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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 26424–26433

Experimental realization of optical eigenmode super-resolution

Kevin Piché, Jonathan Leach, Allan S. Johnson, Jeff Z. Salvail, Mikhail I. Kolobov, and Robert W. Boyd  »View Author Affiliations

Optics Express, Vol. 20, Issue 24, pp. 26424-26433 (2012)

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We experimentally demonstrate the feasibility of a super-resolution technique based on eigenmode decomposition. This technique has been proposed theoretically but, to the best of our knowledge, has not previously been realized experimentally for optical imaging systems with circular apertures. We use a standard diffraction-limited 4f imaging system with circular apertures for which the radial eigenmodes are the circular prolate spheroidal functions. For three original objects with different content of angular information we achieve 45%, 49%, and 89% improvement of resolution over the Rayleigh limit. The work presented can be considered as progress towards the goal of reaching the quantum limits of super-resolution.

© 2012 OSA

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(100.3020) Image processing : Image reconstruction-restoration

ToC Category:
Image Processing

Original Manuscript: August 16, 2012
Revised Manuscript: October 27, 2012
Manuscript Accepted: November 1, 2012
Published: November 8, 2012

Kevin Piché, Jonathan Leach, Allan S. Johnson, Jeff Z. Salvail, Mikhail I. Kolobov, and Robert W. Boyd, "Experimental realization of optical eigenmode super-resolution," Opt. Express 20, 26424-26433 (2012)

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  1. P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys. Rev. A63, 063407 (2001). [CrossRef]
  2. H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett.107, 083603 (2011). [CrossRef] [PubMed]
  3. R. W. Boyd and J. P. Dowling, “Quantum lithography: status of the field,” Quant. Inf. Processing11, 891–901 (2012). [CrossRef]
  4. G. Toraldo and Di Francia, “Resolving power and information,” J. Opt. Soc. Am.45, 497–501 (1955). [CrossRef]
  5. J. L. Harris, “Diffraction and resolving power,” J. Opt. Soc. Am.54, 931–936 (1964). [CrossRef]
  6. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science315, 1686 (2007). [CrossRef] [PubMed]
  7. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966–3969 (2000). [CrossRef] [PubMed]
  8. D. R. Smith, “How to build a superlens,” Science308, 502–503 (2005). [CrossRef] [PubMed]
  9. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308, 534–537 (2005). [CrossRef] [PubMed]
  10. E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Materials11, 432–435 (2012). [CrossRef]
  11. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A79, 013827 (2009). [CrossRef]
  12. F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-rayleigh imaging via N-photon detection,” Phys. Rev. Lett.105, 163602 (2010). [CrossRef]
  13. C. K. Rushforth, “Restoration, resolution, and noise,” J. Opt. Soc. Am.58, 539–545 (1968). [CrossRef]
  14. G. Toraldo and Di Francia, “Degrees of freedom of an image,” J. Opt. Soc. Am.59, 799–804 (1969). [CrossRef]
  15. M. Bertero and E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis,” Opt. Acta29, 727–746 (1982). [CrossRef]
  16. A. C. D. Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, “Optical eigenmode imaging,” Phys. Rev. A84, 021803 (2011). [CrossRef]
  17. M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett.85(18), 3789–3792 (2000). [CrossRef] [PubMed]
  18. I. V. Sokolov and M. I. Kolobov, “Squeezed-light source for superresolving microscopy,” Opt. Lett.29, 703–705 (2004). [CrossRef] [PubMed]
  19. V. N. Beskrovnyy and M. I. Kolobov, “Quantum limits of super-resolution in reconstruction of optical objects,” Phys. Rev. A71(4), 043802 (2005). [CrossRef]
  20. V. N. Beskrovny and M. I. Kolobov, “Quantum theory of super-resolution for optical systems with circular apertures,” Opt. Commun.264(1), 9–12 (2006). [CrossRef]
  21. V. N. Beskrovny and M. I. Kolobov, “Quantum-statistical analysis of superresolution for optical systems with circular symmetry,” Phys. Rev. A78(4), 043824 (2008). [CrossRef]
  22. D. Slepian, “Prolate spheroidal wave functions, Fourier analysis and uncertainty IV,” Bell Syst. Tech. J.43, 3009–3057 (1964).
  23. I. C. Moore and M. Cada, “Prolate spheroidal wave functions, an introduction to the Slepian series and its properties,” Appl. Comput. Harmon. Anal.16, 208–230 (2004). [CrossRef]
  24. G. Walter and T. Soleski, “A new friendly method of computing prolate spheroidal wave functions and wavelets,” Appl. Comput. Harmon. Anal.19, 432–443 (2005). [CrossRef]
  25. H. Xiao, V. Rokhlin, and N. Yarvin, “Prolate spheroidal wavefunctions, quadrature and interpolation,” IOP-Science17, 805–838 (2000).
  26. D. Slepian and E. Sonnenblick, “Eigenvalues associated with prolate spheroidal wave functions of zero order,” Bell Syst. Tech. J.44, 1745–1759 (1965).
  27. B. R. Frieden, “Band-unlimited reconstruction of optical objects and spectra,” J. Opt. Soc. Am.57, 1013–1019 (1967). [CrossRef]
  28. B. R. Frieden, “Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions,” Prog. Opt.9, 311–407 (1971). [CrossRef]
  29. C.-S. Hu, “Prolate spheroidal wave functions of large frequency parameters c = kf and their applications in electromagnetic theory,” IEEE Trans. Antennas Propag.AP-34, 114–119 (1986).
  30. J. C. Heurtley, “Hyperspheroidal functions-optical resonators with circular mirrors,” Proc. Symp. Quasi-Opt.1, 367–375 (1964).

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