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Efficient approximations of the voigt and rautian-sobelman profiles


Sufficiently accurate approximations of the probability integral with complex argument are obtained, which make it possible to calculate the Voigt and Rautian-Sobelman profiles. An efficient method for experimental spectra smoothing is suggested.

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  1. 1.

    I. I. Sobelman, Introduction to the Theory of Atomic Spectra (Nauka, Moscow, 1963; Alpha Science Int., Oxford, 2006).

    Google Scholar 

  2. 2.

    S. G. Rautian and I. I. Sobel’man, “Effect of Collisions on the Doppler Broadening of Spectral Lines,” Usp. Fiz. Nauk 90, 209–236 (1966) [Sov. Phys. Usp. 9, 701 (1967)].

    Google Scholar 

  3. 3.

    Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. Stegun (Nation. Bureau of Standards, New York, 1964; Moscow, Nauka, 1979).

    MATH  Google Scholar 

  4. 4.

    V. P. Kochanov and I. V. Ptashnik, “Approximation of the Width of the Line Profile Narrowed by Collisions,” Opt. Spectrosc. 89, 678 (2000).

    ADS  Article  Google Scholar 

  5. 5.

    S. R. Drayson, “Rapid Computation of the Voigt Profile,” J. Quant. Spectrosc. Rad. Transfer. 16, 611–614 (1976).

    ADS  Article  Google Scholar 

  6. 6.

    J. Humlicek, “An Efficient Method for Evaluation of the Complex Probability Function: The Voigt Function and Its Derivatives,” J. Quant. Spectrosc. Rad. Transfer. 21, 309–313 (1979).

    ADS  Article  Google Scholar 

  7. 7.

    V. N. Faddeeva and N. M. Terent’ev, Tables of Values of the Probability Integral with a Complex Argument (Moscow, Gostekhizdat, 1954) [in Russian].

    Google Scholar 

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Correspondence to V. P. Kochanov.

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Original Russian Text © V.P. Kochanov, 2011, published in Optica Atmosfery i Okeana.

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Kochanov, V.P. Efficient approximations of the voigt and rautian-sobelman profiles. Atmos Ocean Opt 24, 432 (2011).

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  • Neon
  • Experimental Spectrum
  • Oceanic Optic
  • Efficient Approximation
  • Spline Smoothing