Fourth-order optical aberrations and phase-space transformation for reflection and diffraction optics.
One can derive fourth-order optical ray deviations for a mirror or grating from the optical path function by using the analytical code REDUCE. Some of the aberrations are discussed for normal-incidence and grazing-incidence monochromators. The nonlinear transformation of light from the source to the image plane of a mirror or grating is represented by a transformation matrix. The optical properties of a combination of several optical elements are given by the product of the matrices of the individual optical elements. The matrix elements can be interpreted as optical aberrations. A program has been written that optimizes a complete beam line with respect to various optical aberrations by minimizing an appropriate cost function that is built from a weighted sum of the matrix elements.
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