Wavefront reconstruction method for lateral shearing interferometry based on the transport of intensity equation

To address the problems of detail loss due to fitting in traditional phase demodulation of lateral shearing interferometry, as well as the susceptibility of zonal methods to noise that limits reconstruction accuracy, a wavefront reconstruction method based on the transport of intensity equation (TIE) for lateral shearing interferometry is proposed. In this method, a simultaneous phase-shifting lateral shearing interferometry system is first used to acquire four-step phase-shifted interferograms. Through phase-shift demodulation and full-aperture gradient complement, a complete and high-precision differential phase gradient field is obtained. Subsequently, combined with the measured intensity distribution at the focal plane, the anti-noise axial derivative of intensity is reconstructed by inverting the TIE physical model, replacing the finite difference calculation that is susceptible to noise in conventional TIE. Finally, an adaptive step-size iterative strategy based on the maximum likelihood method is employed to solve the TIE equation, achieving high-precision wavefront reconstruction. Simulations and experiments demonstrate that the proposed method combines the advantages of gradient extraction from shearing interferometry and detail preservation from TIE. Compared with the wavefront measured by a commercial ZYGO interferometer, the residual error of the reconstructed wavefront is significantly reduced, and the wavefront details are better reproduced, providing an effective technical approach for high-precision testing of precision optical components such as spherical surfaces.