Projection methods for high numerical aperture phase retrieval

Nguyen, Hieu Thao; Soloviev, O.A.; Luke, Russell; Verhaegen, M.H.G.

doi:10.1088/1361-6420/ac3322

Projection methods for high numerical aperture phase retrieval

Title

Projection methods for high numerical aperture phase retrieval

Author

Nguyen, Hieu Thao (TU Delft Team Raf Van de Plas; Can Tho University)
Soloviev, O.A. (TU Delft Team Michel Verhaegen; Flexible Optical B.V.)
Luke, Russell (University of Göttingen)
Verhaegen, M.H.G. (TU Delft Team Michel Verhaegen)

Date

2021

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.

Subject

High numerical aperture
Inconsistent feasibility
Nonconvex optimization
Phase retrieval
Projection algorithm

To reference this document use:

http://resolver.tudelft.nl/uuid:43ac8e25-4e5f-4269-b316-02aed889932c

DOI

https://doi.org/10.1088/1361-6420/ac3322

ISSN

0266-5611

Source

Inverse Problems: inverse problems, inverse methods and computerized inversion of data, 37 (12)

Part of collection

Institutional Repository