Berreman D W
Appl Opt. 1991 May 1;30(13):1741-5. doi: 10.1364/AO.30.001741.
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.
一种数值孔径不受限的多层反射镜光学系统可实现将一个点聚焦到另一个点上。在轴对称系统中，这是通过在每个反射镜上径向改变多层布拉格间距来实现的。如果波长小于约75埃，实现最佳反射率所需的层对数会超过40。由此产生的反射带宽Δλ/λ将小于1/40，在此带宽范围内光学相位变化约180度。对于如此窄的带宽，针对轴向像点正确改变层间距会在某些区域严重降低反射率，并且对于离轴半径相当小的源点和像点，整个反射镜上的相位相干性也会受到影响。这个问题，可称为色差渐晕，并不局限于轴对称系统，对于任何多层反射光学系统都应进行研究。我们发现，对于使用中等尺寸反射镜的适度大图像，在任何一个反射镜上采用均匀的多层间距比针对一个像点进行校正更好。这将限制数值孔径和分辨率，但会在整个图像上产生均匀的分辨率和强度。对于此类系统，波长越短的X射线所需的层数增加实际上会导致波长小于约75埃时分辨率降低。
