OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 1, Iss. 11 — Nov. 13, 2006

Reduced-complexity representation of the coherent point-spread function in the presence of aberrations and arbitrarily large defocus

Saeed Bagheri, Daniela Pucci de Farias, George Barbastathis, and Mark A. Neifeld  »View Author Affiliations


JOSA A, Vol. 23, Issue 10, pp. 2476-2493 (2006)
http://dx.doi.org/10.1364/JOSAA.23.002476


View Full Text Article

Acrobat PDF (569 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We introduce a method to analyze the diffraction integral for evaluating the point-spread function. Our method is based on the use of higher-order Airy functions along with Zernike and Taylor expansions. Our approach is applicable when we are considering a finite, arbitrary number of aberrations and arbitrarily large defocus simultaneously. We present an upper bound for the complexity and the convergence rate of this method. We also compare the cost and accuracy of this method with those of traditional ones and show the efficiency of our method through these comparisons. In particular, we rigorously show that this method is constructed in a way that the complexity of the analysis (i.e., the number of terms needed for expressing the light disturbance) does not increase as either defocus or resolution of interest increases. This has applications in several fields such as biological microscopy, lithography, and multidomain optimization in optical systems.

© 2006 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.1940) Diffraction and gratings : Diffraction
(070.2590) Fourier optics and signal processing : ABCD transforms

ToC Category:
Fourier Optics and Optical Signal Processing

History
Original Manuscript: December 22, 2005
Revised Manuscript: May 2, 2006
Manuscript Accepted: May 4, 2006

Virtual Issues
Vol. 1, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Saeed Bagheri, Daniela Pucci de Farias, George Barbastathis, and Mark A. Neifeld, "Reduced-complexity representation of the coherent point-spread function in the presence of aberrations and arbitrarily large defocus," J. Opt. Soc. Am. A 23, 2476-2493 (2006)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-23-10-2476


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, UK, 1992).
  2. B. H. W. Hendriks, J. J. H. B. Schleipen, S. Stallinga, and H. van Houten, "Optical pickup for blue optical recording at NA=0.85," Opt. Rev. 6, 211-213 (2001).
  3. H. P. Urbach and D. A. Bernard, "Modeling latent-image formation in photolithography, using the Helmholtz equation," J. Opt. Soc. Am. A 6, 1343-1356 (1989).
  4. W. T. Cathey and E. R. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002).
  5. R. Narayanswamy, G. E. Johnson, P. E. X. Silveira, and H. B. Wach, "Extending the imaging volume for biometric iris recognition," Appl. Opt. 44, 701-712 (2005).
  6. E. R. Dowski and G. E. Johnson, "Wavefront coding: a modern method of achieving high-performance and/or low-cost imaging systems," in Current Developments in Optical Design and Optical Engineering VIII, R. E. Fischer and W. J. Smith, eds., Proc. SPIE 3779, 137-145 (1999).
  7. J. Braat, P. Dirksen, and A. J. E. M. Janssen, "Assessment of an extended Nijboer-Zernike approach for the computation of optical point-spread-functions," J. Opt. Soc. Am. A 19, 858-870 (2002).
  8. A. J. E. M. Janssen, "Extended Nijboer-Zernike approach for the computation of optical point-spread functions," J. Opt. Soc. Am. A 19, 849-857 (2002).
  9. J. Braat, P. Dirksen, A. J. E. M. Janssen, and A. S. van de Nes, "Extended Nijboer-Zernike representation of the vector field in the focal region of an aberrated high-aperture optical system," J. Opt. Soc. Am. A 20, 2281-2292 (2003).
  10. A. J. E. M. Janssen, J. J. M. Braat, and P. Dirksen, "On the computation of the Nijboer-Zernike aberration integrals at arbitrary defocus," J. Mod. Opt. 51, 687-703 (2004).
  11. H. A. Buchdahl, Optical Aberration Coefficients (Oxford U. Press, 1958).
  12. S. Bagheri, P. E. X. Silveira, R. Narayanswamy, and D, P. de Farias, "Analytical optimal solution of the extension of the depth of field using cubic phase wayefront coding" (in preparation; bagheri@mit.edu).
  13. C. L. Tranter, Bessel Functions with Some Physical Applications (Hart, 1969).
  14. A. Gray and G. B. Mathews, A Treatise on Bessel Functions and Their Applications to Physics (Dover, 1966).
  15. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, 1944).
  16. L. Landau, "Monotonicity and bounds on Bessel functions," in Proceedings of Mathematical Physics and Quantum Field Theory, H.Warchall, ed. (2000), Vol. 4, pp. 147-154.

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