Published: 1 May 2012
cosine has developed a software tool for the design and targeted optimization of X-ray multilayers.
Multilayer thin film structures can be used to build effective X-ray mirrors. The process of deciding which multilayer structure (materials, number and thickness of the layers) is best suited for a certain application has traditionally be tackled by formulating a number of educated guesses that are then used to calculate the resulting reflectivity; if the latter is not deemed sufficient for the task at hand, a new guess is formulated and the reflectivity calculated again. This design process, besides requiring considerable experience in deciding which guesses are better than others, is also extremely time consuming.
In 2001 Kozhevnikov, Bukreeva, and Ziegler (http://dx.doi.org/10.1016/S0168-9002(00)01079-2) proposed a new approach to the optimization of wide-band multilayers for X-ray optics. Their approach, based on a combination of theoretical and numerical methods, allows one to calculate the multilayer structure required for a given target reflectivity, energy and incidence angle range. The method is computationally significantly faster, it allows the user to concentrate on the solution of the problem by reducing the number of possible input parameters.
cosine has developed a software tool that applies the method by Kozhevnikov and colleagues. With this tool one can design depth graded multilayer mirrors for X-ray applications with any required reflectivity profile. The user can select a required reflectivity over a certain energy or angular range, and the tool will, by the use of an iterative algorithm, calculate a depth graded multilayer that fulfils the required reflectivity. Other tools to calculate the reflectivity of a depth graded multilayers exist, but none are able to design a multilayer to match a specific reflectivity.
The tool works as follows: The user selects either an energy or an angular range, and the required reflectivity over this range. The user additionally indicates the materials of the multilayer and the material ratios. In a first iteration, requiring only a few seconds, the tool calculates the matching depth graded multilayer. Due to the fact that the full phase profile is not known at the start of the calculation, this first design will come close, but not fully match the requested reflectivity profile. In a second, more computationally demanding step (up to a few hours), the algorithm iterativelly refines the design of the multilayer to fully match the required profile. If a complete match cannot be achieved for physical reasons, the algorithm returns the multilayer structure with the best possible reflectivity.
The advantage of this approach is clear. Many multilayer designs can be quickly investigated, and only when the right design has been found a more complex and longer calculation must be started to nail the details of the design. The tool can be accessed over the web, and the user can get immediate graphical feedback for the first quick iteration. Promising designs can be saved, and then submitted to the cosine computing cluster for detailed calculation.
The tool, developed by Mark Vervest as part of his Master degree, will shortly be made available by cosine to a wider public.
The result of an angle optimization for a Carbon-Nickel multilayer. The requirement was to have 30% reflectivity at 6keV at a grazing incidence angle around one degree.