## Diffraction analysis of random fractal fields

JOSA A, Vol. 15, Issue 3, pp. 669-674 (1998)

http://dx.doi.org/10.1364/JOSAA.15.000669

Enhanced HTML Acrobat PDF (202 KB)

### Abstract

It is shown that optical diffraction can be used to reveal the scaling features not only of deterministic but also of random fractal fields and to determine their main characteristics. The analysis of fractals can be experimentally realized through first-order optical systems.

© 1998 Optical Society of America

**OCIS Codes**

(050.1940) Diffraction and gratings : Diffraction

(050.1970) Diffraction and gratings : Diffractive optics

**History**

Original Manuscript: February 25, 1997

Revised Manuscript: August 18, 1997

Manuscript Accepted: October 6, 1997

Published: March 1, 1998

**Citation**

T. Alieva and F. Agullo-Lopez, "Diffraction analysis of random fractal fields," J. Opt. Soc. Am. A **15**, 669-674 (1998)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-3-669

Sort: Year | Journal | Reset

### References

- B. B. Mandelbrot, The Fractal Geometry of Nature, 2nd ed. (Freeman, New York, 1982), Chap. 1, pp. 1–5.
- A. Lakhtakia, N. S. Holter, V. K. Varadan, V. V. Varadan, “Self-similarity in diffraction by a self-similar fractal screen,” IEEE Trans. Antennas Propag. AP-35, 236–239 (1987). [CrossRef]
- C. Allain, M. Cloitre, “Optical diffraction on fractals,” Phys. Rev. B 33, 3566–3569 (1986). [CrossRef]
- Y. Kim, H. Grebel, D. L. Jaggard, “Diffraction by fractally serrated apertures,” J. Opt. Soc. Am. A 8, 20–26 (1991). [CrossRef]
- Y. Sakurada, J. Uozumi, T. Asakura, “Fresnel diffraction by one-dimensional regular fractals,” Pure Appl. Opt. 1, 29–40 (1992). [CrossRef]
- J. Uozumi, Y. Sakurada, T. Asakura, “Fraunhofer diffraction from apertures bounded by regular fractals,” J. Mod. Opt. 42, 2309–2322 (1995), and references therein. [CrossRef]
- T. Alieva, F. Agullo-Lopez, “Optical wave propagation of fractal fields,” Opt. Commun. 125, 267–274 (1996). [CrossRef]
- M. V. Berry, S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996). [CrossRef]
- T. Alieva, “Fractional Fourier transform as a tool for investigation of fractal objects,” J. Opt. Soc. Am. A 13, 1189–1192 (1996). [CrossRef]
- R. K. Luneburg, Mathematical Theory of Optics (U. of California Press, Berkeley, Calif., 1966), Chap. 4, pp. 217–268.
- K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979), pp. 381–393.
- M. Nazarathy, J. Shamir, “First-order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982). [CrossRef]
- C. Gomez-Reino, “GRIN optics and its application in optical connections,” Int. J. Optoelectron. 7, 607–680 (1992).
- D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transformations and their optical implementation. I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993). [CrossRef]
- A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
- T. Alieva, V. Lopez, F. Agullo-Lopez, L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994). [CrossRef]
- T. Alieva, F. Agullo-Lopez, “Reconstruction of the optical correlation function in a quadratic refractive index medium,” Opt. Commun. 114, 161–169 (1995). [CrossRef]
- S. Abe, J. T. Sheridan, “Almost-Fourier and almost-Fresnel transformations,” Opt. Commun. 113, 385–388 (1995). [CrossRef]
- M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978). [CrossRef]
- A. W. Lohmann, B. H. Soffer, “Relationships between the Radon–Wigner and fractional Fourier transform,” J. Opt. Soc. Am. A 11, 1798–1801 (1994). [CrossRef]
- M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994). [CrossRef] [PubMed]
- J. Feder, Fractals (Plenum, New York, 1988), Chap. 14, pp. 227–237.

## 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.