Phase Retrieval with Application to Optical Imaging: A contemporary overview

TLDR

Phase retrieval, the reconstruction of a function from the magnitude of its Fourier transform, is essential in fields such as electron microscopy, crystallography, astronomy, and optical imaging, yet optical detectors cannot directly capture phase because the electromagnetic field oscillates at ~10^15 Hz, so they only record photon flux proportional to the field’s magnitude squared. To recover optical phase, one typically employs holographic techniques that interfere the unknown wave with a known reference field, enabling phase information to be extracted.

Abstract

The problem of phase retrieval, i.e., the recovery of a function given the magnitude of its Fourier transform, arises in various fields of science and engineering, including electron microscopy, crystallography, astronomy, and optical imaging. Exploring phase retrieval in optical settings, specifically when the light originates from a laser, is natural since optical detection devices [e.g., charge-coupled device (CCD) cameras, photosensitive films, and the human eye] cannot measure the phase of a light wave. This is because, generally, optical measurement devices that rely on converting photons to electrons (current) do not allow for direct recording of the phase: the electromagnetic field oscillates at rates of ~1015 Hz, which no electronic measurement device can follow. Indeed, optical measurement/detection systems measure the photon flux, which is proportional to the magnitude squared of the field, not the phase. Consequently, measuring the phase of optical waves (electromagnetic fields oscillating at 1015 Hz and higher) involves additional complexity, typically by requiring interference with another known field, in the process of holography.