OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 42, Iss. 22 — Aug. 1, 2003
  • pp: 4529–4540

Applicability of the singular-optics concept for diagnostics of random and fractal rough surfaces

Oleg V. Angelsky, Dmitry N. Burkovets, Peter P. Maksimyak, and Steen G. Hanson  »View Author Affiliations

Applied Optics, Vol. 42, Issue 22, pp. 4529-4540 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (4958 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We introduce the singular-optics approach for classification of rough surfaces with large-scale inhomogeneities into random and fractal surfaces. The maps of amplitude zeros of a field versus the parameters of the rough surfaces and the position of the observation zone are obtained and analyzed. It is shown that the local density of amplitude zeros in the scattered field serves as an appropriate parameter with which to classify the surface of interest into a surface with a height distribution that can be described as a random or a fractal process.

© 2003 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4630) Instrumentation, measurement, and metrology : Optical inspection
(170.6960) Medical optics and biotechnology : Tomography
(180.1790) Microscopy : Confocal microscopy
(240.5770) Optics at surfaces : Roughness
(290.0290) Scattering : Scattering

Original Manuscript: December 5, 2002
Revised Manuscript: May 5, 2003
Published: August 1, 2003

Oleg V. Angelsky, Dmitry N. Burkovets, Peter P. Maksimyak, and Steen G. Hanson, "Applicability of the singular-optics concept for diagnostics of random and fractal rough surfaces," Appl. Opt. 42, 4529-4540 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. O. V. Angelsky, S. G. Hanson, P. P. Maksimyak, Use of Optical Correlation Techniques for Characterizing Scattering Objects and Media, Vol. PM71 of SPIE Press Monograph Series (SPIE Press, Bellingham, Wash., 1999).
  2. O. V. Angelsky, P. P. Maksimyak, “Optical diagnostics of random phase objects,” Appl. Opt. 29, 2894–2898 (1990). [CrossRef] [PubMed]
  3. O. V. Angelsky, P. P. Maksimyak, “Optical correlation devices for measuring randomly phased objects,” Opt. Eng. 32, 3235–3243 (1993). [CrossRef]
  4. O. V. Angelsky, P. P. Maksimyak, V. V. Ryukhtin, S. G. Hanson, “New feasibilities for characterizing rough surfaces by optical-correlation techniques,” Appl. Opt. 40, 5693–5707 (2001). [CrossRef]
  5. M. Berry, “Singularities in waves and rays,” in Physics of Defects, R. Bochan, ed. (North-Holland, Amsterdam, 1981), pp. 453–543.
  6. G. Popescu, A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002). [CrossRef] [PubMed]
  7. J. F. Nye, M. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974). [CrossRef]
  8. J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics, Bristol, UK, 1999), p. 328.
  9. I. Freund, N. Shvartsman, V. Freilikher, “Optical dislocation network in highly random media,” Opt. Commun. 101, 247–264 (1993). [CrossRef]
  10. M. Soskin, M. Vasnetsov, “Singular optics as new chapter of modern photonics: optical vortices, fundamentals and applications,” Photon. Sci. News 4(1), 21–27 (1999).
  11. R. F. Voss, “Random fractal forgeries,” in Fundamental Algorithms in Computer Graphics, R. A. Earnshaw, ed. (Springer-Verlag, Berlin, 1985), pp. 13–16 and 805–835.
  12. J. W. Goodman, Statistical Optics, (Wiley, New York, 1985).
  13. S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarsky, Principles of Statistical Radiophysics (Springer-Verlag, Berlin1989).
  14. M. S. Soskin, M. V. Vasnetsov, I. V. Basisty, “Optical wavefront dislocations,” in International Conference on Holography and Correlation Optics, O. V. Angelsky, ed. Proc. SPIE2647, 57–62 (1995). [CrossRef]
  15. N. V. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkunov, B. Y. Zeldovich, “Wavefront dislocations: topological limitations for adaptive system with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983). [CrossRef]
  16. I. V. Basisty, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995). [CrossRef]
  17. N. R. Heckenberg, R. McDuff, C. P. Smith, M. J. Wegener, “Optical Fourier transform recognition of phase singularities in optical fields,” in From Galileo’s Occhialino to Optoelectronics, P. Mazzoldi, ed. (World Scientific, Singapore, 1992), pp. 848–852.
  18. N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef] [PubMed]
  19. A. Arneodo, “Wavelet analysis of fractals: from the mathematical concept to experimental reality,” in Wavelets: Theory and Application, M. Y. Hussaini, ed. (Oxford U. Press, New York, 1996), pp. 352–497.

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