OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 17 — Jun. 10, 1998
  • pp: 3612–3622

Scalar and electromagnetic diffraction point-spread functions

Jakob J. Stamnes and Halvor Heier  »View Author Affiliations


Applied Optics, Vol. 37, Issue 17, pp. 3612-3622 (1998)
http://dx.doi.org/10.1364/AO.37.003612


View Full Text Article

Enhanced HTML    Acrobat PDF (312 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We describe an accurate technique for computing the diffraction point-spread function for optical systems. The approach is based on the combined method of ray tracing and diffraction, which implies that the computation is accomplished in a two-step procedure. First, ray tracing is employed to compute the wave-front error in a reference plane on the image side of the system and to determine the shape of the vignetted pupil. Next the Rayleigh–Sommerfeld diffraction theory, combined with the Kirchhoff approximation and the Stamnes–Spjelkavik–Pedersen method for numerical integration, is applied to compute the field in the region of the image. The method does not rely on small-angle approximations and works well for a pupil of general shape. Both scalar and electromagnetic computations are discussed and numerical results are presented.

© 1998 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(110.0110) Imaging systems : Imaging systems
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(260.5430) Physical optics : Polarization

Citation
Jakob J. Stamnes and Halvor Heier, "Scalar and Electromagnetic Diffraction Point-Spread Functions," Appl. Opt. 37, 3612-3622 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-17-3612


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. H. Hopkins and M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970). [CrossRef]
  2. J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Bristol, 1986), Sec. 12.6.
  3. J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Bristol, 1986), Chap. 3, Sec. 6.3.2.
  4. R. Chander, “On tracing rays with specified endpoints,” Geophysics 41, 173–177 (1975).
  5. V. Cerveny and H. Hron, “The ray series method and dynamic ray tracing for 3-D inhomogeneous media,” Bull. Seism. Soc. Am. 70, 47–77 (1980).
  6. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972).
  7. Equations (4.16a) and (4.18a) in Ref. 2.
  8. Equation (12.3b) in Ref. 2.
  9. H. H. Hopkins, “The numerical evaluation of the frequency response of optical systems,” Proc. Phys. Soc. B 70, 1002–1005 (1957). [CrossRef]
  10. A. C. Ludwig, “Computation of radiation patterns involving double numerical integration,” IEEE Trans. Antennas Propag. AP-16, 767–769 (1968). [CrossRef]
  11. J. J. Stamnes, B. Spjelkavik, and H. M. Pedersen, “Evaluation of diffraction integrals using local phase and amplitude approximations,” Opt. Acta 30, 1331–1358 (1983). [CrossRef]
  12. J. J. Stamnes, Waves in Focal Regions (Adam Hilger, Bristol, 1986), Sec. 7.2.
  13. G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves (Peregrinus, London, 1976).
  14. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), p. 40.
  15. Equation (15.66a) in Ref. 2.
  16. Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981). [CrossRef]
  17. Ref. 2, Sec. 12.2.
  18. M. Mansuripur, “Distribution of light at and near the focus of high numerical aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986). [CrossRef]
  19. V. Dhayalan and J. J. Stamnes, “Focusing of electromagnetic waves in a dielectric slab. I. Exact and asymptotic results,” Pure Appl. Opt. 7, 33–52 (1998). [CrossRef]
  20. J. J. Stamnes and V. Dhayalan, “Focusing of electric-dipole waves,” Pure Appl. Opt. 5, 195–226 (1996). [CrossRef]
  21. V. Dhayalan and J. J. Stamnes, “Focusing of mixed-dipole waves,” Pure Appl. Opt. 6, 317–345 (1997). [CrossRef]
  22. V. Dhayalan and J. J. Stamnes, “Focusing of electric-dipole waves in the Debye and Kirchhoff approximations,” Pure Appl. Opt. 6, 347–372 (1997). [CrossRef]
  23. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959). [CrossRef]
  24. A. Boivin and E. Wolf, “Electromagnetic fields in the neighborhood of the focus of a coherent beam,” Phys. Rev. B 138, 1561–1565 (1965). [CrossRef]
  25. A. Boivin, J. Dow, and E. Wolf, “Energy flow in the neighborhood of the focus of a coherent beam,” J. Opt. Soc. Am. A 57, 1171–1175 (1967). [CrossRef]
  26. A. Yoshida and T. Asakura, “Electromagnetic field in the focal plane of a coherent beam from a wide-angular annular-aperture system,” Optik (Stuttgart) 40, 322–331 (1974).
  27. A. Yoshida and T. Asakura, “Electromagnetic field near the focus of a Gaussian beam,” Optik (Stuttgart) 41, 281–292 (1974).
  28. R. Barakat, “Diffracted electromagnetic fields in the neighborhood of the focus of a paraboloidal mirror having a central obscuration,” Appl. Opt. 26, 3790–3795 (1987). [CrossRef] [PubMed]
  29. H. Ling and S. W. Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. A 1, 965–973 (1984). [CrossRef]
  30. P. Török, P. Varga, Z. Laczic, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12, 2136–2144 (1995). [CrossRef]
  31. P. Török, P. Varga, A. Konkol, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. II,” J. Opt. Soc. Am. A 13, 2232–2238 (1996). [CrossRef]
  32. D. G. Flagello, T. Milster, and A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53–64 (1996). [CrossRef]
  33. S. H. Wiersma and T. D. Visser, “Defocusing of a converging electromagnetic wave by a plane dielectric interface,” J. Opt. Soc. Am. A 13, 320–325 (1996). [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