Determination of x-ray spectra including characteristic line intensities from attenuation data

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Abstract
The Laplace pair transform method for the determination of x-ray spectral shapes has been modified by adding characteristic lines, assuming that the energy of each line is known. Their intensities are parameters to be determined by this extended method. A numerical simulation procedure was used to obtain attenuation data and from this all relevant parameters were determined: four parameters were allocated to the continuum plus one for each line considered. Measured x-ray spectral distributions taken from the literature were used both to generate attenuation data and also to verify the spectrum reconstruction procedure. Percentage differences from both sets of data are less than 8% and they were used to check the goodness of fit of the reconstructed spectra.