Optimum Detection of an Optical Image on a Photoelectric Surface

The detection of an optical image in the presence of uniform background light is based on a likelihood ratio formed of the numbers of photoelectrons emitted from small elements of a photoelectric surface onto which the image is focused. When diffraction is negligible and the surface has unit quantum efficiency, this detector is equipollent with the optimum detector of the image-forming light. Its performance is compared with that of the threshold detector and that of a detector basing its decisions on the total number of photoelectrons from a finite area of the image. The illuminance of the image is postulated to have a Gaussian spatial distribution. All three detectors exhibit nearly the same reliability.