High-precision computation method for key parameters in lateral shearing interferometry

To address the issue of inaccurate calculation of shear quantity and shear angle in lateral shear interferograms due to their discretely distributed edges and unclear gradient changes, this paper proposes a high-precision computation method for key parameters. First, it enhances the clarity of interferogram edges and suppresses internal fringe noise interference by computing the spatial modulation transfer function (MTF) of lateral shear interferograms. Building on this, an improved GrabCut algorithm is employed to iteratively segment the interferogram region from the background, overcoming issues with edge recognition errors caused by insignificant gradient features in interferogram images. Finally, shear quantity and shear angle are computed using effective interferogram edge extraction and circular fitting constraint algorithms, thereby reducing fitting errors or failures due to matrix singularity. Simulation results show that the shear quantity error is within 0.09 pixels, and the shear angle error is within 0.18°. Experimental results indicate that when using a parallel polarized beam splitter with a standard shear ratio of 0.1 for measurement, the shear ratio error is within 0.01 units. When the obtained data are used for wavefront reconstruction, the PV and RMS calculation accuracies are approximately λ/50 and λ/78 (λ=632.8nm), respectively, outperforming mainstream algorithms. This demonstrates that the proposed method maintains excellent performance and effectiveness even in complex scenarios with high-precision requirements.