title: Simplification of vector ray tracing by the groove function.
abstract: Tracing rays through arbitrary diffraction gratings (including holographic gratings of the second generation fabricated on a curved substrate) by the vector form is somewhat complicated. Vector ray tracing utilizes the local groove density, the calculation of which highly depends on how the grooves are generated. Characterizing a grating by its groove function, available for almost arbitrary gratings, is much simpler than doing so by its groove density, essentially being a vector. Applying the concept of Riemann geometry, we give an expression of the groove density by the groove function. The groove function description of a grating can thus be incorporated into vector ray tracing, which is beneficial especially at the design stage. A unified explicit grating ray-tracing formalism is given as well.
authors.affiliation: National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230029, China. ancijade@yahoo.com
authors.forename: Zhongwen
authors.initials: Z
authors.lastname: Hu
authors.forename: Zuping
authors.initials: Z
authors.lastname: Liu
authors.forename: Qiuping
authors.initials: Q
authors.lastname: Wang