## High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination |

Optics Express, Vol. 20, Issue 17, pp. 19050-19059 (2012)

http://dx.doi.org/10.1364/OE.20.019050

Acrobat PDF (1234 KB)

### Abstract

We extend coherent diffraction imaging (CDI) to a high numerical aperture reflection mode geometry for the first time. We derive a coordinate transform that allows us to rewrite the recorded far-field scatter pattern from a tilted object as a uniformly spaced Fourier transform. Using this approach, FFTs in standard iterative phase retrieval algorithms can be used to significantly speed up the image reconstruction times. Moreover, we avoid the isolated sample requirement by imaging a pinhole onto the specimen, in a technique termed apertured illumination CDI. By combining the new coordinate transformation with apertured illumination CDI, we demonstrate rapid high numerical aperture imaging of samples illuminated by visible laser light. Finally, we demonstrate future promise for this technique by using high harmonic beams for high numerical aperture reflection mode imaging.

© 2012 OSA

## 1. Introduction

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

6. 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]

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

12. D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl. **21**, 37–50 (2005). [CrossRef]

13. J. Miao and D. Sayre, “On possible extensions of X-ray crystallography through diffraction-pattern oversampling,” Acta. Crystallogr. A **56**, 596–605 (2000). [CrossRef] [PubMed]

14. P. Fischer, “Studying nanoscale magnetism and its dynamics with soft X-ray microscopy,” IEEE Trans. Magn. **44**, 1900–1904 (2008). [CrossRef]

15. A. Tripathi, J. Mohanty, S. H. Dietze, O. G. Shpyrko, E. Shipton, E. E. Fullerton, S. S. Kim, and I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. U.S.A. **108**, 13393–13398 (2011). [CrossRef] [PubMed]

16. I. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Matter. **8**, 291–298 (2009). [CrossRef]

17. B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” Appl. Phys. Lett. **93**, 214101 (2008). [CrossRef]

18. J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray crystallography to allow the imaging of non-crystalline materials, cells, and single protein complexes,” Annu. Rev. Phys. Chem. **59**, 387–410 (2008). [CrossRef]

19. J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. **107**, 7235–7239 (2010). [CrossRef] [PubMed]

20. T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics **4**, 822–832 (2010). [CrossRef]

22. T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science **336**, 1287–1291 (2012). [CrossRef] [PubMed]

20. T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics **4**, 822–832 (2010). [CrossRef]

24. X. Zhang, A. R. Libertun, A. Paul, E. Gagnon, S. Backus, I. P. Christov, M. M. Murnane, H. C. Kapteyn, R. A. Bartels, Y. Liu, and D. T. Attwood, “Highly coherent light at 13 nm generated by use of quasi-phase-matched high-harmonic generation,” Opt. Lett. **29**, 1357–1399 (2004). [CrossRef] [PubMed]

20. T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics **4**, 822–832 (2010). [CrossRef]

22. T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science **336**, 1287–1291 (2012). [CrossRef] [PubMed]

25. W. Ackermann, “Operation of a free-electron laser from the extreme ultraviolet to the water window,” Nat. Photonics **1**, 336–342 (2007). [CrossRef]

27. D. Alessi, Y. Wang, B. Luther, L. Yin, D. Martz, M. Woolston, Y. Liu, M. Berrill, and J. Rocca, “Efficient Excitation of Gain-Saturated Sub-9-nm-Wavelength Tabletop Soft-X-Ray Lasers and Lasing Down to 7.36 nm,” Phys. Rev. X **1**, 021023 (2011). [CrossRef]

28. M. D. Seaberg, D. E. Adams, E. L. Townsend, D. A. Raymondson, W. F. Schlotter, Y. Liu, C. S. Menoni, L. Rong, C.-C. Chen, J. Miao, H. C. Kapteyn, and M. M. Murnane, “Ultrahigh 22 nm resolution coherent diffractive imaging using a desktop 13 nm high harmonic source,” Opt. Express **19**, 22470–22479 (2011). [CrossRef] [PubMed]

29. S. Roy, D. Parks, K. A. Seu, R. Su, J. J. Turner, W. Chao, E. H. Anderson, S. Cabrini, and S. D. Kevan, “Lensless x-ray imaging in reflection geometry,” Nat. Photonics **5**, 243–245 (2011). [CrossRef]

30. S. Marathe, S. Kim, S. Kim, C. Kim, H. C. Kang, P. V. Nickles, and D. Y. Noh, “Coherent diffraction surface imaging in reflection geometry,” Opt. Express **18**, 7253–7262 (2010). [CrossRef] [PubMed]

29. S. Roy, D. Parks, K. A. Seu, R. Su, J. J. Turner, W. Chao, E. H. Anderson, S. Cabrini, and S. D. Kevan, “Lensless x-ray imaging in reflection geometry,” Nat. Photonics **5**, 243–245 (2011). [CrossRef]

30. S. Marathe, S. Kim, S. Kim, C. Kim, H. C. Kang, P. V. Nickles, and D. Y. Noh, “Coherent diffraction surface imaging in reflection geometry,” Opt. Express **18**, 7253–7262 (2010). [CrossRef] [PubMed]

31. T. Harada, M. Nakasuji, T. Kimura, T. Watanabe, H. Kinoshita, and Y. Nagata, “Imaging of extreme-ultraviolet mask patterns using coherent extreme-ultraviolet scatterometry microscope based on coherent diffraction imaging,” J. Vac. Sci. Technol. B **29**, 06F503 (2011). [CrossRef]

14. P. Fischer, “Studying nanoscale magnetism and its dynamics with soft X-ray microscopy,” IEEE Trans. Magn. **44**, 1900–1904 (2008). [CrossRef]

32. M. Bryan, P. Fry, T. Schrefl, M. R. Gibbs, D. A. Allwood, M.-Y. Im, and P. Fischer, “Transverse field-induced nucleation pad switching modes during domain wall injection,” IEEE Trans. Magn. **46**, 963–967 (2010). [CrossRef]

*μ*m and 100 nm, respectively.

## 2. Transmission mode AICDI

*μ*m wide circular aperture. The aperture is imaged to the sample plane using a one-to-one 4f imaging system. A positive lens placed directly after the sample sends the scattered light into the Fourier plane at the CMOS detector (Mightex Systems MCE-B013, 5.2

*μ*m pixel size). In general the positive lens after the sample is unnecessary, however, the detectors used in this experiment were small enough that a demagnification of the far field was required in order to use a wavelength as large as 633nm. The aperture size is selected to satisfy the oversampling criterion [13

13. J. Miao and D. Sayre, “On possible extensions of X-ray crystallography through diffraction-pattern oversampling,” Acta. Crystallogr. A **56**, 596–605 (2000). [CrossRef] [PubMed]

*μ*m diameter copper wires with an image of the aperture (Fig. 1(a) inset). An example of a scatter pattern obtained is shown in Fig. 1(b). The scatter pattern we obtain is proportional to the modulus of the Fourier transform of the illuminated portion of the sample. We use the RAAR algorithm as outlined in Ref. [12

12. D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl. **21**, 37–50 (2005). [CrossRef]

11. 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]

## 3. Tilted plane correction

*μ*is a parameter that specifies the strength of the interaction with the potential

*V*(

*r*′⃗) and

*f*(

*q⃗*) is the far-field scattering amplitude. We begin by examining the case where a ray is normally incident on the specimen and the sample and detector planes are parallel to each other. A schematic of this geometry is shown in Fig. 2(a) with the following relevant quantities:

*n*̂

*is the normal vector defining the sample plane, S,*

_{S}*n*̂

*is the normal vector defining the detector plane, D,*

_{D}*r*′⃗ describes points on S,

*k⃗*is the incident wavevector,

_{i}*k⃗*is the final scattering vector,

_{f}*q⃗*is the momentum transfer vector (

*k⃗*−

_{f}*k⃗*),

_{i}*ϕ*is the azimuthal angle in S,

*θ*is the angle between

*k⃗*and

_{i}*k⃗*, and

_{f}*α*is the angle between the tilted and untilted sample coordinate systems. We start by writing the momentum transfer vector in a coordinate system where

*k⃗*=

_{i}*k*

_{0}

*z*̂: where

*k*

_{0}is the wavenumber. Our goal here is to identify the unit vectors associated with

*q⃗*(

*x*̂,

*ŷ*,

*z*̂ in Eq. (2)) with those that are associated with

*r*′

*⃗*. In order to take advantage of the FFT algorithm, the real-space sampling grid must be linear in

*r*′⃗ and the frequency-space sampling grid must be linear in

*q⃗*. However, it is clear from Eq. (2) that the spatial frequencies

*q*and

_{x}*q*are linear in sin(

_{y}*θ*) for a given

*ϕ*. At this point, it is instructive to rewrite Eq. (2) in the Cartesian coordinates of the detector where x and y are the detector plane coordinates and

*R*is the distance from the sample to the center of the detector. The values at each pixel of the components of

*q⃗*are clearly spaced non-uniformly on the detector due to the square root term in the denominator of each component. The square root in the denominator is a result of mapping the Ewald sphere onto a flat detector. This should be corrected by a two-dimensional interpolation onto a linearly spaced Cartesian grid. It is also worth noting that the light at the edges has propagated further than light at the center. Because the intensity falls off as 1/

*r*

^{2}, we rescale the data by

*r*

^{2}/

*R*

^{2}in order to correct for this, where

*r*is the distance from the sample to a given pixel on the detector. Written in terms of detector coordinates we have: 1 + (

*x*

^{2}+

*y*

^{2})/

*R*

^{2}. This rescaling should be done on the raw data, but after centering and before doing any transformation of coordinates.

*I*(

*x*,

*y*,

*z*), in terms of the detector coordinates. We then perform the intensity rescaling as where

*I*is now properly scaled as the Fourier transform of the object. The second step is to perform the interpolation in order that the pattern is sampled on a grid that is linear in

_{r}*q⃗*, which can be written as where in the case of a planar sample,

*I*= 0 for

_{r}*q*≠ 0. This allows us to simply use a two-dimensional rather than three-dimensional interpolation. In the case of a three-dimensional sample, a three-dimensional interpolation must be performed [4

_{z}4. K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature **463**, 214–217 (2010). [CrossRef]

*α*about the

*ŷ*′ axis, as would be the case in a reflection geometry (or a tilted sample in transmission). In this case Eq. (2) is still valid in the unprimed coordinate system, however as expected, the coordinate axes associated with

*q⃗*are no longer aligned with the coordinate axes associated with

*r*̂′. To fix this, we simply rewrite

*q⃗*in the sample coordinate system. In practice, this corresponds to rotating

*q⃗*by −

*α*, given by where

*R*is the three-dimensional (gimbal-like) rotation matrix about

_{y}*ŷ*′ and

*q⃗*(

*x*″,

*y*′,

*z*″) is the momentum transfer in the sample coordinate system, in terms of the components of

*q⃗*in the unprimed coordinates. A more general case can be obtained by applying a further rotation

*R*(−

_{x}*β*), allowing for the sample plane to be in any orientation relative to the detector plane. As in the untilted case, a two-dimensional interpolation should be performed (Eq. (5) using

*q⃗*in the sample coordinates) to resample the nonlinearly spaced components of

*q⃗*onto a linearly spaced Cartesian grid. With both rotation matrices applied, the final form of

*q⃗*is:

*q⃗*×

_{i}*n*̂

*≠ 0, can be summarized by the following algorithm: First, write*

_{D}*q⃗*in a plane normal to

*k⃗*then perform rotations on

_{i}*q⃗*in order to represent it in 1) the sample plane and then 2) the detector plane. This transform allows us to write the detected scatter pattern as the Fourier transform of the sample potential. Finally, in order to use the FFT algorithm, an interpolation must be performed to resample the resulting spatial frequencies onto a uniformly spaced grid, once again as in Eq. (5). It is worth noting that the interpolation must be performed with care so that the oversampling ratio does not fall below the minimum requirement. This can be achieved by interpolating onto a grid with a larger number of pixels than the original grid.

## 4. Reflection mode AICDI

*α*= 30 degrees (Fig. 4(a)). The same detector and Fourier transform lens were used as in the transmission setup, but were repositioned such that they were aligned along the specular reflection from the sample (Fig. 4(a)). Thus the NA was kept at 0.22 and the resolution at 1.4

*μ*m. The sample used was a positive 1951 USAF Resolution Target. Figure 3(a) shows a scatter pattern form the vertical bars of group 5 (element 1) of the resolution target. The black dashed lines are overlaid to illustrate the curvature in the diffraction resulting from a tilted sample. In Fig. 3(b) we show the scatter pattern after mapping the diffraction onto a grid that is linear in spatial frequency, as discussed in section 3. After interpolation, the scatter pattern is proportional to the modulus of Fourier transform of the sample. Using the same iterative phase retrieval algorithm as mentioned above, we are able to reconstruct any arbitrary position of the target. These reconstructions are overlaid and shown in Fig. 4(b). An objective based bright-field microscopy image is also shown in Fig. 4(c) for comparison.

## 5. Reflection mode CDI using short wavelength high harmonic beams

*μ*m in width and 20nm high, patterned on a sapphire substrate. Rather than using AICDI, a slightly simpler geometry was used where the beam was loosely focused directly onto the object, with a spot size of approximately 25

*μ*m, so that many pillars were illuminated (Fig. 5(a)). The incident angle of the HHG beam on the sample was 45 deg, and as a result the scatter pattern in Fig. 5(b) displays a high degree of asymmetry, making this specimen a good demonstration of the need for tilted plane correction. Figures 5(b) and 5(c) show uncorrected and corrected scatter patterns respectively. The 27.6 mm square detector with 13.5

*μ*m pixels (Andor iKon) was placed 4.5 cm past the object, resulting in a NA of 0.29. An integration time of 20 minutes was required in order to obtain the diffraction pattern in Fig. 5(b). The missing center in the diffraction pattern is the result of a beam stop used to prevent saturation of the bright zero order peak. The beam stop was placed as close to the detector as possible (≈ 2

*mm*) in order to minimize edge diffraction effects.

## 6. Conclusion

## Acknowledgments

## References and links

1. | J. Miao, P. Charalambous, and J. Kirz, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature |

2. | H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics |

3. | P. Thibault and E. Veit, “X-Ray Diffraction Microscopy,” Annu. Rev. Condens. Matter Phys. |

4. | K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature |

5. | A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. |

6. | 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. |

7. | J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. |

8. | J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. |

9. | V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A |

10. | V. Elser, “Random projections and the optimization of an algorithm for phase retrieval,” J. Phys. A: Math. Gen. |

11. | 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 |

12. | D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl. |

13. | J. Miao and D. Sayre, “On possible extensions of X-ray crystallography through diffraction-pattern oversampling,” Acta. Crystallogr. A |

14. | P. Fischer, “Studying nanoscale magnetism and its dynamics with soft X-ray microscopy,” IEEE Trans. Magn. |

15. | A. Tripathi, J. Mohanty, S. H. Dietze, O. G. Shpyrko, E. Shipton, E. E. Fullerton, S. S. Kim, and I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. U.S.A. |

16. | I. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Matter. |

17. | B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” Appl. Phys. Lett. |

18. | J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray crystallography to allow the imaging of non-crystalline materials, cells, and single protein complexes,” Annu. Rev. Phys. Chem. |

19. | J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. |

20. | T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics |

21. | M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. Murnane, and H. Kapteyn, “Bright, coherent, ultrafast soft x-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. |

22. | T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science |

23. | C. Durfee, A. Rundquist, S. Backus, C. Herne, M. Murnane, and H. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. |

24. | X. Zhang, A. R. Libertun, A. Paul, E. Gagnon, S. Backus, I. P. Christov, M. M. Murnane, H. C. Kapteyn, R. A. Bartels, Y. Liu, and D. T. Attwood, “Highly coherent light at 13 nm generated by use of quasi-phase-matched high-harmonic generation,” Opt. Lett. |

25. | W. Ackermann, “Operation of a free-electron laser from the extreme ultraviolet to the water window,” Nat. Photonics |

26. | S. J. Habib, O. Guilbaud, B. Zielbauer, D. Zimmer, M. Pittman, D. R. Kazamias, C. Montet, and T. Kuehl, “Low energy prepulse for 10 Hz operation of a soft-x-ray laser,” Opt. Express |

27. | D. Alessi, Y. Wang, B. Luther, L. Yin, D. Martz, M. Woolston, Y. Liu, M. Berrill, and J. Rocca, “Efficient Excitation of Gain-Saturated Sub-9-nm-Wavelength Tabletop Soft-X-Ray Lasers and Lasing Down to 7.36 nm,” Phys. Rev. X |

28. | M. D. Seaberg, D. E. Adams, E. L. Townsend, D. A. Raymondson, W. F. Schlotter, Y. Liu, C. S. Menoni, L. Rong, C.-C. Chen, J. Miao, H. C. Kapteyn, and M. M. Murnane, “Ultrahigh 22 nm resolution coherent diffractive imaging using a desktop 13 nm high harmonic source,” Opt. Express |

29. | S. Roy, D. Parks, K. A. Seu, R. Su, J. J. Turner, W. Chao, E. H. Anderson, S. Cabrini, and S. D. Kevan, “Lensless x-ray imaging in reflection geometry,” Nat. Photonics |

30. | S. Marathe, S. Kim, S. Kim, C. Kim, H. C. Kang, P. V. Nickles, and D. Y. Noh, “Coherent diffraction surface imaging in reflection geometry,” Opt. Express |

31. | T. Harada, M. Nakasuji, T. Kimura, T. Watanabe, H. Kinoshita, and Y. Nagata, “Imaging of extreme-ultraviolet mask patterns using coherent extreme-ultraviolet scatterometry microscope based on coherent diffraction imaging,” J. Vac. Sci. Technol. B |

32. | M. Bryan, P. Fry, T. Schrefl, M. R. Gibbs, D. A. Allwood, M.-Y. Im, and P. Fischer, “Transverse field-induced nucleation pad switching modes during domain wall injection,” IEEE Trans. Magn. |

33. | J. M. Cowley, |

**OCIS Codes**

(100.5070) Image processing : Phase retrieval

(190.2620) Nonlinear optics : Harmonic generation and mixing

(340.7460) X-ray optics : X-ray microscopy

(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)

**ToC Category:**

Image Processing

**History**

Original Manuscript: June 21, 2012

Revised Manuscript: July 22, 2012

Manuscript Accepted: July 23, 2012

Published: August 3, 2012

**Virtual Issues**

Vol. 7, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Dennis F. Gardner, Bosheng Zhang, Matthew D. Seaberg, Leigh S. Martin, Daniel E. Adams, Farhad Salmassi, Eric Gullikson, Henry Kapteyn, and Margaret Murnane, "High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination," Opt. Express **20**, 19050-19059 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-17-19050

Sort: Year | Journal | Reset

### References

- J. Miao, P. Charalambous, and J. Kirz, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400, 342–344 (1999). [CrossRef]
- H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics4, 833–839 (2010). [CrossRef]
- P. Thibault and E. Veit, “X-Ray Diffraction Microscopy,” Annu. Rev. Condens. Matter Phys.1, 237–255 (2010). [CrossRef]
- K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature463, 214–217 (2010). [CrossRef]
- A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett.35, 2585–2587 (2010). [CrossRef] [PubMed]
- 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]
- J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett.3, 27–29 (1978). [CrossRef] [PubMed]
- J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21, 2758–2769 (1982). [CrossRef] [PubMed]
- V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A20, 40–55 (2003). [CrossRef]
- V. Elser, “Random projections and the optimization of an algorithm for phase retrieval,” J. Phys. A: Math. Gen.36, 2995–3007 (2003). [CrossRef]
- 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. B68, 140101 (2003). [CrossRef]
- D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl.21, 37–50 (2005). [CrossRef]
- J. Miao and D. Sayre, “On possible extensions of X-ray crystallography through diffraction-pattern oversampling,” Acta. Crystallogr. A56, 596–605 (2000). [CrossRef] [PubMed]
- P. Fischer, “Studying nanoscale magnetism and its dynamics with soft X-ray microscopy,” IEEE Trans. Magn.44, 1900–1904 (2008). [CrossRef]
- A. Tripathi, J. Mohanty, S. H. Dietze, O. G. Shpyrko, E. Shipton, E. E. Fullerton, S. S. Kim, and I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. U.S.A.108, 13393–13398 (2011). [CrossRef] [PubMed]
- I. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Matter.8, 291–298 (2009). [CrossRef]
- B. Abbey, G. J. Williams, M. A. Pfeifer, J. N. Clark, C. T. Putkunz, A. Torrance, I. McNulty, T. M. Levin, A. G. Peele, and K. A. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” Appl. Phys. Lett.93, 214101 (2008). [CrossRef]
- J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray crystallography to allow the imaging of non-crystalline materials, cells, and single protein complexes,” Annu. Rev. Phys. Chem.59, 387–410 (2008). [CrossRef]
- J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A.107, 7235–7239 (2010). [CrossRef] [PubMed]
- T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics4, 822–832 (2010). [CrossRef]
- M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. Murnane, and H. Kapteyn, “Bright, coherent, ultrafast soft x-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett.105, 173901 (2010). [CrossRef]
- T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science336, 1287–1291 (2012). [CrossRef] [PubMed]
- C. Durfee, A. Rundquist, S. Backus, C. Herne, M. Murnane, and H. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett.83, 2187–2190 (1999). [CrossRef]
- X. Zhang, A. R. Libertun, A. Paul, E. Gagnon, S. Backus, I. P. Christov, M. M. Murnane, H. C. Kapteyn, R. A. Bartels, Y. Liu, and D. T. Attwood, “Highly coherent light at 13 nm generated by use of quasi-phase-matched high-harmonic generation,” Opt. Lett.29, 1357–1399 (2004). [CrossRef] [PubMed]
- W. Ackermann and , “Operation of a free-electron laser from the extreme ultraviolet to the water window,” Nat. Photonics1, 336–342 (2007). [CrossRef]
- S. J. Habib, O. Guilbaud, B. Zielbauer, D. Zimmer, M. Pittman, D. R. Kazamias, C. Montet, and T. Kuehl, “Low energy prepulse for 10 Hz operation of a soft-x-ray laser,” Opt. Express20, 10128–10137 (2012). [CrossRef] [PubMed]
- D. Alessi, Y. Wang, B. Luther, L. Yin, D. Martz, M. Woolston, Y. Liu, M. Berrill, and J. Rocca, “Efficient Excitation of Gain-Saturated Sub-9-nm-Wavelength Tabletop Soft-X-Ray Lasers and Lasing Down to 7.36 nm,” Phys. Rev. X1, 021023 (2011). [CrossRef]
- M. D. Seaberg, D. E. Adams, E. L. Townsend, D. A. Raymondson, W. F. Schlotter, Y. Liu, C. S. Menoni, L. Rong, C.-C. Chen, J. Miao, H. C. Kapteyn, and M. M. Murnane, “Ultrahigh 22 nm resolution coherent diffractive imaging using a desktop 13 nm high harmonic source,” Opt. Express19, 22470–22479 (2011). [CrossRef] [PubMed]
- S. Roy, D. Parks, K. A. Seu, R. Su, J. J. Turner, W. Chao, E. H. Anderson, S. Cabrini, and S. D. Kevan, “Lensless x-ray imaging in reflection geometry,” Nat. Photonics5, 243–245 (2011). [CrossRef]
- S. Marathe, S. Kim, S. Kim, C. Kim, H. C. Kang, P. V. Nickles, and D. Y. Noh, “Coherent diffraction surface imaging in reflection geometry,” Opt. Express18, 7253–7262 (2010). [CrossRef] [PubMed]
- T. Harada, M. Nakasuji, T. Kimura, T. Watanabe, H. Kinoshita, and Y. Nagata, “Imaging of extreme-ultraviolet mask patterns using coherent extreme-ultraviolet scatterometry microscope based on coherent diffraction imaging,” J. Vac. Sci. Technol. B29, 06F503 (2011). [CrossRef]
- M. Bryan, P. Fry, T. Schrefl, M. R. Gibbs, D. A. Allwood, M.-Y. Im, and P. Fischer, “Transverse field-induced nucleation pad switching modes during domain wall injection,” IEEE Trans. Magn.46, 963–967 (2010). [CrossRef]
- J. M. Cowley, Diffraction Physics, 3rd ed. (Elsevier Science B.V., Danvers, 1995).

## 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.

« Previous Article | Next Article »

OSA is a member of CrossRef.