Direct-detection synthetic-aperture coherent imaging by phase retrieval

Abstract

Abstract. This paper describes a way to synthesize a larger coherent aperture from smaller apertures combined with motion, when only intensities are measured. It relies on collecting intensity patterns in two planes for each aperture, for example, the aperture plane and an image plane, and using a phase-retrieval algorithm to reconstruct the optical field in the aperture plane. As the sensor moves forward, a larger two-dimensional aperture is synthesized, allowing a much finer resolution image to be reconstructed. An algorithm to correct for the relative pointing (tip and tilt phases) and piston errors between different apertures and at different times is needed to phase up the synthetic aperture. Results of simulations, including the effects of speckle, are shown, and practical considerations are evaluated. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. [DOI: 10.1117/1.OE. 56.11.113111] Keywords: synthetic aperture; imaging; phase retrieval; phase-error correction; image reconstruction; heterodyne.Paper 171359 received Aug. 28, 2017; accepted for publication Nov. 1, 2017; published online Nov. 21, 2017. IntroductionTo achieve fine resolution imagery at a given long distance and in a given wavelength band, one needs a collection system (telescopes) having a large enough effective aperture. As an alternative to building and deploying larger single-aperture systems (which become increasingly bulky, heavy, and costly), one can perform aperture synthesis. This can be done either passively (using reflected sunlight) as in Michelson stellar interferometry or actively as in coherent laser illumination with phase-sensitive detection. Michelson interferometry requires two or more simultaneous apertures having substantial motion of one aperture relative to another and, for a variety of reasons, is poorly suited to looking downward at the earth. One could use laser synthetic-aperture radar (SAR) in which temporal or chirped frequency sensing provides range information and forward motion provides alongtrack resolution; temporal heterodyne sensing over large temporal bandwidths is required for fine range resolution. Digital holography, also known as spatial heterodyne, can achieve fine resolution in angle-angle space by a string of apertures in the cross-track direction combined with aperture synthesis in the along-track direction; it can employ narrow laser bandwidths but must still interfere the return field from the object with a local oscillator (LO), requiring stable LO distribution from a master laser to all the telescopes. One could employ multiple small apertures underneath the wings of an aircraft, or on a group of small satellites, or on a moving ground vehicle, to synthesize a large two-dimensional (2-D) aperture with fine resolution. Images from laser illumination systems exhibit speckle that degrades the effective resolution unless...

Multi-Aperture Joint-Encoding Fourier Ptychography for a Distributed System

“…In recent decades, the space-based electro-optical distributed aperture system (EO-DAS) [20] and synthetic-aperture systems [21][22][23][24] have seen rapid development, achieving better imaging performance with on-orbit self-assembly of relatively small mirror segments mounted on separate low-cost spacecraft [25]. However, it cannot be ignored that the high precision of mirror mounting and the difficulty of sub-aperture co-phase adjustment cause significant problems from fabrication to launch in orbit in such space-based systems.…”