Frequency-modulation spectroscopy for trace species detection: theory and comparison among experimental methods

A variety of frequency-modulation methods for high-sensitivity absorption detection of gas-phase species has evolved in recent years. The distinctions among these methods are mostly semantic. The mathematical derivations for wavelength-modulation spectroscopy and one- and two-tone frequency-modulation spectroscopies are presented; a common terminology is used to permit a comprehensive comparison of predicted detection sensitivities. Applying this formalism, I compare the optimum detection sensitivities of these different methods for a typical laser system, using the same parameters. As long as residual amplitude modulation is minimized by proper adjustment of the detection phase angle, high-frequency wavelength modulation and one- and two-tone frequency-modulation methods all achieve approximately the same sensitivities. The choice among techniques is most strongly driven by the individual laser tuning characteristics, the absorption linewidth, and the detection bandwidth. It is shown that excess laser noise cannot always be excluded from consideration, even at megahertz detection frequencies. Also, detection at harmonics of the modulation or beat frequency may present certain advantages in minimizing residual amplitude-modulation noise.