Focusing of X-rays to nanometre scale focal spots requires high precision X-ray optics. For nanofocusing\nmirrors, height errors in the mirror surface retard or advance the X-ray wavefront and after\npropagation to the focal plane, this distortion of the wavefront causes blurring of the focus resulting\nin a limit on the spatial resolution. We describe here the implementation of a method for correcting\nthe wavefront that is applied before a focusing mirror using custom-designed refracting structures\nwhich locally cancel out the wavefront distortion from the mirror. We demonstrate in measurements\non a synchrotron radiation beamline a reduction in the size of the focal spot of a characterized test\nmirror by a factor of greater than 10 times. This technique could be used to correct existing synchrotron\nbeamline focusing and nanofocusing optics providing a highly stable wavefront with low distortion\nfor obtaining smaller focus sizes. This method could also correct multilayer or focusing crystal\noptics allowing larger numerical apertures to be used in order to reduce the diffraction limited focal\nspot size
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