Lock-in common-mode rejection demodulation: Measurement technique and applications to thermal-wave detection: Theoretical

Abstract

The ability of conventional single-ended photothermal techniques to detect weak inhomogeneities in a given material is mainly limited by two instrumental factors: the signal-to-noise ratio (SNR) and the amplitude dynamic range. The amplitude level is limited by the output signal baseline, and may be too high to monitor relatively small variations introduced by the presence of weak inhomogeneities. The purpose of this work is to introduce a novel photothermal signal generation methodology, the principle of which can be broadly applied to any technique utilizing a lock-in analyzer demodulation scheme of periodic signal wave forms. Unlike the conventional single-ended periodic excitation wave form, which uses a 50% duty-cycle square wave or sinusoidal modulation of the pump laser heating beam, a more complicated periodic modulation wave form is employed, resulting in the equivalent of differential-signal demodulation. The new wave form takes advantage of the real-time differential action performed by the lock-in amplifier weighing function over the two half periods of the modulated signal. This results in enhanced signal dynamic range due to the efficient suppression of the baseline and a substantial improvement in the SNR. The main features of this technique are investigated with a theoretical model for an arbitrary repetitive signal wave form and, in particular, for a photothermal signal. The dependence of the signal on the wave form parameters is also discussed.