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The finite difference methods of computation of X-rays propagation through a system of many lenses

Abstract

The propagation of X-ray waves through an optical system consisting of many beryllium X-ray refrac- tive lenses is considered. In order to calculate the propagation of electromagnetic in the optical sys- tem, two differential equations are considered. First equation for an electric field of a monochromatic wave and the second equation derived for complex phase of the same electric The propagation of X-ray waves through an optical system consisting of many beryllium X-ray refrac- tive lenses is considered. In order to calculate the propagation of electromagnetic in the optical sys- tem, two differential equations are considered. First equation for an electric field of a monochromatic wave and the second equation derived for complex phase of the same electric field. For solving the prob- lems, finite-difference methods are suggested and in- vestigated. It is shown that very small steps of the difference grid are necessary for reliable computa- tion of propagation of X-ray waves through the sys- tem of lenses, when the first equation is used. The reason of such a result is that the electric field of the wave after passing through many lenses is a quickly oscillating function of coordinates. It is shown that much larger steps may be utilized if the second equa- tion is used, because the phase of electric field after passing through many lenses is quickly increasing, but not oscillating function. We suggest and recom- mend using the equation for a phase function instead of the equation for an electric field. The error of simulation obtained for both equations is estimated mathematically and investigated.field. For solving the prob- lems, finite-difference methods are suggested and in- vestigated. It is shown that very small steps of the difference grid are necessary for reliable computa- tion of propagation of X-ray waves through the sys- tem of lenses, when the first equation is used. The reason of such a result is that the electric field of the wave after passing through many lenses is a quickly oscillating function of coordinates. It is shown that much larger steps may be utilized if the second equa- tion is used, because the phase of electric field after passing through many lenses is quickly increasing, but not oscillating function. We suggest and recom- mend using the equation for a phase function instead of the equation for an electric field. The error of simulation obtained for both equations is estimated mathematically and investigated.

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Category:
Conference activity
Type:
materiały konferencyjne indeksowane w Web of Science
Title of issue:
Proceedings of the international conference on Days on Diffraction (DD 2016) strony 440 - 444
Language:
English
Publication year:
2016
Bibliographic description:
Wojda P., Kshevetskii S..: The finite difference methods of computation of X-rays propagation through a system of many lenses, W: Proceedings of the international conference on Days on Diffraction (DD 2016), 2016, IEEE,.
DOI:
Digital Object Identifier (open in new tab) 10.1109/dd.2016.7756890
Verified by:
Gdańsk University of Technology

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