Daigo Kobayashi, Purdue University; Carolin Frueh, Purdue University
Keywords: imaging, light curves, semi-resolved
Abstract:
Optical observations are a cost-efficient way of collecting information about human-made space objects. Ideally, a fully resolved image of any satellite and space-debris object could be created from observations without other guiding information. The challenges are two-fold. For one, the distance between the observer and the objects is generally large or very large, relative to the size of the objects, secondly, in ground-based observations, atmospheric turbulence affects the measurements.
Compressed sensing is a technique known from image compression. Under the condition of sparsity, a resolved image can be recovered from a compressed version, containing only a subset of the information, of the original high-resolution image. The technique is used, e.g. in JPEG images.
In this paper, the classical compressed sensing framework is modified in order to be used for space-object characterization. Two cases are discriminated. For one, for objects in Low-Earth orbit, semi-resolved imaging is available. However, the images are heavily degraded by atmospheric turbulance. The light from different parts of the semi-resolved image is affected by different atmospheric lenses. The details of the atmosphere are generally not known. Crucially adapting the classical compressed sensing framework the atmosphere itself as the so-called sensing matrix, which needs to be estimated alongside the image of the space object, which is sought to be recovered. In the paper, high fidelity simulation of the atmosphere-affected semi-resolved imaging is shown using Kolmogorov turbulence in combination with the multiple-phase screen method. Those images are then used in combination with the modified compressed sensing framework to recover a resolved image of the space object. The method is applicable to large Low Earth objects, which are stabilized during the time of observation.
The second case that is addressed in this paper is the one of high altitude space objects. Here, the entire light of the space object is diffracted and only the Airy disc can be measured. In order words, only non-resolved imaging is available. Light curves, brightness measurements over time, hold all the information that one needs in order to recover a resolved image, however, the information is superimposed and not readily available or extractable. Because the light only travels through the same atmospheric lens when reaching the detector. Therefore, the atmosphere can no longer be understood as the sensing matrix. However, for objects with concavities, such as a box-wing satellite configuration, sparsity in the object signal is reached through self-shadowing, blocking at times large parts of the satellite surface from the observer. In the second part of the paper, compressed sensing is inspiring an entirely new technique recovering so-called net images of an object. Net images are a recovered resolved version of the object, displaying three-dimensional information in the two-dimensional image plane. Three-dimensional information is introduced as different orientations of the satellite need to be observed to create variability in the light curve and various self-shadowing geometries. As depth information is necessarily missing, a two-dimensional display is created. Simulations show the advantage of recovering information on the object which are shadowed more frequently and which are classically harder to resolve in light curve inversion techniques. The performance of the method is shown in simulations of various observation scenarios with a ground-based optical sensor.
Date of Conference: September 27-20, 2022
Track: Non-Resolved Object Characterization