Generalized Jinc functions and their application to focusing and diffraction of circular apertures

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 20, Issue 4, 2003, Pages 661-667

  Cao, Qing ^a  

^a UNIVERSITY OF HAGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGER PROGRAMMING; MATHEMATICAL TECHNIQUES; POLYNOMIALS;

SPHERICAL WAVES;

ELECTROMAGNETIC WAVE DIFFRACTION;

EID: 0041573116     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.20.000661     Document Type: Article

References (22)

1. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, UK, 1975), Chap. 8.
2. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).
3. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 2.
4. A. E. Siegman, Lasers (Oxford U. Press, Oxford, UK, 1986), Sec. 18.4.
5. Y. Li and E. Wolf, "Three-dimensional intensity distribution near the focus in system of different Fresnel numbers," J. Opt. Soc. Am. A 1, 801-808 (1984).
6. Y. Li, "Three-dimensional intensity distribution in low-Fresnel-number focusing systems," J. Opt. Soc. Am. A 4, 1349-1353 (1987).
7. P. Wang, Y. Xu, W. Wang, and Z. Wang, "Analytical expression for Fresnel diffraction," J. Opt. Soc. Am. A 15, 684-688 (1998).
8. J. C. Heurtley, "Analytical expression for Fresnel diffraction: comment," J. Opt. Soc. Am. A 15, 2929-2930 (1998).
9. P. L. Overfelt and D. J. White, "Analytical expression for Fresnel diffraction: comment," J. Opt. Soc. Am. A 16, 613-615 (1999).
10. Y.-T. Wang, Y. C. Pati, and T. Kailath, "Depth of focus and the moment expansion," Opt. Lett. 20, 1841-1843 (1995).
11. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Wiley, New York, 1972).
12. W. H. Southwell, "Validity of the Fresnel approximation in the near field," J. Opt. Soc. Am. 71, 7-14 (1981).
13. J. H. Erkkila and M. E. Rogers, "Diffracted fields in the focal volume of a converging wave," J. Opt. Soc. Am. 71, 904-905 (1981).
14. Y. Li and E. Wolf, "Focal shifts in diffracted converging spherical waves," Opt. Commun. 38, 211-215 (1981).
15. J. J. Stamnes and B. Spjelkavik, "Focusing at small angular apertures in the Debye and Kirchhoff approximations," Opt. Commun. 40, 81-85 (1981).
16. M. P. Givens, "Focal shifts in diffracted converging spherical waves," Opt. Commun. 41, 145-148 (1982).
17. Q. Cao and J. Jahns, "Focusing analysis of the pinhole photon sieve: individual far-field model," J. Opt. Soc. Am. A 19, 2387-2393 (2002).
18. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieve," Nature (London) 414, 184-188 (2001).
19. E. Lalor, "Conditions for the validity of the angular spectrum of plane waves," J. Opt. Soc. Am. 58, 1235-1237 (1968). The Parseval theorem is the special case f(x, y) = g(x, y) of Theorem IV of this reference.
20. W. H. Southwell, "Asymptotic solution of the Huygens-Fresnel integral in circular coordinates," Opt. Lett. 3, 100-102 (1978).
21. 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).
22. 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).