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.

Citations

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