We briefly review previous attempts to obtain useful empirical expressions for the width of the Voigt line. We present a new empirical fit, quite different in form, which is accurate to within ±0.01% for any combination of Lorentz (pressure) and doppler line widths. We also show a simple modification to the expression given by Whiting which attains an accuracy of approx. ±0.02%.

Empirical fits to the Voigt line width: A brief review

Broadening and Shift of Spectral Lines Due to the Presence of Foreign Gases

The static multislit principle is examined, and some ancillary number theoretical concepts are exposed briefly A discussion is also presented of the aberrations which limit the available field area in various spectroscopic systemsA description is given of an apparatus embodying the static multislit principle and designed to give a cathode-ray panoramic display of short segments of the infrared spectrum in the NaCl and KBr prism rangeThe rate at which information about infrared spectra can be obtained in this manner is illustrated by a photograph of the CO2 spectrum which includes both the 14μ and 15μ absorption bands, and which was obtained in 100 milliseconds

Static multislit spectrometry and its application to the panoramic display of infrared spectra.

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.

Simple empirical analytical approximation to the Voigt profile

The equivalent width for lines with the Voigt contour has been evaluated numerically to an accuracy of at least four significant figures. A table is presented from which the equivalent width can be found to an accuracy of at least 0.40 per cent by linear interpolation. The table covers the range from weak to fairly strong absorption and also the range from pure Doppler to nearly pure Lorentz lines shapes. A comparison is made between the numerical results of this work and the Lorentz and Doppler expressions for the equivalent width and other approximate analytic forms.

A table of the equivalent widths of isolated lines with combined Doppler and collision broadened profiles

Methods for the calculation of spectral absorption coefficients for combined Doppler and Lorentz broadening are summarized. The “curves of growth” have been extended to cover the ranges of parameters which arise in spectroscopic studies on flames.

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Radiation from Isolated Spectral Lines with Combined Doppler and Lorentz Broadening

/pdf/approximate-infrared-emissivity-calculations-for-hcl-at-3gsrxa0oht.pdf

Approximate Infrared Emissivity Calculations for HCl at Elevated Temperatures

/pdf/oscillator-strengths-of-the-ultraviolet-g-bands-of-no-34v2xqfrjo.pdf

Oscillator Strengths of the Ultraviolet γ Bands of NO

Radiant Heat Transfer to Receivers Moving along the Axis of a Right Circular Cylindrical Chamber

Equations have been developed for estimating the temperature rise, caused by the absorption of radiant energy, of a small volume element of cool gas or of a liquid droplet moving along the axis of a cylindrical chamber. The absorbing material was assumed to move with constant velocity and to be surrounded at all times by hot radiating gases distributed uniformly throughout the cylindrical chamber. A sample calculation has been carried out for an absorbing volume element of gas moving with a linear velocity of 1.15×104 cm/sec. through a cylindrical chamber (30 cm in length and 14 cm in diameter) filled uniformly with graybody emitters at 3000°K and 20 atmos. pressure. The mass emissivity of the radiating gases was chosen to be 40 sq. cm/g. The upper limit for the temperature rise of the moving gases, caused by the absorption of radiant energy, was found to be about 100°K for the chosen conditions.

S. S. Penner

Papers

Radiation from Isolated Spectral Lines with Combined Doppler and Lorentz Broadening

Approximate Infrared Emissivity Calculations for HCl at Elevated Temperatures

Oscillator Strengths of the Ultraviolet γ Bands of NO

Radiant Heat Transfer to Receivers Moving along the Axis of a Right Circular Cylindrical Chamber

Some Considerations of the Effect of Radiation on the Performance of Liquid Fuel Rockets