Linear mathematical model for the underlying mechanism of extended ptychographic iterative engine

Abstract

A linear model by writing the recorded diffractive intensities as a set of linear equations was put forwarded to determine the complex amplitude of the illumination and sample analytically for the extended ptychographic iterative engine (ePIE) imaging. An efficient computing method that can process large matrices was proposed to improve computing efficiency. The influences of detector noise and the positioning error of the sample were studied to explain why satisfactory reconstruction can be obtained experimentally when the linear equations of diffractive intensities are incorrect. This study demonstrates for the first time that ePIE technique has a unique and deterministic solution even with noisy experimental data, overcoming the main obstacle hindering the application of the ePIE algorithm in optical measurement and optical metrology, where a mathematically unique solution is crucial.