Integer, fractional and fractal Talbot effects

Journal of Modern Optics

Volumn 43, Issue 10, 1996, Pages 2139-2164

  Berry, M V ^a   Klein, S ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; FRACTALS; IMAGE PROCESSING; NUMBER THEORY; OPTICAL WAVEGUIDES;

FRACTAL TALBOT EFFECTS; GOLDEN DISTANCE; SELF-IMAGES OF GRATING;

DIFFRACTION GRATINGS;

EID: 0030263016     PISSN: 09500340     EISSN: 13623044     Source Type: Journal    
DOI: 10.1080/09500349608232876     Document Type: Article

References (30)

1. Talbot, H. F., 1836. Phil. Mag., 9:401–407.
2. Patorski, K., 1989. Prog. Optics, 27:1–108.
3. Rayleigh, Lord. 1881. Phil. Mag., 11:196–205.
4. Hiedemann, E. A., and Breazale, M. A., 1959. J. opt. Soc. Am., 49:372–375.
5. Winthrop, J. T., and Worthington, C. R., 1965. J. opt. Soc. Am., 55:373–381.
6. Mandelbrot, B. B., 1982. The Fractal Geometry of Nature, San Francisco, California:Freeman.
7. Meijas, P. M., and Martinez Herrero, R., 1991. J. opt. Soc. Am. A, 8:266–269.
8. Berry, M. V., and Goldberg, J., 1988. Nonlinearity, 1:1–26.
9. Averbuk, I. Sh., and Perelman, N. F., 1989. Phys. Lett. A, 139:449–453.
10. Mallalieu, M., and Stroud, C. R., Jr. 1995. Phys. Rev. A, 51:1827–1835.
11. Leichtle, C., Averbukj, I. Sh., and Schleich, W. P., 1996. University of Ulm. Preprint
12. Neponen, E., and Turunen, J., 1993. Optics Commun., 98:132–140.
13. Abramowitz, M., and Stegun, I. A., 1972. Handbook of Mathematical Functions, Washington, DC:US National Bureau of Standards.
14. Patorski, K., 1983. Optica Acta, 30:1255–1258.
15. Latimer, P., and Crouse, R. F., 1992. J. opt. Soc. Am., 31:80–89.
16. Smirnov, A. P., 1977. Opt. Spectrosc. (USSR), 43:446–448.
17. Lang, S., 1970. Algebraic Number Theory, Reading, Massachusetts:Addison-Wesley.
18. Hannay, J. H., and Berry, M. V., 1980. Physica D, 1:267–290.
19. Wolfram, S., 1991. Mathematica:a System for Doing Mathematics by Computer, Reading, Massachusetts:Addison-Wesley.
20. Wronkowski, L., 1988. J. mod. Optics, 35:1417–1422.
21. Arrizon, V., and Lopez-Olagasti, E., 1995. J. opt. Soc. Am. A, 12:801–804.
22. Smirnov, A. P., 1978. Opt. Spectrosc. (USSR), 44:208–212.
23. Berry, M. V., and Lewis, Z. V., 1980. Proc. R. Soc. A, 370:459–484.
24. Hardy, G. H., and Wright, E. M., 1988. An Introduction to the Theory of Numbers, fifth edition, Oxford:Clarendon.
25. Berry, M. V., and Upstill, C., 1980. Prog. Optics, 18:257–346.
26. Born, M., and Wolf, E., 1959. Principles of Optics, Oxford:Pergamon.
27. Smirnov, A. P., 1979. Opt. Spectrosc. (USSR), 46:319–322.
28. Clauser, J. F., and Reinsch, M. W., 1992. Appl. Phys. B, 54:380–395.
29. Falconer, K., 1990. Fractal Geometry:Mathematical Foundations and Applications, New York:Wiley.
30. Berry, M. V., 1996. Quantum fractals in boxes. J. Phys A., submitted to