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.

© 2011 OSA

1. K. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 8732 (2010). [CrossRef]
2. D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, 2006). [CrossRef]
3. I. A. Vartanyants and A. Singer, “Coherence properties of hard x-ray synchrotron sources and x-ray free-electron lasers,” N. J. Phys. 12, 035004 (2010). [CrossRef]
4. J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synch. Radiat. 11, 476–482 (2004). [CrossRef]
5. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005). [CrossRef] [PubMed]
6. F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005). [CrossRef] [PubMed]
7. A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synch. Radiat. 17, 299–307 (2010). [CrossRef]
8. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999). [CrossRef]
9. B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008). [CrossRef]
10. G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75, 104102 (2007). [CrossRef]
11. K. Giewekemeyer, H. Neubauer, S. Kalbfleisch, S. P. Krger, and T. Salditt, “Holographic and diffractive x-ray imaging using waveguides as quasi-point sources,” N. J. Phys. 12, 035008 (2010). [CrossRef]
12. J. R. Fienup, “Reconstruction of an object from the modulus of its fourier transform,” Opt. Lett. 3, 27–29 (1978). [CrossRef] [PubMed]
13. H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys. 2, 101–104 (2006). [CrossRef]
14. S. Marchesini, “Invited article: A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007). [CrossRef] [PubMed]
15. J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801– (2007). [CrossRef] [PubMed]
16. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008). [CrossRef] [PubMed]
17. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinearoptimization approach,” Opt. Express 16, 7264–7278 (2008). [CrossRef] [PubMed]
18. A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, E. Weckert, S. Schrder, M. Burghammer, and C. G. Schroer, “Hard x-ray nanobeam characterization by coherent diffraction microscopy,” Appl. Phys. Lett. 96, 091102 (2010). [CrossRef]
19. C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy 110, 325–329 (2010). [CrossRef] [PubMed]
20. S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, and T. Salditt, “The holography endstation of beamline P10 at PETRA III,” SRI 2009, AIP Conf. Proc. 1234, 433–436 (2010). [CrossRef]
21. S. P. Krger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T. Salditt, “Sub-15 nm beam confinement by twocrossed x-ray waveguides,” Opt. Express 18, 13492–13501 (2010). [CrossRef]
22. C. Fuhse, C. Ollinger, and T. Salditt, “Waveguide-based off-axis holography with hard x rays,” Phys. Rev. Lett. 97, 254801 (2006). [CrossRef]
23. C. Fuhse and T. Salditt, “Finite-difference field calculations for two-dimensionally confined x-ray waveguides,” Appl. Opt. 45, 4603–4608 (2006). [CrossRef] [PubMed]
24. L. D. Caro, C. Giannini, S. D. Fonzo, W. Yark, A. Cedola, and S. Lagomarsino, “Spatial coherence of x-ray planar waveguide exiting radiation,” Opt. Commun. 217, 31–45 (2003). [CrossRef]
25. I. Bukreeva, A. Popov, D. Pelliccia, A. Cedola, S. B. Dabagov, and S. Lagomarsino, “Wave-field formation in a hollow x-ray waveguide,” Phys. Rev. Lett. 97, 184801 (2006).
26. Y. V. Kopylov, A. V. Popov, and A. V. Vinogradov, “Application of the parabolic wave equation to x-ray diffraction optics,” Opt. Commun. 118, 619–636 (1995). [CrossRef]
27. H. Mimura, H. Yumoto, S. Matsuyama, Y. Sano, K. Yamamura, Y. Mori, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “Efficient focusing of hard x-rays to 25 nm by a total reflection mirror,” Appl. Phys. Lett. 90, 051903 (2007). [CrossRef]
28. L. D. Caro, C. Giannini, D. Pelliccia, C. Mocuta, T. H. Metzger, A. Guagliardi, A. Cedola, I. Burkeeva, and S. Lagomarsino, “In-line holography and coherent diffractive imaging with x-ray waveguides,” Phys. Rev. B 77, 081408 (2008). [CrossRef]
29. T. Salditt, S. P. Krger, C. Fuhse, and C. Bhtz, “High-transmission planar x-ray waveguides,” Phys. Rev. Lett. 100, 184801–4 (2008). [CrossRef] [PubMed]
30. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Oxford University Press, 2007).
31. S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003). [CrossRef] [PubMed]
32. T. Weitkamp, “Imaging and tomography with high resolution using coherent hard synchrotron radiation,” Ph.D. thesis, Universitt Hamburg (2002).

Adv. Phys.

• K. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 8732 (2010). [CrossRef]

Appl. Opt.

• C. Fuhse and T. Salditt, “Finite-difference field calculations for two-dimensionally confined x-ray waveguides,” Appl. Opt. 45, 4603–4608 (2006). [CrossRef] [PubMed]

Appl. Phys. Lett.

• A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, E. Weckert, S. Schrder, M. Burghammer, and C. G. Schroer, “Hard x-ray nanobeam characterization by coherent diffraction microscopy,” Appl. Phys. Lett. 96, 091102 (2010). [CrossRef]
• H. Mimura, H. Yumoto, S. Matsuyama, Y. Sano, K. Yamamura, Y. Mori, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “Efficient focusing of hard x-rays to 25 nm by a total reflection mirror,” Appl. Phys. Lett. 90, 051903 (2007). [CrossRef]

J. Synch. Radiat.

• J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synch. Radiat. 11, 476–482 (2004). [CrossRef]
• A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synch. Radiat. 17, 299–307 (2010). [CrossRef]

N. J. Phys.

• K. Giewekemeyer, H. Neubauer, S. Kalbfleisch, S. P. Krger, and T. Salditt, “Holographic and diffractive x-ray imaging using waveguides as quasi-point sources,” N. J. Phys. 12, 035008 (2010). [CrossRef]
• I. A. Vartanyants and A. Singer, “Coherence properties of hard x-ray synchrotron sources and x-ray free-electron lasers,” N. J. Phys. 12, 035004 (2010). [CrossRef]

Nat. Phys.

• H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys. 2, 101–104 (2006). [CrossRef]
• B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008). [CrossRef]

Nature

• J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999). [CrossRef]

Opt. Commun.

• L. D. Caro, C. Giannini, S. D. Fonzo, W. Yark, A. Cedola, and S. Lagomarsino, “Spatial coherence of x-ray planar waveguide exiting radiation,” Opt. Commun. 217, 31–45 (2003). [CrossRef]
• Y. V. Kopylov, A. V. Popov, and A. V. Vinogradov, “Application of the parabolic wave equation to x-ray diffraction optics,” Opt. Commun. 118, 619–636 (1995). [CrossRef]

Opt. Express

• S. P. Krger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T. Salditt, “Sub-15 nm beam confinement by twocrossed x-ray waveguides,” Opt. Express 18, 13492–13501 (2010). [CrossRef]
• S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003). [CrossRef] [PubMed]
• T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005). [CrossRef] [PubMed]
• M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinearoptimization approach,” Opt. Express 16, 7264–7278 (2008). [CrossRef] [PubMed]

Opt. Lett.

• J. R. Fienup, “Reconstruction of an object from the modulus of its fourier transform,” Opt. Lett. 3, 27–29 (1978). [CrossRef] [PubMed]

Phys. Rev. B

• G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75, 104102 (2007). [CrossRef]
• L. D. Caro, C. Giannini, D. Pelliccia, C. Mocuta, T. H. Metzger, A. Guagliardi, A. Cedola, I. Burkeeva, and S. Lagomarsino, “In-line holography and coherent diffractive imaging with x-ray waveguides,” Phys. Rev. B 77, 081408 (2008). [CrossRef]

Phys. Rev. Lett.

• T. Salditt, S. P. Krger, C. Fuhse, and C. Bhtz, “High-transmission planar x-ray waveguides,” Phys. Rev. Lett. 100, 184801–4 (2008). [CrossRef] [PubMed]
• C. Fuhse, C. Ollinger, and T. Salditt, “Waveguide-based off-axis holography with hard x rays,” Phys. Rev. Lett. 97, 254801 (2006). [CrossRef]
• I. Bukreeva, A. Popov, D. Pelliccia, A. Cedola, S. B. Dabagov, and S. Lagomarsino, “Wave-field formation in a hollow x-ray waveguide,” Phys. Rev. Lett. 97, 184801 (2006).
• F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005). [CrossRef] [PubMed]
• J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801– (2007). [CrossRef] [PubMed]

Rev. Sci. Instrum.

• S. Marchesini, “Invited article: A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007). [CrossRef] [PubMed]

Science

• P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008). [CrossRef] [PubMed]

SRI 2009, AIP Conf. Proc.

• S. Kalbfleisch, M. Osterhoff, K. Giewekemeyer, H. Neubauer, S. P. Krger, B. Hartmann, M. Bartels, M. Sprung, O. Leupold, F. Siewert, and T. Salditt, “The holography endstation of beamline P10 at PETRA III,” SRI 2009, AIP Conf. Proc. 1234, 433–436 (2010). [CrossRef]

Ultramicroscopy

• C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy 110, 325–329 (2010). [CrossRef] [PubMed]

Other

• E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Oxford University Press, 2007).
• T. Weitkamp, “Imaging and tomography with high resolution using coherent hard synchrotron radiation,” Ph.D. thesis, Universitt Hamburg (2002).
• D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, 2006). [CrossRef]

Click here to see a list of articles that cite this paper

Related Journal Articles

• Introduction (OE)
• Phase-sensitive imaging and phase tomography using X-ray interferometers (OE)
• Coherence-contrast x-ray imaging based on x-ray interferometry (AO)
• X-ray phase imaging with a grating interferometer (OE)
• A two-directional approach for grating based differential phase contrast imaging using hard x-rays (OE)

Related Conference Papers

• Delay Lines with Tailored High Dispersion Orders for Periodic Optical Pulses
• Microscale Diffraction Measurements with a High Harmonic Soft X-ray Source
• Uniform Fiber Bragg Grating Based Tunable Dispersion Compensator and its Application to Tunable Pulse Repetition-Rate Multiplication
• Delay Lines with Tailored High Dispersion Orders for Periodic Optical Pulses
• Front and Backside Structured Gratings for X-Ray Phase Contrast Imaging