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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 21 — Oct. 8, 2012
  • pp: 24038–24048
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Quantitative X-ray wavefront measurements of Fresnel zone plate and K-B mirrors using phase retrieval

Xiaojing Huang, Michael Wojcik, Nicolas Burdet, Isaac Peterson, Graeme R. Morrison, David J. Vine, Daniel Legnini, Ross Harder, Yong S. Chu, and Ian K. Robinson  »View Author Affiliations


Optics Express, Vol. 20, Issue 21, pp. 24038-24048 (2012)
http://dx.doi.org/10.1364/OE.20.024038


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Abstract

A scanning coherent diffraction imaging method was used to reconstruct the X-ray wavefronts produced by a Fresnel zone plate (FZP) and by Kirkpatrick-Baez (KB) focusing mirrors. The ptychographical measurement was conducted repeatedly by placing a lithographed test sample at different defocused planes. The wavefronts, recovered by phase-retrieval at well-separated planes, show good consistency with numerical propagation results, which provides a self-verification. The validity of the obtained FZP wavefront was further confirmed with theoretical predictions.

© 2012 OSA

1. Introduction

Recent developments in optics fabrication techniques have provided focused X-ray beam sizes in tens-of-nanometer size range, by a variety of formations: compound refractive lens [1

1. C. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, and B. Lengeler, “Hard x-ray nanoprobe based on refractive x-ray lenses,” Appl. Phys. Lett. 87, 124103 (2005). [CrossRef]

], Kinoform lens [2

2. K. Evans-Lutterodt, A. Stein, J. Ablett, N. Bozovic, A. Taylor, and D. Tennant, “Using Compound Kinoform Hard-X-Ray Lenses to Exceed the Critical Angle Limit,” Phys. Rev. Lett. 99(13), 134801 (2007). [CrossRef] [PubMed]

], Kirkpatrick-Baez mirrors [3

3. 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]

], Fresnel zone plate [4

4. W. Chao, P. Fischer, T. Tyliszczak, S. Rekawa, E. Anderson, and P. Naulleau, “Real space soft x-ray imaging at 10 nm spatial resolution,” Opt. Express 20(9), 9777–9783 (2012). [CrossRef] [PubMed]

, 5

5. T. Chen, Y. Chen, C. Wang, I. Kempson, W. Lee, Y. Chu, Y. Hwu, and G. Margaritondo, “Full-field microimaging with 8 keV X-rays achieves a spatial resolutions better than 20 nm,” Opt. Express 19(21), 19919–19924 (2011). [CrossRef] [PubMed]

] and multilayer Laue lens [6

6. H. Yan, V. Rose, D. Shu, E. Lima, H. Kang, R. Conley, C. Liu, N. Jahedi, A. Macrander, G. Stephenson, M. Holt, Y. Chu, M. Lu, and J. Maser, “Two dimensional hard x-ray nanofocusing with crossed multilayer Laue lenses,” Opt. Express 19(16), 15069–15076 (2011). [CrossRef] [PubMed]

]. Characterization of the resulting X-ray focused beam wavefront is of fundamental importance for evaluating the fabrication and alignment qualities of focusing optical elements [7

7. H. Quiney, A. Peele, Z. Cai, D. Paterson, and K. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2, 101–104 (2006). [CrossRef]

17

17. A. Morgan, A. Martin, A. D’Alfonso, C. Putkunz, and L. Allen, “Direct exit-wave reconstruction from a single defocused image,” Ultramicroscopy 111, 1455–1460 (2011). [CrossRef] [PubMed]

].

Quantitative wavefront measurement is also extremely valuable for the purpose of reliably obtaining artifact-free images with arbitrary sizes. In lens-less coherent diffraction imaging (CDI) methods specifically, the image obtained through phase retrieval is the product of the object and the illumination function. If the incident X-ray wavefront is not sufficiently uniform over the sample, the beam structure will be present mixed in with the image of the object. Phase-retrieval based approaches for wavefront measurement can reconstruct the complex wavefront using the far-field diffraction intensity of the beam itself with a priori knowledge of the optics aperture [7

7. H. Quiney, A. Peele, Z. Cai, D. Paterson, and K. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2, 101–104 (2006). [CrossRef]

]. The accurately determined wavefront function can then serve as a scannable probe [18

18. 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(2), 025506 (2006). [CrossRef] [PubMed]

, 19

19. B. Abbey, K. Nugent, G. Williams, J. Clark, A. Peele, M. Pfeifer, M. D. Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008). [CrossRef]

], and thus release the limitation on field of view to imaging samples with arbitrary sizes. Alternatively, introducing translational diversity into coherent diffraction imaging measurement provides extra constraints arising from overlapping, redundantly illuminated sample sections. This general ptychographic approach can remove requirements on the maximum sample dimensions [20

20. J. Rodenburg, A. Hurst, A. Cullis, B. 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]

]. This redundancy also enables the factorisation of the illuminating beam while recovering the object image simultaneously [21

21. 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]

27

27. P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011). [CrossRef] [PubMed]

]. Because they also characterize the incident beam wavefront, these generalized ptychography approaches have been shown to be very robust for handling noise and eliminating ambiguities. Widely used algorithms are based on the Difference Map [21

21. 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]

] and the extended Ptychographic Iterative Engine (ePIE) [23

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

].

2. Experimental setup

Fig. 1(a) (b) illustrate the experimental setup at the 34-ID-C beamline of Advanced Photon Source, Argonne National Laboratory. The coherence and illumination-defining slits are 54.5 m (Zv) away from the center of the Undulator A. The vertical full width at half maximum (FWHM) X-ray beam source size is 26 μm [28

28. APS Science 2011 (Argonne National Laboratory, 2012).

]. To increase the horizontal coherence length, a 100 μm wide beam was selected horizontally by slits in front of a mirror, located 27.5 m in front of the coherence-defining entrance slits. With this setup, the half width at half maximum (HWHM) transverse coherence lengths can be estimated using 2λZ/ln2/(πD) [29

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

] to be 20 ×154 μm (horizontal × vertical), where D is the characteristic source size. The slit gaps were adjusted to select the coherent part of the incident X-ray beam.

Fig. 1 Sketch of the experimental setup with Fresnel zone plate (a) and KB mirrors (b). (c) SEM image of the test pattern. (d) (e) typical reconstructed magnitude and phase images using data measured with FZP.

An X-ray energy of 9 keV (λ = 0.138 nm) was selected by the beamline Si(111) double crystal monochromator [30

30. T. Kupp, B. Blank, A. Deyhim, C. Benson, I. Robinson, and P. Fuoss, “Development of a double crystal monochromator,” AIP Conf. Proc. CP705, 651–654 (2004). [CrossRef]

], which provides sufficient longitudinal (temporal) coherence for this experiment.

A customized test pattern (shown in Fig. 1 (c)) was designed by us and fabricated by Zone-Plates Ltd [31

31. ZonePlates Ltd, 8 South Way, Claverings Industrial Estate, London N9 OAB, UK., URL http://www.zoneplates.com.

] using electron beam lithography and Reactive Ion Etching (RIE). The pattern was prepared in 1.5 μm thick tungsten film evaporated on to a 1 μm thick silicon nitride window, to provide about 70% intensity transmission and about 0.8 π phase shift to a 9 keV X-ray beam. The test pattern was illuminated by an X-ray beam focused by the optics under investigation: the FZP or the KB mirror system. The ptychographical measurement was performed by translating the sample in the transverse plane. The sample was scanned using nPoint NPXY100Z25A piezo stage, which was mounted on the top of a set of XYZ step-motors for larger range movements. The scanning trajectory follows concentric circles, with 5n points on the nth ring and a radius increment of 0.5 μm for FZP and 0.75 μm for KB mirrors.

A Princeton Instrument PI-MTE 1300B charge-coupling device (CCD) with 20×20 μm pixel size was placed 2.31 m downstream from the test sample. The detector region-of-interest (ROI) was set to 400×400 pixels for FZP and 280×280 pixels for KB mirror measurements, which gives the real-space pixel size of 40 nm and 56.8 nm, respectively.

3. Focused wavefront from the Fresnel zone plate

The FZP we used in this work contains 2 μm thick alternating gold and diamond zones [32

32. M. Wojcik, V. Joshi, A. Sumant, R. Divan, L. Ocola, M. Lu, and D. Mancini, “Nanofabrication of x-ray zone plates using ultrananocrystalline diamond molds and electroforming,” J. Vac. Sci. Technol. B 28(6), C6P30–C6P35 (2010). [CrossRef]

]. The diameter is 180 μm with 80 nm outer-most zone width and a 30 μm diameter central stop. With 9 keV X-rays, the first-order focus length is 104.5 mm. It was fabricated using ultra-nanocrystalline diamond (UNCD) as the dielectric mold material into which Au is electroplated. UNCD is a chemical vapor deposition (CVD) diamond composed of 2–5 nm grains of diamond bonded together with graphitic type bonds [33

33. J. Butler and A. Sumant, “The CVD of Nanodiamond Materials,” J. Chem. Vap. Deposition 14, 145–160 (2008). [CrossRef]

]. A 2-μm-thick layer of UNCD was prepared on 40 nm of tungsten and 1 μm of Si3N4 supported by a Si substrate. These layers were released to form a membrane by back etching the Si substrate. The sample was then coated with hydrogen silsesquioxane (HSQ) acting as the resist material and exposed using a 100 keV e-beam lithography system. After development, UNCD was etched with oxygen plasma designed for high anisotropy and selectivity. The resulting mold was filled by electroplating gold using tungsten as the conductive base. The HSQ was removed and the resulting FZP consists of alternating Au and UNCD zones.

The zone plate was mounted 286 mm downstream of the beam defining slits, about 104 mm before the sample. Considering the transverse coherence lengths at the zone plate plane are not sufficient to cover its entire 180 μm diameter, the beam-defining slits were set to 20×100 μm (horizontal × vertical) to select the coherent beam and produce a partial illumination of the FZP [16

16. F. Mastropietro, D. Carbone, A. Diaz, J. Eymery, A. Sentenac, T. H. Metzger, V. Chamard, and V. Favre-Nicolin, “Coherent x-ray wavefront reconstruction of a partially illuminated Fresnel zone plate,” Opt. Express 19(20), 19223–19232 (2011). [CrossRef] [PubMed]

]. Another option is to increase the horizontal coherence length by narrowing the white beam slits. But the incident x-ray flux will drop dramatically. For the interest of having more flux, the experiment utilized the partial illumination setup. The illumination-defining slits were offset by 35 μm in the horizontal direction to avoid the central stop and produce the separation between the first order focussed beam and the zeroth order direction beam, which is blocked by a 40 μm diameter order sorting aperture (OSA) mounted 85 mm away from the FZP, 19 mm in front of the sample.

Fig. 2 (a)(b)(c) The phase-retrieved probe for FZP with the test sample placed at 0.0 mm, −6.0 mm and −12.32 mm. (e)(f) The simulated probes propagated from (a). (d) The propagation distances were determined by minimizing the standard deviation between propagated and phase-retrieved probes.
Fig. 3 Comparison of phase-retrieved and numerically propagated probes along the central vertical lines: the amplitude (a) and phase (b) plots at z = −5.947 mm, the amplitude (c) and phase (d) plots at z = −12.401 mm.

The fully recovered complex wavefront allows one to propagate it to any other plane in both the forward and backward directions. We propagated the reconstructed probe at z = 0 mm with 10 μm propagation step size in 20 mm range. Fig. 4 (a) and (b) shows horizontally-integrated and vertically-integrated intensities of the propagation profiles. In order to precisely locate the focal planes, a finer propagation with 1 μm step size was perform in the neighborhood of z = 0 mm. The propagation was repeated with 10 individually phase-retrieved probes obtained from different random starts, and the vertical and horizontal waist planes with narrowest peaks were selected from each propagation. Averaging these propagation results reveals that the vertical and horizontal foci locate at 65 μm and 322 μm upstream of z = 0 mm plane, and the separation of those 2 focal planes is 257 ±68 μm. The horizontal and vertical focus sizes are 730 nm and 168 nm, respectively, as shown in Fig. 5 (a) and (b).

Fig. 4 Propagation of the phase-retrieved probe obtained at z = 0.0 mm: (a) intensity along the vertical direction, horizontally integrated, (b) intensity along the horizontal direction, vertically integrated.
Fig. 5 Estimation of focal sizes of the phase-retrieved wavefront (a)(b) and the simulated wavefront (c)(d).

Considering the focused wavefront as a demagnified image of the light source, if the horizontal and vertical X-ray sources located at different distances from the FZP, it can cause separated foci in the different directions. In the 34-ID-C beamline, the undulator center served as the vertical source, and a horizontal secondary source of 100 μm was set by a white-beam slit at the beamline mirror location. A simple calculation using the lens law gives that the separation of horizontal and vertical focal planes should be 195 μm, which agrees with the experimental result of 257±68 μm within measurement uncertainty. This 62 μm discrepancy may be due to fabrication or alignment issues with the FZP (see below) or due to incorrect functioning of the secondary source, which will be investigated further.

The focusing performance of the FZP can be simulated using its fabrication and experimental setup parameters [16

16. F. Mastropietro, D. Carbone, A. Diaz, J. Eymery, A. Sentenac, T. H. Metzger, V. Chamard, and V. Favre-Nicolin, “Coherent x-ray wavefront reconstruction of a partially illuminated Fresnel zone plate,” Opt. Express 19(20), 19223–19232 (2011). [CrossRef] [PubMed]

]. A perfect FZP with 80 nm outer-most zone width and 180 μm diameter was simulated using alternating gold and diamond zone with 2 μm thickness. A uniform plane wave illumination was assumed in front of the 20 × 100 μm (horizontal × vertical) beam-defining slits. It then propagated 286 mm to the FZP. The wavefront modified by the FZP continued to propagate by 85 mm, where the outer wavefront was masked out by a 30 μm diameter OSA. The wavefront propagated by another 19.5 mm to reach the focal plane. Notice that the phase-retrieved wavefront presents alternatively dim horizontal fringes, especially in the top-half plane as shown in Fig. 6 (a). The missing fringes and asymmetry in the probe implies a phase-ramp might be introduced by FZP imperfection. Such a phase ramp with 2π extent and 90 μm width was added into the FZP simulation, and the simulated focus is shown in Fig. 6 (b). The major features are consistent with the phase-retrieved the probe (Fig. 6 (c) (d)). The horizontal and vertical focus sizes of the simulated wavefront are 712 nm and 173 nm, respectively (Fig. 5 (c) (d)), which agree very well with the focus sizes of the recovered probe, 730 nm×168 nm (Fig. 5 (a) (b)), considering that the reconstruction pixel resolution is 40 nm. Reliable quantitative imaging of the astigmatic source attests to the high quality of the fabrication of the FZP used. Its diamond substrate may be particularly stable against beam induced damage.

Fig. 6 Comparison between the recovered wavefront (a) through phase-retrieval and the simulated wavefront of FZP focused beam (b). The central 8 ×8 μm area is shown. (c) The amplitude plotted along the horizontal central line. (d) The amplitude plotted along the vertical central line.

4. Focused wavefront from Kirkpatrick Baez mirrors

Ptychographical measurements were conducted with Kirkpatrick-Baez (KB) mirrors using the same concept. The experimental setup was identical to FZP experiment, except for no OSA inserted in the optics path. The bendable KB mirrors [35

35. P. Eng, M. Newvile, M. Rivers, and S. Sutton, “Dynamicaly figured Kirkpatrick Baez X-ray micro-focusing optic,” Proc. SPIE 3449, 145–156 (1998). [CrossRef]

] were coated with 50 nm platinum on top of a 10 nm chrome under-layer. The center of the 100 mm long vertical focusing mirror was placed 220 mm in front of the sample plane. The 100 mm long horizontal focusing mirror was 120 mm in front of the sample plane. The incident angle was set to 3 μrad for both of them. The illumination-defining slits were 120 mm upstream of the entrance side of the vertical focusing mirror, and the entrance slit opening was set to 20 ×20 μm. The same lithographed test object was used to measure the wavefront in the sample plane.

The scan trajectory covered 10 ×10 μm range with 0.75 μm step size for radius increment, which created 141 frames of diffraction patterns for each complete ptychographcial scan. The measurement was repeated at z = −10.0 mm, 0.0 mm and +10.5 mm. The phase-retrieved X-ray beam wavefronts are shown in Fig. 7 (a)(b)(c). The reconstructed images of the test pattern are shown in Fig. 8. The recovered probe at z = 0.0 mm was numerically propagated to the −10 mm and +10.5 mm planes. The propagated wavefronts are shown in Fig. 7 (d) and (e), which are in good agreement with the reconstructed probes. Although the lack of metrology measurement of KB mirrors prevents numerical simulation of their focusing behavior [12

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

], the consistency between recovered and propagated probes provides satisfactory confidence for the measurement.

Fig. 7 (a)(b)(c) The reconstructed probe of the KB mirrors with the sample placed at −10 mm, 0.0 mm and 10.5 mm. (d)(e) The simulated probes propagated from (b). (f)(g) The integrated vertical and horizontal amplitude through focus.
Fig. 8 Typical images of the reconstructed magnitude (a) and phase (b) using data measured with KB mirrors.

The phase-retrieved probe was propagated in a range of 100 mm with 100 μm propagation step size. The horizontally and vertically integrated intensities at different planes are shown in Fig. 7 (f) and (g). We found that the vertical focal plane was located at z = −18.6 mm, and the horizontal focal plane was at z = −27.8 mm. The horizontal and vertical focal sizes were estimated to be 0.94 μm and 1.32 μm, respectively, as shown in Fig. 9. These numbers are systematically smaller than the 1.6 μm size routinely obtained by scanning a 100 μm tungsten wire through the focus during the alignment of the KB benders. This discrepancy is understood to come from partial penetration of the X-ray beam into the edge of the wire.

Fig. 9 Horizontal (a) and vertical (b) focal sizes of the Kirkpatrick-Baez (KB) mirror system at their corresponding focal planes.

5. Conclusion

Ptychographical measurements of the focused X-ray beam produced by Fresnel zone plate and KB mirrors were conducted with a test sample at various defocused planes. Phase-retrieved wavefronts at the different planes show good agreement with numerical propagations starting from the smallest recovered probe. For the FZP, the recovered focus is also consistent with a numerically simulated wave function of its focal plane. Both measurements confirm that the ptychographical approach is capable of providing robust and reliable X-ray probe functions. The repeated measurements at different defocused planes produce a convincing verification of the analytical method recovering the correct probe phase information, which is important in describing the focus.

Acknowledgments

This project is supported by the European Research Council as an FP7 Advanced grant “Nanosculpture”, code 227711. The measurements were carried out at APS beamline 34-ID-C, built with US National Science Foundation grant DMR-9724294 and operated by the US Department of Energy, Office of Basic Energy Sciences, under contract no. DE-AC0206CH11357. X. H. and Y. S. C. are supported by Brookhaven Science Associates, LLC under Contract No DE-AC02-98CH10886.

References and links

1.

C. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, and B. Lengeler, “Hard x-ray nanoprobe based on refractive x-ray lenses,” Appl. Phys. Lett. 87, 124103 (2005). [CrossRef]

2.

K. Evans-Lutterodt, A. Stein, J. Ablett, N. Bozovic, A. Taylor, and D. Tennant, “Using Compound Kinoform Hard-X-Ray Lenses to Exceed the Critical Angle Limit,” Phys. Rev. Lett. 99(13), 134801 (2007). [CrossRef] [PubMed]

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4.

W. Chao, P. Fischer, T. Tyliszczak, S. Rekawa, E. Anderson, and P. Naulleau, “Real space soft x-ray imaging at 10 nm spatial resolution,” Opt. Express 20(9), 9777–9783 (2012). [CrossRef] [PubMed]

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C. 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]

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17.

A. Morgan, A. Martin, A. D’Alfonso, C. Putkunz, and L. Allen, “Direct exit-wave reconstruction from a single defocused image,” Ultramicroscopy 111, 1455–1460 (2011). [CrossRef] [PubMed]

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Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Coherent x-ray wavefront reconstruction of a partially illuminated Fresnel zone plate,” Phys. Rev. B 83(21), 214109 (2011). [CrossRef]

27.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011). [CrossRef] [PubMed]

28.

APS Science 2011 (Argonne National Laboratory, 2012).

29.

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

30.

T. Kupp, B. Blank, A. Deyhim, C. Benson, I. Robinson, and P. Fuoss, “Development of a double crystal monochromator,” AIP Conf. Proc. CP705, 651–654 (2004). [CrossRef]

31.

ZonePlates Ltd, 8 South Way, Claverings Industrial Estate, London N9 OAB, UK., URL http://www.zoneplates.com.

32.

M. Wojcik, V. Joshi, A. Sumant, R. Divan, L. Ocola, M. Lu, and D. Mancini, “Nanofabrication of x-ray zone plates using ultrananocrystalline diamond molds and electroforming,” J. Vac. Sci. Technol. B 28(6), C6P30–C6P35 (2010). [CrossRef]

33.

J. Butler and A. Sumant, “The CVD of Nanodiamond Materials,” J. Chem. Vap. Deposition 14, 145–160 (2008). [CrossRef]

34.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2004).

35.

P. Eng, M. Newvile, M. Rivers, and S. Sutton, “Dynamicaly figured Kirkpatrick Baez X-ray micro-focusing optic,” Proc. SPIE 3449, 145–156 (1998). [CrossRef]

OCIS Codes
(100.5070) Image processing : Phase retrieval
(340.0340) X-ray optics : X-ray optics
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
X-ray Optics

History
Original Manuscript: July 3, 2012
Revised Manuscript: August 13, 2012
Manuscript Accepted: September 4, 2012
Published: October 5, 2012

Citation
Xiaojing Huang, Michael Wojcik, Nicolas Burdet, Isaac Peterson, Graeme R. Morrison, David J. Vine, Daniel Legnini, Ross Harder, Yong S. Chu, and Ian K. Robinson, "Quantitative X-ray wavefront measurements of Fresnel zone plate and K-B mirrors using phase retrieval," Opt. Express 20, 24038-24048 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-24038


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  29. K. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys.59, 1–99 (2010). [CrossRef]
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  33. J. Butler and A. Sumant, “The CVD of Nanodiamond Materials,” J. Chem. Vap. Deposition14, 145–160 (2008). [CrossRef]
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  35. P. Eng, M. Newvile, M. Rivers, and S. Sutton, “Dynamicaly figured Kirkpatrick Baez X-ray micro-focusing optic,” Proc. SPIE3449, 145–156 (1998). [CrossRef]

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