Special relativity effects for space-based coherent lidar experiments

There is a great need to develop a system that can measure accurately atmospheric wind profiles because an accurate data of wind profiles in the atmosphere constitutes single most input for reliable simulations of global climate numerical methods. Also such data helps us understand atmospheric circulation and climate dynamics better. Because of this need for accurate wind measurements, a space-based Laser Atmospheric Winds Sounder (LAWS) is being designed at MSFC to measure wind profiles in the lower atmosphere of the earth with an accuracy of 1 m/s at lower altitudes to 5m/s at higher altitudes. This system uses an orbiting spacecraft with a pulsed laser source and measures the Doppler shift between the transmitted and received frequencies to estimate the atmospheric wind velocities. If a significant return from the ground (sea) is possible, the spacecraft speed and height are estimated from it and these results and the Doppler shift are then used to estimate the wind velocities in the atmosphere. It is expected that at the proposed wavelengths, there will be enough backscatter from the aerosols but there may no be significant return from the ground. So a coherent (heterodyne) detection system is being proposed for signal processing because it can provide high signal to noise ratio and sensitivity and thus make the best use of low ground return. However, for a heterodyne detection scheme to provide the best results, it is important that the receiving aperture be aligned properly for the proposed wind sounder, this amounts to only a few microradians tolerance in alignment. It is suspected that the satellite motion relative to the ground may introduce errors in the order of a few microradians because of special relativity. Hence, the problem of laser scattering off a moving fixed target when the source and receiver are moving, which was not treated in the past in the literature, was analyzed in the following, using relativistic electrodynamics and applied to the case of the space-based coherent lidar, assuming flat ground. Here an interest in developing analytical expression for the location of the receiving point for the return with respect to the satellite, receiving angle and Doppler shift in frequency and amount of tip, all as measured in the satellite moving coordinate system and the diffuse scattering angle at the ground which does not require any compensation. All the three cases of retro-reflection, specular reflection and diffuse scattering by the ground should be treated though retro-reflection and diffuse scattering are more important.