The occurrence of maximum quantum or thermal detection efficiency (defined here as the ratio of utilized photons or energy to the total emitted by a Planckian radiator) was determined theoretically as a function of the absorption edge and bandwidth of the detector, and the temperature of the Planckian radiator. It is assumed that the quantum or thermal efficiency of the detector is constant within the bandwidth in question and zero elsewhere. The application of the specific results derived here is limited to source-detector combinations where the source spectral energy or photon distribution approximates that of a Planckian radiator. A “noise level” and its effect on the efficiency are not considered in the present analysis. The outcome of the analysis is a series of “displacement laws” which are similar to the Wien displacement law, λmT=0.2898 cm °K.
It is shown that the temperature should be increased for maximum efficiency as the bandwidth of the detector is increased.
ALAN D. WILSON, "Occurrence of Maximum Quantum and Thermal Detection Efficiencies Attainable with a Planckian Radiator," J. Opt. Soc. Am. 54, 482-485 (1964)