Optimize Imaging Quality in Long Baseline Interferometry
Professor David Hyland
University of Michigan
Department of Aerospace Engineeing
The NASA Origins program undertaking, with its sequence of ever more demanding missions, ST-3, SIM, NGST, etc., culminating in Terrestrial Planet Finder (TPF) and Planet Imager (PI) will involve multi-spacecraft, distributed space systems that must be intelligently coordinated to accomplish interferometrically-based imaging of distant exosolar planets and other phenomena relating to the origins and development of life in the universe. These astronomical systems will not be "space missions" in the conventional sense, but will actually constitute permanent observational installations. The Origins installations will have to operate unmanned and in very remote locations (thus precluding frequent mission support communications with Earth), without possibility of repair or rescue and over long periods of time. System operations will involve coordination of numerous free-flying space segments to accomplish the system-wide observational goals, as well as a complex hierarchy of supporting tasks and functions, all to be accomplished without frequent human intervention or decision-making and in the face of inevitable, unforeseen circumstances, hardware failures and similar emergencies.
The above challenges for future distributed, formation-flying space systems strongly urge the development of truly, self-reliant control. In the case of imaging interferometry systems, such self-reliance means the ability to devise and execute, without need of ground-control intervention, whatever formation maneuvers are needed to produce an image, of acceptable quality, of the designated object. Current work in formation flying control has focused on control optimization to execute prescribed maneuvers with minimum time or fuel. We need to start including some measure of imaging performance, as well as fuel and time in our control design optimizations.
The work discussed here contributes to formation flying control algorithms and architectures by incorporating into the formation flying control formulation a "figure of merit" that also includes imaging performance of the system i.e. the quality of the image so-far attainable through the course of the observations taken over the current formation flying maneuver. Optimization of this integrated figure of merit would enable more "self-reliant" formation flying control that assures the system will carry out maneuvers to acquire an image of acceptable quality as rapidly as possible and without frequent re-direction from ground control.
Composition of this figure of merit entails two steps: (1) Transformation of interferometric measurements of mutual intensity on the observation plane (or surface) to the mutual intensity on the image plane (using the van Cittert-Zernike result or its generalization) and (2) computation, from the image plane intensity, of a measure of image definition/completeness. Some important generalizations of (1) are formulated. Work in item (2) addresses measures of image quality that can cope with unknown image content e.g. one may be observing a previously unknown terrestrial-sized planet yet one needs assurance that the image will be "sharp". Various measures of contrast are addressed, in particular, image entropy in the information theoretic sense and a generalization of the Modulation Transfer Function (MTF) to the case of a distributed, interferometric constellation. The selected integrated measure of image quality is a complex function of the formation flying patterns and maneuvers reflecting, for example, the set of points swept out by the light collecting elements of the constellation on the observation surface.
With above figure of merit that integrates imaging quality we formulate the optimal control problem to obtain optimally efficient image-building formation maneuvers. It appears that when the extended MTF is adopted as the image quality metric, the formation flying problem can be recognized as a generalized traveling salesman problem, involving multiple salesmen. We explore a few exact solutions obtainable for two light collecting spacecraft and outline an approximate approach to the general problem.
Friday, February 16, 2001
3:30 - 5:00 p.m.