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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 (ooouuu)

∗∗

, Jiancheng Lai (555ïïï¤¤¤),

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

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

k,top

, and the other is the diffusely reﬂected

light I

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

Σ,bottom

is mainly

unpolarized. Therefore, the parallel component to the

scattering plane of the diffusely reﬂected light I

k,bottom

is equal to the perpendicular component I

⊥,bottom

, that

is I

k,bottom

= I

⊥,bottom

= 0.5I

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

= I

k,top

+ I

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

⊥

= I

⊥,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

k,top

−

⊥

. This equa-

tion holds true as long as the intensities of parallel and

1671-7694/2010/030278-04

° 2010 Chinese Optics Letters

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