RAPID AND ACCURATE CALCULATION OF A SPEED DEPENDENT SPECTRAL LINE SHAPE

Use of the Voigt profile with the Lorentz width allowed to vary with the speed of collision has been hampered by the lack of fast accurate algorithms. Such an algorithm has been written assuming a quadratic dependence of the Lorentz width upon the speed of collision that is accurate to one part in 10 000 and is generally only a factor of four or so slower than the equivalent Voigt calculation with the Letchworth and Benner algorithm.a The only exception to the accuracy is far from line center near the Doppler limit when the speed dependent parameter is quite large. At this point the spectral line has fallen by at least 17 orders of magnitude from the line center and is generally insignificant. Gauss-Hermite quadrature of third to seventeenth order, Taylor series expansion about precomputed points and spline interpolation are used in the computation of both the real and imaginary parts for various regions.b