Photon detectors: Thermal background noise-equivalent power with frequency-dependent detector efficiency

Background thermal noise often becomes the limiting factor while detecting low signals of photon flux from a distant thermal source. This cannot be eliminated by simply cooling the photodetector. A general method is developed here to calculate the background thermal noise and the noise equivalent power (NEP) for background source temperature T, with any given frequency-dependent quantum efficiency function eta(v) for the photodetector. Applications of our analysis to some specific model forms of eta(v), with finite bandwidths, show that earlier calculations are highly inadequate for peak efficiency frequencies v(o) < k(B)T/h, where k(B) is the Boltzmann constant and h is the Planck constant. The NEP, which determines the limit on the lowest signal power that can be detected by any given photodetector, is much higher in these frequency regions compared to earlier approximate estimates.