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Multiple scattering in optical

coherence tomography signal: Monte

Carlo modeling and experimental

study

Gang Yao, Lihong V. Wang

Gang Yao, Lihong V. Wang, "Multiple scattering in optical coherence

tomography signal: Monte Carlo modeling and experimental study," Proc.

SPIE 3598, Coherence Domain Optical Methods in Biomedical Science and

Clinical Applications III, (30 April 1999); doi: 10.1117/12.347489

Event: BiOS '99 International Biomedical Optics Symposium, 1999, San Jose,

CA, United States

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Multiple Scattering in Optical Coherence Tomography Signal:

Monte Carlo Modeling and Experimental Study

Gang Yao, Lihong Wang*

Optical Imaging Laboratory, Biomedical Engineering Program, Texas A&M University

233 Zachry Engineering Center, College Station, TX 77843-3120

ABSTRACT

The angle biased Monte Carlo technique is applied to simulate the OCT signal from homogeneous turbid medium. The OCT

signal is divided into two categories: one is from a specific imaging target layer in the turbid medium (Class I photon); the

other is from the other background medium (Class II photon). The Class II signal has wider spatial and angular distribution

than the Class I signal. And it experiences more scattering events. The multiple scattered photons will decrease the contrast

of the OCT image and their contributions become dominant at larger depths. The average number of scattering events

increases with the probing depth for both Class I and Class II lights. Experimental study is conducted by measuring the

depth-resolved degree of polarization (DOP) of the back-scattered signal from the turbid media. The DOP is derived from

the Stokes vector measurements. The incident light is linear polarized and could be depolarize by the multiple scattering.

The DOP decreases to 0.5

when

Class I signal is equal to the Class II signal. Experiments in the Intralipid solution with

different scattering coefficient show the imaging depth is limited to 3 -

optical depths.

Keywords: Optical coherence tomography, Monte Carlo, multiple scattering, depolarization, stokes vector

1. INTRODUCTORY

Because of its high spatial resolution and high dynamic range, optical coherence tomography (OCT)' has drawn much

attention recently. Unfortunately, its applications in highly scattering biological tissue are limited by its penetration depth

unlike its successful applications in transparent tissues such as the ocular organs.23 It is believed that multiple scattering that

becomes dominant at large depths is the fundamental limitation for OCT to achieve a large probing depth in turbid media.4

In order to understand the governing physical process and better interpret the OCT signal in highly scattering media, a

couple of theoretical models have been developed. Pan et at5 established the relationship between the path-length resolved

reflectance signal with the OCT signal using linear system theory. They used Monte Carlo technique to simulate the path-

length resolved reflectance but did not separate the effects of the singly scattered light and the multiply scattered light.

Recently, Schmitt et al 6

described

an OCT model based on the Huygens-Fresnel diffraction optics. They split the OCT

signal as the summation of singly back-scattered light (coherent) and multiply scattered light (partially coherent). The effect

of multiple scattering on the formation of speckle patterns and the degradation of image contrast were demonstrated.

In reality, light scattering in turbid media is a complex process, and it is only an approximation to assume that the OCT

signal is from single back-scattering alone. A photon still contributes to the OCT signal after a limited number of scattering

events. A more realistic model is needed to study the OCT signal from the turbid media.

In this paper, we simulate the light scattering process in homogeneous turbid media by Monte Carlo method.7 The OCT

signal is divided into two classes: one is the light coming from the target layer in the medium; and the other is the light

coming from the background other than the target layer. Angle biasing technique8 is applied to speed up the simulation and

reduce the statistical variance. A polarization sensitive OCT is used to measure the depth resolved degree of polarization

(DOP) of back-scattering signal from turbid media. The DOP is derived from the Stokes vector of the back-scattered signal.

Because the multiple scattering will depolarize the incident light, the change of polarization degree is a sensitive indication

ofthe dominance ofthe multiple scattering events.

Correspondence: Email: 1wangtamu.edu, Tel: (409)847-9040, Fax: (409)845-4450

Part

of the SPIE Conference on Coherence Domain Optical Methods in Biomedical

Science and Clinical Applications Ill • San Jose, California • January 1999

SPIE Vol. 3598 • 0277-786X/99/$10.00

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2. THEORETICAL STUDY

2.1 OCT model

An OCT system is a Michelson interferometer illuminated by a low-coherence light source. The light from the reference

arm and the sampling arm can interfere at the detector only when the difference of their optical path-lengths is within the

coherence length of the light source. The interference signal is used to construct a tomographic image of the sample.

Therefore, the spatial resolution of OCT is determined by the coherence length of the light source.

In the simulation, it is assumed that the probing fiber is in direct contact with the

turbid medium. For simplicity, the fiber is assumed to emit a pencil beam. The

radius of the probing fiber is 10 rim, and the receiving angle is 5°. The light

back-scattered from the sample is divided into two different classes: Class I and

Class II (Fig. 1).

The Class I light is the light scattered from a specific layer whose central depth

corresponds to the path-length of the reference arm and whose thickness is

determined by

\ItJ

(1)

Fig.1. Composition of the OCT signal,

where I represents the light from the

specified target layer (Class I), and H

represents the light from the rest of the

medium (Class II).

where n is the refractive index of the medium, l is the coherence length of the

light source in vacuum, and Az is the thickness of the layer. Because the photons

scattered from this layer contain information about the local optical properties,

the Class I light is considered the useful signal that provides direct imaging

information. The Class II light is the light scattered from the rest of the medium whose optical path-length is within the

range of [p—4/2, p+l!2], where p is the path-length of the reference arm. Because the path-length difference between this

part of the light and the reference light is within the coherence length, the Class II light affects the OCT signal. The Class Ii

light may be from anywhere above the specific layer in the turbid medium, i.e., it does not contain information about the

specific probing depth in the medium. Therefore, this part of the light is responsible for the degradation of the contrast of

OCT images and may overwhelm the Class I signal at large probing depths.

The OCT signal can be written as:5

Jd(r) =

1s 'r +2(JsIr)1I2 Re[Vrnc(r)],

(2)

where t is the time delay between the reference arm and the sampling arm; i. and I. are the ensemble averaged light

intensities from the reference arm and the sampling arm, respectively; and Vmc i5 the mutual coherence function of the light

from the two arms and is assumed to be rectangular for simplicity. Equation (2) indicates that the OCT signal is proportional

to the square root ofthe diffuse reflectance h. In our model, I. is the summation ofthe Class I light (li) and the Class II light

(12):

Is = Ii + '2

(3)

The light whose path-length difference with the reference path-length is beyond the coherence length is simply discarded

because it does not contribute to the OCT signal.

2.2 Angle biased Monte Carlo simulation

Monte Carlo simulation has been proved to be an accurate method to study photon-tissue interaction. Because biological

tissues usually have very large anisotropy factors, light undergoes highly forward scattering and has a small chance to be

back-scattered. However, OCT modeling requires very high spatial resolution (of the order of the coherence length).

Therefore, it would be a very time consuming task to use the conventional Monte Carlo algorithm. In order to accelerate the

computation, we applied a variance reduction technique called "angle biased" sampling.8 The basic idea is to use an

artificial scattering phase function to replace the true phase function when sampling the scattering angle and then update the

photon weight according to:

2nAz=l,

I_AZ

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