Abstract

A range sensing technique is demonstrated that finds the 3-D shape of diffusely reflecting objects. The technique works sequentially in depth direction and is based on structured illumination and focus sensing. A TV camera and analog electronics are used to find the locations in focus of each step of a focus series in TV real time. The depth resolution is not very high, however, the technique is simple, rapid, and well suited to get an overview of a scene in robot vision.

© 1988 Optical Society of America

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References

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  1. T. C. Strand, “Optical Three-Dimensional Sensing for Machine Vision,” Opt. Eng. 24, 33 (1985).
    [CrossRef]
  2. R. A. Jarvis, “A Perspective on Range Finding Techniques for Computer Vision,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-5, 122 (1983).
    [CrossRef]
  3. G. Bickel, G. Hdusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
    [CrossRef]
  4. W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).
  5. P. Chavel, T. C. Strand, “Range Measurement Using Talbot Diffraction Imaging of Gratings,” Appl. Opt. 23, 862 (1984).
    [CrossRef] [PubMed]
  6. J. R. Leger, M. A. Snyder, “Real-Time Depth Measurement and Display Using Fresnel Diffraction and White-Light Processing,” Appl. Opt. 23, 1655 (1984).
    [CrossRef] [PubMed]
  7. J. C. Davis, C. Buckberry, “Full Field Range Measurement in Real Time Using a Fresnel-Talbot Fringe System,” VDI Ber. (Ver. Dtsch. Ing.) 617, 77 (1986).
  8. H. H. Hopkins, “The Frequency Response of a Defocused Optical System,” Proc. R. Soc. London Ser. A 231, 91 (1955).
    [CrossRef]

1986 (2)

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

J. C. Davis, C. Buckberry, “Full Field Range Measurement in Real Time Using a Fresnel-Talbot Fringe System,” VDI Ber. (Ver. Dtsch. Ing.) 617, 77 (1986).

1985 (2)

G. Bickel, G. Hdusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

T. C. Strand, “Optical Three-Dimensional Sensing for Machine Vision,” Opt. Eng. 24, 33 (1985).
[CrossRef]

1984 (2)

1983 (1)

R. A. Jarvis, “A Perspective on Range Finding Techniques for Computer Vision,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-5, 122 (1983).
[CrossRef]

1955 (1)

H. H. Hopkins, “The Frequency Response of a Defocused Optical System,” Proc. R. Soc. London Ser. A 231, 91 (1955).
[CrossRef]

Bickel, G.

G. Bickel, G. Hdusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

Buckberry, C.

J. C. Davis, C. Buckberry, “Full Field Range Measurement in Real Time Using a Fresnel-Talbot Fringe System,” VDI Ber. (Ver. Dtsch. Ing.) 617, 77 (1986).

Chavel, P.

Davis, J. C.

J. C. Davis, C. Buckberry, “Full Field Range Measurement in Real Time Using a Fresnel-Talbot Fringe System,” VDI Ber. (Ver. Dtsch. Ing.) 617, 77 (1986).

Dremel, W.

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

Häusler, G.

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

Hdusler, G.

G. Bickel, G. Hdusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, “The Frequency Response of a Defocused Optical System,” Proc. R. Soc. London Ser. A 231, 91 (1955).
[CrossRef]

Jarvis, R. A.

R. A. Jarvis, “A Perspective on Range Finding Techniques for Computer Vision,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-5, 122 (1983).
[CrossRef]

Leger, J. R.

Maul, M.

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

G. Bickel, G. Hdusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

Snyder, M. A.

Strand, T. C.

Appl. Opt. (2)

IEEE Trans. Pattern Anal. Machine Intell. (1)

R. A. Jarvis, “A Perspective on Range Finding Techniques for Computer Vision,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-5, 122 (1983).
[CrossRef]

Opt. Eng. (2)

G. Bickel, G. Hdusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

T. C. Strand, “Optical Three-Dimensional Sensing for Machine Vision,” Opt. Eng. 24, 33 (1985).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

H. H. Hopkins, “The Frequency Response of a Defocused Optical System,” Proc. R. Soc. London Ser. A 231, 91 (1955).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

VDI Ber. (Ver. Dtsch. Ing.) (1)

J. C. Davis, C. Buckberry, “Full Field Range Measurement in Real Time Using a Fresnel-Talbot Fringe System,” VDI Ber. (Ver. Dtsch. Ing.) 617, 77 (1986).

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Figures (7)

Fig. 1
Fig. 1

Schematic optical setup of the range sensing technique based on grid projection, confocal imaging, and focus detection.

Fig. 2
Fig. 2

Incoherent imaging with defocus: normalized transmitted grating modulation Dn as a function of normalized defocus a for four specific normalized grating frequencies sG.

Fig. 3
Fig. 3

Range sensing by grid projection with small depth of focus: depth resolution Δz at 0% contrast threshold vs sinu imaging aperture for four practical grating frequencies (λ = 0.5 μm).

Fig. 4
Fig. 4

Focus detection: (a) For a coarse grid (compared to the cutoff frequency of the system) a fixed threshold is sufficient to detect focused grid lines even at local varying reflectance R of the object. (b) For a fine grid the threshold has to vary according to the mean local brightness of the image to become independent of object reflectance R.

Fig. 5
Fig. 5

Schematic diagram of the detection electronics. An analog video comparator finds the periods of maximum grating contrast in the video signal.

Fig. 6
Fig. 6

Experimental result. The object is a plane tilted by φ ≈ 30° against the grid. The left part of the plane had a distance 50 mm larger than the right part. Reflectance R of the object decreases stepwise from left to right with Rmax/Rmin ≈ 8. (a) Video image, center of the object in focus; (b) corresponding binary output of the comparator; the detected region is bright; (c) pseudo 3-D plot of the collected data set z(x,y). Note that z(x,y) is independent of the local reflectance.

Fig. 7
Fig. 7

Experimental result. The object is a socket (a) with the projected grid focused on its top; (b) corresponding binary output of the comparator; the detected region is bright; (c) pseudo 3-D reconstruction of the object from the measured data set z(x,y).

Equations (10)

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D ( s , α ) = sin [ α · s · ( 2 - s ) ] 2 · α · s ,             s 2.
s : = ν ν c ,             ν c = sin u λ .
α : = π · δ z δ z R ,             δ z R = λ sin 2 u .
D n ( s G , α ) = D ( s G , α ) D ( s G , 0 ) = sin σ σ ;
Δ α ( s G ; T = 0 ) = π s G · ( 2 - s G ) .
Δ z ( ν G ; T = 0 ) = 1 ν G · ( 2 · sin u - λ · ν G ) .
Δ z ( ν G ; T = 0 ) 1 2 · ν G · sin u .
V ( t ) = R ( t ) · [ 1 + D ( t ) · cos ( 2 · π · t / t G ) ] + B ,
ρ = 1 - T - / R ( t ) .
z ( x , y ) = i z i · d i / i d i ,

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