Abstract

Speckle noise is shown to constitute a fundamental limit to laser range finders based on triangulation. A model is derived that relates the magnitude of this noise to the optical geometry used. Synchronized laser scanners are shown to have inherent speckle noise reduction properties. Experimental results are presented.

© 1991 Optical Society of America

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References

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  1. M. Rioux, G. Bechthold, D. Taylor, M. Duggan, “Design of a large depth of view three-dimensional camera for robot vision,” Opt. Eng. 26, 1245–1250 (1987).
  2. W. Dremel, G. Hausler, M. Maul, “Triangulation with large dynamical range,” in Proceedings on Optical Techniques in Industrial Inspection, P. Cielo, ed., Proc. Soc. Photo-Opt. Instrum. Eng.665, 182–187 (1986).
  3. R. Baribeau, “Industrial applications of auto-synchronized 3-D camera,” presented at the Workshop on Range Image Understanding, Vision Interface ’89, London, Ontario, Canadax1989.
  4. M. Rioux, L. Cournoyer, The NRC Three-Dimensional Data Files, NRC 29077 (June1988).
  5. L. B. Jeunhomme, Single-Mode Fiber Optics (Marcel Dekker, New York, 1983).
  6. R. E. Wagner, W. J. Tomlinson, “Coupling efficiency of optics in single-mode fiber components,” Appl. Opt. 21, 2671–2688 (1982).
    [CrossRef] [PubMed]
  7. F. Blais, M. Rioux, “Real-time numerical peak detector,” Signal Process. 11, 145–155 (1986).
    [CrossRef]
  8. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975).
    [CrossRef]
  9. L. Leushacke, M. Kirchner, “Three-dimensional correlation coefficients of speckle intensity for rectangular and circular apertures,” J. Opt. Soc. Am. A 7, 827–832 (1990).
    [CrossRef]
  10. J. W. Goodman, Statsitical Optics (Wiley, New York, 1985).
  11. R. Baribeau, M. Rioux, “Centroid fluctuations of speckled targets,” submitted to Appl. Opt.30, 0000–0000 (1991).
    [CrossRef]
  12. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
    [CrossRef]
  13. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).
  14. B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, New York, 1983).
    [CrossRef]

1990

1987

M. Rioux, G. Bechthold, D. Taylor, M. Duggan, “Design of a large depth of view three-dimensional camera for robot vision,” Opt. Eng. 26, 1245–1250 (1987).

1986

F. Blais, M. Rioux, “Real-time numerical peak detector,” Signal Process. 11, 145–155 (1986).
[CrossRef]

1982

1976

Baribeau, R.

R. Baribeau, “Industrial applications of auto-synchronized 3-D camera,” presented at the Workshop on Range Image Understanding, Vision Interface ’89, London, Ontario, Canadax1989.

R. Baribeau, M. Rioux, “Centroid fluctuations of speckled targets,” submitted to Appl. Opt.30, 0000–0000 (1991).
[CrossRef]

Bechthold, G.

M. Rioux, G. Bechthold, D. Taylor, M. Duggan, “Design of a large depth of view three-dimensional camera for robot vision,” Opt. Eng. 26, 1245–1250 (1987).

Blais, F.

F. Blais, M. Rioux, “Real-time numerical peak detector,” Signal Process. 11, 145–155 (1986).
[CrossRef]

Cournoyer, L.

M. Rioux, L. Cournoyer, The NRC Three-Dimensional Data Files, NRC 29077 (June1988).

Dremel, W.

W. Dremel, G. Hausler, M. Maul, “Triangulation with large dynamical range,” in Proceedings on Optical Techniques in Industrial Inspection, P. Cielo, ed., Proc. Soc. Photo-Opt. Instrum. Eng.665, 182–187 (1986).

Duggan, M.

M. Rioux, G. Bechthold, D. Taylor, M. Duggan, “Design of a large depth of view three-dimensional camera for robot vision,” Opt. Eng. 26, 1245–1250 (1987).

Frieden, B. R.

B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, New York, 1983).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
[CrossRef]

J. W. Goodman, Statsitical Optics (Wiley, New York, 1985).

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975).
[CrossRef]

Hausler, G.

W. Dremel, G. Hausler, M. Maul, “Triangulation with large dynamical range,” in Proceedings on Optical Techniques in Industrial Inspection, P. Cielo, ed., Proc. Soc. Photo-Opt. Instrum. Eng.665, 182–187 (1986).

Jeunhomme, L. B.

L. B. Jeunhomme, Single-Mode Fiber Optics (Marcel Dekker, New York, 1983).

Kirchner, M.

Leushacke, L.

Maul, M.

W. Dremel, G. Hausler, M. Maul, “Triangulation with large dynamical range,” in Proceedings on Optical Techniques in Industrial Inspection, P. Cielo, ed., Proc. Soc. Photo-Opt. Instrum. Eng.665, 182–187 (1986).

Rioux, M.

M. Rioux, G. Bechthold, D. Taylor, M. Duggan, “Design of a large depth of view three-dimensional camera for robot vision,” Opt. Eng. 26, 1245–1250 (1987).

F. Blais, M. Rioux, “Real-time numerical peak detector,” Signal Process. 11, 145–155 (1986).
[CrossRef]

M. Rioux, L. Cournoyer, The NRC Three-Dimensional Data Files, NRC 29077 (June1988).

R. Baribeau, M. Rioux, “Centroid fluctuations of speckled targets,” submitted to Appl. Opt.30, 0000–0000 (1991).
[CrossRef]

Taylor, D.

M. Rioux, G. Bechthold, D. Taylor, M. Duggan, “Design of a large depth of view three-dimensional camera for robot vision,” Opt. Eng. 26, 1245–1250 (1987).

Tomlinson, W. J.

Wagner, R. E.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

M. Rioux, G. Bechthold, D. Taylor, M. Duggan, “Design of a large depth of view three-dimensional camera for robot vision,” Opt. Eng. 26, 1245–1250 (1987).

Signal Process.

F. Blais, M. Rioux, “Real-time numerical peak detector,” Signal Process. 11, 145–155 (1986).
[CrossRef]

Other

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975).
[CrossRef]

J. W. Goodman, Statsitical Optics (Wiley, New York, 1985).

R. Baribeau, M. Rioux, “Centroid fluctuations of speckled targets,” submitted to Appl. Opt.30, 0000–0000 (1991).
[CrossRef]

W. Dremel, G. Hausler, M. Maul, “Triangulation with large dynamical range,” in Proceedings on Optical Techniques in Industrial Inspection, P. Cielo, ed., Proc. Soc. Photo-Opt. Instrum. Eng.665, 182–187 (1986).

R. Baribeau, “Industrial applications of auto-synchronized 3-D camera,” presented at the Workshop on Range Image Understanding, Vision Interface ’89, London, Ontario, Canadax1989.

M. Rioux, L. Cournoyer, The NRC Three-Dimensional Data Files, NRC 29077 (June1988).

L. B. Jeunhomme, Single-Mode Fiber Optics (Marcel Dekker, New York, 1983).

M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).

B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, New York, 1983).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Laser triangulation geometry.

Fig. 2
Fig. 2

Autosynchronized scanning geometry.

Fig. 3
Fig. 3

Speckle reduction by spatial averaging.

Fig. 4
Fig. 4

Range fluctuations as a function of spatial averaging distance (relative units).

Fig. 5
Fig. 5

Range fluctuations as a function of spatial averaging distance as measured in one experiment.

Equations (30)

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M R δ p δ z = f 0 sin γ l cos β .
A = k = i + 1 i + 4 S k - k = i - 4 i - 1 S k ,
B = k = i + 2 i + 5 S k - k = i - 3 i S k ,
Δ = A A - B .
p = ( i + Δ ) a .
I ( p , q ) = I ¯ ( p , q ) ,
I ( p , q ) I ( p + Δ p , q + Δ q ) = I ¯ 2 ( p , q ) [ 1 + μ ( Δ p , Δ q ) 2 ] .
I ¯ ( p , q ) = 1 2 π b 2 cos β exp ( - ( p - p ¯ ) 2 b 2 - q 2 2 b 2 cos 2 β ) ,
A c = - - μ ( Δ p , Δ q ) 2 d ( Δ p ) d ( Δ q ) ,
A c = 4 π λ 2 f 0 2 ϕ 2 cos β .
- p M - I ( p , q ) d q d p = p M - I ( p , q ) d q d p .
σ 2 = A c 8 cos β .
Δ = 1 1 + S i S i + 1 .
S i = p m - a p M - I ( p , q ) d q d p ,
δ Δ = 1 2 ( S N ) rms - 1 .
δ Δ 1 2 [ A c ( 4 π ) 1 / 2 a b cos β ] 1 / 2 .
a / b < ( π ) 1 / 2 ,
σ z = 1 ( 2 π ) 1 / 2 λ ϕ l sin γ .
σ ( L ) = σ 0 ( 1 - s t ) ,
σ ( L ) = σ 0 d 0 L { i 1 erfc ( 0 ) - i 1 erfc [ ( 2 ) 1 / 2 L d 0 ] } ,
σ speckle 2 = σ observed 2 - σ nonspeckle 2 ,
2 0 p M - I ( p , q ) d q d p = 0 - I ( p , q ) d q d p - - 0 - I ( p , q ) d q d p .
p M = - - sgn ( p ) I ( p , q ) d q d p 2 - I ( 0 , q ) d q ,
sgn ( p ) = { 1 if p > 0 , 0 if p = 0 , - 1 if p < 0.
p M = - - Λ ( p ) I ( p , q ) d q d p ,
Λ ( p ) = sgn ( p ) 2 - I ¯ ( 0 , q ) d q .
p M 2 = - - - - Λ ( p 1 ) Λ ( p 2 ) I ( p 1 , q 1 ) × I ( p 2 q 2 ) d q 1 d p 1 d q 2 d p 2 .
p M 2 = - - Λ ( p 1 ) I ¯ ( p 1 , q 1 ) 2 - - Λ ( p 2 ) × μ ( p 2 - p 1 , q 2 - q 1 ) 2 d q 2 d p 2 d q 1 d p 1 .
p M 2 = A c - Λ 2 ( p ) I ¯ 2 ( p , q ) d q d p ,
p M 2 = A c 8 cos β .

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