title: Generalized groove density equation concerning bending-grating-related imaging properties.
abstract: Varied-line-spacing gratings are used in soft-x-ray monochromators and spectrometers because of their ability to correct various aberrations by varying the groove density. A curved grating blank in a Rowland circle mounting could eliminate primary aberrations. Bending a plane constant-groove-density grating into a desirable surface can eliminate higher-order aberrations as a result of the change in surface profile and groove density. This provides a simple means for improving the imaging properties. When used in a monochromator, the grating can be bent to different degrees to minimize aberrations at all wavelengths. General formulas concerning the transformations of groove function, groove density, and groove spacing are presented for the bending grating. Analytic results with a numerical example show the significant properties of the system.
authors.affiliation: National Synchroton Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui. figo_abin@163.com
authors.forename: Bin
authors.initials: B
authors.lastname: Liu
authors.forename: Qiuping
authors.initials: Q
authors.lastname: Wang
authors.forename: Shaojun
authors.initials: S
authors.lastname: Fu
authors.forename: Zhongwen
authors.initials: Z
authors.lastname: Hu