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Voigt Profiles of Spectral Lines: Accuracy of Line Parameters as a Function of Peak Transmittance

Volume 35, Number 4 (Aug. 1981) Page 443-444

Wilczek, Elizabeth; Belbruno, Joseph J.; Gelfand, Jack

There exists an optimum line depth for the determination of spectral line parameters. Below this value, the signal becomes comparable to the noise in the continuum. Conversely, in deep lines saturation magnifies, in the extracted parameters, the effect of a given fractional noise in the transmittance spectrum. A previous study has reported an analytical expression for the error in the absorption coefficient as a function of the value of the transmittance at that particular point. This analysis, based upon the derivative of the expression for transmittance as a function of the absorption coefficient, indicated an optimum range of 20 to 50% transmission. Computer fitting techniques make it possible to least squares fit an absorption line to the expected line profile. This procedure enables one to make use of the information contained in all of the data points to ascertain spectral parameters such as linewidth, line strength, and center frequency. We report accuracy estimates as a function of the transmittance at the center frequency for all three line parameters. Curve fitting was via a least squares routine previously reported.