The theoretical angular resolution of an optical imaging instrument such as a telescope is given by the ratio of the imaging wavelength lambda over the aperture diameter D of the instrument. For real-world instrument, optical aberrations often prevent this so-called diffraction-limit resolution lambda/D from being achieved. These aberrations may arise both from the instrument itself and from the propagation medium of the light. The aberrations can be compensated either during the image acquisition by real-time techniques or a posteriori, i.e., by post-processing. Most of these techniques require the measurement of the aberrations, also called wave-front, by a wave-front sensor (WFS). The focal-plane family of sensors was born from the very natural idea that an image of a given object contains information not only about the object, but also about the wave-front. A focal-plane sensor thus requires little or no optics other than the imaging sensor; it is also the only way to be sensitive to all aberrations down to the focal plane. The first practical method for wave-front sensing from focal-plane data was proposed by Gerchberg and Saxton (1972). This so-called “phase-retrieval” method has two major limitations. Firstly, it only works with a point source. Secondly, there is generally a sign ambiguity in the recovered phase, i.e., the solution is not unique, as will be detailed below. Gonsalves (1982) showed that by using a second image with an additional known phase variation with respect to the first image (such as defocus), it is possible to estimate the unknown phase even when the object is extended and unknown. The presence of this second image additionally removes the above-mentioned sign ambiguity of the solution. This technique is referred to as “phase diversity”. This contribution attempts to provide a survey of the phase diversity technique, with an emphasis on its wave-front sensing capabilities. Section 1 gives an introduction to the image formation for the considered instruments (i.e. those working with spatially incoherent light, such as telescopes), reviews the sources of image degradation, and states the inverse (estimation) problem to be solved in phase diversity. Section 2 reviews the domains of application of phase diversity. Then, Sections 3 and 4 review the wave-front estimation methods associated with this technique and their properties, while Section 5 examines the possible object estimation (i.e., image restoration) methods. Section 6 gives some background on the various minimization algorithms that have been used for phase diversity. Section 7 illustrates the use of phase diversity on experimental data for wave-front sensing. Finally, Sections 8 and 9 highlight two fields of phase diversity wave-front sensing that have witnessed noteworthy advances: Section 8 reviews the methods used to estimate the large-amplitude aberrations that one faces when imaging through turbulence, and proposes a novel approach for this difficult problem. And Section 9 reviews the developments of phase diversity for a recent application: the phasing (also called cophasing) of multi-aperture telescopes.

/pdf/phase-diversity-a-technique-for-wave-front-sensing-and-for-5c3wfiatbq.pdf

Imaging Technology and Telescopes

Phase Diversity: A Technique for Wave-Front Sensing and for Diffraction-Limited Imaging

Telescopes and imaging interferometers with sparsely filled apertures can be lighter weight and less expensive than conventional filled-aperture telescopes. However, their greatly reduced MTF’s cause significant blurring and loss of contrast in the collected imagery. Image reconstruction algorithms can correct the blurring completely when the signal-to-noise (SNR) is high, but only partially when the SNR is low. This paper compares both linear (Wiener) and nonlinear (iterative maximum likelihood) algorithms for image reconstruction under a variety of circumstances. These include high and low SNR, Gaussian noise and Poisson-noise dominated, and a variety of aperture configurations and degrees of sparsity. The quality metric employed to compare algorithms is image utility as quantified by the National Imagery Interpretability Rating Scale (NIIRS). On balance, a linear reconstruction algorithm with a power-law power-spectrum estimate performed best.

Comparison of reconstruction algorithms for images from sparse-aperture systems

Orbital debris in low Earth orbit is of growing concern to operational satellites from the government and commercial sector. With an uptick in worldwide satellite launches and the growing adoption of the CubeSat standard, the number of small objects in orbit are increasing at a faster pace than ever. As a result, a cascading collision event seems inevitable in the near future. The United States Strategic Command tracks and determines the orbit of resident space objects using a worldwide network of radar and optical sensors. However, in order to better protect space assets, there has been increased interest in not just knowing where a space object is, but what the object is. The optical and spectral characteristics of solar light re ected o of satellites or debris can provide information on the physical state or identity of the object. These same optical signatures can be used for mission support of operational satellite missions—down to satellites as small as CubeSats. Optical observation of CubeSats could provide independent monitoring of spin rate, deployable status, identi cation of individual CubeSats in a swarm, or possibly attitude information. This thesis rst introduces the reader to a review of available observation techniques followed by the basics of observational astronomy relevant to satellite tracking. The thesis then presents the OSCOM system—a system for Optical tracking and Spectral characterization of CubeSats for Operational Missions. OSCOM is a ground-based system capable of observing and characterizing small debris and CubeSats with commercially available optical telescopes and detectors. The system is just as applicable for larger satellites which have higher signal to noise ratio. The OSCOM system has been used to successfully collect time-series photometry of more than 60 unique satellites of all sizes. Selected photometry results are presented along with a discussion of the technical details required for optical observation of small satellites.

https://commons.erau.edu/cgi/viewcontent.cgi?article=1211&context=edt

Optical Tracking and Spectral Characterization of Cubesats for Operational Missions

This study concerns the wrinkling performance of thin membranes for use as novel reectors in space-based telescopes. We introduce small-scale experiments for inducing and interrogating wrinkling patterns in at membranes, and we capture these details computationally by performing a range of nite element analysis. The overall aim is to assess the sophistication of modelling, to verify the feasibility of a small-diameter reector concept proposed in accompanying work.

Imaging Technology and Telescopes

Citations

Phase Diversity: A Technique for Wave-Front Sensing and for Diffraction-Limited Imaging

Comparison of reconstruction algorithms for images from sparse-aperture systems

Optical Tracking and Spectral Characterization of Cubesats for Operational Missions

Small-diameter membrane reflector wrinkling

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