Photoelectric astrometry: a comparison of methods for precise image location

Abstract

AbstractSeveral techniques for obtaining the precise location of a noisy image (of a star, spectral line, solar limb, etc.) are described by means of characteristic “weighting functions”. The imprecision of an image location estimate can be expressed in terms of the weighting function and the image shape and noise covariance. It is limited by the intrinsic imprecision of the image, which is attained with an optimum weighting function, computable from the image characteristics. The hypothetical optimum method is compared with some commonly used location methods, such as computing the median or centre of gravity, least-squares fitting and cross correlating, and hardware techniques including the quadrant detector and rotating knife-edge. One- and two-dimensional Gaussian images are considered as well as diffraction and seeing images. The general results apply also to photographic astrometry, measurement of radial velocities, timing of pulses, etc.