30 January 2002 Markov chain Monte Carlo algorithms for optimizing grazing incidence optics for wide-field x-ray survey imaging
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We have been working on the design of a wide-field, short focal length, grazing incidence mirror shell set with a desired rms image spot size of 15 arcsec. The baseline design consists of Wolter I type mirror shells with polynomial perturbations applied to the baseline design. The overall optimization technique is to efficiently optimize the polynomial coefficients that directly influence the angular resolution without stepping through the entire multi-dimensional coefficient space. We have previously investigated the use of Response Surface Designs and Artificial Neural Networks as a means for optimizing the polynomial coefficients. The results have been published elsewhere. Here we have investigated Markov chain Monte Carlo (MCMC) algorithms as a method for optimizing the multi-dimensional coefficient space. Although MCMC algorithms are traditionally used to explore probability densities that result from a particular model specification, they can be used to create irreducible algorithms for optimizing arbitrary, bounded functions. In situations where very little is known, a priori, about a function and where the function may have multiple minimums, the irreducible nature of the MCMC algorithm combined with the ability to adapt MCMC algorithms offers a promising framework for optimizing this multi-dimensional complex function.
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Peter W. A. Roming, John C. Liechty, David H. Sohn, Jared R. Shoemaker, David N. Burrows, Gordon P. Garmire, "Markov chain Monte Carlo algorithms for optimizing grazing incidence optics for wide-field x-ray survey imaging", Proc. SPIE 4496, X-Ray Optics for Astronomy: Telescopes, Multilayers, Spectrometers, and Missions, (30 January 2002); doi: 10.1117/12.454361; https://doi.org/10.1117/12.454361

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