Relationship between shear ratio and reconstruction accuracy in lateral shearing interferometry

Abstract

The shear ratio is an essential parameter of the lateral shearing interferometry system that affects dynamic range, signal-to-noise ratio, and accuracy. Some qualitative conclusions about the shear ratio’s influence can be found in existing reports, but no systematical analysis or quantified universal conclusion has been given. Using the sheared phase to reconstruct wavefront is the unique feature of the shearing interferometry, but it also affects the measurement accuracy significantly. The wavefront reconstruction methods can be divided into zonal and modal methods. We use the FFT reconstruction method and the least-square reconstruction method as the typical methods of modal and zonal methods to analyze the source of the reconstruction error and its relationship with the shear ratio. We conclude that the FFT reconstruction method and the least-square reconstruction method are equivalent to each other. The lost information during the shearing corresponds to some incalculable spectral values in the frequency domain and the pistons of different subgrids in the spatial domain. More spectral information will be lost if the shear ratio increased, which leads to more significant reconstruction errors. When the shear ratios are 1.6% and 6.3%, the corresponding relative reconstruction errors are about 1% and 1%, respectively. The error will be lower if the test wavefront can be represented by a limited amount of basis functions.