OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 33, Iss. 7 — Mar. 1, 1994
  • pp: 1306–1314

Laser triangulation: fundamental uncertainty in distance measurement

Rainer G. Dorsch, Gerd Häusler, and Jürgen M. Herrmann  »View Author Affiliations

Applied Optics, Vol. 33, Issue 7, pp. 1306-1314 (1994)

View Full Text Article

Enhanced HTML    Acrobat PDF (1735 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We discuss the uncertainty limit in distance sensing by laser triangulation. The uncertainty in distance measurement of laser triangulation sensors and other coherent sensors is limited by speckle noise. Speckle arises because of the coherent illumination in combination with rough surfaces. A minimum limit on the distance uncertainty is derived through speckle statistics. This uncertainty is a function of wavelength, observation aperture, and speckle contrast in the spot image. Surprisingly, it is the same distance uncertainty that we obtained from a single-photon experiment and from Heisenberg’s uncertainty principle. Experiments confirm the theory. An uncertainty principle connecting lateral resolution and distance uncertainty is introduced. Design criteria for a sensor with minimum distance uncertainty are determined: small temporal coherence, small spatial coherence, a large observation aperture.

© 1994 Optical Society of America

Original Manuscript: October 26, 1992
Revised Manuscript: May 11, 1993
Published: March 1, 1994

Rainer G. Dorsch, Gerd Häusler, and Jürgen M. Herrmann, "Laser triangulation: fundamental uncertainty in distance measurement," Appl. Opt. 33, 1306-1314 (1994)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Parthasarathy, J. Birk, J. Dessimoz, “Laser rangefinder for robot control and inspection,” in Robot Vision, A. Rosenfeld, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 336, 2–10 (1982).
  2. G. Bickel, G. Häusler, M. Maul, “Triangulation with expanded range of depth,” Opt. Eng. 24, 975–977 (1985).
  3. J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multistrip structured light,” Opt. Eng. 24, 966–974 (1985).
  4. G. Seitz, H. Tiziani, R. Litschel, “3-D-Koordinatenmessung durch optische Triangulation,” Feinwerktechnik Messtechnik 94, 423–425 (1986).
  5. G. Häusler, W. Heckel, “Light sectioning with large depth and high resolution,” Appl. Opt. 27, 5165–5169 (1988). [CrossRef] [PubMed]
  6. W. Dremel, G. Häusler, M. Maul, “Triangulation with large dynamical range,” in Optical Techniques for Industrial Inspection, P. G. Cielo, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182–187 (1986).
  7. G. Häusler, J. M. Herrmann, “Range sensing by shearing interferometery: influence of speckle,” Appl. Opt. 27, 4631–4637 (1988). [CrossRef] [PubMed]
  8. G. Häusler, J. M. Herrmann, “3-D sensing with a confocal optical ‘macroscope’,” in Optics in Complex Systems, F. Lanz, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1319, 359 (1990).
  9. J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975).
  10. R. Baribeau, M. Rioux, “Influence of speckle on laser range finders,” Appl. Opt. 30, 2873–2878 (1991). [CrossRef] [PubMed]
  11. G. Häusler, “About fundamental limits of three-dimensional sensing or nature makes no presents,” in Optics in Complex Systems, F. Lanz, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1319, 352–353 (1990).
  12. G. Häusler, J. M. Herrmann, “Physical limits of 3-D sensing,” in Optics, Illumination, and Image Sensing for Machine Vision VII, O. J. Svetkoff, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1822, 150–158 (1992).
  13. K. Nakagawa, N. Nagamatsu, T. Asakura, Y. Shindo, “An effect of the extended detecting aperture on the contrast of monochromatic and white-light speckles,” J. Opt. (Paris) 13, 147–153 (1982). [CrossRef]
  14. N. Nagamatsu, K. Nakagawa, T. Asakura, “The autocorrelation function of polychromatic laser speckle patterns near the image plane,” Opt. Quantum Electron. 15, 507–512 (1983). [CrossRef]
  15. H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975). [CrossRef]
  16. O. Falconi, “Maximum sensitivities of optical direction and twist measuring instruments,” J. Opt. Soc. Am. 54, 1315–1320 (1964). [CrossRef]
  17. E. Ingelstam, “An optical uncertainty principle and its application to the amount of information obtainable from multiple-beam interferences,” Ark. Fys. 7, 309–322 (1953).
  18. B. S. Thornton, “An uncertainty relation in interferometry,” Opt. Acta 4, 41–42 (1957). [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