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. 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]
2. H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics4, 833–839 (2010). [CrossRef]
3. P. Thibault and E. Veit, “X-Ray Diffraction Microscopy,” Annu. Rev. Condens. Matter Phys.1, 237–255 (2010). [CrossRef]
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,” Nature463, 214–217 (2010). [CrossRef]
5. 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]
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]
8. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21, 2758–2769 (1982). [CrossRef] [PubMed]
9. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A20, 40–55 (2003). [CrossRef]
10. V. Elser, “Random projections and the optimization of an algorithm for phase retrieval,” J. Phys. A: Math. Gen.36, 2995–3007 (2003). [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. B68, 140101 (2003). [CrossRef]
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. A56, 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. Photonics4, 822–832 (2010). [CrossRef]
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.105, 173901 (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,” Science336, 1287–1291 (2012). [CrossRef] [PubMed]
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.83, 2187–2190 (1999). [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]
25. W. Ackermann and , “Operation of a free-electron laser from the extreme ultraviolet to the water window,” Nat. Photonics1, 336–342 (2007). [CrossRef]
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. Express20, 10128–10137 (2012). [CrossRef] [PubMed]
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. X1, 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. Express19, 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. Photonics5, 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. Express18, 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. B29, 06F503 (2011). [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]
33. J. M. Cowley, Diffraction Physics, 3rd ed. (Elsevier Science B.V., Danvers, 1995).

Acta. Crystallogr. A

• J. Miao and D. Sayre, “On possible extensions of X-ray crystallography through diffraction-pattern oversampling,” Acta. Crystallogr. A56, 596–605 (2000). [CrossRef] [PubMed]

Annu. Rev. Condens. Matter Phys.

• P. Thibault and E. Veit, “X-Ray Diffraction Microscopy,” Annu. Rev. Condens. Matter Phys.1, 237–255 (2010). [CrossRef]

Annu. Rev. Phys. Chem.

• 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]

Appl. Opt.

• J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21, 2758–2769 (1982). [CrossRef] [PubMed]

Appl. Phys. Lett.

• 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]

IEEE Trans. Magn.

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

Inverse Probl.

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

J. Opt. Soc. Am. A

• V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A20, 40–55 (2003). [CrossRef]

J. Phys. A: Math. Gen.

• V. Elser, “Random projections and the optimization of an algorithm for phase retrieval,” J. Phys. A: Math. Gen.36, 2995–3007 (2003). [CrossRef]

J. Vac. Sci. Technol. B

• 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]

Nat. Matter.

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

Nat. Photonics

• H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics4, 833–839 (2010). [CrossRef]
• 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]
• 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]
• W. Ackermann and , “Operation of a free-electron laser from the extreme ultraviolet to the water window,” Nat. Photonics1, 336–342 (2007). [CrossRef]

Nat. Phys.

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

Nature

• J. Miao, P. Charalambous, and J. Kirz, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400, 342–344 (1999). [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]

Opt. Express

• 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]
• 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. 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]

Opt. Lett.

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

Phys. Rev. B

• 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]

Phys. Rev. Lett.

• 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]
• 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]

Phys. Rev. X

• 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]

Proc. Natl. Acad. Sci. U.S.A.

• 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]
• 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]

Science

• 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]

Other

• J. M. Cowley, Diffraction Physics, 3rd ed. (Elsevier Science B.V., Danvers, 1995).

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