Encircled energy in systems with truncated-Gaussian apertures of different Fresnel numbers. I. Generalization of the Q2n function of E. Wolf and the Yn function of H. H. Hopkins

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

Volumn 24, Issue 7, 2007, Pages 2023-2032

  Li, Yajun ^a  

^a NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; FOCUSING; GAUSSIAN BEAMS; GRAPH THEORY; OPTIMIZATION;

ENCIRCLED ENERGY; FRESNEL NUMBERS;

DIFFRACTION;

EID: 34548297618     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.24.002023     Document Type: Article

References (16)

1. E. Wolf, "Light distribution near focus in an error-free diffraction image," Proc. R. Soc. London, Ser. A 204, 533-548 (1951).
2. H. H. Hopkins, "The disturbance near the focus of waves of radically nonuniform amplitude," Proc. Phys. Soc. London, Sect. B 62, 22 (1949).
3. G. N. Watson, A Treatise of the Theory of Bessel Functions (Cambridge U. Press, 1962) pp. 537-550.
4. M. Bom and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Sec. 8.2.2.
5. Y. Li and E. Wolf, "Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers," J. Opt. Soc. Am. A 1, 801-808 (1984).
6. Y. Li, "Encircled energy for systems with truncated-Gaussian apertures of different Frasnel numbers. II. Maximizing beam energy concentration on a target," J. Opt. Soc. Am. A 24, 2033-2042 (2007).
7. Y. Li, "Three-dimensional intensity distribution in low-Fresnel-number focusing systems," J. Opt. Soc. Am. A 4, 1349-1363 (1987).
8. J. Walker, The Analytical Theory of Light (Cambridge U. Press, 1904) p. 133.
9. J. P. Campbell and L. G. DeShazer, "Near field of truncated-Gaussian apertures," J. Opt. Soc. Am. 59, 1427-1429 (1969).
10. G. O. Olaofe, "Diffraction by Gaussian apertures," J. Opt. Soc. Am. 60, 1654-1657 (1970).
11. R. G. Schell and G. Tyras, "Irradiance from an aperture with a truncated-Gaussian field distribution," J. Opt. Soc. Am. 61, 31-35 (1971).
12. D. A. Holmes, J. E. Korka, and P. V. Avizonis, "Parametric study of apertured focused Gaussian beams," Appl. Opt. 11, 565-574 (1972).
13. Y. Li, "Establishment of the maximum encircled energy in the geometrical focal plane," Opt. Acta 31, 1107-1118 (1984).
14. Y. Li, "Degeneracy in the Fraunhofer diffraction of truncated Gaussian beams," J. Opt. Soc. Am. A 4, 1237-1242 (1987).
15. E. Collect and E. Wolf, "Symmetry properties of focused fields," Opt. Lett. 5, 264-266 (1980).
16. L. Råde and B. Wintergreen, BETA Mathematics Handbook, 2nd ed. (CRC, 1989), See. 8.4.