Ultimate sensitivity of heterodyne spectrometers

Low noise heterodyne receivers are now used in a large variety of instruments such as radiotelescopes, far infrared laser side bands spectrometers, supersonic nozzle beams Fourier transform spectrometers, lidars or plasmas diagnostics devices. Numerous papers have been devoted to the analysis of heterodyne receivers in the attempt to reach ultimate performances. These previous papers usually retain the restrictive hypothesis of vanishingly small signal powers. Such a condition occurs only in a restrictive number of applications, radioastronomic systems being probably among the most representative examples. Spectroscopic instruments operate usually in a different regime. The signal to be detected consists of a small variation in the source power. The absolute value of this source power largely depends on the available technology in the spectral range of interest. The purpose of this paper is to analyze the behavior of heterodyne detection in the general case. The results apply to a large category of systems including spectroscopic instruments. The influence of crucial parameters such as source power and predetection bandwidth is analysed in details. The theory is experimentally tested on an example of ultra low noise receiver designed for far infrared laser side bands spectroscopy. Some numerical calculations are proposed, illustrating methods for an optimal sizing of receiver's predetection bandwidth and the estimation of ultimate sensitivity of spectrometers.