Based on polynomial approximation, method of reconstruction of soft X-ray and extreme ultraviolet radiation spectrum from a diffraction pattern obtained using a transmission diffraction grating

Abstract

A transmission diffraction grating is a useful tool for studying spectra in the soft X-ray and extreme ultraviolet range, created by the radiation of small–sized sources, such as laser produced plasma, vacuum spark, Z-pinch, X-pinch, etc. In almost all such experiments, a distance between the source and the grating is much larger than the size of the source, so the incident wave can be considered plane with sufficient accuracy, the distance from the recording detector to the grating is also much larger than the size of the grating and, therefore, Fraunhofer diffraction takes place here and the presence of a focusing element is not required.The interpretation of the results obtained using such a grating is difficult due to the fact that different diffraction orders overlap in the registered diffraction pattern. Therefore, there is a problem of reconstruction the true spectrum from an experimental diffraction pattern. In this paper, this problem is solved by approximating the function of the radiation intensity recorded on the diffraction pattern by a polynomial. In this case, due to the properties of the transmission diffraction grating, the desired function describing the spectrum being reconstructed is also a polynomial, which can be calculated according to the developed algorithm. Both the direct conversion of the spectrum into the diffraction pattern and the reverse conversion of the diffraction pattern into the spectrum do not change the radius of convergence, since multiplication is carried out by multipliers uniformly bounded from above and below. It follows from this that minor errors in the definition of the function describing the diffraction pattern cannot lead to significant errors in the reconstructed spectrum.