Evaluation of the light field distribution in scattering medium
using
simulation method
C. Su 
, H.S. Ding , J. Bai , B. Chance 
Department of Electrical Engineering, Tsinghua University
Beijing, 100084, P.R.China;
Department of Biochemistry and Biophysics,
University of Pennsylvania
Philadelphia PA 19104 USA
Studying the characteristics of light propagation through the scattering medium or biological tissue using simulation method has theoretical and practical significance in the application of biomedical area. There will exist a optical field distribution in a homogeneous and isotropic medium placed two or more coherent light sources. If the homogeneity of the medium is destroyed, the optical field is then distorted. Therefore, by analyzing the degree of the distortion, the localized heterogeneity or the shape of the tumor may be detected.
Phase modulation spectroscopy measures transport delay in terms of phase shifts. Two coherent light sources with constant phase difference can give particularly optical field distributions. The unsymmetric light amplitude and phase due to the existence of the localized absorber can be detected very sensitively in the middle of the array of in-phase and anti-phase source. Light propagation in highly scattering medium can be described by the diffusion approximation similar to the Boltzmann transport equation in thermodynamics, but the analytical expressions derived are relatively complicated.
In this paper, we present a simple optical simulation method to estimate the optical field distribution of the scattering medium. Theoretical analysis and simulation have shown that in a homogeneous system, two-element optical sources with the same intensity and definite initial phase, 0 and pi radians, may create a phase jump of pi radians and a null amplitude in the midplane of in- and anti-phase sources. Also the amplitude or the phase is related to the optical characteristics of medium and external parameters such as wave frequency. Detecting the phase transition has a number of advantages over the amplitude transition. Furthermore, the fixed null line can vary with the scanning time by using dynamic scanning similar to radar scanning. This makes it easy to detect the absorber for fixed source position. The phenomena above are demonstrated by our experiment. This simple optical simulation method provides a basis for localization information on the detection of heterogeneity or small tumors within the human breast or in the human brain.