Determination of the absorption and reduced scattering coefficients by CW spatially resolved spectroscopy with long source-detector distances at high and low internal reflection

Abstract

Many studies on CW spatially resolved spectroscopy (CW-SRS) have been conducted to noninvasively determine the optical properties, particularly the absorption and reduced scattering coefficients, μa and μs′, of biological tissues. To determine both μa and μs′, conventional CW-SRS employs measurements of the diffuse reflectances at short source-detector (SD) distances in the non-diffusion regime. In contrast, CW-SRS with long SD distances in the diffusion regime can determine only the effective attenuation coefficients, μeff = (3μaμs′)1/2 without separating μa and μs′. This study proposes a new method to separately determine μa and μs′ using CW-SRS with long SD distances, extending to conditions with high and low internal reflection at the boundary of homogeneous semi-infinite media. The proposed method used two ratios of the diffuse reflectances at two long SD distances, and μa and μs′ were determined by fitting the theoretical ratios to the measured values. Numerical simulations were conducted to validate the proposed method. As a light propagation model, the analytical solution of the time-dependent photon diffusion equation under the partial-current boundary condition (TD-DE-PCBC), which is verified for high internal reflection, was employed. Simulated measurements of the two ratios were compared with the calculated ratios (so-called look-up tables) using the TD-DE-PCBC to determine both μa and μs of the media. Simulation results demonstrate the validity of the proposed method. The effects of deviations in the SD distances and internal reflection coefficients were evaluated. Changes in the light propagation paths in the medium are discussed, and methods to realize the proposed method are suggested.