Laser Doppler velocimetry: analytical solution to the optical system including the effects of partial coherence of the target

Within the framework of ABCD matrix theory, analytical expressions are derived for the time-lagged covariance of a classical laser Doppler velocimetry system as a function of the laser spot size, the limiting aperture, and the measurement aperture size. Both partial and fully developed speckle as well as planar and rotating targets, are considered. Further, error estimates are presented that indicate how well one can determine in practice the velocity of both planar and rotating targets, and a comparison with time-of-flight velocimetry is given.