Calculating photocount distributions by saddlepoint methods

Abstract

Probability generating functions of the number of photoelectrons emitted by a detector during a given interval can often be relatively easily calculated from a physical model of the emissive processes, but inverting them analytically to obtain the distributions of the number of so-called “photocounts” is usually complicated or impossible. Techniques for computing those distributions can be based on numerical evaluation of the inversion integral along a suitably chosen contour passing through a saddlepoint of the integrand and lying as close as possible to a path of steepest descent of that integrand. The method can be extended to include the effects of additive Gaussian noise, intersymbol interference, and postdetector filtering.