical tomographical techniques—diffuse optical
tomography1,2 DOT and optical coherence tomography
OCT.3,4
DOT works in the diffusive regime and provides maps of
tissues’ optical properties through model-based reconstruc-
tion from measurements at a large number of source-
detection pairs. It can image a few centimeters into tissue
using near-infrared light. However, the spatial resolution
achieved is relatively poor, typically on the order of millime-
ters 1/10 of the imaged depth, due to the nature of diffu-
sion. The time-resolved DOT measures the temporal point
spread function TPSF of the emitted light through a me-
dium in response to an ultrashort laser pulse. It is expected to
outperform the cw and frequency-domain versions since it
carries information of the whole spectrum simultaneously.
TPSFs were measured by sophisticated high-sensitivity de-
tection systems, such as a streak camera5 and a time-
correlated single-photon counting system.6 However, the
slow frame rate and the high cost limited their application.
Recently, time-gated optical image intensifier7 has been uti-
lized to develop fast parallel time-resolved DOT. However,
the gate width is 200 ps, corresponding to a path length as
long as 6 cm in air. A finer temporal resolution is preferred to
resolve tissues’ structure better.
In this letter, we propose to measure TPSFs using low-
coherence interferometry, where a temporal resolution
smaller than 100 fs can be easily achieved using ordinary
low-coherence sources, such as a superluminescent diode, a
femtosecond laser, or a wavelength-swept laser. This method
has high sensitivity 90–140 dB due to the amplification of
signal by a strong reference signal. Also, it can provide a
wide dynamic range because the interference signal is pro-
portional to the amplitude, instead of the intensity, of the
light emitted from the sample. This detection scheme is the
basis for OCT.
OCT works in the ballistic regime, where the measured
photons are assumed to take straight paths. It is able to pro-
vide micron-scale resolution imaging of tissues’ scattering
structure. However, like other ballistic imaging modalities,
its imaging depth is limited to 1 mm, due to the rapid
exponential attenuation of ballistic photons. In a highly scat-
tering medium, the image quality degrades quickly after light
penetrates several hundreds of micrometer because of mul-
tiple scattering.8 The multiple-scattered light can interfere
with the reference light just like the single-scattered light.9 It
is also difficult to extract absorption information from OCT.
Spectral information has previously been exploited to solve
this problem at the cost of spatial resolution.10 However, this
method is susceptible to the spectral variation of the scatter-
ing coefficient s, and is also unable to detect absorbers
whose absorption coefficient a does not change much in the
source bandwidth.
OCCT bridges the gap between DOT and OCT. It works
in the quasidiffusive regime,11 where most photons are mul-
tiply scattered, however not totally diffused. The side-
scattered photons are also collected. It makes full use of the
multiple-scattered photons by adopting a DOT-like model-
based reconstruction, and provides a tomographic imaging
technique that provides deeper penetration than OCT and
finer spatial resolution than DOT. In addition, because the
full inverse transient radiative transfer problem is solved dur-
ing the reconstruction, it can potentially map all the optical
properties.
Our OCCT system Fig. 1 is based on a fiber-optic
Mach-Zehnder interferometer. It is seeded by a broadband
superluminescent diode IPSDD0803, InPhenix, center
wavelength 0=829 nm, bandwidth =36.4 nm. There-
fore, the achievable temporal resolution here is 56 fs, which
can be further reduced by increasing the source bandwidth.
The cross interference between light traveling through a
fixed-length reference arm and the sample arm is recorded by
a homemade spectrometer using a fast line-scan camera
Aviiva M2, Atmel, 12 bits, 2042 pixels. This spectral-
domain detection has been proven to be faster and more sen-
sitive than its time-domain counterpart.12,13 The polarization
and dispersion differences between the two arms are care-
fully compensated for. The TPSF is calculated from the re-aElectronic mail: lhwang@biomed.wustl.edu
APPLIED PHYSICS LETTERS 91, 141107 2007
0003-6951/2007/9114/141107/3/$23.00 © 2007 American Institute of Physics91, 141107-1 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP:  131.215.70.231 On: Wed, 06 Jul 2016
22:59:18
corded spectrum through Fourier transform. The illumination
and collection optics are prealigned coaxially. Both are
scanned laterally in the x-y plane by a translation stage
with a step size of 100 m. This system can be easily paral-
lelized, for example, using a coherent fiber bundle, in the
future to increase the frame rate.
Unlike DOT, OCCT cannot use diffusion theory to
model the underlying photon-migration problem because the
diffusion approximations are invalid for the early arriving
photons. We must resort to the full transient radiative trans-
port equation RTE. As an initial demonstration of the
OCCT concept, we aim to image the spatial distribution of
absorption perturbation ar here. Perturbations in scatter-
ing coefficient s and the scattering phase function can be
mapped by following similar procedures. From the RTE, the
change in the measurement due to this absorption perturba-
tion within the acceptance angle d is obtained under the
first Born approximation as
Trd,td = − 
d

V

4

t
nˆrd · sˆdSrs, sˆs,tsGr, sˆ,t;rs, sˆs,tsarGrd, sˆd,td;r, sˆ,tdtddVdd
= − 
V
ar
d

4

t
nˆrd · sˆdSrs, sˆs,tsGr, sˆ,t;rs, sˆs,tsGrd, sˆd,td;r, sˆ,tdtddddV
= − 
V
arJ0r;rd,tddV , 1
where nˆ is the inward normal of the detection surface. S is
the source term, while G is the Green’s function solution for
the transient RTE. The integration involving S and G can be
merged into a single term J0r ;rd , td, which physically
means the portion of measured signal that has been affected
by the perturbation at r. Equation 1 represents a linear in-
verse problem, which is widely studied in DOT. J0, often
referred to as the sensitivity function, is calculated through a
time-resolved Monte Carlo method.14 The experimental
boundary condition is also included in our Monte Carlo
simulation. The simultaneous iterative reconstruction tech-
nique is used to solve ar, since it, in general, yields
better images than the regularized pseudoinverse approach
and the algebraic reconstruction technique. In real experi-
ment, we used M0T /T0 instead of T directly for inversion,
in order to make our reconstruction less susceptible to the
boundary condition of the object. Here, T0 and M0 are the
unperturbed measurements obtained through experiment and
simulation, respectively.
A highly scattering tissue-mimicking phantom was con-
structed using aqueous suspension of 1 m polystyrene mi-
crospheres. The optical properties calculated using the Mie
theory were s=113.6 cm−1 and scattering anisotropy g
=0.90, whereas the absorption is negligible. The phantom
used in our experiment was 2.6 mm thick, corresponding to
30 scattering mean-free-paths. The integration time for re-
cording a single spectrum was 1 ms. The TPSF for a single
source-detector pair was the average based on 500 recorded
spectra, where averaging alleviated the speckle noise.
Figure 2a shows the TPSFs detected at the source-detector
pairs with lateral shift x ranging from −0.5 to 0.5 mm. The
measurements at x=0, 0.2, and 0.4 mm, after compensation
for the depth-dependent decay due to the finite spectral reso-
lution, match the predictions from the Monte Carlo simula-
tion well, as shown in Figs. 2b–2d.
FIG. 1. Color online Optical coherence computed tomography OCCT
system. TPSFs at different source-detection pairs are measured by spectral-
domain low-coherence interferometry. SLD: superluminescent diode; FC:
fiber coupler; PC: polarization controller; DC: dispersion compensation; G:
gratings; LSC: Line-scan camera; L1–L8: lenses.
FIG. 2. Color online TPSFs measured in OCCT. a TPSFs obtained at
source-detector pairs with lateral shift x=−0.5–0.5 mm. TPSFs measured at
b x=0 mm, c x=0.2 mm, and d x=0.4 mm is compared with the pre-
dictions from the Monte Carlo simulation.
141107-2 L. Li and L. V. Wang Appl. Phys. Lett. 91, 141107 2007
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22:59:18
A 100 m hair fiber was immersed parallel to the y axis
inside the scattering medium described above. Three tomog-
raphic images were obtained when this hair fiber was placed
at three different depths with a 0.5 mm separation. For each
position, data were collected at 1111 source-detector pairs,
which covered a 1 mm range along the x axis. Figure 3a
shows the combined three reconstructed OCCT images
thresholded at 50% of the peak value in the image. The hair
fiber was clearly identified at all three expected positions.
The full width at half maximum of the imaged hair is
200 m along the z direction and 180 m along the x direc-
tion, both of which are 100 m wider than the diameter of
the hair fiber. Under the assumption of a linear system a
result of the Born approximation, the spatial resolution of
our OCCT system is estimated to be 100 m. This resolu-
tion maintains well throughout the imaged area. Figure 3b
shows the reconstructed image of two hair fibers in the scat-
tering medium, with a 1.3 mm separation in both the x and z
directions. Transmitted light was measured at 2121
source-detector pairs, which covered a 2 mm range along the
x axis. This demonstrates that OCCT is capable of mapping
multiple absorption perturbations simultaneously.
Previous development of imaging modalities for the qua-
sidiffusive regime is limited to laminar optical tomography
LOT15,16, which uses cw measurements. The image quality
relies on proper regularization and decays with depth. Since
time-resolved measurements are adopted in OCCT, the in-
verse problem is less ill-posed and the reconstruction is more
robust. OCCT is also less sensitive to specular reflections
than LOT, since the unwanted reflections fall outside the
time gate.
Another unique advantage of OCCT is that it can be
scaled up to image thicker tissues by relaxing the temporal
resolution because the light detected at each time point in-
creases with increasing time gate. Of course, this is done at
the cost of spatial resolution. The scaled-up OCCT is prom-
ising to provide a low-cost alternative to the current time-
domain DOT. Detection of light after penetrating 1.5 cm
chicken tissue was previously reported by relaxing the time
gate to 900 fs.17
The linear perturbation assumption is known to fail
when perturbations are large. In this case, the above predic-
tion of spatial resolution would also fail because the system
would become nonlinear and the neighboring targets would
affect each other’s image. Therefore, the nonlinear image
reconstruction problem needs to be solved through matching
the prediction and the measurement using the forward model
iteratively. The current Monte Carlo based forward model,
although accurate, suffers from stochastic noise. To achieve
acceptable smooth time-resolved simulation for the quasidif-
fusive regime is extremely computation intensive. As a re-
sult, our current experiments are limited to imaging line ob-
jects parallel with the y axis by using a sensitivity function
integrated along the y axis. Thus, a fast forward model is
desirable for expanding the application of OCCT. Recently,
with the advancement in time-resolved optical image tech-
niques, researchers have started to develop various numerical
solutions for solving the full transient RTE based on the dis-
crete transfer method, the discrete ordinates method, and fi-
nite volume method.8 However, further studies are needed to
clarify their applications in the content of biomedical optical
imaging, especially for the quasidiffusive regime. Their ac-
curacy need to be tested against the Monte Carlo method, a
well-accepted golden standard.
In conclusion, we demonstrated OCCT as a
50-fs-time-resolved tomographic modality to provide tomo-
graphical images of absorption perturbations in the quasidif-
fusive regime. This technique is important for functional
studies e.g., hemodynamics and molecular imaging based
on absorption-modulated probes in human skin and small
animals. A reflection-mode OCCT, as well as its scaled-up
version and proper fast forward model, is actively pursued in
our group.
We thank Dr. Youzhi Li and Dr. Ku Geng for fruitful
discussion and insightful suggestions. This work was sup-
ported in part by the National Institutes of Health under
Grant No. R01 CA092415 and R01 CA106728.
1A. Yodh and D. Boas, Biomedical Photonics Handbook CRC,
Boca Raton, 2003, Chap. 21, p. 71.
2A. Gibson, J. Hebden, and S. Arridge, Phys. Med. Biol. 50, R1 2005.
3D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M.
Hee, T. Flotte, K. Gregory, C. Puliafito, and J. Fujimoto, Science 254,
1178 1991.
4B. Bouma and G. Tearney, Handbook of Optical Coherence Tomography
Dekker, New York, 2002.
5J. Hebden and D. Delpy, Opt. Lett. 19, 311 1994.
6F. Schmidt, M. Fry, E. Hillman, J. Hebdan, and D. Delpy, Rev. Sci.
Instrum. 71, 256 2000.
7C. D’Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R.
Cubeddu, J. Phys. D 36, 1676 2003.
8M. Yadlowshy, J. Schmitt, and R. Bonner, Appl. Opt. 34, 5699 1995.
9B. Karamata, M. Laubscher, M. Leutenegger, S. Bourquin, T. Lasser, and
P. Lambelet, J. Opt. Soc. Am. A 22, 1369 2005.
10U. Morgner, W. Drexler, F. Kärtner, X. Li, C. Pitris, E. Ippen, and
J. Fujimoto, Opt. Lett. 25, 111 2000.
11L. V. Wang and H.-I. Wu, Biomedical Optics: Principles and Imaging
Wiley, New Jersey, 2007, Chap. 5, p. 114.
12J. deBoer, B. Cense, B. Park, M. Pierce, G. Tearney, and B. Bouma,
Opt. Lett. 28, 2067 2003.
13R. Leitgeb, C. Hitzenberger, and A. Fercher, Opt. Express 11, 889 2003.
14G. Yao and L. Wang, Phys. Med. Biol. 44, 2307 1999.
15A. Dunn and D. Boas, Opt. Lett. 25, 1777 2000.
16E. Hillman, D. Boas, M. Dale, and A. Dunn, Opt. Lett. 29, 1650 2004.
17M. Hee, J. Izatt, E. Swanson, and J. Fujimoto, Opt. Lett. 18, 1107 1993.
18S. Mishra, P. Chugh, P. Kumar, and K. Mitra, Int. J. Heat Mass Transfer
49, 1820 2006.
FIG. 3. Reconstructed OCCT images of hair fibers in high-scattering tissue
mimicking phantom. a OCCT images of a 100 m hair fiber at three
different depths with 0.5 mm separation. b OCCT images of two hair
fibers with 1.3 mm separation along both the x and z directions.
141107-3 L. Li and L. V. Wang Appl. Phys. Lett. 91, 141107 2007
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22:59:18


Optical coherence computed tomography

We proposed a novel time-resolved optical tomography, optical coherence computed tomography. It married the key concepts of time-resolved diffuse optical tomography and optical coherence tomography. Both ballistic and multiple-scattered photons were measured at multiple source-detection positions by low-coherence interferometry. It measures the reemitted light with a temporal resolution of 56 femtoseconds, which is much better than the resolution of conventional time-resolved detection systems. A light-tissue interaction model was established using the time-resolved Monte Carlo method. The optical properties were then reconstructed by solving the inverse time-resolved radiative transport problem under the first Born approximation. Our initial results showed the potential of this technology to bridge the gap between diffuse optical tomography and optical coherence tomography

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Optical coherence computed tomography

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