On the design of wide-field x-ray telescopes
X-ray telescopes having a relatively wide field-of-view and spatial resolution vs. polar off-axis angle curves much flatter than the parabolic dependence characteristic of Wolter I designs are of great interest for surveys of the X-ray sky and potentially for study of the Sun's X-ray emission. We discuss the various considerations affecting the design of such telescopes, including the possible use of polynomial mirror surface prescriptions, a method of optimizing the polynomial coefficients, scaling laws for mirror segment length vs. intersection radius, the loss of on-axis spatial resolution, and the positioning of focal plane detectors.
Markov chain Monte Carlo algorithms for optimizing grazing incidence optics for wide-field x-ray survey imaging
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.
Geometrical aberration of a generalized Wolter type I telescope.
Using two hyperboloids, we can control spherical aberration and coma of an imaging x-ray telescope. The coma-free condition is satisfied only at a particular radius of the first mirror. The best performance is obtained when we allow the coma-free condition at the outer edge and cancel about half of the defocused image for the largest height of an object by introducing spherical aberration.