The use of joint probability densities are examined as a method for the complete description of background. The requirements for the complete description leads to an infinite dimensional analysis of background. The relationships between joint probability densities, the autocorrelation function and the Wiener spectra are explored to obtain some insight into the nature of background from measured Wiener spectra. Techniques for theoretical and experimental determination of probability of detection and probability of false alarm are considered.
HERMAN G. ELDERING, "Method for the Complete Description of Infrared Sky Backgrounds," J. Opt. Soc. Am. 51, 1424-1429 (1961)