Sparsity-based single-shot subwavelength coherent diffractive imaging

Nature Materials

Volumn 11, Issue 5, 2012, Pages 455-459

  Szameit, A ^a,b   Shechtman, Y ^a   Osherovich, E ^a   Bullkich, E ^a   Sidorenko, P ^a   Dana, H ^a   Steiner, S ^b   Kley, E B ^b   Gazit, S ^a   Cohen Hyams, T ^a   Shoham, S ^a   Zibulevsky, M ^a   Yavneh, I ^a   Eldar, Y C ^a   Cohen, O ^a   Segev, M ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRONS; FREE ELECTRON LASERS; IMAGING TECHNIQUES;

COHERENT DIFFRACTIVE IMAGING; DIFFRACTION LIMITS; FAR-FIELD INTENSITY; INTENSITY PATTERNS; SINGLE-SHOT MEASUREMENTS; STRUCTURE OF MOLECULES; SUBWAVELENGTH RESOLUTION; X-RAY FREE ELECTRON LASERS;

DIFFRACTION;

ALGORITHM; ARTICLE; IMAGE PROCESSING; METHODOLOGY; STATISTICS; X RAY DIFFRACTION;

ALGORITHMS; IMAGE PROCESSING, COMPUTER-ASSISTED; X-RAY DIFFRACTION;

EID: 84860121825     PISSN: 14761122     EISSN: 14764660     Source Type: Journal    
DOI: 10.1038/nmat3289     Document Type: Article

References (36)

1. Abbe, E. Beiträge zur Theorie des Mikroskops und der Mikroskopischen Wahrnehmung. Arch. Mikrosk. Anatomie 9, 413-468 (1873).
2. Lipson, S. G. , Lipson, H. & Tannhauser, D. S. Optical Physics 3rd edn (Cambridge Univ. Press, 1995).
3. Lewis, A. , Isaacson, M. , Harotunian, A. & Muray, A. Development of a 500-Å spatial-resolution light-microscope: I. Light is efficiently transmitted through l=16 diameter apertures. Ultramicroscopy 13, 227-231 (1984).
4. Betzig, E. , Trautman, J. K. , Harris, T. D. , Weiner, J. S. & Kostelak, R. L. Breaking the diffraction barrier: Optical microscopy on a nanometric scale. Science 251, 1468-1470 (1991). (Pubitemid 121000433)
5. Di Francia, G. T. Super-gain antennas and optical resolving power. Nuovo Cimento 9, 426-438 (1955).
6. Lezec, H. J. et al. Beaming light from a subwavelength aperture. Science 297, 820-823 (2002).
7. Huang, F. M. & Zheludev, N. I. Super-resolution without evanescent waves. Nano Lett. 9, 1249-1254 (2009).
8. Hell, S. W. & Wichmann, J. Breaking the diffraction resolution limit by stimulated emission: Stimulated-emission-depletion microscopy. Opt. Lett. 19, 780-783 (1994).
9. Yildiz, A. et al. Myosin V walks hand-overhand: Single fluorophore imaging with 1. 5nm localization. Science 300, 2061-2065 (2003). (Pubitemid 36760126)
10. Hell, S. W. , Schmidt, R. & Egner, A. Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses. Nature Photon. 3, 381-387 (2009).
11. Harris, J. L. Diffraction and resolving power. J. Opt. Soc. Am. 54, 931-936 (1964).
12. Papoulis, A. A new algorithm in spectral analysis and band-limited extrapolation. IEEE Trans. Circuits Syst. 22, 735-742 (1975).
13. Gerchberg, R. W. Super-resolution through error energy reduction. J. Mod. Opt. 21, 709-720 (1974).
14. Goodman, J. W. Introduction to Fourier Optics 3rd edn (Roberts, 2005).
15. Gazit, S. , Szameit, A. , Eldar, Y. C. & Segev, M. Super-resolution and reconstruction of sparse subwavelength images. Opt. Exp. 17, 23920-23946 (2009).
16. Candes, E. J. , Romberg, J. & Tao, T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52, 489-509 (2006). (Pubitemid 43174093)
17. Donoho, D. L. Compressed sensing. IEEE Trans. Inf. Theory 52, 1289-1306 (2006).
18. Candes, E. J. & Tao, T. Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inf. Theory 52, 5406-5425 (2006). (Pubitemid 46445381)
19. Candes, E. J. & Wakin, M. B. An introduction to compressive sampling. IEEE Signal Process. Mag. 25, 21-30 (2008).
20. Duarte, M. & Eldar, Y. C. Structured compressed sensing: From theory to applications. Trans. Signal Process. 59, 4053-4085 (2011).
21. Szameit, A. et al. Far-field microscopy of sparse subwavelength objects, Preprint at http://arxiv. org/abs/1010. 0631v1 (2010).
22. Shechtman, Y. , Gazit, S. , Szameit, A. , Eldar, Y. C. & Segev, M. Super-resolution and reconstruction of sparse images carried by incoherent light. Opt. Lett. 35, 1148-1150 (2010).
23. Shechtman, Y. , Eldar, Y. C. , Szameit, A. & Segev, M. Sparsity-based subwavelength imaging with partially spatially incoherent light via quadratic compressed sensing. Opt. Exp. 19, 14807-14822 (2011).
24. Derin, S. D. , Wang, Z. , Do, M. & Popescu, G. Cell imaging beyond the diffraction limit using sparse deconvolution spatial light interference microscopy. Biomedical Opt. Exp. 2, 1815-1827 (2011).
25. Sayre, D. Some implications of a theorem due to Shannon. Acta Crystallogr. 5, 843 (1952).
26. Miao, J. , Charalambous, P. , Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens. Nature 400, 342-344 (1999). (Pubitemid 29344194)
27. Quiney, H. M. Coherent diffractive imaging using short wavelength light sources: A tutorial review. J. Mod. Opt. 57, 1109-1149 (2010).
28. Chapman, H. N. & Nugent, K. A. Coherent lensless X-ray imaging. Nature Photon. 4, 833-839 (2010).
29. Sandberg, R. L. et al. Lensless diffractive imaging using tabletop coherent high-harmonic soft-X-ray beams. Phys. Rev. Lett. 99, 098103 (2007).
30. Chapman, H. N. et al. Femtosecond time-delay X-ray holography. Nature 448, 676-679 (2007). (Pubitemid 47236865)
31. Neutze, R. , Wouts, R. , van der Spoel, D. , Weckert, E. & Hajdu, J. Potential for biomolecular imaging with femtosecond X-ray pulses. Nature 406, 752-757 (2000).
32. Chapman, H. M. et al. Femtosecond X-ray protein nanocrystallography. Nature 470, 73-77 (2011).
33. Vetterli, M. , Marziliano, P. & Blu, T. Sampling signals with finite rate of innovation. IEEE Trans. Signal Process. 50, 1417-1428 (2002). (Pubitemid 34822552)
34. Gleichman, S. & Eldar, Y. C. Blind compressed sensing. IEEE Trans. Inform. Theory 57, 6958-6975 (2011).
35. Aharon, M. , Elad, M. & Bruckstein, A. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54, 4311-4322 (2006). (Pubitemid 44637761)
36. Sidorenko, P. et al. The 2010 Frontiers Optics Conference, OSA Technical Digest (Optical Society of America, 2010), Paper FTuE2.