Atmospheric Phase Error in Coherent Laser Radar

Coherent laser radar (ladar) deduces the shape, velocity and vibration of a remote target by measuring the round-trip optical phase or the Doppler shift of target-scattered light. Phase fluctuations from wind-driven atmospheric turbulence generate micro-Doppler or velocity error at mum/sec levels. The turbulence-induced noise spectra of all geometric phase components of the ladar, the average phase power spectral densities of arbitrary ladar receiver modes, and the resultant Doppler noise spectra, are derived in the Rytov approximation for any isotropic stationary turbulence, any wind velocity profile, any Fresnel number and any source illumination pattern. In Kolmogorov turbulence the piston phase noise spectrum, and the average phase shift over a time interval, are well-approximated by simple universal asymptotic forms dependent only on atmospheric coherence length, turbulence-weighted average wind speed Vmacr, and aperture size D. The spectrum slope changes at a critical frequency of order Vmacr/D. The approximate results do not depend on the usually-unknown outer scale of turbulence