Theory and practice of elliptically bent x-ray mirrors

We report the results of our research and development in techniques for pro ducing elliptical x-ray mirrors by controlled bending of a flat substrate. We review the theory and technique of mirror bending with emphasis on the o ptical engineering issues and describe our design concepts for both metal a nd ceramic mirrors. We provide analysis of the various classes of error tha t must be addressed to obtain a high quality elliptical surface and a corre spondingly fine focus of the x-ray beam. We describe particular mirrors tha t have been built, using these techniques, to meet the requirements of the scientific program at the Advanced Light Source at Lawrence Berkeley Nation al Laboratory. For these examples, we show optical metrology results indica ting the achievement of surface accuracy values around and, in some cases, below 1 mu rad as well as x-ray measurements showing submicrometer focal sp ots. (C) 2000 Society of Photo-Optical Instrumentation Engineers. [S0091-32 86(00)01410-0].