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Applied Optics

Applied Optics


  • Vol. 38, Iss. 27 — Sep. 20, 1999
  • pp: 5803–5815

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

Pawel Kluczynski and Ove Axner  »View Author Affiliations

Applied Optics, Vol. 38, Issue 27, pp. 5803-5815 (1999)

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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.

© 1999 Optical Society of America

OCIS Codes
(020.3690) Atomic and molecular physics : Line shapes and shifts
(300.1030) Spectroscopy : Absorption
(300.6260) Spectroscopy : Spectroscopy, diode lasers

Original Manuscript: December 8, 1998
Revised Manuscript: May 21, 1999
Published: September 20, 1999

Pawel Kluczynski and Ove Axner, "Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals," Appl. Opt. 38, 5803-5815 (1999)

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  48. An alternative definition of the 2f and the 4f WM-signal fractions, which can be considered more convenient under some experimental conditions, is to relate the actually measured nth signal component to the zeroth signal component rather than to the unmodulated signal, as was done in Eqs. (18)–(21), i.e., as SAS,neven(ν̅d, ν̅a) = ΓAS,neven(ν̅d, ν̅a)SAS,0even(ν̅d, ν̅a). This will, however, give the same expression for the nf WM-signal fractions as do expressions (48) and (49) under the conditions considered [i.e., when T0e ≫ Tkk>0e and IL,0e > IL,1e ≫ IL,2e].
  49. Our choice of expression for the modulated laser intensity [Eq. (6)] however, suggests that the linear intensity modulation, given by IL,0(νc)κ1νa cos(ϕ1), should depend on the laser intensity at the center frequency. This is, however, not the case in reality but rather an artifact from our method of writing the intensity modulation. To correct for this artifact when calculating the nf WM spectra, we use the following expression for the wavelength dependence of the intensity-modulation coefficient: κ1(νd) = κ1(0)/[1 + κ1(0)νd].

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