Statistical analysis for coherent optical-imaging systems with registration errors

Abstract

Coherent images of diffuse objects exhibit two fundamental noise artifacts: speckle noise that is due to the use of coherent illumination and photon noise that is due to fundamental limitations in the detection of electromagnetic radiation. Because of the nature of speckle noise, slight changes in the source-scene–sensor geometry can give rise to independent speckle-noise realizations, which can, in turn, be used to form ensemble averages and reduce the speckle-induced degradations. The very nature of this procedure, however, can result in a collection of images that are not registered relative to one another, and new distortions, unrelated to the speckle effect, will be seen in the resulting images. Our goal, therefore, is to present a statistical analysis of coherent optical-imaging systems that collect and average independent, photon-limited speckle images with registration errors and to use this analysis in the derivation of mean-square-error and signal-to-noise ratio expressions that are applicable for both image-domain and spatial-frequency-domain analyses.