Inversion of Phase Factor in Interferometric Imaging Based on Analysis of Interferential Extrema

The phase factor in optical interferometric imaging serves as a direct metric of the target’s phase across various spatial frequencies, making accurate acquisition of the phase factor crucial for reconstructing spatial target images. Current phase factor measurement methods rely on precise zero optical path difference (OPD) positions or require phase reference sources, imposing stringent conditions on precise OPD control or limiting application scenarios, which hinder the utilization of interferometric imaging. To tackle this challenge, we analyze the spatiotemporal coherence characteristics of time-delayed interference signals in interferometric imaging contexts and derive the modulation relationship between the interferential phase factor and the extrema of time-delayed interference. By decoupling these two aspects, we propose a phase factor inversion method for interferometric imaging based on the analysis of time-delayed extrema sequences, which do not rely on precise zero OPD positions. This method only requires the acquisition of interference fringe extrema sequences to invert the phase factor, significantly reducing the complexity of measuring the phase factor in interferometric imaging. Experimental results indicate that the phase inversion accuracy offered by this method surpasses <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.1\pi $ </tex-math></inline-formula>, satisfying the requirements for image reconstruction in interferometric imaging. This method introduces a novel phase measurement (PM) approach for applications of interferometric imaging.