278 CHINESE OPTICS LETTERS / Vol. 8, No. 3 / March 10, 2010
Fourier analysis of elastic light scattering
spectrum of epithelial cell nuclei
Qinghua Wang (uuu)
∗
, Zhenhua Li (ooouuu)
∗∗
, Jiancheng Lai (555ïï襤¤),
and Anzhi He (åååSSS)
Department of Information Physics and Engineering, Nanjing University of Science and Technology,
Nanjing 210094, China
∗
E-mail: qhwang@mail.njust.edu.cn;
∗∗
e-mail: lizhenhua@mail.njust.edu.cn
Received June 9, 2009
A new method for simultaneously determining the size and refractive index of epithelial cell nuclei is
presented. The function of the modified elastic light scattering spectrum is regarded as a function of
wave number factor, Q=2λ
−1
sin(θ/2). The modified spectrum has a constant oscillation period with its
frequency proportional to the average diameter of cell nuclei. To the same average diameter, the different
relative refractive indexes of epithelial cell nuclei only induce the horizontal shift of the spectra. Both the
oscillation frequency and the horizontal shift are quantified by the fast Fourier transform on the modified
sp ectra. The average diameter can be figured out through the peak frequency divided by the value of the
refractive index of the surrounding medium. The phase angle of the peak frequency has an approximate
linear relationship with the relative refractive index of epithelial cell nuclei.
OCIS co des: 070.4790, 290.5825, 300.6300.
doi: 10.3788/COL20100803.0278.
The epithelium is the tissue composed of cells that line
the cavities and surfaces of structures throughout the
body. More than 85% of all cancers originate in the
epithelium
[1,2]
. The early form of carcinoma defined by
the absence of invasion of surrounding tissues is called
carcinoma in situ (CIS). The keystone for the early de-
tection of cancer is to diagnose CIS in time. The treat-
ment for CIS is usually simple and completely effective.
When treated in the stage of CIS, the patient can make a
full recovery. Elastic light-scattering (ELS) spectroscopy
shows significant promise as a fast and noninvasive tool
for early cancer diagnosis and has attracted considerable
attention at present
[3−5]
. In the measurement of ELS
spectroscopy, epithelial cell nuclei can be considered as
spheroidal Mie scatterers
[6]
. The increase of the average
size and the relative refractive index value of cell nuclei
will indicate the dysplasia of epithelial tissue
[7,8]
.
In the determination of cell configuration with ELS
spectroscopy, the inverse method of light scattering spec-
troscopy plays an important role
[9,10]
. The inversion of
light scattering based on Mie theory is a nonlinear prob-
lem related to multiple parameters, which we used to
solve the Fredholm integral equation of the first kind.
To deal with such a typical ill-posed problem, more re-
cent work is based on assuming a relative refractive index
of cell nuclei to retrieve its average size with Tikhonov
regularization methods
[11,12]
. However, these methods
are unreliable for ascertaining the relative refractive in-
dex of cell nuclei. In this letter, the function of the
modified ELS spectrum is regarded as a function of wave
number factor. Then the average size and the relative
refractive index can be simultaneously determined with
the Fourier transformation on the modified spectrum.
Figure 1 illustrates a typical schematic diagram of ELS
spectroscopy system to measure the average size of ep-
ithelial cell nuclei. The light from a broadband light
source arrives at the collimating lens through a fiber-
optic cable. Then, the parallel light beam through a
broadband polarizer illuminates a circular spot on the
surface of epithelial tissue at a certain angle from the
normal direction. After impinging on the epithelial tis-
sue, the light scattered normal to the surface passes
through an analyzer and is focused on the fiber end
face connected with a spectroscope. The polarizer keeps
stationary and transmits light polarized parallel to the
scattering plane (defined by the directions of the inci-
dent light and the scattering light), whereas the collec-
tion analyzer can be rotated to make its transmission
axis parallel or perpendicular to the transmission axis
of the incident polarizer. With the parallel-polarized
incident light I
i
k
illuminating, the scattering light in the
normal direction consists of two components. One is the
single scattering light from epithelial cell nuclei in the
top layer, which preserves its original polarization state,
marked as I
s
k,top
, and the other is the diffusely reflected
light I
s
Σ,bottom
, which travels into the sample deeper and
re-emits at the surface. As a result of multiple scat-
tering, the diffusely reflected light I
s
Σ,bottom
is mainly
unpolarized. Therefore, the parallel component to the
scattering plane of the diffusely reflected light I
s
k,bottom
is equal to the perpendicular component I
s
⊥,bottom
, that
is I
s
k,bottom
= I
s
⊥,bottom
= 0.5I
s
Σ,bottom
. In the first mea-
surement when the polarization of the collection analyzer
is parallel to the scattering plane, the measured scatter-
ing light is I
c
k
= I
s
k,top
+ I
s
k,bottom
. In the second mea-
surement when the polarization of the collection analyzer
is perpendicular to the scattering plane, the measured
scattering light is I
c
⊥
= I
s
⊥,bottom
. By subtracting the
second measured light intensity from the first measured
light intensity, the single scattering light from epithelial
cell nuclei in the top layer is
I
s
k,top
=
I
c
k
−
I
c
⊥
. This equa-
tion holds true as long as the intensities of parallel and
1671-7694/2010/030278-04
c
° 2010 Chinese Optics Letters
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