Estimation and Detection of Optical Signals Distorted by Diffraction, Background Noise, and Detection Noise

摘要

Estimation and detection of optical signals distorted by diffraction, additive background noise, and multiplicative (detection) noise are studied. Assuming that the output of the detector is a Poisson process, that the signal and noise are additive, and that they have prescribed means and covariance matrices, the optimum linear estimate of the optical signal or object is obtained. In the physical detection process, the interaction between the incident radiation and the detector produces an effect called multiplicative noise which must be taken into account in obtaining the optimum linear estimate. The performance of the estimation procedure is evaluated for several special cases. Both white and colored noise are considered in the estimation problem. The problem of discriminating between optical signals is considered. Optimum procedures are derived for detecting known and unknown optical using fixed-sample detectors. The properties of sequential detectors which are optimum for the detection of random or unknown optical signals are investigated. A comparison is made of the average test lengths of these optimum random signal detectors with those of a detector designed for particular optical signals. The test lengths of the fixed-sample detector and sequential detector are compared for a particular example. (Author)