HEAD 2000, November 2000
Session 16. Workshops
Display, Tuesday, November 7, 2000, 8:00am-6:00pm, Bora Bora Ballroom

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[16.08] Markov Chain Monte Carlo Algorithms for Optimizing Grazing Incidence Optics for Wide-Field X-Ray Survey Imaging

P.W.A. Roming, J.C. Liechty, G. Kinney, D.H. Sohn, D.N. Burrows, G.P. Garmire (Penn State University)

Discussions of optimizing wide-field x-ray optics, with field-of-views less-than 1.1 degree-squared, have been made previously in the literature. However, very little has been published about the optimization of wide-field x-ray optics with larger field-of-views, which technology could greatly enhance x-ray surveys. We have been working on the design of a wide-field (3.1 degree-squared field-of-view), short focal length (190.5 cm), 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 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 which 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. We report our findings to date.

This work has been funded by NASA grant NAG5-5093

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