Doppler shift analysis for a holographic aperture ladar system

Since the invention of the laser, laser radars (ladars) have been investigated following the extensive development path of radar systems. Ladar systems have progressed from simple direct detect systems to more complicated synthetic aperture heterodyne systems. Developments in digital processing allowed a new type of synthetic aperture ladar known as holographic aperture ladar where the heterodyne detection of temporal synthetic aperture ladar was combined with the holographic digital recording methods. Using holographic aperture ladar increases cross-range resolution, but by using a low bandwidth spatial receiver array instead of a high bandwidth point receiver increases the system\u27s Doppler effect vulnerability for each sub-aperture image. The Doppler frequency offsets are due to projected line of sight velocities across the target. In a broadside imaging configuration, one side of the target will appear to be approaching the target while the other appears to be receding. The projected line of sight velocity is zero at the center of the target (normal to the LOS), and has maximum values at the edges of the target field. This produces an approximately linear differential Doppler frequency shift across the target in the dimension of travel. This spatially dependent, sinusoidal signal is temporally integrated over the fixed integration time of the imaging array which maps the sinusoidal signal into a spatial sinc pattern across the target\u27s image. Since the targets edges have the highest projected velocities, the sinc pattern appears as a loss in target information effectively reducing the field of view. Faster platform velocities and longer integration times produce larger compressions in the field of view. This paper describes the velocity and integration time required to limit the field of view reduction to a selected value. The first null in the cross sectional sinc pattern is assumed to be a good measure for the compression of the field of view. Analytic expressions and numerical simulations are developed for the impact of differential Doppler frequencies and then verified with laboratory experiments. Four integration times were analyzed in this experiment. Since the motion is relative, the target\u27s velocity varied. The integration times were 0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms and the velocities varied between 0 and 14 cm/s. The results of this experiment were in good agreement with the theory and simulation and confirm that selection of faster effective integration times is required to limit data loss due to platform motion