Special relativity corrections for space-based lidars

The theory of special relativity is used to analyze some of the physical phenomena associated with space-based coherent Doppler lidars aimed at Earth and the atmosphere. Two important cases of diffuse scattering and retroreflection by lidar targets are treated. For the case of diffuse scattering, we show that for a coaligned transmitter and receiver on the moving satellite, there is no angle between transmitted and returned radiation. However, the ray that enters the receiver does not correspond to a retroreflected ray by the target. For the retroreflection case there is misalignment between the transmitted ray and the received ray. In addition, the Doppler shift in the frequency and the amount of tip for the receiver aperture when needed are calculated. The error in estimating wind because of the Doppler shift in the frequency due to special relativity effects is examined. The results are then applied to a proposed space-based pulsed coherent Doppler lidar at NASA's Marshall Space Flight Center for wind and aerosol backscatter measurements. The lidar uses an orbiting spacecraft with a pulsed laser source and measures the Doppler shift between the transmitted and the received frequencies to determine the atmospheric wind velocities. We show that the special relativity effects are small for the proposed system.