Analysis of the forward problem with diffuse photon density waves in turbid media by use of a diffraction tomography model

Abstract

We extend our previously developed diffraction tomography model of diffuse photon density wave propagation in turbid media to analyze the forward problem associated with detecting and resolving both absorptive and scattering inhomogeneities. Our results assume that detection occurs in a plane but no restrictions are placed on the illumination source geometry. We then specialize these results to plane-wave illumination and derive the turbid media version of the Fourier diffraction theorem. We also develop a shot-noise-limited Fourier-domain signal-to-noise-ratio (SNR) expression to determine how background, system, and inhomogeneity parameters affect one’s ability to detect and resolve inhomogeneities. We show that, in general, scattering inhomogeneities are more easily resolved than absorbing inhomogeneities. We also show that lower temporal modulation frequencies enhance one’s ability to detect and resolve inhomogeneities. These theoretical results are compared with previously published image-domain SNR results, and qualitative agreement is demonstrated.