Optical properties of tissues quantified
by Fourier-transform light scattering
Huafeng Ding,1Freddy Nguyen,2Stephen A. Boppart,2and Gabriel Popescu1,*
1Quantitative Light Imaging Laboratory, Beckman Institute for Advanced Science and Technology,
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
2Biophotonics Imaging Laboratory, Beckman Institute for Advanced Science and Technology,
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
* Corresponding author: firstname.lastname@example.org
Received February 6, 2009; accepted March 2, 2009;
posted March 25, 2009 (Doc. ID 107291); published April 22, 2009
We employ Fourier-transform light scattering, a technique recently developed in our laboratory, to study the
scattering properties of rat organ tissues. Using the knowledge of the complex field associated with high-
resolution microscope images of tissue slices, we extracted the scattering mean-free path lsand anisotropy
factor g, which characterize the bulk tissue for three different rat organs. This “bottom up” approach to mea-
suring tissue scattering parameters allows for predicting the wave transport phenomena within the organ of
interest at a multitude of scales—from organelle to organ level. © 2009 Optical Society of America
OCIS codes: 290.5820, 170.3660, 170.6935, 170.0180, 180.3170.
Upon propagation through inhomogeneous media,
optical fields undergo modifications in terms of irra-
diance, phase, spectrum, direction, polarization, and
coherence, which can reveal information about the
sample of interest. Light scattering by cells and tis-
sues evolved as a dynamic area of study, especially
because this type of investigation can potentially of-
fer a noninvasive window into function and pathology
[1–9]. Despite all these efforts, light-scattering-based
techniques currently have limited use in the clinic. A
great challenge is posed by the insufficient knowl-
edge of the tissues’s optical properties.
Recent phase-sensitive methods have been em-
ployed to directly extract the refractive index of cells
and tissues . These approaches have been ex-
tended further to three-dimensional (3D) reconstruc-
tions of cell refractive index [11,12]. Starting from
the measured 3D refractive index distribution, the
angular scattering has been retrieved via the Born
approximation . Based on diffraction phase mi-
croscopy (DPM) , we developed Fourier-transform
light scattering (FTLS) as an experimental approach
for studying inhomogeneous and dynamic media .
In FTLS the optical phase and amplitude of a coher-
ent image field are quantified and propagated nu-
merically to the scattering plane.
In this Letter, we use FTLS to extract quantita-
tively the scattering mean-free path lsand anisotropy
factor g from tissue slices of different organs. This di-
rect measurement of tissue scattering parameters al-
lows for predicting the wave transport phenomena
within the organ of interest at a multitude of scales.
Figure 1 depicts our experimental setup, presented
in more detail previously . Briefly, the fiber-
coupled second harmonic of a diode-pumped Nd:YAG
laser ??=532 nm? is collimated and used to illumi-
nate the sample in transmission. At the sample
plane, the laser beam is larger than a centimeter,
with a total power of approximately 3 mW. An ampli-
tude diffraction grating G (110 grooves/mm) is placed
at the image plane. To establish a common-path
Mach–Zehnder interferometer, a standard spatial fil-
tering lens set L1–L2(i.e., 4-f system) with focal
lengths of 60 and 300 mm is used to select the two
diffraction orders and generate the final interfero-
gram at the CCD plane. The zeroth-order beam is
low-pass filtered using a pinhole (25 ?m diameter) at
the spatial filter (SF) plane, which is the Fourier
plane of L1. Thus, at the CCD plane this zeroth-order
beam approaches a uniform, i.e., reference, field. Si-
multaneously, the SF allows for passing the entire
frequency content of the first diffraction-order beam
and blocks all the other orders. The two beams propa-
gate along a common optical path, significantly re-
ducing the longitudinal phase noise. From a single
CCD exposure, we obtain the spatially resolved
phase and amplitude associated with the image field,
Figures 2(a)–2(c) show examples of quantitative
phase images associated with 5 ?m tissue slices for
three different organs from a rat, which were pre-
pared according to a standard procedure under a pro-
tocol approved by the Institutional Animal Care and
Use Committee at the University of Illinois at
Urbana-Champaign. The scattered intensity for each
slice is obtained by Fourier transforming the complex
BS, beam splitter; S, sample; O, objective lens; M, mirror;
TL, tube lens; I, iris; G, grating; SF, spatial filter; L1 and
Schematic of the FTLS setup. FC, fiber collimator;
OPTICS LETTERS / Vol. 34, No. 9 / May 1, 2009
0146-9592/09/091372-3/$15.00 © 2009 Optical Society of America
In Eq. (1), q is the momentum transfer of modulus
q=?4?/??sin??/2?, with ? as the scattering angle. The
scattering maps associated with the phase images
[Figs. 2(a)–2(c)] are shown in Figs. 2(d)–2(f).
The scattering mean-free path lswas measured by
quantifying the attenuation owing to scattering for
=−d/ln ?I?d?/I0?, where d is the thickness of the tis-
sue, I?d? is the irradiance of the unscattered light af-
ter transmission through the tissue, and I0is the to-
tal irradiance, i.e., the sum of the scattered and
unscattered components. The unscattered intensity
I?d? is evaluated by integrating the angular scatter-
ing over the diffraction spot around the origin. The
resulting lsvalues for 20 samples for each organ from
the same rat are summarized in Fig. 3(a). Ritz et al.
 report much-larger values for lsof pig liver. How-
ever, their wavelength is in the near-IR, which is ex-
pected to scatter less strongly than our green light.
Parsa et al. , on the other hand, report ls
=60 ?m at our wavelength by using the integrating
sphere and diffusion model. This lsvalue is a factor of
?4 larger than our values [Fig. 3(a)]. We believe that
differences in sample preparation may explain this
The anisotropy factor g is defined as the average
cosine of the scattering angle,
slice via theLambert–Beerlaw,
where p is the normalized angular scattering, i.e., the
phase function. Note that since Eq. (1) applies to tis-
sue slices of thickness d?ls, it cannot be used di-
rectly in Eq. (2) to extract g since g values in this case
will be thickness dependent. This is so because the
calculation in Eq. (2) is defined over tissue of thick-
ness d=ls, which describes the average scattering
properties of the tissue (i.e., independent of how the
tissue is cut). Under the weakly scattering regime of
interest here, this angular-scattering distribution p
is obtained by propagating the complex field numeri-
cally through N=ls/d layers of d=5 ?m thickness,
Equation (3) applies to a slice of thickness ls. It re-
flects that by propagating through N weakly scatter-
ing layers of tissue, the total phase accumulation is
the sum of the phase shifts from each layer, as is typi-
cally assumed in phase imaging of transparent struc-
tures . In essence, Eq. (1) describes the tissue
slice angular scattering, while Eq. (3) characterizes
the bulk tissue. The angular-scattering distribution,
or phase function, p??? is obtained by performing azi-
muthal averaging of the scattering map, p?q?, associ-
ated with each tissue sample [Figs. 2(a)–2(c)]. The
maximum scattering angle was determined by the
NA of the objective lens and is about 18° for our cur-
rent setup. The angular-scattering data were further
fitted with Gegenbauer kernel (GK) phase function
free path ls, (b) anisotropy factors, and (c) transport mean-
free path for the three rat organs with 20 samples per
group. The error bars correspond to the standard devia-
tions ?N=20?. (d)–(f) The angular-scattering plots associ-
ated with the scattering maps in Figs. 2(d)–2(f). The
dashed curves indicate fits with the GK phase function.
FTLS measurements of the (a) scattering mean-
?512?512 pixels? for rat kidney, liver, and brain, respec-
tively. Scale bar shows 25 ?m; (d)–(f) The scattering maps
(logarithmic scale) associated with the phase images (a)–
(c). Scale bar shows 0.14 rad.
(a)–(c) Examples of quantitative phase images
May 1, 2009 / Vol. 34, No. 9 / OPTICS LETTERS
P??? = ag Download full-text
?1 − g2?2a
??1 + g2− 2g cos?????a+1???1 + g?2a− ?1 − g?2a?.
Note that g can be estimated directly from the
angular-scattering data via its definition [Eq. (2)].
However, because of the limited angular range mea-
sured, g tends to be overestimated by this method,
and thus the GK fit offers a more reliable alternative
than the widely used Henyey–Greenstein (HG) phase
function (with the parameter a=1/2). The represen-
tative fitting plots for each sample are shown in Figs.
3(d)–3(f). The final values of g are included in Fig.
3(b) and agree very well with previous reports in the
From these measurements of thin singly scattering
slices we inferred the behavior of light transport in
thick strongly scattering tissue. Thus the transport
mean-free path, which is the renormalized scattering
length to account for the anisotropic phase function,
can be obtained as l?=ls/?1−g?. The l?values for 20
samples from each organ are shown in Fig. 3(c),
which show larger standard deviations compared to
lsand g. These larger fluctuations are due to the com-
bined effect of measuring both g and ls.
In summary, we showed that FTLS can quantify
the angular-scattering properties of thin tissues,
which in turn provides the scattering mean-free path
lsand anisotropy factor g, for the macroscopic (bulk)
organ. We note that based on the knowledge of ls, g,
and l?, one can predict the outcome of a broad range
of scattering experiments on large samples ?size
?l?? via numerical solutions to the transport equa-
tion or analytical solutions to the diffusion equation.
We envision that the FTLS measurements of un-
stained tissue biopsies, which are broadly available,
will provide not only diagnosis value but also possibly
the premise for a large scattering database, where
various tissue types, healthy and diseased, will be
fully characterized in terms of their scattering prop-
erties. At the opposite end of the spatial scales, FTLS
can be used in combination with high-resolution mi-
croscopes to describe the angular (and dynamic) scat-
tering of subcellular structures. For example, we
have recently demonstrated that FTLS is sensitive to
spatiotemporal organization of actin cytoskeleton
. Thus, FTLS can be used to study tissue optics
from microscopic (organelle) to macroscopic (organ)
This research was supported in part by the Na-
tional Science Foundation (NSF) (CAREER 08-
46660) and the Grainger Foundation.
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