Phase retrieval algorithm for wavefront reconstruction using four scattering spots

Subject of research. A method of wavefront reconstruction using the known intensity distribution of several scattering spots with the extended iterative Misell algorithm was considered. The input data for wavefront recovery were the intensity distribution in four scattering spots with various defocusing values. The recovery error and convergence criterion for wavefronts with spans of different magnitudes were analyzed. This study aimed to analyze the numerical parameters of the Misell algorithm, namely, the convergence criterion of the method and the effect of the error in determining the center of the scattering spot on the result of restoring the telescope wavefront from four known intensity distributions in defocused scattering spots. The influence of the scattering spot center determination error on the result of the reconstruction was analyzed. Method. Wavefronts with spans up to 5 lambda were modeled using arbitrary sets of Zernike polynomial coefficients, and then the known defocusing was added to these wavefronts and the scattering spots were calculated. The wavefronts were reconstructed by known scattering spots with the extended Misell algorithm, and then they were approximated using Zernike polynomials. The coefficients obtained through the algorithm application were compared with those obtained by simulating the spots, and the error was estimated. The influence of the numerical parameters of the algorithm on the error of the wavefront reconstruction was analyzed. Main results. The extended Misell algorithm enables the successful reconstruction of the wavefront using known intensity distributions in four defocused scattering spots. The convergence criterion 10(-6)lambda is optimal and provides a root-mean-square relative error of less than 0.0005%. The error of the Zernike polynomial approximation is no more than 10(-6)lambda for the wavefront with spans up to 5 lambda. The error of the scattering spot center determination does not affect the recovery result for the wavefront with spans up to 3.5 lambda. For the wavefront with spans from3.5 lambda to 5 lambda, the acceptable scattering spot center error is up to 4 pixels. Practical relevance. Wavefront reconstruction using four defocused scattering spots can be efficiently applied for the wavefronts with spans up to 5 lambda and can be used for telescope alignment during operation when other methods are difficult to implement.