Abstract
•Add the global searching with k-means clustering into the current diversity phase retrieval (PDPR).•High robustnessvalidation by testing up to 500 different phase aberrations that is rarely reported in other PDPR methods.•GreatlyImprove the wavefront aberration detection accuracy from 56.4% (classic PDPR methods) to 84.8%.
Phase diversity phase retrieval (PDPR) has been a popular technique for quantitatively measuring wavefront errors of optical imaging systems by extracting the phase information from several designated intensity measurements. As the problem is inverse and non-convex in general, the accuracy and robustness of most such algorithms rely greatly on the initial conditions. In this work, we propose a new strategy that combines Limited-Memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) with the initial points generated by k-means clustering method and three various channels to improve the overall performance. Experimental results show that, for 500 different phase aberrations with root mean square (RMS) value bounded within [0.2λ, 0.3λ], the minimum, the maximum and the mean RMS residual errors reach 0.017λ, 0.066λ and 0.039λ, respectively, and 84.8% of the RMS residual errors are less than 0.05λ. We have further investigated and analyzed the proposed method in details to quantitatively demonstrate its performance: statistical results reveal that our proposed PDPR with k-means clustering enhanced method has excellent robustness in terms of initial points and other influential factors, and the accuracy can outperform its counterpart methods such as classic L-BFGS and modified BFGS.