OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 3 — Mar. 1, 2014
  • pp: 470–474

K-means clustering for support construction in diffractive imaging

Shunsuke Hattanda, Hiroyuki Shioya, Yosuke Maehara, and Kazutoshi Gohara  »View Author Affiliations


JOSA A, Vol. 31, Issue 3, pp. 470-474 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000470


View Full Text Article

Enhanced HTML    Acrobat PDF (531 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A method for constructing an object support based on K-means clustering of the object-intensity distribution is newly presented in diffractive imaging. This releases the adjustment of unknown parameters in the support construction, and it is well incorporated with the Gerchberg and Saxton diagram. A simple numerical simulation reveals that the proposed method is effective for dynamically constructing the support without an initial prior support.

© 2014 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(100.3008) Image processing : Image recognition, algorithms and filters

ToC Category:
Image Processing

History
Original Manuscript: October 9, 2013
Revised Manuscript: November 27, 2013
Manuscript Accepted: December 6, 2013
Published: February 5, 2014

Citation
Shunsuke Hattanda, Hiroyuki Shioya, Yosuke Maehara, and Kazutoshi Gohara, "K-means clustering for support construction in diffractive imaging," J. Opt. Soc. Am. A 31, 470-474 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-3-470


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5, 843 (1952). [CrossRef]
  2. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  3. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998). [CrossRef]
  4. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999). [CrossRef]
  5. J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002). [CrossRef]
  6. J. Miao, T. Ishikawa, E. H. Anderson, and K. O. Hodgson, “Phase retrieval of diffraction patterns from noncrystalline samples using the oversampling method,” Phys. Rev. B 67, 174104 (2003). [CrossRef]
  7. Y. Nishino, J. Miao, and T. Ishikawa, “Image reconstruction of nanostructured nonperiodic objects only from oversampled hard x-ray diffraction intensities,” Phys. Rev. B 68, 220101(R) (2003). [CrossRef]
  8. H. N. Chapman, A. Barty, M. J. Bogan, S. Boutet, M. Frank, S. P. Hau-Riege, S. Marchesini, B. W. Woods, S. Bajt, W. H. Benner, R. A. London, E. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szöke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006). [CrossRef]
  9. U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2002). [CrossRef]
  10. J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003). [CrossRef]
  11. O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92, 024106 (2008). [CrossRef]
  12. S. Morishita, J. Yamasaki, K. Nakamura, T. Kato, and N. Tanaka, “Diffractive imaging of the dumbbell structure in silicon by spherical-aberation-corrected electron diffraction,” Appl. Phys. Lett. 93, 183103 (2008). [CrossRef]
  13. R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Lensless diffractive imaging using tabletop coherent high-harmonic soft-x-ray beams,” Phys. Rev. Lett. 99, 098103 (2007). [CrossRef]
  14. J. C. H. Spence, Science of Microscopy, P. W. Hawkes and J. C. H. Spence, eds. (Springer, 2007).
  15. A. Walter, “The question of phase retrieval in optics,” Opt. Acta 10, 41–49 (1963). [CrossRef]
  16. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef]
  17. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978). [CrossRef]
  18. J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Opt. Eng. 18, 185529 (1979). [CrossRef]
  19. B. R. Frieden and D. G. Currie, “On unfolding the autocorrelation function,” J. Opt. Soc. Am. 66, 1111 (1976). [CrossRef]
  20. R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I. Underlying theory,” Optik 61, 247–262 (1982).
  21. K. L. Garden and R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. II. One dimensional considerations,” Optik 62, 131–142 (1982).
  22. W. R. Fright and R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. III. Computational examples for two dimension,” Optik 62, 219–230 (1982).
  23. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40–55 (2003). [CrossRef]
  24. H. Shioya, Y. Maehara, and K. Gohara, “Spherical shell structure of distribution of images reconstructed by diffractive imaging,” J. Opt. Soc. Am. A 27, 1214–1218 (2010). [CrossRef]
  25. J. R. Fienup, T. R. Crimmins, and W. Holsztynski, “Reconstruction of the support an object from the support of its autocorrelation,” J. Opt. Soc. Am. A 72, 610–624 (1982).
  26. J. R. Fienup, “Phase retrieval using boundary conditions,” J. Opt. Soc. Am. A 3, 284–288 (1986). [CrossRef]
  27. J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986). [CrossRef]
  28. T. R. Crimmins, J. R. Fienup, and B. J. Thelen, “Improved bounds on object support from autocorrelation support and application to phase retrieval,” J. Opt. Soc. Am. A 7, 3–13 (1990). [CrossRef]
  29. 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]
  30. G. Oszlanyi and A. Suto, “Ab initio structure solution by charge flipping,” Acta Crystallogr. Sect. A 60, 134–141 (2004). [CrossRef]
  31. J. S. Wu, U. Weierstall, J. C. Spence, and C. T. Koch, “Iterative phase retrieval without support,” Opt. Lett. 29, 2737–2739 (2004). [CrossRef]
  32. J. B. MacQueen, “Some methods for classification and analysis of multivariate observations,” in Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability (University of California, 1967), pp. 281–297.
  33. A. K. Jain, N. M. Murty, and P. J. Flynn, “Data clustering: a review,” ACM Comput. Surv. 31, 264–323 (1999). [CrossRef]
  34. J. A. Hartigan, Clustering Algorithms (Wiley, 1975).
  35. J. A. Hartigan and M. A. Wong, “A K-means clustering algorithm,” J. R. Stat. Soc. Ser. C 28, 100–108 (1979). [CrossRef]

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.

CrossCheck Deposited