A quantitative estimation of the limiting stellar magnitude in the photon counting mode

The paper is concerned with the problem of determining the threshold magnitude of an object that is accessible for photoelectric observations in the photon counting mode. The principal quantitative characteristics of the detection of a weak star against the background of the sky are calculated. These characteristics include the probability of a false alarm, the correct detection probability, and the signal-to-noise ratio of the detection criterion optimized on the basis of the Neyman-Pearson theory.