Ray-tracing analysis in aberration of a laterally- graded multilayer mirror

A laterally- graded multilayer mirror, which has a multilayer film on a curved surface substrate, is one of the candidates of focusing elements producing an ultimate hard-X-ray beam. Aberration, which multilayer mirrors natively have, should be seriously considered when we challenge several nanometer-size X-ray beams. X-rays, inserting a multilayer structure, are reflected at a relatively large angle by the effect of interferences among X-rays slightly reflected on each boundary. However, if focal points of X-rays reflected at bottom boundary and uppermost surfaces might be different, the X-rays are not allowed to be focused at the same point. This is due to refractions inside the multilayer film. Now, there is no rigorous numerical method to determine clearly the behavior of such reflection of X-rays. In this study, we code a ray-tracing simulator to analyze such aberration effect and carry out several simulations. The results conclude that aberration of an ideal laterally- graded multilayer mirror has insignificant effects on the focused beam size.