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Manuscript Title: Calculation of the energy response of a spectrometer.
Authors: J. Lotrian, M. Leriche, J. Cariou
Program title: AFER
Catalogue identifier: ACXA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 12(1976)231
Programming language: Fortran.
Computer: IBM 1130.
Operating system: V2M11.
RAM: 8K words
Word size: 16
Peripherals: disc, graph plotter.
Keywords: Plasma physics, Radiative transfer, Spectral line width, Data interpretation, Quantitative Spectroscopy, Convulsion integral.
Classification: 19.4, 21.2.

Nature of problem:
This program computes the convolution integral of an idealized spectrograph (or spectrometer) apparatus function with a Voigt line profile (lorentzian and gaussian shaped line). On this basis one could evaluate the validity to derive the total integrated intensity of an emission (or absorption) line from the peak value of the recorded signal (irradiance for a spectrograph, radiant power for a spectrometer).

Solution method:
The various functions and convolution integrals, i.e. source function (convolution of a gaussian line shape with a Lorentz line) and apparatus function (convolution of entrance slit function, grating function, exit slit function) are evaluated by FOURIER transform. These direct and inverse Fourier transforms are computed numerically using the dicrete Fourier transform with a method derived from the Cooley-Tukey algorithm.

For our physical problem, according to the computer used for each function calculated, the number of samples is limited to 512 (2**9). The final response is given with 256 (1 22**9) points. With a trivial change the program can compute with an other resolution for the total bandpass, or with other forms of the various functions.

Running time:
The test run takes about 140 s on the IBM 1130.