Wavelength modulation absorption spectrometry from optically saturated collision-broadened transitions

A theoretical investigation of the influence of optical saturation on wavelength modulation absorption spectrometry (WMAS) signals from collision-broadened transitions is presented. Expressions are derived for the nth Fourier coefficient of the analytical detector signal, and thereby also for the nth harmonic signal from a WMAS instrumentation (i.e. the nf-WMAS signal), from a wavelength modulated collision-broadened transition exposed to optical saturation. The flux- (or irradiance-) and modulation-amplitude dependences of the nf-WMAS signal on resonance are scrutinized in detail. It is shown that the nth Fourier coefficient of the wavelength modulated analytical detector signal from an optically saturated collision-broadened transition can be written as a product of a flux-dependent (φ) bleaching function, given by (1+φ/φsat)-1 and identical to that appearing for ordinary, unmodulated absorption spectrometry (AS), and a flux-, detuning-, and modulation-amplitude-dependent wavelength modulated peak-normalized saturation-broadened Lorentzian lineshape function, specific for the WMAS technique. It is found that the nf-WMAS signal on resonance decreases faster than an ordinary AS signal as a function of laser flux when smaller-than-optimum modulation amplitudes are used, but slower when larger-than-optimum modulation amplitudes are used. When optimum (or close-to-optimum) modulation amplitudes are being used, on the other hand, the flux dependence of the WMAS signal resembles to a large degree that of ordinary AS. The conditions for when WMAS from collision-broadened transitions has the same flux dependence as ordinary AS are identified.