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A Simple Analytical Approximation to an Inhomogeneously-Broadened Dispersion Spectrum. Application to Absorption-Dispersion Admixtures

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An Erratum to this article was published on 16 June 2017

Abstract

A simple analytical approximation to an inhomogeneously-broadened dispersion signal is proposed and tested with resonance lines broadened by unresolved hyperfine structure. Spectral parameters may be rapidly and accurately extracted using a nonlinear least-squares fitting algorithm. Combining the new approximation to a dispersion signal with a well-known approximation to the absorption signal allows dispersion-absorption admixtures, a problem of growing importance, to be analyzed quickly and accurately. For pure dispersion signals, the maximum difference between the fit and the signal for unresolved lines is 1.1 % of the maximum intensity. For pure absorption, the difference is 0.33 % of the peak-to-peak intensity, and for admixtures up to 40 % dispersion (maximum intensity/peak-to-peak intensity), the difference is 0.7 %. The accuracy of the recovered spectral parameters depends on the degree of inhomogeneously-broadened and the percentage admixture, but they are generally about 1 % at most. A significant finding of the work is that the parameters pertinent to the dispersion or the absorption are insignificantly different when fitting isolated lines vs. fitting admixtures. Admixtures with added noise or an unsuspected extraneous line are investigated.

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Notes

  1. To simplify the presentation, we abbreviate the Voigt, Lorentzian, Gaussian, and sum-function line shape functions as simply the Voigt, Lorentzian, Gaussian, and sum-function, respectively. To distinguish between the absorption and dispersion, we refer, to the Voigt absorption or the Lorentzian dispersion, etc. Furthermore, we shall write that “\(\Delta H_{pp}^0\) increases …” rather than “the value of \(\Delta H_{pp}^0\) increases …,” etc.

  2. Sigma-Aldrich, Merck KGaA, Darmstadt, Germany.

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  1. Department of Physics and Astronomy, California State University at Northridge, Northridge, CA, 91330, USA

    Barney L. Bales

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An erratum to this article is available at http://dx.doi.org/10.1007/s12013-017-0805-6.

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Bales, B.L. A Simple Analytical Approximation to an Inhomogeneously-Broadened Dispersion Spectrum. Application to Absorption-Dispersion Admixtures. Cell Biochem Biophys 75, 171–184 (2017). https://doi.org/10.1007/s12013-016-0760-7

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  • DOI: https://doi.org/10.1007/s12013-016-0760-7

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