Tomography formula for biochemical imaging of thin tissue with diffuse-photon density waves

Using the transport theory to describe the near infrared light propagating in tissue with finite parallel-plane geometry, and taking the zero-boundary condition, we obtain the analytical expression of average photon density and Green's function incorporating the boundary effects in the homogeneous tissure. Making use of perturbation theory we also obtain the analytical expression of scattered wave induced by the heterogeneity, and present the 2-dimensional spatial transform of scattered wave with respect to transverse coordinate. If the information of heterogeneity on depth and thickness is available, diffraction tomography formula is presented to save the time of image reconstruction; if the information is unknown, we suggest to obtain the inhomogeneous function from the one-dimensional integral equation of 2-dimensional spatial transform of scattered wave applying the direct matrix method or iterative method for image reconstruction. This approach avoids directly solving three-dimensional integral equation of scattered wave. In our proposed approach the strong points of the direct matrix method, iterative method, and diffraction tomography are fully combined.