Complex wave and phase retrieval from a single off-axis interferogram

Single-frame transmission and phase imaging using off-axis holography with undetected photons

Imaging with undetected photons relies upon nonlinear interferometry to extract the spatial image from an infrared probe beam and reveal it in the interference pattern of an easier-to-detect visible beam. Typically, the transmission and phase images are extracted using phase-shifting techniques and combining interferograms from multiple frames. Here we show that off-axis digital holography enables reconstruction of both transmission and phase images at the infrared wavelength from a single interferogram, and hence a single frame, recorded in the visible. This eliminates the need for phase stepping and multiple acquisitions, thereby greatly reducing total measurement time for imaging with long acquisition times at low flux or enabling video-rate imaging at higher flux. With this single-frame acquisition technique, we are able to reconstruct transmission images of an object in the infrared beam with a signal-to-noise ratio of 3.680 ± 0.004 at 10 frames per second, and record a dynamic scene in the infrared beam at 33 frames per second.

On the use of deep learning for phase recovery

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.