LADAR Detection Statistics in the Presence of Pointing Errors.

The probability of detection of optically rough targets by pulsed LADAR systems that employ direct detection is considered here. It is assumed that the LADAR operates under conditions of both unintentional pointing off-set bias i.e., bore-sight error and jitter. Under these conditions, the probability of detection of targets in both the near and far field of the collecting aperture i.e., for resolved, partially resolved, and unresolved targets and for both large and small photoelectron counts is derived, and, in many cases of practical interest, accurate, elementary analytic approximations that are useful for parametric system studies are obtained. As such, the approximate engineering expressions derived here will be useful, for example, to those performing engineering modeling of space-based LADAR systems. A number of appendices are included to serve as technical references, where some key results employed in the main body of the report are derived. In particular, an interesting new mathematical result involving the complementary incomplete gamma function and an analytic expression for the probability distribution function of a signal photocount obeying Bose-Einstein statistics such as that arising from unresolved targets immersed in Poisson noise are derived. Optical radar, Detection statistics, LADAR, Statistical optics, Pointing errors