Wavefront reconstruction based on multi-directional orthogonal lateral shearing interferometry

Abstract

The shear wavefront propagates in a single direction, influenced by the phase deviation of the missing orthogonal direction in the interference pattern. Furthermore, the restriction of phase sampling points in the shear direction has a certain impact on attaining high spatial resolution in wavefront reconstruction. To attain high-precision wavefront reconstruction, it is necessary to acquire additional sampled data from various orthogonal shear directions. During our investigation, a wavefront reconstruction method was proposed for multi-directional orthogonal lateral shearing interferometry. This method establishes a relationship model that corresponds to multi-directional differential wavefront and differential Zernike polynomials. Using the principle of wavefront reconstruction with differential Zernike polynomials, it allows for the reconstruction of wavefronts from any orthogonal-direction lateral shearing interference patterns. To validate the efficacy of the proposed method, the wavefront reconstruction accuracy of various sets of arbitrarily oriented shearing interferograms was simulated and analyzed. Additionally, the results were compared to those obtained from the average differential wavefront of multiple orthogonal shearing interferograms. The results show that by choosing multiple orthogonal shear directions to improve phase sampling data, wavefront reconstruction can be successfully accomplished using any number of orthogonal lateral shearing interferograms. This effectively reduces the impact of both random and systematic errors on the spatial resolution of the wavefront during the reconstruction process. Ultimately, the accuracy of the proposed method was confirmed through experimental validation. After comparing the repeatability measurement with the results obtained from the ZYGO interferometer, it was discovered that the precision of the relative measurement error in RMS was superior to 0.01λ.