Wavefront restoration from lateral shearing data using spectral interpolation

TL;DR

This paper presents a spectral interpolation method that reduces the number of interferograms needed for wavefront restoration in lateral-shear interferometry, using origin-shift, natural extension, and least-squares techniques.

Contribution

It introduces a novel spectral interpolation approach with origin-shift to accurately restore wavefronts from fewer interferograms, improving efficiency over previous methods.

Findings

Accurately restored wavefronts from only two interferograms.

Validated the method through numerical simulations.

Potential to enhance lateral-shear interferometry applications.

Abstract

Although a lateral-shear interferometer is robust against optical component vibrations, its interferogram provides information about differential wavefronts rather than the wavefronts themselves, resulting in the loss of specific frequency components. Previous studies have addressed this limitation by measuring four interferograms with different shear amounts to accurately restore the two-dimensional wavefront. This study proposes a technique that employs spectral interpolation to reduce the number of required interferograms. The proposed approach introduces an origin-shift technique for accurate spectral interpolation, which in turn is implemented by combining two methods: natural extension and least-squares determination of ambiguities in uniform biases. Numerical simulations confirmed that the proposed method accurately restored a two-dimensional wavefront from just two interferograms, thereby indicating its potential to address the limitations of the lateral-shear interferometer.