Remote Angular Frequency Measurement Through Turbulence

A performance model is developed for an angular frequency measurement technique based on photon correlation. The purpose of the technique is to measure the rate of rotation of a remote diffusely reflecting target. Coherent illumination of the target produces a speckle pattern that is sampled temporally and spatially by an array of photodetectors. The collected data are processed to obtain an estimate of the spatiotemporal cross correlation function for the speckle irradiance. The position of the correlation peak for a particular time delay provides a measure of the speckle velocity, which, combined with the known range and transverse velocity of the target, allows the transverse component of the target's angular frequency (i.e., rotation rate) vector to be calculated. The performance model includes the effects of atmospheric turbulence, clear-weather atmospheric attentuation, dark count, background radiation, dead time, spatiotemporal integration, photon noise, and classical measurement noise. Expressions for the signal-to-noise ratio, signal biasing, angular frequency resolution, and the maximum measurable angular frequency are derived.