Experiments on sparsity assisted phase retrieval of phase objects

Abstract

Iterative phase retrieval algorithms such as the Gerchberg–Saxton method and the Fienup hybrid input–output method are known to suffer from the twin image stagnation problem, particularly when the solution to be recovered is complex valued and has centrosymmetric support. Recently we showed that the twin image stagnation problem can be addressed using image sparsity ideas (Gaur et al 2015 J. Opt. Soc. Am. A 32 1922). In this work we test this sparsity assisted phase retrieval method with experimental single shot Fourier transform intensity data frames corresponding to phase objects displayed on a spatial light modulator. The standard iterative phase retrieval algorithms are combined with an image sparsity based penalty in an adaptive manner. Illustrations for both binary and continuous phase objects are provided. It is observed that image sparsity constraint has an important role to play in obtaining meaningful phase recovery without encountering the well-known stagnation problems. The results are valuable for enabling single shot coherent diffraction imaging of phase objects for applications involving illumination wavelengths over a wide range of electromagnetic spectrum.

Single-beam digital holographic reconstruction: a phase-support enhanced complex wavefront on phase-only function for twin-image elimination

“…Several techniques have been developed to reduce or eliminate twin-image artifacts. These include conventional diffraction methods such as the Fresnel or the angular spectrum method (ASM), 14 – 19 linear filtering, 20 , 21 iterative phase retrieval (ItPR) methods, 22 – 28 deep learning, 29 – 32 sparsity-based phase retrieval, 33 – 35 and complex wavefront filtering 25 , 36 – 38 ASM involves computing wave propagation through Fourier transforms, enabling analysis of diffraction patterns and reconstructing wavefronts at various distances.…”

“…By contrast, the sparsity-based method exploits the inherent sparsity within the object domain to improve holographic reconstruction 33 – 35 It can provide high-quality reconstructions with reduced artifacts. However, its performance may vary depending on the sparsity level of the object.…”