Theory of the Cavity Microwave Spectrometer and Molecular Frequency Standard

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Abstract
A short section of a wave guide is considered as a nonresonant absorption cell and then as a resonant cavity. It is shown that the latter gives a better signal‐to‐noise ratio by a factor which depends upon the relative intensity of the various noise sources but which increases with the Q. It is shown that the voltage signal‐to‐noise ratio is proportional to the square root of the product of the volume and the Q and otherwise is independent of the shape. This result leads to the conclusion that it is possible in theory to build microwave spectrometers having signal‐to‐noise ratios some 50 db larger or capable of detecting absorption coefficients some 300 times smaller than spectrometers which are now widely used. However, practical considerations probably would prevent this advantage from being realized completely. These results are applied to a frequency standard using an absorption line. It is shown that it is possible to build a standard using the 3,3 line of NH3 with a fractional stability of about 4×10−12 over an extended interval of time. Some discussion of spectrometers with long nonresonant cells is also included.