Minimum Detectable Absorption in Microwave Spectroscopy and an Analysis of the Stark Modulation Method

It is shown that the minimum detectable absorption coefficient for an isolated spectral line as measured in a matched wave guide of optimum length is [4kTNΔf/(P0/e)]αc,where N is the noise factor and Δf the band width of the receiver, αc is the attenuation constant for the wave guide, and P0/e is the average microwave power available at the receiver. The equivalence between cavity and wave guide methods is developed. The Stark modulation method of Hughes and Wilson is analyzed, assuming a quadratic Stark effect, and expressions are developed for the modulation factor of a microwave at twice and four times the frequency of the Stark field. For a matched guide the modulation factor is αgl/4. Also the shift in line position is calculated, and finally, the directions in which improvement in sensitivity may be expected are indicated.