A detailed characterization of the coherent x-ray wavefront produced by a partially illuminated Fresnel zone plate is presented. We show, by numerical and experimental approaches, how the beam size and the focal depth are strongly influenced by the illumination conditions, while the phase of the focal spot remains constant. These results confirm that the partial illumination can be used for coherent diffraction experiments. Finally, we demonstrate the possibility of reconstructing the complex-valued illumination function by simple measurement of the far field intensity in the specific case of partial illumination.

© 2011 OSA

1. K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99 (2010). [CrossRef]
2. V. L. R. Jacques, S. Ravy, D. L. Bolloc’h, E. Pinsolle, M. Sauvage-Simkin, and F. Livet, “Bulk dislocation core dissociation probed by coherent x rays in silicon,” Phys. Rev. Lett. 106, 065502 (2011). [CrossRef] [PubMed]
3. V. Chamard, J. Stangl, S. Labat, B. Mandl, R. T. Lechner, and T. H. Metzger, “Evidence of stacking-fault distribution along an InAs nanowire using micro-focused coherent x-ray diffraction,” J. Appl. Cryst. 41, 272–280 (2008). [CrossRef]
4. 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]
5. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010). [CrossRef] [PubMed]
6. S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004). [CrossRef] [PubMed]
7. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006). [CrossRef]
8. V. Favre-Nicolin, J. Eymery, R. Koester, and P. Gentile, “Coherent-diffraction imaging of single nanowires of diameter 95 nanometers,” Phys. Rev. B 79, 195401 (2009).
9. M. C. Newton, S. J. Leake, R. Harder, and I. K. Robinson, “Three-dimensional imaging of strain in a single ZnO nanorod,” Nat. Mater. 9, 120–124 (2010). [CrossRef]
10. P. Godard, D. Carbone, M. Allain, F. Mastropietro, G. Chen, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional x-ray Bragg ptychography: high-resolution imaging of extended crystalline nanostructures,” Submitted to Nat. Commun. [PubMed]
11. V. Chamard, J. Stangl, G. Carbone, A. Diaz, G. Chen, C. Alfonso, C. Mocuta, and T. H. Metzger, “Three-dimensional x-Ray Fourier transform holography: the Bragg case,” Phys. Rev. Lett. 104, 165501 (2010). [CrossRef] [PubMed]
12. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
13. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
14. S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003). [CrossRef]
15. S. Takagi, “A dynamical theory of diffraction for a distorted crystal,” J. Phys. Soc. Jpn. 26, 1239–1253 (1969). [CrossRef]
16. A. Snigirev, V. Kohn, I. Snigireva, A. Souvorov, and B. Lengeler, “Focusing high-energy x-rays by compound refractive lenses,” Appl. Opt. 37, 653–662 (1998). [CrossRef]
17. K. Yamauchi, H. M. Mimura, K. Yamamura, Y. Sano, H. Yumoto, S. Matsuyama, K. Endo, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and Y. Mori “Development of elliptical Kirkpatrick-Baez mirrors for hard x-ray nanofocusing,” Frontiers in Optics , OSA Technical Digest Series (Optical Society of America, 2005), paper FTuS4.
18. D. M. Paganin, Coherent X-ray Optics , Oxford series on synchrotron radiation (Oxford University Press, 2006), Vol. 6. [CrossRef]
19. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft x-ray microscopy at a spatial resolution better than 15nm,” Nature 435, 1210–1213 (2005). [CrossRef] [PubMed]
20. E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999). [CrossRef]
21. C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schöder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008). [CrossRef] [PubMed]
22. I. A. Vartanyants and I. K. Robinson, “Partial coherence effects on the imaging of small crystals using coherent x-ray diffraction,” J. Phys. Condens. Matter 13, 10593–10611 (2001). [CrossRef]
23. A. Diaz, C. Mocuta, J. Stangl, B. Mandl, C. David, J. Vila-Comamala, V. Chamard, T. H. Metzger, and G. Bauer, “Coherent diffraction imaging of a single epitaxial InAs nanowire using a focused x-ray beam,” Phys. Rev. B 79, 125324 (2009). [CrossRef]
24. Http://www.esrf.eu/UserAndScience/Experiments/StructMaterials/ID01 .
25. G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006). [CrossRef] [PubMed]
26. K. A. Nugent, A. G. Peele, H. M. Quiney, and H. N. Chapman, “Diffraction with wavefront curvature: a path to unique phase recovery,” Acta Cryst. A 61, 373–381 (2005). [CrossRef]
27. V. Chamard, A. Diaz, J. Stangl, and S. Labat, “Structural investigation of InAs nanowires with coherent x-rays,” J. Strain Anal. Eng. Des. 44, 533–542 (2009). [CrossRef]
28. 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]
29. 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]
30. 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]
31. 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. Synchrotron Radiat. 17, 299–307 (2010). [CrossRef] [PubMed]
32. S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard x-rays by 100keV e-beam lithography and electroplating,” J. Synchrotron Radiat. 18, 442–446 (2011). [CrossRef] [PubMed]
33. C. David, B. Nöhammer, E. Ziegler, and O. Hignette, “Tunable diffractive optical elements for hard x-rays,” Proc. SPIE 4499, 96–104 (2001). [CrossRef]
34. C. Ponchut, J. M. Rigal, J. Clément, E. Papillon, A. Homs, and S. Petitdemange, “Maxipix, a fast readout photon-counting x-ray area detector for synchrotron applications,” J. Instrum. 6, C01069 (2011). [CrossRef]
35. J. Vila-Comamala, S. Gorelick, E. Färm, C. M. Kewish, A. Diaz, R. Barrett, V. A. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Opt. Express 19, 175–184 (2011). [CrossRef] [PubMed]
36. O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, “Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels,” Acta Cryst. A 63, 306–314 (2007). [CrossRef]
37. D. L. Bolloc’h, F. Livet, F. Bley, T. Schülli, M. Veron, and T. H. Metzger, “X-ray diffraction from rectangular slits,” J. Synchrotron Radiat. 9, 258–265 (2002). [CrossRef] [PubMed]

Acta Cryst. A

• K. A. Nugent, A. G. Peele, H. M. Quiney, and H. N. Chapman, “Diffraction with wavefront curvature: a path to unique phase recovery,” Acta Cryst. A 61, 373–381 (2005). [CrossRef]
• O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, “Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels,” Acta Cryst. A 63, 306–314 (2007). [CrossRef]

Adv. Phys.

• K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99 (2010). [CrossRef]

Appl. Opt.

• J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
• A. Snigirev, V. Kohn, I. Snigireva, A. Souvorov, and B. Lengeler, “Focusing high-energy x-rays by compound refractive lenses,” Appl. Opt. 37, 653–662 (1998). [CrossRef]

J. Appl. Cryst.

• V. Chamard, J. Stangl, S. Labat, B. Mandl, R. T. Lechner, and T. H. Metzger, “Evidence of stacking-fault distribution along an InAs nanowire using micro-focused coherent x-ray diffraction,” J. Appl. Cryst. 41, 272–280 (2008). [CrossRef]

J. Instrum.

• C. Ponchut, J. M. Rigal, J. Clément, E. Papillon, A. Homs, and S. Petitdemange, “Maxipix, a fast readout photon-counting x-ray area detector for synchrotron applications,” J. Instrum. 6, C01069 (2011). [CrossRef]

J. Phys. Condens. Matter

• I. A. Vartanyants and I. K. Robinson, “Partial coherence effects on the imaging of small crystals using coherent x-ray diffraction,” J. Phys. Condens. Matter 13, 10593–10611 (2001). [CrossRef]

J. Phys. Soc. Jpn.

• S. Takagi, “A dynamical theory of diffraction for a distorted crystal,” J. Phys. Soc. Jpn. 26, 1239–1253 (1969). [CrossRef]

J. Strain Anal. Eng. Des.

• V. Chamard, A. Diaz, J. Stangl, and S. Labat, “Structural investigation of InAs nanowires with coherent x-rays,” J. Strain Anal. Eng. Des. 44, 533–542 (2009). [CrossRef]

J. Synchrotron Radiat.

• 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. Synchrotron Radiat. 17, 299–307 (2010). [CrossRef] [PubMed]
• S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard x-rays by 100keV e-beam lithography and electroplating,” J. Synchrotron Radiat. 18, 442–446 (2011). [CrossRef] [PubMed]
• D. L. Bolloc’h, F. Livet, F. Bley, T. Schülli, M. Veron, and T. H. Metzger, “X-ray diffraction from rectangular slits,” J. Synchrotron Radiat. 9, 258–265 (2002). [CrossRef] [PubMed]

Nat. Mater.

• M. C. Newton, S. J. Leake, R. Harder, and I. K. Robinson, “Three-dimensional imaging of strain in a single ZnO nanorod,” Nat. Mater. 9, 120–124 (2010). [CrossRef]

Nat. Phys.

• F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006). [CrossRef]
• 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]

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]
• M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010). [CrossRef] [PubMed]
• S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature 432, 885–888 (2004). [CrossRef] [PubMed]
• W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft x-ray microscopy at a spatial resolution better than 15nm,” Nature 435, 1210–1213 (2005). [CrossRef] [PubMed]
• E. D. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999). [CrossRef]

Opt. Express

• J. Vila-Comamala, S. Gorelick, E. Färm, C. M. Kewish, A. Diaz, R. Barrett, V. A. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Opt. Express 19, 175–184 (2011). [CrossRef] [PubMed]

Optik

• R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Phys. Rev. B

• S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003). [CrossRef]
• V. Favre-Nicolin, J. Eymery, R. Koester, and P. Gentile, “Coherent-diffraction imaging of single nanowires of diameter 95 nanometers,” Phys. Rev. B 79, 195401 (2009).
• A. Diaz, C. Mocuta, J. Stangl, B. Mandl, C. David, J. Vila-Comamala, V. Chamard, T. H. Metzger, and G. Bauer, “Coherent diffraction imaging of a single epitaxial InAs nanowire using a focused x-ray beam,” Phys. Rev. B 79, 125324 (2009). [CrossRef]

Phys. Rev. Lett.

• C. G. Schroer, P. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schöder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008). [CrossRef] [PubMed]
• G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006). [CrossRef] [PubMed]
• V. L. R. Jacques, S. Ravy, D. L. Bolloc’h, E. Pinsolle, M. Sauvage-Simkin, and F. Livet, “Bulk dislocation core dissociation probed by coherent x rays in silicon,” Phys. Rev. Lett. 106, 065502 (2011). [CrossRef] [PubMed]
• V. Chamard, J. Stangl, G. Carbone, A. Diaz, G. Chen, C. Alfonso, C. Mocuta, and T. H. Metzger, “Three-dimensional x-Ray Fourier transform holography: the Bragg case,” Phys. Rev. Lett. 104, 165501 (2010). [CrossRef] [PubMed]

Proc. SPIE

• C. David, B. Nöhammer, E. Ziegler, and O. Hignette, “Tunable diffractive optical elements for hard x-rays,” Proc. SPIE 4499, 96–104 (2001). [CrossRef]

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]

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

• Http://www.esrf.eu/UserAndScience/Experiments/StructMaterials/ID01 .
• P. Godard, D. Carbone, M. Allain, F. Mastropietro, G. Chen, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional x-ray Bragg ptychography: high-resolution imaging of extended crystalline nanostructures,” Submitted to Nat. Commun. [PubMed]
• K. Yamauchi, H. M. Mimura, K. Yamamura, Y. Sano, H. Yumoto, S. Matsuyama, K. Endo, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and Y. Mori “Development of elliptical Kirkpatrick-Baez mirrors for hard x-ray nanofocusing,” Frontiers in Optics , OSA Technical Digest Series (Optical Society of America, 2005), paper FTuS4.
• D. M. Paganin, Coherent X-ray Optics , Oxford series on synchrotron radiation (Oxford University Press, 2006), Vol. 6. [CrossRef]

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

Related Journal Articles

• Lobster-Eye X-Ray Optics: A Rapid Evaluation of the Image Distribution (AO)
• Pinhole-Array X-Ray Spectrometer for Laser-Fusion Experiments (AO)
• Adaptive Image Interpolation for Full-Field Digital X-ray Mammography (AO)
• Fast Imaging of Hard X Rays with a Laboratory Microscope (AO)
• Development of thermally formed glass optics for astronomical hard X-ray telescopes (OE)

Related Conference Papers

• Microscale Diffraction Measurements with a High Harmonic Soft X-ray Source
• Microscale Diffraction Measurements with a High Harmonic Soft X-ray Source
• Focusing coherent XUV light to micron spot size with an intensity of 1014 W/cm2
• High-resolution EUV imaging using high harmonic generation
• Focusing coherent XUV light to micron spot size with an intensity of 1014 W/cm2