Abstract

We have studied the spatial coherence properties of a nano-focused x-ray beam by grating (Talbot) interferometry in projection geometry. The beam is focused by a fixed curvature mirror system optimized for high flux density under conditions of partial coherence. The spatial coherence of the divergent exit wave emitted from the mirror focus is measured by Talbot interferometry The results are compared to numerical calculations of coherence propagation. In view of imaging applications, the magnified in-line image of a test pattern formed under conditions of partial coherence is analyzed quantitatively. Finally, additional coherence filtering by use of x-ray waveguides is demonstrated. By insertion of x-ray waveguides, the beam diameter can be reduced from typical values of 200 nm to values below 15 nm. In proportion to the reduction in the focal spot size, the numerical aperture (NA) of the projection imaging system is increased, as well as the coherence length, as quantified by grating interferometry.

Highlights

  • The high degree of spatial coherence required by modern lensless x-ray imaging techniques calls for suitable methods to quantify wavefront distortion and spatial coherence [1,2,3]

  • We have studied the spatial coherence properties of a nano-focused x-ray beam by grating (Talbot) interferometry in projection geometry

  • The spatial coherence of the divergent exit wave emitted from the mirror focus is measured by Talbot interferometry The results are compared to numerical calculations of coherence propagation

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Summary

Introduction

The high degree of spatial coherence required by modern lensless x-ray imaging techniques calls for suitable methods to quantify wavefront distortion and spatial coherence [1,2,3]. The mutual intensity function Γ or the complex degree of coherence needs to be quantified to control the coherence of the wavefront To this end, powerful methods based on interferometry have been developed [4,5,6,7]. We extend the methods of coherence characterization by the Talbot effect to nano-focused beams with highly curved divergent wavefronts behind the focus. In its advanced variants [16, 17], ptychography is capable to reconstruct the unknown complex-valued illumination function probed by scanning along with an generally unknown object through the beam This approach has been used to characterize nanoscale wavefronts [18, 19].

Experimental setup and parameters
Intensity distribution of the KB focus
Coherence measured by Talbot effect
Holographic imaging of a double slit
Coherence filtering by a waveguide
Summary and conclusion

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