Diffraction tomographic imaging with photon density waves: an explicit solution

An explicit formula is derived for reconstructing tissue inhomogeneities from scattered photon-density waves. When intensity-modulated light is used as a source, such waves obey a Helmholtz equation with a complex wave number. A process of analytical continuation in the spatial-frequency domain is used to make this wave number real, whereupon inversion formulas based on conventional diffraction tomography are applied to invert the data to yield an image. In this way an explicit solution to the inverse problem can be derived within the Born approximation. Here the spatially varying quantity imaged is a linear combination of the transport scattering and absorption coefficients. Data are assumed measured at one modulation frequency, but multiple modulation frequencies could in principle be used to generate independent images of the scattering and absorption coefficients. (C) 1998 Optical Society of America.