Wavefront Reconstruction for Fractional Lateral Shear Measurements using Weighted Integer Shear Averages

TL;DR

This paper introduces a weighted integer shear averaging technique for wavefront reconstruction in lateral shearing interferometry, effectively reducing errors caused by fractional shear values and improving accuracy over traditional methods.

Contribution

It proposes a novel weighted averaging approach that cancels dominant error terms, enhancing wavefront reconstruction accuracy for fractional shear measurements.

Findings

Two-shear averaging removes first-order errors.

Three-shear averaging removes second-order errors.

Significantly lower RMS error compared to conventional methods.

Abstract

Wavefront reconstruction in lateral shearing interferometry typically assumes that the shear amount is an integer multiple of the sampling interval. When the shear is fractional, approximating it with the nearest integer value leads to noticeable reconstruction errors. To address this, we propose a weighted integer shear averaging method. The approach combines reconstructions from nearby integer shears with carefully chosen weights designed to cancel the dominant error terms. Analytical error analysis shows that two-shear averaging removes first-order errors, while three-shear averaging removes second-order errors. Numerical simulations with a test wavefront confirm that the method achieves significantly lower RMS error than conventional single-shear reconstruction. The technique is simple, computationally efficient, and can be readily extended to two-dimensional interferometry. This makes weighted integer shear averaging a practical and accurate tool for wavefront reconstruction when fractional shear is unavoidable.