Mathematical uniqueness of multimode ptychographic imaging

Abstract

By writing diffracted intensities as a set of linear equations with the self-correlation of sample’s Fourier components as unknown terms and the self-correlation of illumination’s Fourier components as coefficients, it was found that the number of unknown terms to be determined is much larger in partially coherent PIE than that in purely coherent PIE. When a partially coherent illumination composed of N modes was applied a unique reconstruction can be determined by scanning the sample to at least 4 N positions and recording 4 N frames of diffraction patterns. While mathematically illustrating the physical mechanism of multimode ptychography and numerically demonstrating its capability in generating unique reconstruction under partially coherent illumination, this study showed for the first time that multimode ptychography could be an analytic imaging method.