OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 24, Iss. 14 — Jul. 15, 1985
  • pp: 2181–2188

Rough surface interferometry with a two-wavelength heterodyne speckle interferometer

A. F. Fercher, H. Z. Hu, and U. Vry  »View Author Affiliations

Applied Optics, Vol. 24, Issue 14, pp. 2181-2188 (1985)

View Full Text Article

Enhanced HTML    Acrobat PDF (1085 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



If a rough surface is illuminated by a coherent lightwave of wavelength λ1, it is not possible to determine the surface profile from the phases of the speckle field formed by the scattered light. If the rough surface is illuminated, however, by an additional coherent wave of wavelength λ1, the phase differences between the two speckle fields do contain information about the macroscopic surface profile even if subject to a statistical error. It is shown that (1) the macroscopic surface profile may be determined from the phase differences if the effective wavelength Λ = λ1λ2/|λ1−λ2| is sufficiently larger than the standard deviation of the microscopic profile of the illuminated surface, and (2) the statistical error is reasonably small if the phase measurements are obtained from speckles of sufficient intensity. Using a heterodyne interferometer we demonstrate the feasibility of this technique. In the first experiment we determine the radius of curvature of a rough spherical surface. In the second experiment the macroscopic surface contour on two ophthalmic lenses of the same power variation, one with a grounded surface and the other with a polished surface, was determined.

© 1985 Optical Society of America

Original Manuscript: December 24, 1984
Published: July 15, 1985

A. F. Fercher, H. Z. Hu, and U. Vry, "Rough surface interferometry with a two-wavelength heterodyne speckle interferometer," Appl. Opt. 24, 2181-2188 (1985)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. Fujii, T. Asakura, “Effect of Surface Roughness on the Statistical Distribution of Image Speckle Intensity,” Opt. Commun. 11, 35 (1974);J. W. Goodman, “Dependence of Image Speckle Contrast on Surface Roughness,” Opt. Commun. 14, 324 (1975). [CrossRef]
  2. J. M. Burch, “Dependence of Image Speckle Contrast on Surface Roughness,” in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel Press, Newcastle-upon-Tyne, 1970), p. 213.
  3. C. R. Munnerlyn, M. Latta, “Rough Surface Interferometry Using a CO2 Laser Source,” Appl. Opt. 7, 1858 (1968). [CrossRef] [PubMed]
  4. O. Kwon, J. C. Wyant, C. R. Hayslett, “Rough Surface Interferometry at 10.6 μm,” Appl. Opt. 19, 1862 (1980). [CrossRef] [PubMed]
  5. M. V. R. K. Murty, R. P. Shukla, “An Oblique Incidence Interferometer,” Opt. Eng. 15, 461 (1976). [CrossRef]
  6. K. G. Birch, “Oblique Incidence Interferometry Applied to Non-Optical Surfaces,” J. Phys. E 6, 1045 (1973). [CrossRef]
  7. G. Schulz, J. Schwider, “Interferometric Testing of Smooth Surfaces,” Prog. Opt. 13, 93 (1976). [CrossRef]
  8. C. Polhemus, “Two-Wavelength Interferometry,” Appl. Opt. 12, 2071 (1973). [CrossRef] [PubMed]
  9. J. C. Wyant, “Testing Aspherics Using Two-Wavelength Holography,” Appl. Opt. 10, 2113 (1971). [CrossRef] [PubMed]
  10. W. Schmidt, A. F. Fercher, “Holographic Generation of Depth Contours Using a Flash-Lamp-Pumped Dye Laser,” Opt. Commun. 3, 363 (1971). [CrossRef]
  11. F. M. Kuchel, H. J. Tiziani, “Real-Time Contour Holography Using BSO Crystals,” Opt. Commun. 38, 17 (1981). [CrossRef]
  12. J. S. Zelenka, J. R. Varner, “A New Method for Generating Depth Contours Holographically,” Appl. Opt. 7, 2107 (1968). [CrossRef] [PubMed]
  13. A. F. Fercher, H. Z. Hu, “Two-Wavelength Heterodyne Interferometry,” in Optoelectronics in Engineering, W. Waidelich, Ed. (Springer, Berlin, 1984), p. 142.
  14. R. E. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London, 1983).
  15. H. Z. Hu, “Polarization Heterodyne Interferometry Using a Simple Rotating Analyzer. 1: Theory and Error Analysis,” Appl. Opt. 22, 2052 (1983). [CrossRef] [PubMed]
  16. E. W. Marchand, E. Wolf, “Radiometry with Sources of Any State of Coherence,” J. Opt. Soc. Am. 64, 1219 (1974). [CrossRef]
  17. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), p. 328.
  18. S. Donati, G. Martini, “Speckle-Pattern Intensity and Phase: Second-order Conditional Statistics,” J. Opt. Soc. Am. 69, 1690 (1979). [CrossRef]
  19. J. W. Goodman, “Statiscal Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), p. 9. [CrossRef]
  20. J. W. Goodman, Stanford Electronic Laboratories TR 2303-1, SEL-63-140 (1963).
  21. N. George, A. Jain, “Space and Wavelength Dependence of Speckle Intensity,” Appl. Phys. 4, 201 (1974). [CrossRef]
  22. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 59.
  23. I. S. Reed, “On a Moment Theorem for Complex Gaussian Processes,”\ IRE Trans. Inf. Theory IT-8, 194 (1962). [CrossRef]
  24. M. Giglio, S. Musazzi, U. Perini, “Surface Roughness Measurements by Means of Speckle Wavelength Decorrelation,” Opt. Commun. 28, 166 (1979). [CrossRef]

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