Single-look tracking noise for intensity and binary centroiding algorithms for resolved targets and performance comparison between shared- and separate-aperture active tracking

摘要

Abstract: Expressions are derived for the single look tracking noise (SLTN) for an unthresholded intensity centroid algorithm and a binary centroid with a lower threshold. The SLTN is defined as the rss value of the rms errors due to (1) photoelectron statistics, (2) background in the tracking gate, and (3) non- coincidence of the object boundaries and the focal plane array (FPA) detector pixels. The expressions, eqs. (27) and (28) below, are applied to typical directed energy weapon scenarios where the objects are pulse-illuminated distant, Lambertian targets. We find for both algorithms that the SLTN decreases with increasing illuminator energy to a terminal value set by the boundary mismatch error (3) above, but for a fixed illumination and pixel footprint on the target this error is smaller for the intensity algorithm. For each algorithm, the footprint can be optimized to obtain a minimal SLTN, and in the cases studied the binary SLTN was consistently lower than the intensity SLTN. Furthermore, the dependence on illuminator pulse energy E is approximately 1/$ROOT@E for the intensity, approximately 1/E$+2/3$/ for the binary centroid. Finally, the SLTN is approximately proportional to 1/D$ROOT$eta@, where D is the collecting aperture and $eta is the tracker photon efficiency (transmission X quantum). Thus the advantage of a `shared' DEW tracker compared to `separate' is typically a factor 5 or less. !8