Comparison of different phase retrieval algorithms based on ENZ theory

In optical imaging, phase information of light waves is critical for object recognition. The phase retrieval problem can be reformulated as an optimization problem by utilizing the Extended Nijboer-Zernike theory (ENZ). To address the issues of slow convergence and large residuals in solving Zernike polynomials using the classical quasi-Newton method, this study proposes the implementation of the momentum and Adam methods. Through comparative experiments, it was demonstrated that the momentum and Adam methods can effectively enhance convergence speed, reduce final residuals, and achieve superior convergence results compared to the quasi-Newton method. Furthermore, the momentum method was observed to approximate the optimal solution more closely than the Adam method did. This study presents improved methods for applying ENZ in phase retrieval, potentially enhancing the precision and efficiency of optical imaging techniques.