Scatting theory for reflective Fourier ptychographic diffraction tomography

A forward model is presented to an inverse scattering problem that arises in the application of reflective Fourier ptychographic microscopy. The model allows us to determine the 3D distributions of refractive index for weakly scattering semi-transparent objects using Fourier ptychographic tomography. The derivation results show that both transmission types reported previously and reflective type present in this article are corresponding to a specific application in Wolf's work (Emil Wolf, Opt. Commun. 1969 1(4) pp. 153-156). The transmission type measures the forward scattering field while the reflective type measures the backward scattering field. This model is also available for holographic method