Abstract

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

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    [CrossRef] [PubMed]
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  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).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1991

1988

1986

G. Seitz, H. Tiziani, R. Litschel, “3-D-Koordinatenmessung durch optische Triangulation,” Feinwerktechnik Messtechnik 94, 423–425 (1986).

1985

G. Bickel, G. Häusler, M. Maul, “Triangulation with expanded range of depth,” Opt. Eng. 24, 975–977 (1985).

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multistrip structured light,” Opt. Eng. 24, 966–974 (1985).

1983

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]

1982

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]

1975

H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[CrossRef]

1964

1957

B. S. Thornton, “An uncertainty relation in interferometry,” Opt. Acta 4, 41–42 (1957).
[CrossRef]

1953

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).

Asakura, T.

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]

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]

Baribeau, R.

Bickel, G.

G. Bickel, G. Häusler, M. Maul, “Triangulation with expanded range of depth,” Opt. Eng. 24, 975–977 (1985).

Birk, J.

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).

Case, S. K.

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multistrip structured light,” Opt. Eng. 24, 966–974 (1985).

Dessimoz, J.

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).

Dremel, W.

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).

Falconi, O.

Häusler, G.

G. Häusler, J. M. Herrmann, “Range sensing by shearing interferometery: influence of speckle,” Appl. Opt. 27, 4631–4637 (1988).
[CrossRef] [PubMed]

G. Häusler, W. Heckel, “Light sectioning with large depth and high resolution,” Appl. Opt. 27, 5165–5169 (1988).
[CrossRef] [PubMed]

G. Bickel, G. Häusler, M. Maul, “Triangulation with expanded range of depth,” Opt. Eng. 24, 975–977 (1985).

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).

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).

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).

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).

Heckel, W.

Herrmann, J. M.

G. Häusler, J. M. Herrmann, “Range sensing by shearing interferometery: influence of speckle,” Appl. Opt. 27, 4631–4637 (1988).
[CrossRef] [PubMed]

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).

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).

Ingelstam, E.

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).

Jalkio, J. A.

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multistrip structured light,” Opt. Eng. 24, 966–974 (1985).

Kim, R. C.

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multistrip structured light,” Opt. Eng. 24, 966–974 (1985).

Litschel, R.

G. Seitz, H. Tiziani, R. Litschel, “3-D-Koordinatenmessung durch optische Triangulation,” Feinwerktechnik Messtechnik 94, 423–425 (1986).

Maul, M.

G. Bickel, G. Häusler, M. Maul, “Triangulation with expanded range of depth,” Opt. Eng. 24, 975–977 (1985).

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).

Nagamatsu, N.

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]

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]

Nakagawa, K.

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]

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]

Parthasarathy, S.

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).

Pedersen, H. M.

H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[CrossRef]

Rioux, M.

Seitz, G.

G. Seitz, H. Tiziani, R. Litschel, “3-D-Koordinatenmessung durch optische Triangulation,” Feinwerktechnik Messtechnik 94, 423–425 (1986).

Shindo, Y.

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]

Thornton, B. S.

B. S. Thornton, “An uncertainty relation in interferometry,” Opt. Acta 4, 41–42 (1957).
[CrossRef]

Tiziani, H.

G. Seitz, H. Tiziani, R. Litschel, “3-D-Koordinatenmessung durch optische Triangulation,” Feinwerktechnik Messtechnik 94, 423–425 (1986).

Appl. Opt.

Ark. Fys

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).

Feinwerktechnik Messtechnik

G. Seitz, H. Tiziani, R. Litschel, “3-D-Koordinatenmessung durch optische Triangulation,” Feinwerktechnik Messtechnik 94, 423–425 (1986).

J. Opt. (Paris)

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]

J. Opt. Soc. Am.

Opt. Acta

B. S. Thornton, “An uncertainty relation in interferometry,” Opt. Acta 4, 41–42 (1957).
[CrossRef]

H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[CrossRef]

Opt. Eng.

G. Bickel, G. Häusler, M. Maul, “Triangulation with expanded range of depth,” Opt. Eng. 24, 975–977 (1985).

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multistrip structured light,” Opt. Eng. 24, 966–974 (1985).

Opt. Quantum Electron.

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]

Other

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).

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).

J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975).

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).

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).

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).

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