Line shape of amplitude or frequency-modulated spectral profiles including resonator distortions

We report experiments and an improved method of analysis for any harmonics of frequency-modulated spectral line shapes allowing for very precise determinations of the resonance frequency of single absorption lines for gigahertz spectroscopy in the gas phase. Resonator perturbations are implemented into the formalism of modulation spectroscopy by means of a full complex transmission function being able to model the asymmetrically distorted absorption line shapes for arbitrary modulation depths, modulation frequencies, and resonator reflectivities. Exact equations of the in-phase and the quadrature modulation signal, taking into account a full resonator transmission function, are simultaneously adjusted to two-channel lock-in measurements performed in the gigahertz regime to obtain the spectral line position. The determination of the absorption line position of the rotational transition J' = 7 ← J" = 6 of (16)O(12)C(32)S in the vibrational ground state is investigated while changing the resonator distortions. The results are subjected to the approach proposed here and compared to standard methods known from the literature.