Open AccessComputational expressions for signals in frequency-modulation spectroscopy
Author(s) -
Massimiliano Rosa,
Matthew T. Reiten
Publication year - 2015
Publication title -
applied optics
Language(s) - English
Resource type - Journals
ISSN - 0003-6935
DOI - 10.1364/ao.54.005031
Subject(s) - modulation index , modulation (music) , frequency modulation , phase modulation , signal (programming language) , optics , physics , doppler effect , limit (mathematics) , interpolation (computer graphics) , line (geometry) , doppler broadening , amplitude modulation , computer science , mathematics , acoustics , mathematical analysis , telecommunications , spectral line , pulse width modulation , radio frequency , geometry , quantum mechanics , power (physics) , phase noise , frame (networking) , programming language
General expressions for the signals in frequency-modulation spectroscopy (FMS) appear in the literature but are often reduced to simple analytical equations following the assumption of a weak modulation index. This is little help to the experimentalist who wants to predict signals for modulation depths of the order of unity or greater, where strong FMS signals reside. Here, we develop general formulas for FMS signals in the case of an absorber with a Voigt line shape and then link these expressions to an example and existing numerical code for the line shape. The resulting computational recipe is easy to implement and exercised here to show where the larger FMS signals are found over the coordinates of modulation index and modulation frequency. One can also estimate from provided curves the in-phase FMS signal over a wide range of modulation parameters at either the Lorentzian-broadening or Doppler-broadening limit, or anywhere in between by interpolation.