Co-phasing of the segmented mirror and image retrieval based on phase diversity using a modified algorithm.

The conventional Broyden–Fletcher–Goldfarb–Shanno (BFGS) method used to solve the cost function of a phase diversity (PD) algorithm converges to a global optimum only when the cost function is convex. We present a modified BFGS method, which has fine global convergences for both convex and nonconvex functions, guarantees that the solutions will converge to the global minimum, corresponding to the actual wavefront coefficients, and apply it to minimize the PD cost function to co-phase the segmented active optics system and recover the unknown object under different noise levels. The noise amplification effect on the accuracy of the algorithm is removed by our proposed estimated strategy of the regularization parameter for the PD problem. The vast contrast results demonstrate that the modified method has a much higher accuracy than the conventional BFGS method for the nonconvex condition even under a considerably high noise level.