Projection methods for high numerical aperture phase retrieval. (9th November 2021)

• Record Type: Journal Article
• Authors: Hieu Thao, Nguyen; Soloviev, Oleg; Luke, Russell; Verhaegen, Michel
• Is Part Of: Inverse problems. Volume 37:Number 12(2021)
• Publication Date: 2021-11-09
• Subjects: phase retrieval -- high numerical aperture -- projection algorithm -- nonconvex optimization -- inconsistent feasibility; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac3322
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We develop for the first time a mathematical framework in which the class of projection algorithms can be applied to high numerical aperture (NA) phase retrieval. Within this framework, we first analyze the basic steps of solving the high-NA phase retrieval problem by projection algorithms and establish the closed forms of all the relevant projection operators. We then study the geometry of the high-NA phase retrieval problem and the obtained results are subsequently used to establish convergence criteria of projection algorithms in the presence of noise. Making use of the vectorial point-spread-function (PSF) is, on the one hand, the key difference between this paper and the literature of phase retrieval mathematics which deals with the scalar PSF. The results of this paper, on the other hand, can be viewed as extensions of those concerning projection methods for low-NA phase retrieval. Importantly, the improved performance of projection methods over the other classes of phase retrieval algorithms in the low-NA setting now also becomes applicable to the high-NA case. This is demonstrated by the accompanying numerical results which show that available solution approaches for high-NA phase retrieval are outperformed by projection methods.