Second-Order Statistics of the Performance of the Starfire Optical Range Adaptive Optics System

Abstract

Early in the development of adaptive optics technology, the goal was to obtain good instantaneous results, i.e., well-compensated short-exposure images. The next goal was expressed in terms of average results, for example, acquiring good long-exposure images. The next logical step in characterizing and improving adaptive optics (AO) system performance is to investigate the second-order statistics. For example, we are interested not only in the average point spread function (PSF), but also the variance of the PSF. Depending on the application, we may be interested in the second-order statistics of other widely used measures of AO system performance such as the optical transfer function (OTF), Strehl ratio, image width, and encircled energy. The variance of the PSF/OTF is of interest when post-processing AO-compensated images.1 The variance of the OTF appears explicitly in the denominator of the image spectrum signal-to-noise ratio.2 Some researchers have suggested that AO may be useful in the area of optical communications to deep space probes.3 In such an application, one is interested in the statistical variation of the coupling efficiency of the compensated beam to an optical receiver and the frequency, duration, and distribution of signal excursions below threshold levels.4