Extraction of the anisotropy factor and refractive index of biological tissue in the near-infrared region from diffusion approximation in the spatial frequency domain

In order to characterize biological tissue or to model light propagation in tissue medium it is necessary to define four key optical parameters, namely, absorption coefficient μ_a, reduced scattering coefficient μ_s’, anisotropy factor g (or scattering phase function), and refractive index n. Successful derivation of these valuable parameters can provide comprehensive information regarding the condition of tissue during disease pathogenesis and therapy and help to build accurate light propagation simulator. Usually, absorption and reduced scattering coefficients are investigated while the other two are assuming to be constant factors (g ≈ 0.9, n ≈ 1.4) across the near-infrared region. In order to quantify the g and n spectrum of a sample, we propose the use of spatial frequency domain (SFD). In SFD, periodic illumination patterns (structured illumination) at different spatial frequencies and wavelengths are serially projected onto the sample surface. Then, the collected diffusely reflected light is analyzed via the diffusion equation (or Monte Carlo simulation) in SFD to separately recover the sample's absorption and scattering properties over a wide field of view. This work aimed to use the solution of the diffusion equation (DE) developed for the diffuse reflectance in SFD to estimate the wavelength-dependent variability of the g and n parameters of various turbid samples in the near-infrared spectral region. Since the solution of DE contains four unknown parameters, we use four different spatial frequencies to extract these four components; four equations at four different frequencies with four unknown parameters are solved at each of the four discrete wavelengths used. During data processing of n, its wavelength-dependence was fitted using the dispersion model of Sellmeier. While there are several approaches to retrieving information about g and n, the work in SFD offers an easier and more straightforward framework and grants expanded capability to this domain by enlarging its measurement range.