Annular apertures for angular tracking

Abstract

The estimation of the angular position of a target based on its image is considered when the image is formed with a telescope possessing an annular pupil and is sensed with a four-quadrant noncoherent detector. The Cramér-Rao lower bound on the estimation error is calculated as a function of the linear obscuration ratio ∊ for unresolved targets in the shot-noise limit. The ratio influences the error both via the shape of the telescope point spread function (PSF) and via the SNR. The error increase associated with the PSF becomes significant for ∊ ≳ 0.5.