The joint probability of finding m2 photons in detection interval 2 and m1 photons in detection interval 1 was previously determined by the author [ J. Mod. Opt. 34, 91 ( 1987)] in terms of a series expansion of the time-integrated intensity correlation function with coefficients given by a class of orthogonal polynomials in the discrete variables m2 and m1. This expansion is now used to obtain an expression for the average of two general functions υ(m2) and u(m1), 〈υ(m2)u(m1)〉. These functions are specialized to cover two important situations: singly and doubly clipped covariances for essentially arbitrary counting times. In the doubly clipped case, different clipping levels are permitted in the two channels in order to study the influence of clipping mismatch. Numerical calculations, in the form of graphs, are used to illustrate typical behavior.
© 1988 Optical Society of America
Original Manuscript: February 17, 1987
Manuscript Accepted: March 18, 1988
Published: August 1, 1988
Richard Barakat, "Clipped photon-counting covariance functions," J. Opt. Soc. Am. A 5, 1248-1253 (1988)