Linear mathematical model for the unique solution of 3D ptychographic iterative engine

Abstract

Diffraction intensities of the 3D ptychographic iterative engine (3PIE) were written as a set of linear equations of the selfcorrelations of Fourier components of all sample slices, and an effective computing method was developed to solve these linear equations for the transmission functions of all sample slices analytically. With both theoretical analysis and numerical simulations, this study revealed the underlying physics and mathematics of 3PIE and demonstrated for the first time, to our knowledge, that 3PIE can generate mathematically unique reconstruction even with noisy data.