Multilayer reflecting x-ray optical systems: chromatic vignetting by narrow reflection bands

A multilayer mirror reflecting optical system of unlimited numerical aperture can be made to focus one point onto another. On an axially symmetric system this is done by radially varying the multilayer Bragg spacing on each mirror. If the wavelength is less than approximately 75 A, the number of layer pairs required for optimal reflectance rises above 40. The resulting reflection bandwidth Deltalambda/lambda will be <1/40, over which the optical phase changes by approximately 180 degrees . With such a narrow band, correct variation of layer spacing for an axial image point would seriously reduce the reflectance in some regions, and the phase coherence across the mirror, for source and image points within a rather small radius off-axis. This problem, which might be called chromatic vignetting, is not restricted to axially symmetric systems and should be investigated for any multilayer reflecting optical system. We find that for moderately large images with mirrors of moderate size it is better to use uniform multilayer spacing across any one mirror than to correct for one image point. This will limit the numerical aperture and resolution but will result in uniform resolution and intensity over the entire image. The increasing number of layers required for x-rays of shorter wavelengths actually results in a decrease in resolution with wavelengths shorter than approximately 75 A for such systems.