Cumulative distributions of the number of photoelectrons ejected during a fixed interval can be computed by numerical contour integration in the complex plane when the light incident upon the detector is a combination of coherent light and incoherent background light with arbitrary spectral density. The integrand involves the probability-generating function of the distribution, and a method for computing it in terms of the solution of a certain integral equation is described. The method is related to those for the estimation of a stochastic process in the presence of white noise. An approximation valid for large values of the time–bandwidth product is also described.
© 1985 Optical Society of America
Original Manuscript: July 23, 1984
Manuscript Accepted: January 10, 1985
Published: May 1, 1985
Carl W. Helstrom, "Computation of photoelectron counting distributions by numerical contour integration," J. Opt. Soc. Am. A 2, 674-682 (1985)