Generalizing Fienup’s symmetry-breaking approach for geometry analysis and neural network design

Develop a generalized framework that extends Fienup’s boundary-condition-based symmetry-breaking approach—which reduces wavefront estimation to solving a system of linear equations—so that it enables systematic analysis of optimal pupil geometry and the co-design of reconstruction neural networks for phase retrieval from a single Fourier magnitude measurement.

Background

Symmetry breaking has long been used in optical phase retrieval, notably in Fienup’s work, where boundary conditions of the autocorrelation function are employed and the resulting constraints are solved via linear systems. While effective, this approach is tied to linear formulations and specific boundary-condition constructions.

The paper argues that pupil geometry critically determines uniqueness for wavefront estimation and proposes an optics–algorithm co-design using non-centrosymmetric pupils and neural networks. In contrasting with prior symmetry-breaking methods, the authors explicitly note that generalizing the linear boundary-condition framework to analyze optimal aperture geometry or to facilitate neural network design remains unclear, motivating a formal statement of this unresolved problem.