Signal-to-Noise Relationships for Coaxial Systems that Heterodyne Backscatter from the Atmosphere

Abstract

This paper analyzes the signal-to-noise ratio for a coaxial laser system that heterodynes the signal backscattered from the atmospheric aerosol. The laser radiation, which is assumed to have a wavefront with a gaussian amplitude distribution, is transmitted into the atmosphere through a telescope. Radiation is collected by the same telescope and directed onto a detector where it is mixed with a local oscillator beam originating from the same laser source. The signal-to-noise ratio at the output of the detector is calculated under shot noise limited conditions. The calculation is general and applies for both near and far fields and for focused and unfocused systems. Three specific cases are considered. These are a pulsed system, a cw system illuminating an infinite target, and a cw system illuminating a target of finite extent.