Theory and practice of elliptically bent x-ray mirrors

We report the results of our research and development in techniques for producing elliptical x-ray mirrors by controlled bending of a flat substrate. We review the theory and technique of mirror bending with emphasis on the optical engineering issues and describe our design concepts for both metal and ceramic mirrors. We provide analysis of the various classes of error that must be addressed to obtain a high quality elliptical surface and a correspondingly fine focus of the x-ray beam. We describe particular mirrors that have been built, using these techniques, to meet the requirements of the scientific program at the Advanced Light Source at Lawrence Berkeley National Laboratory. For these examples, we show optical metrology results indicating the achievement of surface accuracy values around and, in some cases, below 1 mu rad as well as x-ray measurements showing submicrometer focal spots. (C) 2000 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(00)01410-0].