Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and provide an outlook on how to better use DL to improve the reliability and efficiency of PR. Furthermore, we present a live-updating resource (https://github.com/kqwang/phase-recovery) for readers to learn more about PR.

High-speed and high-resolution imaging techniques have been long sought for material metrology and biological structure observation. Such examples include the inspection of large area subwavelength structures and optical metasurfaces widely used in integrated photonics,^1,2 monitoring fast semiconductor wet etching process,³ microdroplet evaporation dynamics,⁴ observation of live cell morphology, fast dynamics in a large cell population,^5,6 and tracking of high-speed cell motions.^7,8 Conventionally used techniques for material metrology, including scanning electron microscopy (SEM) and atomic force microscopy (AFM), are limited in throughput and speed. In addition, once the structures are encapsulated in dielectric claddings, which are the standard practice for photonic devices, SEM or AFM characterization becomes impractical, as the cladding often obscures the electron imaging contrast between core and cladding and prohibits physical contact of the AFM probe with the structure. On the other hand, the challenge for light microscopy is that many subwavelength structures and living cells share the common feature of being transparent and thin. Under conventional bright-field microscopes, those structures cannot be well resolved due to their weak light absorption. With chemical staining, fluorescence microscopy can be applied to image these structures. However, for certain live cell imaging and most material metrology applications, label-free or noninvasive imaging is favored for minimizing sample perturbation. Furthermore, fluorescence-based imaging techniques are usually slow, thus limiting their use in high-speed imaging applications.

Optical diffraction tomography (ODT) is an emerging microscopy technique for three-dimensional (3D) refractive index (RI) mapping of transparent specimens. Recently, the digital micromirror device (DMD) based scheme for angle-controlled plane wave illumination has been proposed to improve the imaging speed and stability of ODT. However, undesired diffraction noise always exists in the reported DMD-based illumination scheme, which leads to a limited contrast ratio of the measurement fringe and hence inaccurate RI mapping. Here we present a novel spatial filtering method, based on a second DMD, to dynamically remove the diffraction noise. The reported results illustrate significantly enhanced image quality of the obtained interferograms and the subsequently derived phase maps. And moreover, with this method, we demonstrate mapping of 3D RI distribution of polystyrene beads as well as biological cells with high accuracy. Importantly, with the proper hardware configuration, our method does not compromise the 3D imaging speed advantage promised by the DMD-based illumination scheme. Specifically, we have been able to successfully obtain interferograms at over 1 kHz speed, which is critical for potential high-throughput label-free 3D image cytometry applications.

Quantitative phase microscopy (QPM) has emerged as an important tool for material metrology and biological imaging. For broader adoption in those applications, we have proposed and demonstrated a new portable off-axis QPM method, which works in both transmission and reflection modes to meet different sample measurement requirements. The temporal and spatial sensitivities of our system, as quantified by optical path-length difference values, are 0.65 nm and 1.04 nm, respectively. To demonstrate its applicability for a wide range of applications, we deployed our system for profiling transistor gold electrode samples, observing red blood cell membrane fluctuations, imaging living cells flowing in a microfluidic chip, etc. Our portable QPM system has a low-cost design and involves a simple and robust phase-retrieval algorithm that we envision will allow for broader deployment at different environmental settings, including in resource-limited sites and integration with other metrology or imaging modalities.