Solution to the shearing problem via guided diffusion

Wavefront reconstruction from lateral shearing interferometry (LSI) represents a challenging ill-posed inverse problem due to shear-periodic information loss and noise sensitivity. Conventional techniques typically mandate multiple shearograms or impose rigid, potentially biasing priors. We introduce Pseudoinverse-Guided Diffusion Models (ΠGDM), a novel framework leveraging a pre-trained unconditional diffusion model as a robust data driven prior. By integrating the LSI physics via Vector-Jacobian Product guidance, ΠGDM ensures measurement consistency while plausibly recovering missing spatial frequencies. We comprehensively benchmark ΠGDM against four distinct methods: classical Zonal integration, Fourier, Tikhonov regularization, and a supervised deep learning network. Simulations and experimental validation using a Michelson-based setup demonstrate that ΠGDM yields superior fidelity and noise robustness from single shearograms. Crucially, it offers a versatile, zero shot alternative to supervised methods, achieving high-precision metrology without requiring task-specific training.