Signal-to-noise ratio in lock-in amplifier synchronous detection: A generalized communications systems approach with applications to frequency, time, and hybrid (rate window) photothermal measurements

Abstract

Detailed analytical models of signal‐to‐noise ratios (SNR) of the conventional frequency domain (FD) and time domain (TD) photothermal measurement methodologies are developed and compared to the rate‐window photothermal method, both theoretically and experimentally. The conclusions of this study demonstrate that the lock‐in amplifier (LIA) rate‐window measurement mode in general, and the digital LIA mode, in particular, exhibits superior SNR to both the conventional frequency‐scanned LIA FD method and to the transient, time‐averaged TD method. Between the pulse‐duration‐scanned and pulse‐repetition‐period scanned rate‐window methodologies, the former clearly exhibits superior SNR. The theoretical conclusions are in agreement with experimental SNRs using the implementation of the foregoing measurement methodologies with simple infrared photothermal radiometric setups.