Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals

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A theoretical description of the wavelength-modulation (WM) spectrometry technique is given. The formalism is based on Fourier analysis and can therefore correctly handle arbitrary large frequency-modulation amplitudes. It can also deal with associated intensity modulations as well as wavelength-dependent transmission effects. It elucidates clearly how various Fourier components of these entities combine with those of the line-shape function to yield separately the final analytical and background nf WM signals. Explicit expressions are given for the 2f and the 4f signals. It is shown, among other things, that the 4f technique in general gives rise to smaller background signals (and therefore larger signal-to-background ratios) than does the 2f technique when the background is dominated by etalon effects from short cavities and that a finite intensity modulation necessarily leads to an out-of-phase nf WM signal. The formalism is also able to elucidate clearly that a linear intensity modulation is not sufficient to cause any 2f background residual-amplitude-modulation signals (as was the general consensus until recently in the literature) but that 2f background signals instead can exist only in systems with either wavelength-dependent transmission or a laser with nonlinear intensity modulation.