Relativity effects for space-based coherent lidar experiments

An effort was initiated last year in the Astrionics Laboratory at Marshall Space Flight Center to examine and incorporate, if necessary, the effects of relativity in the design of space-based lidar systems. A space-based lidar system, named AEOLUS, is under development at Marshall Space Flight Center and it will be used to accurately measure atmospheric wind profiles. Effects of relativity were also observed in the performance of space-based systems, for example in case of global positioning systems, and corrections were incorporated into the design of instruments. During the last summer, the effects of special relativity on the design of space-based lidar systems were studied in detail, by analyzing the problem of laser scattering off a fixed target when the source and a co-located receiver are moving on a spacecraft. Since the proposed lidar system uses a coherent detection system, errors even in the order of a few microradians must be corrected to achieve a good signal-to-noise ratio. Previous analysis assumed that the ground is flat and the spacecraft is moving parallel to the ground, and developed analytical expressions for the location, direction and Doppler shift of the returning radiation. Because of the assumptions used in that analysis, only special relativity effects were involved. In this report, that analysis is extended to include general relativity and calculate its effects on the design.