Analytische Betrachtung optisch abbildender Sensorsysteme im Rahmen der AsteroidFinder-Mission

Kurzfassung

This work outlines an analytical consideration of optical sensor systems applied to the satellite camera of the AsteroidFinder mission. The basic for this analysis is the question whether the optical sensor system of the AsteroidFinder mission supports a space-based detection of space debris which is defined as the secondary goal of the mission. The primary goal is the discovery of Inner Earth Objects. Aerospace has become more and more dangerous due to the increasing number of space debris. Thus, a deeper involvement in space debris investigations is required. Up to now, space debris is detected, observed and cataloged solely by ground-based optical or radar instruments. Here, the AsteroidFinder mission with its planned space-based detection will go a step further. Assuming that a detection is possible, the image a space debris would create on the CCD was simulated by an IDL-program. As this image underlies all impairments caused by the optics, in this work the basics for a precise description of optoelectronic systems was elaborated with special regard to diffraction aspects. While derivating the total PSF of the system the thematic priority was given by the optics' PSF, especially by the comparison of the two diffraction integrals by Kirchhoff and Fresnel, where Fresnel is the quadratic approximation of the Kirchhoff's diffraction integral. With this approximation a lot of calculations concerning camera systems can be simplified. However, Fresnel approximations cannot be applied to arbitrary camera systems. For configurations with wide aperture, e.g., the usage of Fresnel is not possible without accepting an unagreeable deviation. In this work, investigations of the real and complex integrands lead to a formula from which the minimal F-number (respectively the maximum aperture radius) is derived, so that Fresnel approximations can be surely applied to a system. The analytical results are supported by numerical calculations and audited for three camera configurations outlined for remote sensing. To answer the question whether the detection of space debris with the optical sensor of the AsteroidFinder mission is feasible at all, radiometrical and statistical analyses have been performed. For the radiometrical investigations a theory including the effects of diffraction and noise was developed and exemplified by an IDL-simulation. Based on the radiometrical results, statistical investigations have been performed in which the mean time-span could be determined which is needed to detect a space debris particle. The results indicate that it is well possible to detect space debris with the optical sensor system of the AsteroidFinder mission, although the mission itself is not optimally designed for this task.