OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 6, Iss. 9 — Oct. 3, 2011
« Show journal navigation

Full optical characterization of coherent x-ray nanobeams by ptychographic imaging

Susanne Hönig, Robert Hoppe, Jens Patommel, Andreas Schropp, Sandra Stephan, Sebastian Schöder, Manfred Burghammer, and Christian G. Schroer  »View Author Affiliations


Optics Express, Vol. 19, Issue 17, pp. 16324-16329 (2011)
http://dx.doi.org/10.1364/OE.19.016324


View Full Text Article

Acrobat PDF (1144 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Scanning coherent diffraction microscopy (ptychography) is an emerging hard x-ray microscopy technique that yields spatial resolutions well below the lateral size of the probing nanobeam. Besides a high resolution image of the object, the complex wave field of the probe can be reconstructed at the position of the object. By verifying the consistency of several independent wave field measurements along the optical axis, we address the question of how well the reconstruction represents the nanobeam. With a single ptychogram the wave field can be properly determined over a large range along the optical axis, also at positions inaccessible otherwise.

© 2011 OSA

1. Introduction

Hard x-ray scanning microscopy is used in a variety of scientific fields such as physics and chemistry, as well as biomedical, earth, environmental, materials, and nanoscience [1

1. C. Quitmann, C. David, F. Nolting, F. Pfeiffer, and M. Stampanoni, Proceedings of the 9th International Conference on X-ray Microscopy, Journal of Physics: Conference Series (IOP, Bristol, 2009), vol. 186.

]. Due to their large penetration depth x rays are ideally suited for non-destructive microscopy of the bulk of an object [2

2. A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011). [CrossRef]

, 3

3. 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, 436–440 (2010). [CrossRef] [PubMed]

] or to image in-situ a specimen inside a special sample environment [4

4. J.-D. Grunwaldt and C. G. Schroer, “Hard and soft x-ray microscopy and tomography in catalysis: Bridging the different time and length scales,” Chem. Soc. Rev. 39, 4741 (2010). [CrossRef] [PubMed]

]. Different x-ray analytical techniques, such as x-ray diffraction, x-ray fluorescence analysis, and x-ray absorption spectroscopy, yield structural, elemental, and chemical contrast, respectively [5

5. P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008). [CrossRef] [PubMed]

8

8. C. G. Schroer, M. Kuhlmann, T. F. Günzler, B. Lengeler, M. Richwin, B. Griesebock, D. Lützenkirchen-Hecht, R. Frahm, E. Ziegler, A. Mashayekhi, D. Haeffner, J.-D. Grunwaldt, and A. Baiker, “Mapping the chemical states of an element inside a sample using tomographic x-ray absorption spectroscopy,” Appl. Phys. Lett. 82, 3360–3362 (2003). [CrossRef]

].

In scanning microscopy, the x-ray beam from a highly brilliant synchrotron radiation source is focused by an x-ray optic onto the sample in a strongly reducing geometry. Ideally, the beam size at the sample is limited by diffraction at the aperture of the optic. In that case, the smallest beam sizes and highest spatial resolutions are achieved. While the short wavelength allows in principle to reach diffraction limited beams in the sub-nanometer range [9

9. F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, “Nanometer focusing properties of Fesnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73, 245331 (2006). [CrossRef]

11

11. H. Yan, J. Maser, A. Macrander, Q. Shen, S. Vogt, G. B. Stephenson, and H. C. Kang, “Takagi-taupin description of x-ray dynamical diffraction from diffractive optics with large numerical aperture,” Phys. Rev. B 76, 115438 (2007). [CrossRef]

], todays x-ray optics are mainly technology limited, reaching focal spot sizes well below 100 nm [12

12. C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, “Hard x-ray nanoprobe based on refractive x-ray lenses,” Appl. Phys. Lett. 87, 124103 (2005). [CrossRef]

14

14. H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2010). [CrossRef]

].

Generally, the spatial resolution of a scanning microscope is limited by the size of the probe, i. e., the structural variations inside the sample are convolved with the nanobeam. The exact knowledge of the optical field around the focus is crucial to properly interpret and deconvolve the scanning micrographs, and to understand and correct for aberrations of x-ray optics. This complex wave field can be determined using ptychographic scanning diffraction microscopy [15

15. 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]

20

20. 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]

]. In this coherent imaging technique [15

15. 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]

, 21

21. J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004). [CrossRef]

], a sample is scanned through the nanobeam, recording at each scanning position a far-field diffraction pattern [Fig. 1(a)]. From these data, the complex transmission function [Fig. 1(b)] of the object and the complex wave field of the illuminating beam [Fig. 1(c)] can be reconstructed. With the complex wave field reconstructed in the object plane, in principle, the full caustic of the nanobeam can be reconstructed by numerical propagation, giving a full optical characterization of the nanobeam and the aberrations of the instrument [15

15. 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]

20

20. 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]

, 22

22. C. M. Kewish, M. Guizar-Sicairos, C. Liu, J. Qian, B. Shi, C. Benson, A. M. Khounsary, J. Vila-Comamala, O. Bunk, J. R. Fienup, A. T. Macrander, and L. Assoufid, “Reconstruction of an astigmatic hard x-ray beam alignment of K-B mirrors from ptychographic coherent diffraction data,” Opt. Express 18, 23420–23427 (2010). [CrossRef] [PubMed]

].

Fig. 1 (Color) (a) Ptychography: the sample is scanned trough the focused x-ray beam. Diffraction patterns are recorded in the far field at each scanning position. Ptychographic reconstruction: (b) phase of a test object (microchip [2]) and (c) reconstructed complex wave field both at position −500 μm upstream of the focal plane of the microscope. The rectangle in (b) delineates the area covered by the ptychographic scan.

In this article we address the question of how reliable the reconstruction of the complex optical wave field is, considering that the reconstructed object function often suffers from artifacts due to positioning errors of the scanner and mechanical instabilities during the exposure [19

19. 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. Schöder, M. Burghammer, and C. G. Schroer, “Hard x-ray nanobeam characterization by coherent diffraction microscopy,” Appl. Phys. Lett. 96, 091102 (2010). [CrossRef]

]. While the object function can be verified by other microscopy techniques, there is no independent other method that yields the same wealth of information for the wave field. Therefore, here, we propose a verification by self-consistency: ptychograms of a test object are recorded at different positions along the beam, reaching well into the far field of the nanobeam. The resulting complex wave fields are then used to predict the wave fields at the other positions along the beam by numerical (Fresnel-Kirchhoff) propagation. A comparison with the measured wave fields shows how consistent these results describe a common nanobeam.

2. Ptychographic Experiments

The ptychography experiments were carried out at the hard x-ray scanning microscope at beam-line ID13 of the European Synchrotron Radiation Facility (ESRF). The hard x rays from an undulator source were monochromatized (energy E = 15.25 keV, wave length λ = 0.813 Å) by a channel-cut monochromator (Si 111) located at 31 m from the source and focused in the x-ray scanning microscope (location: L s = 96 m from the source) by nanofocusing refractive x-ray lenses made of silicon [12

12. C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, “Hard x-ray nanoprobe based on refractive x-ray lenses,” Appl. Phys. Lett. 87, 124103 (2005). [CrossRef]

]. Two such cylinder lenses are aligned in a crossed geometry [cf. Fig. 1(a)] to generate a nearly Gaussian point focus about 13 mm behind the last lens with full width at half maximum (FWHM) lateral extensions of 74 × 81 nm2 in the horizontal and vertical directions (H × V), respectively. Due to the generally small numerical aperture (NA ≈ 10−3) of hard x-ray optics, the depth of focus is slightly larger than 100 μm. This also justifies the use of the paraxial approximation in numerical propagation.

The effective FWHM source size d s is 150 μm horizontally and 50 μm vertically as measured by fringe visibility experiments [23

23. V. Kohn, I. Snigireva, and A. Snigirev, “Direct measurement of transverse coherence length of hard X rays from interference fringes,” Phys. Rev. Lett. 85, 2745–2748 (2000). [CrossRef] [PubMed]

], resulting in a lateral coherence length at the instrument of 53 × 160 μm2 (H × V), here, defined by lt=λLsds. As this lateral coherence length at the instrument is much larger than the aperture of the optic [40 × 36 μm2 (H × V)], the focus is diffraction limited and the focused beam has a high degree of lateral coherence. The coherence in the focus is determined by propagating the mutual intensity from the source, through the focusing optic to the focus as described in [24

24. C. G. Schroer, P. Boye, J. 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]

]. At the focus, the lateral coherence length is 325 × 990 nm2 (H × V), well exceeding the size of the central maximum of the focus.

Ptychograms were recorded at different positions of the object along the optical axis, e. g., −1000, −500, 0, 500, and 1000 μm from the focal plane. As a test object a front-end processed microchip (512 Mb DDR 2 RAM by Qimonda in 80 nm technology) was used [2

2. A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011). [CrossRef]

]. For each ptychogram an area of 2 × 2 μm2 was scanned in 50 × 50 steps (step size 40 nm), recording at each position of the scan a far-field diffraction pattern with a single photon counting MAXIPIX detector placed at a distance L = 1.9 m downstream of the focus (exposure time 0.3 s per point). The overall acquisition time including overheads was 43 min. The MAXIPIX detector has N 2 = 256 × 256 pixels (pixel size d 2 = 55 × 55 μm2). As the translation along the optical axis was not perfectly aligned with the beam, the scanned area on the sample varied slightly for the different ptychograms.

3. Reconstruction and Consistency of Optical Wave Field

All ptychograms were reconstructed using the algorithm by Maiden and Rodenburg [17

17. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009). [CrossRef] [PubMed]

] (100 iterations). Figure 1(b) exemplarily shows the reconstructed test object 500 μm upstream of the focus (position −500 μm) together with the reconstructed x-ray wave field at that position along the optical axis [Fig. 1(c)]. The pixel size in both reconstructions is λL/(Nd) = 11.0 nm. Due to the extended illumination, the object is also reconstructed beyond the scanned area [cf. Fig. 1(b)]. The strongly phase shifting plug vias in the microchip (cf. [2

2. A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011). [CrossRef]

] for a detailed description of the sample) are visible as dark vertically elongated dots in Fig. 1(b). Due to mechanical instabilities of the x-ray microscope, they show slight artifacts in the form of horizontally displaced fringes. Therefore, it is important to verify that similar artifacts do not appear in the reconstructed wave field. This is done here, assuming that artifacts in the reconstructed wave field would yield inconsistencies when propagated to another position along the optical axis.

The first row of Fig. 2 shows the complex wave fields reconstructed from the different ptychograms along the optical axis. For comparison, the second row of Fig. 2 shows the wave fields calculated by propagating that at the focal position to the different positions along the optical axis. The propagation is done using Fresnel-Kirchhoff integration (scalar field) in paraxial approximation. This is very well justified in the hard x-ray range at the 10 nm resolution level. As the overall phase in each reconstructed optical field is arbitrary, it was fixed to match that in the propagated optical fields. In addition, the optical axis was centered to the nearest pixel in each of the reconstructed and propagated wave fields.

Fig. 2 (Color) First row: ptychographic reconstructions of the x-ray wave field measured independently at different positions from the focus along the optical axis. Second row: given the wave field in the focus (0 μm), the wave fields at the other positions are obtained by Fresnel-Kirchhoff propagation. Complex amplitudes are coded according to the color wheel. Comparing the propagated and reconstructed wave fields shows excellent agreement. The reconstructed projected vertical beam profile (intensity) is shown at the bottom.

Figure 2 shows a striking correspondence of the measured and propagated wave fields along the caustic. Exemplarily, the difference of two corresponding wave fields is shown in Fig. 3. The measured and propagated wave fields [Fig. 3(a) and 3(b)] can hardly be distinguished visually. The difference [Fig. 3(c) and 3(d)] amounts to about 10% in relative L 2 norm and is mainly a result of sub-pixel misalignment. This is shown in Fig. 3(d): each of the Fresnel zones in the difference image changes phase by about 180° between upper right and lower left [cf. color wheel in Fig. 3(c)]. This means that the propagated field is slightly shifted towards the upper right with respect to the measured field, making it smaller in amplitude at the lower left and higher at the upper right.

Fig. 3 (Color) (a) illumination reconstructed (measured) at position −1000 μm upstream of the focus and (b) that obtained by propagation from the wave field in the focus (same as in Fig. 2). (c) Difference between reconstructed and propagated illumination at that position on the same color scale as in (a) and (b). (d) difference with 10× enhanced contrast. The 180° phase shift of the Fresnel zones (cf. color wheel) from upper right to lower left in the difference map indicates a (sub-pixel) misalignment along the lower-left-upper-right diagonal.

Similarly consistent results are obtained by choosing any reconstructed wave field and propagating it to the other positions along the beam. In the case shown here, the reconstruction is faithful over a range larger than 20 times the depth of focus. Ptychographic reconstruction of the correct illumination fails when a significant part of the illumination falls out of the field of view (FOV) that is limited by the angle d/L subtended by a pixel of the detector (FOV = λL/d), i. e., when the sampling requirements for the far-field diffraction patterns are no longer met (cf. also [25

25. K. Giewekemeyer, M. Beckers, T. Gorniak, M. Grunze, T. Salditt, and A. Rosenhahn, “Ptychographic coherent x-ray diffractive imaging in the water window,” Opt. Express 19, 1037–1050 (2011). [CrossRef] [PubMed]

]). In the given example, this gradually happens around 1500 μm from the focus. When the optical wave field falls fully into the field of view — this is very well fulfilled in focus — the caustic can be calculated over much longer distances by appropriately zero padding the FOV before numerical propagation. This allows one to propagate the wave field to the exit plane of the nanofocusing optic.

4. Conclusion

In conclusion, ptychography is very well suited to reliably reconstruct the complex wave field in a confined beam, even when mechanical instabilities and unwanted sample motion introduce artifacts in the reconstruction of the object. No prior knowledge of the test sample is required, except that it should be optically thin and have a sufficiently high structural diversity on the length scales of the beam. In addition, the test object does not have to be in focus: reliable beam reconstructions can be made from a distance. This is important, for example, when the beam is to be assessed at a position that is not accessible by a test sample, e. g., at the exit of a wave guide [26

26. T. Salditt, S. P. Krueger, C. Fuhse, and C. Bahtz, “High-transmission planar x-ray waveguides,” Phys. Rev. Lett. 100, 184801 (2008).

] or a pinhole [18

18. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009). [CrossRef] [PubMed]

]. The only restriction is the size of the beam at the sample position that must be compatible with the sampling of the far-field diffraction patterns. The method is not limited to the hard x-ray range, but can be applied in other (longer) wavelength regimes as well.

Acknowledgments

The authors thank L. Lardière and D. Samberg for their excellent technical support. The beam time was granted as part of the long-term project MI-836 of the ESRF. This work is supported by the BMBF grants 05KS7OD1 and 05KS10OD1 and by VI-203 of the Helmholtz-Society. The GPU implementation of the numerical algorithms is supported within the NVIDIA Professor Partnership of C. S..

References and links

1.

C. Quitmann, C. David, F. Nolting, F. Pfeiffer, and M. Stampanoni, Proceedings of the 9th International Conference on X-ray Microscopy, Journal of Physics: Conference Series (IOP, Bristol, 2009), vol. 186.

2.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011). [CrossRef]

3.

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, 436–440 (2010). [CrossRef] [PubMed]

4.

J.-D. Grunwaldt and C. G. Schroer, “Hard and soft x-ray microscopy and tomography in catalysis: Bridging the different time and length scales,” Chem. Soc. Rev. 39, 4741 (2010). [CrossRef] [PubMed]

5.

P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008). [CrossRef] [PubMed]

6.

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006). [CrossRef]

7.

A. Carmona, P. Cloetens, G. Deves, S. Bohic, and R. Ortega, “Nano-imaging of trace metals by synchrotron x-ray fluorescence into dopaminergic single cells and neurite-like processes,” J. Anal. At. Spectrom. 23, 1083–1088 (2008). [CrossRef]

8.

C. G. Schroer, M. Kuhlmann, T. F. Günzler, B. Lengeler, M. Richwin, B. Griesebock, D. Lützenkirchen-Hecht, R. Frahm, E. Ziegler, A. Mashayekhi, D. Haeffner, J.-D. Grunwaldt, and A. Baiker, “Mapping the chemical states of an element inside a sample using tomographic x-ray absorption spectroscopy,” Appl. Phys. Lett. 82, 3360–3362 (2003). [CrossRef]

9.

F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, “Nanometer focusing properties of Fesnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73, 245331 (2006). [CrossRef]

10.

C. G. Schroer, “Focusing hard x rays to nanometer dimensions using Fresnel zone plates,” Phys. Rev. B 74, 033405 (2006). [CrossRef]

11.

H. Yan, J. Maser, A. Macrander, Q. Shen, S. Vogt, G. B. Stephenson, and H. C. Kang, “Takagi-taupin description of x-ray dynamical diffraction from diffractive optics with large numerical aperture,” Phys. Rev. B 76, 115438 (2007). [CrossRef]

12.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, “Hard x-ray nanoprobe based on refractive x-ray lenses,” Appl. Phys. Lett. 87, 124103 (2005). [CrossRef]

13.

H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer laue lens,” Appl. Phys. Lett. 92, 221114 (2008). [CrossRef]

14.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2010). [CrossRef]

15.

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]

16.

M. Guizar-Sicairos and J. R. Fienup, “Measurement of coherent x-ray focused beams by phase retrieval with transverse translation diversity,” Opt. Express 17, 2670–2685 (2009). [CrossRef] [PubMed]

17.

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009). [CrossRef] [PubMed]

18.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009). [CrossRef] [PubMed]

19.

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. Schöder, M. Burghammer, and C. G. Schroer, “Hard x-ray nanobeam characterization by coherent diffraction microscopy,” Appl. Phys. Lett. 96, 091102 (2010). [CrossRef]

20.

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]

21.

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004). [CrossRef]

22.

C. M. Kewish, M. Guizar-Sicairos, C. Liu, J. Qian, B. Shi, C. Benson, A. M. Khounsary, J. Vila-Comamala, O. Bunk, J. R. Fienup, A. T. Macrander, and L. Assoufid, “Reconstruction of an astigmatic hard x-ray beam alignment of K-B mirrors from ptychographic coherent diffraction data,” Opt. Express 18, 23420–23427 (2010). [CrossRef] [PubMed]

23.

V. Kohn, I. Snigireva, and A. Snigirev, “Direct measurement of transverse coherence length of hard X rays from interference fringes,” Phys. Rev. Lett. 85, 2745–2748 (2000). [CrossRef] [PubMed]

24.

C. G. Schroer, P. Boye, J. 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]

25.

K. Giewekemeyer, M. Beckers, T. Gorniak, M. Grunze, T. Salditt, and A. Rosenhahn, “Ptychographic coherent x-ray diffractive imaging in the water window,” Opt. Express 19, 1037–1050 (2011). [CrossRef] [PubMed]

26.

T. Salditt, S. P. Krueger, C. Fuhse, and C. Bahtz, “High-transmission planar x-ray waveguides,” Phys. Rev. Lett. 100, 184801 (2008).

OCIS Codes
(100.5070) Image processing : Phase retrieval
(110.1650) Imaging systems : Coherence imaging
(340.7460) X-ray optics : X-ray microscopy

ToC Category:
X-ray Optics

History
Original Manuscript: April 4, 2011
Revised Manuscript: July 2, 2011
Manuscript Accepted: August 1, 2011
Published: August 10, 2011

Virtual Issues
Vol. 6, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Susanne Hönig, Robert Hoppe, Jens Patommel, Andreas Schropp, Sandra Stephan, Sebastian Schöder, Manfred Burghammer, and Christian G. Schroer, "Full optical characterization of coherent x-ray nanobeams by ptychographic imaging," Opt. Express 19, 16324-16329 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-17-16324


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. Quitmann, C. David, F. Nolting, F. Pfeiffer, and M. Stampanoni, Proceedings of the 9th International Conference on X-ray Microscopy, Journal of Physics: Conference Series (IOP, Bristol, 2009), vol. 186.
  2. A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard x-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011). [CrossRef]
  3. 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, 436–440 (2010). [CrossRef] [PubMed]
  4. J.-D. Grunwaldt and C. G. Schroer, “Hard and soft x-ray microscopy and tomography in catalysis: Bridging the different time and length scales,” Chem. Soc. Rev. 39, 4741 (2010). [CrossRef] [PubMed]
  5. P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008). [CrossRef] [PubMed]
  6. C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006). [CrossRef]
  7. A. Carmona, P. Cloetens, G. Deves, S. Bohic, and R. Ortega, “Nano-imaging of trace metals by synchrotron x-ray fluorescence into dopaminergic single cells and neurite-like processes,” J. Anal. At. Spectrom. 23, 1083–1088 (2008). [CrossRef]
  8. C. G. Schroer, M. Kuhlmann, T. F. Günzler, B. Lengeler, M. Richwin, B. Griesebock, D. Lützenkirchen-Hecht, R. Frahm, E. Ziegler, A. Mashayekhi, D. Haeffner, J.-D. Grunwaldt, and A. Baiker, “Mapping the chemical states of an element inside a sample using tomographic x-ray absorption spectroscopy,” Appl. Phys. Lett. 82, 3360–3362 (2003). [CrossRef]
  9. F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, “Nanometer focusing properties of Fesnel zone plates described by dynamical diffraction theory,” Phys. Rev. B 73, 245331 (2006). [CrossRef]
  10. C. G. Schroer, “Focusing hard x rays to nanometer dimensions using Fresnel zone plates,” Phys. Rev. B 74, 033405 (2006). [CrossRef]
  11. H. Yan, J. Maser, A. Macrander, Q. Shen, S. Vogt, G. B. Stephenson, and H. C. Kang, “Takagi-taupin description of x-ray dynamical diffraction from diffractive optics with large numerical aperture,” Phys. Rev. B 76, 115438 (2007). [CrossRef]
  12. C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, “Hard x-ray nanoprobe based on refractive x-ray lenses,” Appl. Phys. Lett. 87, 124103 (2005). [CrossRef]
  13. H. C. Kang, H. Yan, R. P. Winarski, M. V. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. T. Macrander, and G. B. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer laue lens,” Appl. Phys. Lett. 92, 221114 (2008). [CrossRef]
  14. H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6, 122–125 (2010). [CrossRef]
  15. 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]
  16. M. Guizar-Sicairos and J. R. Fienup, “Measurement of coherent x-ray focused beams by phase retrieval with transverse translation diversity,” Opt. Express 17, 2670–2685 (2009). [CrossRef] [PubMed]
  17. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009). [CrossRef] [PubMed]
  18. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009). [CrossRef] [PubMed]
  19. 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. Schöder, M. Burghammer, and C. G. Schroer, “Hard x-ray nanobeam characterization by coherent diffraction microscopy,” Appl. Phys. Lett. 96, 091102 (2010). [CrossRef]
  20. 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]
  21. J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004). [CrossRef]
  22. C. M. Kewish, M. Guizar-Sicairos, C. Liu, J. Qian, B. Shi, C. Benson, A. M. Khounsary, J. Vila-Comamala, O. Bunk, J. R. Fienup, A. T. Macrander, and L. Assoufid, “Reconstruction of an astigmatic hard x-ray beam alignment of K-B mirrors from ptychographic coherent diffraction data,” Opt. Express 18, 23420–23427 (2010). [CrossRef] [PubMed]
  23. V. Kohn, I. Snigireva, and A. Snigirev, “Direct measurement of transverse coherence length of hard X rays from interference fringes,” Phys. Rev. Lett. 85, 2745–2748 (2000). [CrossRef] [PubMed]
  24. C. G. Schroer, P. Boye, J. 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]
  25. K. Giewekemeyer, M. Beckers, T. Gorniak, M. Grunze, T. Salditt, and A. Rosenhahn, “Ptychographic coherent x-ray diffractive imaging in the water window,” Opt. Express 19, 1037–1050 (2011). [CrossRef] [PubMed]
  26. T. Salditt, S. P. Krueger, C. Fuhse, and C. Bahtz, “High-transmission planar x-ray waveguides,” Phys. Rev. Lett. 100, 184801 (2008).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited