OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 3, Iss. 4 — Apr. 23, 2008

Defocus measurement for random self-affine fractal surfaces

Jun Wang, Wei Zhou, Lennie E. N. Lim, and Anand K. Asundi  »View Author Affiliations

Optics Express, Vol. 16, Issue 5, pp. 2928-2932 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (400 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We studied correlation between fractal dimensions and image contrast for metallic surfaces. The study has led to an interesting finding that the maximum fractal dimension of the object surface under imaging gives the best focal plane. The significant finding can be made use of to estimate the best focal plane or measure the focus error with high sensitivity of a few microns, which are well within depth of field of the microscopic imaging system.

© 2008 Optical Society of America

OCIS Codes
(080.1010) Geometric optics : Aberrations (global)
(110.0180) Imaging systems : Microscopy
(110.2960) Imaging systems : Image analysis

ToC Category:
Imaging Systems

Original Manuscript: January 4, 2008
Revised Manuscript: February 8, 2008
Manuscript Accepted: February 14, 2008
Published: February 19, 2008

Virtual Issues
Vol. 3, Iss. 4 Virtual Journal for Biomedical Optics

Jun Wang, Wei Zhou, Lennie E. Lim, and Anand K. Asundi, "Defocus measurement for random self-affine fractal surfaces," Opt. Express 16, 2928-2932 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. B. Mandelbrot, The Fractal Geometry of Nature, (W. H. Freeman, San Francisco, New York, 1982).
  2. P. Kotowski, "Fractal dimension of metallic fracture surface," Int. J. Fract. 141, 269-286 (2006). [CrossRef]
  3. A. Helalizadeh, H. Muller-Steinhagen, and M. Jamialahmadi, "Application of fractal theory for characterisation of crystalline deposits," Chem. Eng. Sci. 61, 2069-2078 (2006). [CrossRef]
  4. D. K. Goswami and B. N. Dev, "Nanoscale self-affine surface smoothing by ion bombardment," Phys. Rev. B 68, 033401 (2003). [CrossRef]
  5. J. Henry, "Accuracy issues in chemical and dimensional metrology in the SEM and TEM," Meas. Sci. Technol. 18, 2755-2761 (2007). [CrossRef]
  6. G. V. Duinen, M. V Heel, and A. Patwardhan, "Magnification variations due to illumination curvature and object defocus in transmission electron microscopy," Opt. Express 13, 9085 (2005). [CrossRef] [PubMed]
  7. R. N. Bracewell, Fourier Analysis and Imaging, (Kluwer, New York, 2003).
  8. J. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, New York, 1996).
  9. G. Franceschetti and D. Riccio, Scattering, Natural Surfaces and Fractals, (Elsevier, 2007).
  10. S. S. Chen, J. M. Keller, and R. M. Crownover, "On the calculation of fractal features from images," IEEE T. Pattern Anal. 15, 1087-1090 (1993). [CrossRef]
  11. N. Sarkar and B. B. Chaudhuri, "An efficient approach to estimate fractal dimension of textural images," Pattern Recogn. 25, 1035-1044 (1992). [CrossRef]
  12. http://cse.naro.affrc.go.jp/sasaki/fractal/fractal-e.html.
  13. V. Krishnakumar and A. K. Asundi, "Defocus measurement using spackle correlation," J. Mod. Opt. 48, 935-940 (2001).

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.


Fig. 1. Fig. 2. Fig. 3.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited