The detection and resolution of optical signals

The principles of statistical signal-detection theory are applied to the detection of optical signals by postulating the photoelectric effect as the mechanism for the interaction of the electromagnetic field of the light with matter. The data with which the detection system works are the numbers of photoelectric events in various parts of a receptor on which the light falls after passing through an aperture. The theory prescribes how the data should be processed and measures the detectability of the signals in terms of an SNR. The theory is applied to the detection of a point source and of an array of incoherent point sources, all against a uniform background. The resolution of two weak close point sources of radiation observed against a uniform background is also treated as a problem in the testing of hypotheses, and the reliability of the system derived on this basis is measured by an SNR that is a function of the angular separation of the sources. The estimation of the parameters of an optical signal is discussed from the standpoint of statistical estimation theory. Estimation of the angular position of a point source against a uniform background is treated as an example.