A mathematical apparatus for solving problems of X-ray wave propagation through complex optical systems, when the lens thickness can change with jumps, is developed and presented. The developed method is based on the use of the superposition of oriented Gaussian beams, which satisfy the Helmholtz equation with high accuracy. The wave propagation in air and through kinoform and ordinary lenses is considered. Focusing and imaging properties are compared for both types of X-ray optics. The diffraction effects arising due to thickness jumps in the kinoform lenses and the influence of these jumps on the X-ray focusing and imaging are investigated. The prospect of using the developed theory for X-ray optics applications is discussed.
Keywords: Gaussian beams; Helmholtz equation; X-ray optics; X-ray wave propagation; focusing; imaging.