Detector, linear heterodyne

Now, the effective linear response function h(t) can be identified with g(t) as defined in Eqs. (25) and (29) h(t) = g(t). The primary sample response is the heterodyne diffraction efficiencyy (t) = Chet(t)- The instantaneous contribution of the temperature grating to the diffraction efficiency is expressed by the 5-function in g(t) [Eq. (25)]. After the sample, an unavoidable noise term e(t) is added. The continuous yff) is sampled by integrating with an ideal detector over time intervals At to finally obtain the time-discrete sequence y[n]. 

In an FM MMW spectrometer the spectral source frequency is modulated at a certain rate /, typically 1 kHz. This gives rise to sidebands of the spectral source frequency above and below the carrier frequency. The frequency modulated MMW carrier has in its modulation envelope phase and amplitude relationships to the carrier. Mixing in the non-linear junction of the detector yields the modulation signals altered by their interaction with the cavity and gas inside it, with their preserved amplitude and phase relationship to the original modulation signals. Those properties are measured by passing the heterodyne mixer output and the thermal noise contribution from the mixer, to a filtered phase-sensitive detection system, with the original modulation as reference. 

General considerations [7.60] show that all vth law detectors behave in an essentially similar manner to the full-wave square-law detector in terms of the ratio of (SNR). and (SNR) . For large values of (SNR)j, therefore, (SNR) is expected to be directly proportional to (SNR)j. Thus, if a half-wave linear device were used instead of the full-wave square-law device considered previously, we would expect results similar to those obtained earlier. This provides a wide choice for designing a heterodyne-nonlinear detector combination, perhaps in a single package. 

---