OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 1 — Jan. 7, 2008
  • pp: 58–66

Quantum limits of superresolution for imaging discrete subwavelength structures

Mikhail I. Kolobov  »View Author Affiliations

Optics Express, Vol. 16, Issue 1, pp. 58-66 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (121 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present the quantum theory of superresolution for discrete subwavelength structures. It allows to formulate, in particular, the standard quantum limit of superresolution achieved for illumination of the structure by light in coherent state. Our theory is based on discrete prolate spheroidal sequences and functions which are the proper basis set of the problem. We demonstrate that the superresolution factor is much higher for discrete structures than for continuous objects for the same signal-to-noise ratio. This result is a clear illustration of the crucial role of a priori information in superresolution problems.

© 2008 Optical Society of America

OCIS Codes
(100.6640) Image processing : Superresolution
(270.0270) Quantum optics : Quantum optics
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Imaging Systems

Original Manuscript: November 14, 2007
Revised Manuscript: December 17, 2007
Manuscript Accepted: December 20, 2007
Published: January 2, 2008

Mikhail I. Kolobov, "Quantum limits of superresolution for imaging discrete subwavelength structures," Opt. Express 16, 58-66 (2008)

Sort:  Year  |  Journal  |  Reset  


  1. F. Thomas, "Multilevel subwavelength optical data storage using reflective nanostructures," presented at the 2005 INSIC Symposium "Alternative Data Storage," Monterey, USA, 2005.
  2. H. Kostal, J. J. Wang, and F. Thomas, "Manufacture of multi-level encoded subwavelength optical data storage media," invited paper at the Topical Meeting "Advanced Imaging Techniques" of the European Optical Society, London, UK, 2005.
  3. A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, "High-density optical data storage," Rep. Prog. Phys. 69, 2323-2363 (2006). [CrossRef]
  4. M. I. Kolobov and C. Fabre, "Quantum limits on optical resolution," Phys. Rev. Lett. 85, 3789-3792 (2000). [CrossRef] [PubMed]
  5. V. N. Beskrovnyy and M. I. Kolobov, "Quantum limits of super-resolution in reconstruction of optical objects," Phys. Rev. A 71, 043802(1-10) (2005). [CrossRef]
  6. M. I. Kolobov and V. N. Beskrovnyy, "Quantum theory of super-resolution for optical systems with circular apertures," Opt. Commun. 264, 9-12 (2006). [CrossRef]
  7. I. V. Sokolov and M. I. Kolobov, "Squeezed-light source for superresolving microscopy," Opt. Lett. 29, 703-705 (2004). [CrossRef] [PubMed]
  8. M. Bertero and C. De Mol, "Super-resolution by data inversion," in Progress in Optics, edited by E.Wolf (North-Holland, Amsterdam, 1996), Vol. XXXVI, pp. 129-178.
  9. B. R. Frieden, "Restoring with maximum likelihood and maximum entropy," J. Opt. Soc. Am. 62, 511-518 (1972). [CrossRef] [PubMed]
  10. M. Bertero, C. De Mol, and E. R. Pike, "Linear inverse problems with discrete data. I: General formulation and singular system analysis," Inverse Problems 1, 301-330 (1985). [CrossRef]
  11. D. Slepian, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-V: The discrete case", Bell System Tech. J. 57, 1371-1430 (1978).
  12. A. Papoulis and M. S. Bertran, "Digital filtering and prolate functions," IEEE Trans.Circuit Theory, CT- 19, 674-681 (1972). [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.


Fig. 1. Fig. 2.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited