Abstract

A simple empirical analytical approximation to the Voigt profile is proposed as a weighted sum of Lorentzian and Gaussian functions. It is prevalent in the analysis of complicated experimental spectra such as that with multibroadening mechanisms and congested or overlapped lines. The maximum errors of width, area, and peak relative to those from direct convolution of the Voigt profile are 0.01%, 0.2%, and 0.55%, respectively. The relative width error of the present approximation is smaller and its convergence of absolute strength calculation, i.e. the area under the profile, faster than for the other methods that we considered, such as Gautsch’s algorithm, which is developed by introduction of a complex probability function.

© 2001 Optical Society of America

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References

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  1. D. W. Posener, “The shape of spectral lines: tables of the Voigt profile a/π ∫ e−y2dy/a2 + (x−y)2,” Aust. J. Phys. 12, 184–196 (1959).
    [CrossRef]
  2. D. G. Hummer, “The Voigt function—an eight-significant-figure table and generating procedure,” Mem. R. Astron. Soc. 70, 1–32 (1965).
  3. J. F. Kielkopf, “New approximation to the Voigt function with applications to spectral-line,” J. Opt. Soc. Am. 63, 987–995 (1973).
    [CrossRef]
  4. E. E. Whiting, “An empirical approximation to the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379–1384 (1968).
    [CrossRef]
  5. C. Young, “Note: Calculation of the absorption coefficient for lines with combined Doppler and Lorentz broadening,” J. Quant. Spectrosc. Radiat. Transfer 5, 549–552 (1965).
    [CrossRef]
  6. B. H. Armstrong, “Spectrum line profiles: the Voigt function,” J. Quant. Spectrosc. Radiat. Transfer 7, 61–88 (1967).
    [CrossRef]
  7. W. Gautschi, “Algorithm 363, complex error function [S15],” Commun. ACM 12, 635 (1969).
    [CrossRef]
  8. S. R. Drayson, “Note: Rapid computation of the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 16, 611–614 (1976).
    [CrossRef]
  9. A. K. Hui, B. H. Armstrong, and A. A. Wray, “Rapid computation of the Voigt and complex error functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509–516 (1978).
    [CrossRef]
  10. J. H. Pierluissi and P. C. Vanderwood, “Note: Fast calculation algorithm for the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 18, 555–558 (1977).
    [CrossRef]
  11. J. Humlicek, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Transfer 21, 309–313 (1979).
    [CrossRef]
  12. J. Humlicek, “Optimized computation of the Voigt and complex probability functions,” J. Quant. Spectrosc. Radiat. Transfer 27, 437–444 (1982).
    [CrossRef]
  13. A. H. Karp, “Efficient computation of spectral line shapes,” J. Quant. Spectrosc. Radiat. Transfer 20, 379–384 (1978).
    [CrossRef]
  14. W. G. Mankin, “Fourier transform method for calculating the transmittance of inhomogeneous atmospheres,” Appl. Opt. 18, 3426–3433 (1979).
    [CrossRef] [PubMed]
  15. S. S. Penner and R. W. Kavanagh, “Radiation from isolated spectral lines with combined Doppler and Lorentz broadening,” J. Opt. Soc. Am. 43, 385–388 (1953).
    [CrossRef]
  16. C. Chiarella and A. Reichel, “On the evaluation of Voigt spectral line functions,” Mon. Not. R. Astron. Soc. 134, 83–86 (1966).
  17. F. Matta and A. Reichel, “Uniform computation of the error function and other related functions,” Math. Comput. 25, 339–344 (1971).
    [CrossRef]
  18. V. N. Faddeyeva and N. M. Terentev, Tables of Values of the Function w(z) for Complex Argument (Pergamon, Oxford, 1961).
  19. F. Schreier, “The Voigt and complex error functions: a comparison of computational methods,” J. Quant. Spectrosc. Radiat. Transfer 48, 743–762 (1992).
    [CrossRef]
  20. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), p. 297.
  21. J. J. Olivero and R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
    [CrossRef]
  22. Z. A. Liu, Y. Y. Liu, F. Y. Li, J. R. Li, B. Z. Gong, and Y. Q. Chen, “Measurement of pressure broadening coefficients of NO by intracavity laser magnetic resonance with a CO laser,” Chem. Phys. Lett. 183, 340–344 (1991).
    [CrossRef]
  23. Y. Q. Chen, Y. Y. Liu, F. Y. Li, J. R. Li, and K. L. He, “Determination of pressure broadening coefficients of NO2 by laser magnetic resonance,” Chin. Phys. Lett. 5, 277–280 (1988).
    [CrossRef]
  24. J. T. Twitty, P. L. Rarig, and R. E. Thompson, “Note: A comparison of fast codes for the evaluation of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transfer 24, 529–532 (1980).
    [CrossRef]
  25. C.-H. Xu, Introduction to Computational Methods (Higher Education Press, Beijing, China, 1995), pp. 88–105.
  26. A. Klim, “A comparison of methods for the calculation of Voigt profiles,” J. Quant. Spectrosc. Radiat. Transfer 26, 537–545 (1981).
    [CrossRef]
  27. T. K. Fang and T. N. Chang, “Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution,” Phys. Rev. A 57, 4407–4412 (1998).
    [CrossRef]
  28. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
    [CrossRef]
  29. Y. Y. Liu, J. L. Lin, and Y. Q. Guo, “Measurement of the pressure self-broadening coefficient of NO by saturation spectroscopy of LMR,” Can. J. Phys. 78, 985–995 (2000).
    [CrossRef]

2000 (1)

Y. Y. Liu, J. L. Lin, and Y. Q. Guo, “Measurement of the pressure self-broadening coefficient of NO by saturation spectroscopy of LMR,” Can. J. Phys. 78, 985–995 (2000).
[CrossRef]

1998 (1)

T. K. Fang and T. N. Chang, “Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution,” Phys. Rev. A 57, 4407–4412 (1998).
[CrossRef]

1992 (1)

F. Schreier, “The Voigt and complex error functions: a comparison of computational methods,” J. Quant. Spectrosc. Radiat. Transfer 48, 743–762 (1992).
[CrossRef]

1991 (1)

Z. A. Liu, Y. Y. Liu, F. Y. Li, J. R. Li, B. Z. Gong, and Y. Q. Chen, “Measurement of pressure broadening coefficients of NO by intracavity laser magnetic resonance with a CO laser,” Chem. Phys. Lett. 183, 340–344 (1991).
[CrossRef]

1988 (1)

Y. Q. Chen, Y. Y. Liu, F. Y. Li, J. R. Li, and K. L. He, “Determination of pressure broadening coefficients of NO2 by laser magnetic resonance,” Chin. Phys. Lett. 5, 277–280 (1988).
[CrossRef]

1982 (1)

J. Humlicek, “Optimized computation of the Voigt and complex probability functions,” J. Quant. Spectrosc. Radiat. Transfer 27, 437–444 (1982).
[CrossRef]

1981 (1)

A. Klim, “A comparison of methods for the calculation of Voigt profiles,” J. Quant. Spectrosc. Radiat. Transfer 26, 537–545 (1981).
[CrossRef]

1980 (1)

J. T. Twitty, P. L. Rarig, and R. E. Thompson, “Note: A comparison of fast codes for the evaluation of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transfer 24, 529–532 (1980).
[CrossRef]

1979 (2)

J. Humlicek, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Transfer 21, 309–313 (1979).
[CrossRef]

W. G. Mankin, “Fourier transform method for calculating the transmittance of inhomogeneous atmospheres,” Appl. Opt. 18, 3426–3433 (1979).
[CrossRef] [PubMed]

1978 (2)

A. K. Hui, B. H. Armstrong, and A. A. Wray, “Rapid computation of the Voigt and complex error functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509–516 (1978).
[CrossRef]

A. H. Karp, “Efficient computation of spectral line shapes,” J. Quant. Spectrosc. Radiat. Transfer 20, 379–384 (1978).
[CrossRef]

1977 (2)

J. J. Olivero and R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

J. H. Pierluissi and P. C. Vanderwood, “Note: Fast calculation algorithm for the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 18, 555–558 (1977).
[CrossRef]

1976 (1)

S. R. Drayson, “Note: Rapid computation of the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 16, 611–614 (1976).
[CrossRef]

1973 (1)

1971 (1)

F. Matta and A. Reichel, “Uniform computation of the error function and other related functions,” Math. Comput. 25, 339–344 (1971).
[CrossRef]

1969 (1)

W. Gautschi, “Algorithm 363, complex error function [S15],” Commun. ACM 12, 635 (1969).
[CrossRef]

1968 (1)

E. E. Whiting, “An empirical approximation to the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379–1384 (1968).
[CrossRef]

1967 (1)

B. H. Armstrong, “Spectrum line profiles: the Voigt function,” J. Quant. Spectrosc. Radiat. Transfer 7, 61–88 (1967).
[CrossRef]

1966 (1)

C. Chiarella and A. Reichel, “On the evaluation of Voigt spectral line functions,” Mon. Not. R. Astron. Soc. 134, 83–86 (1966).

1965 (2)

C. Young, “Note: Calculation of the absorption coefficient for lines with combined Doppler and Lorentz broadening,” J. Quant. Spectrosc. Radiat. Transfer 5, 549–552 (1965).
[CrossRef]

D. G. Hummer, “The Voigt function—an eight-significant-figure table and generating procedure,” Mem. R. Astron. Soc. 70, 1–32 (1965).

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

1959 (1)

D. W. Posener, “The shape of spectral lines: tables of the Voigt profile a/π ∫ e−y2dy/a2 + (x−y)2,” Aust. J. Phys. 12, 184–196 (1959).
[CrossRef]

1953 (1)

Armstrong, B. H.

A. K. Hui, B. H. Armstrong, and A. A. Wray, “Rapid computation of the Voigt and complex error functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509–516 (1978).
[CrossRef]

B. H. Armstrong, “Spectrum line profiles: the Voigt function,” J. Quant. Spectrosc. Radiat. Transfer 7, 61–88 (1967).
[CrossRef]

Chang, T. N.

T. K. Fang and T. N. Chang, “Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution,” Phys. Rev. A 57, 4407–4412 (1998).
[CrossRef]

Chen, Y. Q.

Z. A. Liu, Y. Y. Liu, F. Y. Li, J. R. Li, B. Z. Gong, and Y. Q. Chen, “Measurement of pressure broadening coefficients of NO by intracavity laser magnetic resonance with a CO laser,” Chem. Phys. Lett. 183, 340–344 (1991).
[CrossRef]

Y. Q. Chen, Y. Y. Liu, F. Y. Li, J. R. Li, and K. L. He, “Determination of pressure broadening coefficients of NO2 by laser magnetic resonance,” Chin. Phys. Lett. 5, 277–280 (1988).
[CrossRef]

Chiarella, C.

C. Chiarella and A. Reichel, “On the evaluation of Voigt spectral line functions,” Mon. Not. R. Astron. Soc. 134, 83–86 (1966).

Drayson, S. R.

S. R. Drayson, “Note: Rapid computation of the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 16, 611–614 (1976).
[CrossRef]

Fang, T. K.

T. K. Fang and T. N. Chang, “Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution,” Phys. Rev. A 57, 4407–4412 (1998).
[CrossRef]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Gautschi, W.

W. Gautschi, “Algorithm 363, complex error function [S15],” Commun. ACM 12, 635 (1969).
[CrossRef]

Gong, B. Z.

Z. A. Liu, Y. Y. Liu, F. Y. Li, J. R. Li, B. Z. Gong, and Y. Q. Chen, “Measurement of pressure broadening coefficients of NO by intracavity laser magnetic resonance with a CO laser,” Chem. Phys. Lett. 183, 340–344 (1991).
[CrossRef]

Guo, Y. Q.

Y. Y. Liu, J. L. Lin, and Y. Q. Guo, “Measurement of the pressure self-broadening coefficient of NO by saturation spectroscopy of LMR,” Can. J. Phys. 78, 985–995 (2000).
[CrossRef]

He, K. L.

Y. Q. Chen, Y. Y. Liu, F. Y. Li, J. R. Li, and K. L. He, “Determination of pressure broadening coefficients of NO2 by laser magnetic resonance,” Chin. Phys. Lett. 5, 277–280 (1988).
[CrossRef]

Hui, A. K.

A. K. Hui, B. H. Armstrong, and A. A. Wray, “Rapid computation of the Voigt and complex error functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509–516 (1978).
[CrossRef]

Humlicek, J.

J. Humlicek, “Optimized computation of the Voigt and complex probability functions,” J. Quant. Spectrosc. Radiat. Transfer 27, 437–444 (1982).
[CrossRef]

J. Humlicek, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Transfer 21, 309–313 (1979).
[CrossRef]

Hummer, D. G.

D. G. Hummer, “The Voigt function—an eight-significant-figure table and generating procedure,” Mem. R. Astron. Soc. 70, 1–32 (1965).

Karp, A. H.

A. H. Karp, “Efficient computation of spectral line shapes,” J. Quant. Spectrosc. Radiat. Transfer 20, 379–384 (1978).
[CrossRef]

Kavanagh, R. W.

Kielkopf, J. F.

Klim, A.

A. Klim, “A comparison of methods for the calculation of Voigt profiles,” J. Quant. Spectrosc. Radiat. Transfer 26, 537–545 (1981).
[CrossRef]

Li, F. Y.

Z. A. Liu, Y. Y. Liu, F. Y. Li, J. R. Li, B. Z. Gong, and Y. Q. Chen, “Measurement of pressure broadening coefficients of NO by intracavity laser magnetic resonance with a CO laser,” Chem. Phys. Lett. 183, 340–344 (1991).
[CrossRef]

Y. Q. Chen, Y. Y. Liu, F. Y. Li, J. R. Li, and K. L. He, “Determination of pressure broadening coefficients of NO2 by laser magnetic resonance,” Chin. Phys. Lett. 5, 277–280 (1988).
[CrossRef]

Li, J. R.

Z. A. Liu, Y. Y. Liu, F. Y. Li, J. R. Li, B. Z. Gong, and Y. Q. Chen, “Measurement of pressure broadening coefficients of NO by intracavity laser magnetic resonance with a CO laser,” Chem. Phys. Lett. 183, 340–344 (1991).
[CrossRef]

Y. Q. Chen, Y. Y. Liu, F. Y. Li, J. R. Li, and K. L. He, “Determination of pressure broadening coefficients of NO2 by laser magnetic resonance,” Chin. Phys. Lett. 5, 277–280 (1988).
[CrossRef]

Lin, J. L.

Y. Y. Liu, J. L. Lin, and Y. Q. Guo, “Measurement of the pressure self-broadening coefficient of NO by saturation spectroscopy of LMR,” Can. J. Phys. 78, 985–995 (2000).
[CrossRef]

Liu, Y. Y.

Y. Y. Liu, J. L. Lin, and Y. Q. Guo, “Measurement of the pressure self-broadening coefficient of NO by saturation spectroscopy of LMR,” Can. J. Phys. 78, 985–995 (2000).
[CrossRef]

Z. A. Liu, Y. Y. Liu, F. Y. Li, J. R. Li, B. Z. Gong, and Y. Q. Chen, “Measurement of pressure broadening coefficients of NO by intracavity laser magnetic resonance with a CO laser,” Chem. Phys. Lett. 183, 340–344 (1991).
[CrossRef]

Y. Q. Chen, Y. Y. Liu, F. Y. Li, J. R. Li, and K. L. He, “Determination of pressure broadening coefficients of NO2 by laser magnetic resonance,” Chin. Phys. Lett. 5, 277–280 (1988).
[CrossRef]

Liu, Z. A.

Z. A. Liu, Y. Y. Liu, F. Y. Li, J. R. Li, B. Z. Gong, and Y. Q. Chen, “Measurement of pressure broadening coefficients of NO by intracavity laser magnetic resonance with a CO laser,” Chem. Phys. Lett. 183, 340–344 (1991).
[CrossRef]

Longbothum, R. L.

J. J. Olivero and R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Mankin, W. G.

Matta, F.

F. Matta and A. Reichel, “Uniform computation of the error function and other related functions,” Math. Comput. 25, 339–344 (1971).
[CrossRef]

Olivero, J. J.

J. J. Olivero and R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Penner, S. S.

Pierluissi, J. H.

J. H. Pierluissi and P. C. Vanderwood, “Note: Fast calculation algorithm for the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 18, 555–558 (1977).
[CrossRef]

Posener, D. W.

D. W. Posener, “The shape of spectral lines: tables of the Voigt profile a/π ∫ e−y2dy/a2 + (x−y)2,” Aust. J. Phys. 12, 184–196 (1959).
[CrossRef]

Rarig, P. L.

J. T. Twitty, P. L. Rarig, and R. E. Thompson, “Note: A comparison of fast codes for the evaluation of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transfer 24, 529–532 (1980).
[CrossRef]

Reichel, A.

F. Matta and A. Reichel, “Uniform computation of the error function and other related functions,” Math. Comput. 25, 339–344 (1971).
[CrossRef]

C. Chiarella and A. Reichel, “On the evaluation of Voigt spectral line functions,” Mon. Not. R. Astron. Soc. 134, 83–86 (1966).

Schreier, F.

F. Schreier, “The Voigt and complex error functions: a comparison of computational methods,” J. Quant. Spectrosc. Radiat. Transfer 48, 743–762 (1992).
[CrossRef]

Thompson, R. E.

J. T. Twitty, P. L. Rarig, and R. E. Thompson, “Note: A comparison of fast codes for the evaluation of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transfer 24, 529–532 (1980).
[CrossRef]

Twitty, J. T.

J. T. Twitty, P. L. Rarig, and R. E. Thompson, “Note: A comparison of fast codes for the evaluation of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transfer 24, 529–532 (1980).
[CrossRef]

Vanderwood, P. C.

J. H. Pierluissi and P. C. Vanderwood, “Note: Fast calculation algorithm for the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 18, 555–558 (1977).
[CrossRef]

Whiting, E. E.

E. E. Whiting, “An empirical approximation to the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379–1384 (1968).
[CrossRef]

Wray, A. A.

A. K. Hui, B. H. Armstrong, and A. A. Wray, “Rapid computation of the Voigt and complex error functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509–516 (1978).
[CrossRef]

Young, C.

C. Young, “Note: Calculation of the absorption coefficient for lines with combined Doppler and Lorentz broadening,” J. Quant. Spectrosc. Radiat. Transfer 5, 549–552 (1965).
[CrossRef]

Appl. Opt. (1)

Aust. J. Phys. (1)

D. W. Posener, “The shape of spectral lines: tables of the Voigt profile a/π ∫ e−y2dy/a2 + (x−y)2,” Aust. J. Phys. 12, 184–196 (1959).
[CrossRef]

Can. J. Phys. (1)

Y. Y. Liu, J. L. Lin, and Y. Q. Guo, “Measurement of the pressure self-broadening coefficient of NO by saturation spectroscopy of LMR,” Can. J. Phys. 78, 985–995 (2000).
[CrossRef]

Chem. Phys. Lett. (1)

Z. A. Liu, Y. Y. Liu, F. Y. Li, J. R. Li, B. Z. Gong, and Y. Q. Chen, “Measurement of pressure broadening coefficients of NO by intracavity laser magnetic resonance with a CO laser,” Chem. Phys. Lett. 183, 340–344 (1991).
[CrossRef]

Chin. Phys. Lett. (1)

Y. Q. Chen, Y. Y. Liu, F. Y. Li, J. R. Li, and K. L. He, “Determination of pressure broadening coefficients of NO2 by laser magnetic resonance,” Chin. Phys. Lett. 5, 277–280 (1988).
[CrossRef]

Commun. ACM (1)

W. Gautschi, “Algorithm 363, complex error function [S15],” Commun. ACM 12, 635 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Quant. Spectrosc. Radiat. Transfer (13)

J. J. Olivero and R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

F. Schreier, “The Voigt and complex error functions: a comparison of computational methods,” J. Quant. Spectrosc. Radiat. Transfer 48, 743–762 (1992).
[CrossRef]

A. Klim, “A comparison of methods for the calculation of Voigt profiles,” J. Quant. Spectrosc. Radiat. Transfer 26, 537–545 (1981).
[CrossRef]

S. R. Drayson, “Note: Rapid computation of the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 16, 611–614 (1976).
[CrossRef]

A. K. Hui, B. H. Armstrong, and A. A. Wray, “Rapid computation of the Voigt and complex error functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509–516 (1978).
[CrossRef]

J. H. Pierluissi and P. C. Vanderwood, “Note: Fast calculation algorithm for the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 18, 555–558 (1977).
[CrossRef]

J. Humlicek, “An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives,” J. Quant. Spectrosc. Radiat. Transfer 21, 309–313 (1979).
[CrossRef]

J. Humlicek, “Optimized computation of the Voigt and complex probability functions,” J. Quant. Spectrosc. Radiat. Transfer 27, 437–444 (1982).
[CrossRef]

A. H. Karp, “Efficient computation of spectral line shapes,” J. Quant. Spectrosc. Radiat. Transfer 20, 379–384 (1978).
[CrossRef]

J. T. Twitty, P. L. Rarig, and R. E. Thompson, “Note: A comparison of fast codes for the evaluation of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transfer 24, 529–532 (1980).
[CrossRef]

E. E. Whiting, “An empirical approximation to the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 8, 1379–1384 (1968).
[CrossRef]

C. Young, “Note: Calculation of the absorption coefficient for lines with combined Doppler and Lorentz broadening,” J. Quant. Spectrosc. Radiat. Transfer 5, 549–552 (1965).
[CrossRef]

B. H. Armstrong, “Spectrum line profiles: the Voigt function,” J. Quant. Spectrosc. Radiat. Transfer 7, 61–88 (1967).
[CrossRef]

Math. Comput. (1)

F. Matta and A. Reichel, “Uniform computation of the error function and other related functions,” Math. Comput. 25, 339–344 (1971).
[CrossRef]

Mem. R. Astron. Soc. (1)

D. G. Hummer, “The Voigt function—an eight-significant-figure table and generating procedure,” Mem. R. Astron. Soc. 70, 1–32 (1965).

Mon. Not. R. Astron. Soc. (1)

C. Chiarella and A. Reichel, “On the evaluation of Voigt spectral line functions,” Mon. Not. R. Astron. Soc. 134, 83–86 (1966).

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Phys. Rev. A (1)

T. K. Fang and T. N. Chang, “Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution,” Phys. Rev. A 57, 4407–4412 (1998).
[CrossRef]

Other (3)

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), p. 297.

V. N. Faddeyeva and N. M. Terentev, Tables of Values of the Function w(z) for Complex Argument (Pergamon, Oxford, 1961).

C.-H. Xu, Introduction to Computational Methods (Higher Education Press, Beijing, China, 1995), pp. 88–105.

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Figures (5)

Fig. 1
Fig. 1

Comparison of three line profiles with the normalized intensity and the same width.

Fig. 2
Fig. 2

Weight coefficients cL and cG versus d.

Fig. 3
Fig. 3

Width errors of the combination approach to the actual Voigt profile.

Fig. 4
Fig. 4

Relative errors of area and peak intensity of the combination approach compared with area and peak intensity of the Voigt profile.

Fig. 5
Fig. 5

Comparison of relative width errors of various approaches.

Tables (3)

Tables Icon

Table 1 Maximum and Minimum Relative Errors of Width, Area, and Peak of the Sum Approach

Tables Icon

Table 2 Maximum Relative Errors of Width of Various Approximation Methods with Respect to the Actual Voigt Profile

Tables Icon

Table 3 Number of the Convergence Termsa for Area Computation at Some Values of and δ νD for Methods That Converge Slowlyb

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

fν(ν-ν0, δνL, δνD)
=fLfG=ln 2aπ3/2 -+ [-ln(2)(ν-ν0)2/δνD2](ν-ν)2+δνL2 dν,
fV(x, y)=ln 2πδνD Re[w(z)],
fVx=-2ln 2πδνD Re[zw(z)].
fV=[(1-η)G(x/ln 2)+ηL(x/ln 2)] aπδνLF(a),
η=11+g/a(g=δνD/δνV),
fV(ν-ν0, δνL, δνD)
=fV(ν-ν0, δνV)=cLfL(ν-ν0, δνV)
+cGfG(ν-ν0, δνV)
=cL 1π δνV(ν-ν0)2+δνV2
+cG ln 2πδνV exp-ln(2)(ν-ν0)2δνV2.
cL=f1(d),cG=f2(d),
cL=0.68188(17)+0.61293(31)*d-0.18384(39)*d2-0.11568(44)*d3,
cG=0.32460(17)-0.61825(31)*d+0.17681(39)*d2+0.12109(44)*d3.

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