Abstract

A new rotary encoder is proposed which detects displacement of speckle arising in the diffraction field of a cylinder illuminated by a narrow laser beam. The displacement is detected from the peak position of the cross-correlation between the outputs of a linear image sensor. The speckle displacement due to small rotation of the cylinder is derived first. In experiments correlation is computed on a microcomputer for investigating the sensitivity and repeatability. A He–Ne laser and a laser diode are used for metal and paper surfaces. Acceleration and extension of the measurement range has also been possible by developing a real-time correlator.

© 1989 Optical Society of America

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References

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  1. I. Yamaguchi, “Real-Time Measurement of In-Plane Translation and Tilt by Electronic Speckle Correlation,” Jpn. J. Appl. Phys. 19, L133–L136 (1980).
    [Crossref]
  2. I. Yamaguchi, “Automatic Measurement of In-Plane Translation by Speckle Correlation Using a Linear Image Sensor,” J. Phys. E. 19, 944–949 (1986).
    [Crossref]
  3. I. Yamaguchi, “A Laser-Speckle Strain Gauge,” J. Phys. E. 14, 1270–1273 (1980).
    [Crossref]
  4. I. Yamaguchi, “Simplified Laser-Speckle Strain Gauge,” Opt. Eng. 21, 436–440 (1982).
    [Crossref]
  5. I. Yamaguchi, “Advances in the Laser Speckle Strain Gauge,” Opt. Eng. 27, 214–218 (1988).
    [Crossref]
  6. E. Ingelstam, S. -I. Ragnarsson, “Eye Refraction Examined by Aid of Speckle Pattern Produced by Coherent Light,” Vision Res. 12, 411–420 (1972).
    [Crossref] [PubMed]
  7. A. F. Fercher, H. Sprongl, “Automatic Measurement of Vertex Refraction with Coherent Light,” Opt. Acta. 22, 799–806 (1975).
    [Crossref]
  8. A. Hayashi, Y. Kitagawa, “High-Resolution Rotation-Angle Measurement of a Cylinder Using Speckle Displacement Detection,” Appl. Opt. 22, 3520–3525 (1983).
    [Crossref] [PubMed]
  9. I. Yamaguchi, “Speckle Displacement and Decorrelation in the Diffraction and Image Fields for Small Object Deformation,” Opt. Acta 28, 1359–1376 (1981).
    [Crossref]

1988 (1)

I. Yamaguchi, “Advances in the Laser Speckle Strain Gauge,” Opt. Eng. 27, 214–218 (1988).
[Crossref]

1986 (1)

I. Yamaguchi, “Automatic Measurement of In-Plane Translation by Speckle Correlation Using a Linear Image Sensor,” J. Phys. E. 19, 944–949 (1986).
[Crossref]

1983 (1)

1982 (1)

I. Yamaguchi, “Simplified Laser-Speckle Strain Gauge,” Opt. Eng. 21, 436–440 (1982).
[Crossref]

1981 (1)

I. Yamaguchi, “Speckle Displacement and Decorrelation in the Diffraction and Image Fields for Small Object Deformation,” Opt. Acta 28, 1359–1376 (1981).
[Crossref]

1980 (2)

I. Yamaguchi, “Real-Time Measurement of In-Plane Translation and Tilt by Electronic Speckle Correlation,” Jpn. J. Appl. Phys. 19, L133–L136 (1980).
[Crossref]

I. Yamaguchi, “A Laser-Speckle Strain Gauge,” J. Phys. E. 14, 1270–1273 (1980).
[Crossref]

1975 (1)

A. F. Fercher, H. Sprongl, “Automatic Measurement of Vertex Refraction with Coherent Light,” Opt. Acta. 22, 799–806 (1975).
[Crossref]

1972 (1)

E. Ingelstam, S. -I. Ragnarsson, “Eye Refraction Examined by Aid of Speckle Pattern Produced by Coherent Light,” Vision Res. 12, 411–420 (1972).
[Crossref] [PubMed]

Fercher, A. F.

A. F. Fercher, H. Sprongl, “Automatic Measurement of Vertex Refraction with Coherent Light,” Opt. Acta. 22, 799–806 (1975).
[Crossref]

Hayashi, A.

Ingelstam, E.

E. Ingelstam, S. -I. Ragnarsson, “Eye Refraction Examined by Aid of Speckle Pattern Produced by Coherent Light,” Vision Res. 12, 411–420 (1972).
[Crossref] [PubMed]

Kitagawa, Y.

Ragnarsson, S. -I.

E. Ingelstam, S. -I. Ragnarsson, “Eye Refraction Examined by Aid of Speckle Pattern Produced by Coherent Light,” Vision Res. 12, 411–420 (1972).
[Crossref] [PubMed]

Sprongl, H.

A. F. Fercher, H. Sprongl, “Automatic Measurement of Vertex Refraction with Coherent Light,” Opt. Acta. 22, 799–806 (1975).
[Crossref]

Yamaguchi, I.

I. Yamaguchi, “Advances in the Laser Speckle Strain Gauge,” Opt. Eng. 27, 214–218 (1988).
[Crossref]

I. Yamaguchi, “Automatic Measurement of In-Plane Translation by Speckle Correlation Using a Linear Image Sensor,” J. Phys. E. 19, 944–949 (1986).
[Crossref]

I. Yamaguchi, “Simplified Laser-Speckle Strain Gauge,” Opt. Eng. 21, 436–440 (1982).
[Crossref]

I. Yamaguchi, “Speckle Displacement and Decorrelation in the Diffraction and Image Fields for Small Object Deformation,” Opt. Acta 28, 1359–1376 (1981).
[Crossref]

I. Yamaguchi, “Real-Time Measurement of In-Plane Translation and Tilt by Electronic Speckle Correlation,” Jpn. J. Appl. Phys. 19, L133–L136 (1980).
[Crossref]

I. Yamaguchi, “A Laser-Speckle Strain Gauge,” J. Phys. E. 14, 1270–1273 (1980).
[Crossref]

Appl. Opt. (1)

J. Phys. E. (2)

I. Yamaguchi, “Automatic Measurement of In-Plane Translation by Speckle Correlation Using a Linear Image Sensor,” J. Phys. E. 19, 944–949 (1986).
[Crossref]

I. Yamaguchi, “A Laser-Speckle Strain Gauge,” J. Phys. E. 14, 1270–1273 (1980).
[Crossref]

Jpn. J. Appl. Phys. (1)

I. Yamaguchi, “Real-Time Measurement of In-Plane Translation and Tilt by Electronic Speckle Correlation,” Jpn. J. Appl. Phys. 19, L133–L136 (1980).
[Crossref]

Opt. Acta (1)

I. Yamaguchi, “Speckle Displacement and Decorrelation in the Diffraction and Image Fields for Small Object Deformation,” Opt. Acta 28, 1359–1376 (1981).
[Crossref]

Opt. Acta. (1)

A. F. Fercher, H. Sprongl, “Automatic Measurement of Vertex Refraction with Coherent Light,” Opt. Acta. 22, 799–806 (1975).
[Crossref]

Opt. Eng. (2)

I. Yamaguchi, “Simplified Laser-Speckle Strain Gauge,” Opt. Eng. 21, 436–440 (1982).
[Crossref]

I. Yamaguchi, “Advances in the Laser Speckle Strain Gauge,” Opt. Eng. 27, 214–218 (1988).
[Crossref]

Vision Res. (1)

E. Ingelstam, S. -I. Ragnarsson, “Eye Refraction Examined by Aid of Speckle Pattern Produced by Coherent Light,” Vision Res. 12, 411–420 (1972).
[Crossref] [PubMed]

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Figures (12)

Fig. 1
Fig. 1

Schematics of a speckle rotary encoder.

Fig. 2
Fig. 2

Coordinate systems for deriving speckle displacement.

Fig. 3
Fig. 3

Position and height of the cross-correlation peak for various angles of rotation obtained from a He–Ne laser incident on a aluminum cylinder.

Fig. 4
Fig. 4

Same as Fig. 3, but obtained from a cylinder covered with a paper sheet (b).

Fig. 5
Fig. 5

Same as Fig. 3, but obtained from a laser diode.

Fig. 6
Fig. 6

Same as Fig. 4, but obtained from a laser diode.

Fig. 7
Fig. 7

Repeatability of measurement at a fixed position obtained from the configuration of Fig. 5.

Fig. 8
Fig. 8

Repeatability of measurement at a fixed position obtained from a He–Ne laser.

Fig. 9
Fig. 9

Results from the measurement at various positions of a cylinder.

Fig. 10
Fig. 10

Block diagram of a real time binary correlator for outputs of a linear image sensor.

Fig. 11
Fig. 11

Result from application of a real time correlator to rotation of a metal cylinder.

Fig. 12
Fig. 12

Same as Fig. 11, but for finer rotation angle.

Equations (15)

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U ( X ) = I 0 ( φ R ) exp [ i ϕ ( φ R ) ] exp { i k [ L A ( φ ) + L B ( φ , X ) ] } R d φ ,
I 1 ( X ) I 2 ( X + X ¯ ) = I 1 ( X ) I 2 ( X + X ¯ ) + | U 1 ( X ) U 2 * ( X + X ¯ ) | 2 ,
U 1 ( X ) U 2 * ( X + X ¯ ) = R 2 I 0 ( φ R ) I 0 ( φ R ) exp ( i { ϕ ( φ R ) ϕ [ ( φ Δ φ ) R ] } ) exp { i k [ L A ( φ ) L A ( φ Δ φ ) + L B ( φ , X ) L B ( φ Δ φ , X + X ¯ ) ] } d φ d φ .
exp { i [ ϕ ( φ ) ϕ ( φ Δ φ ) ] R } = δ [ ( φ φ + Δ φ ) R ] .
U 1 ( X ) U 2 * ( X + X ¯ ) = R 2 I 0 ( φ R ) I 0 [ ( φ + Δ φ ) R ] exp { i k [ L A ( φ ) L A ( φ + Δ φ ) + L B ( φ , X ) L B ( φ + Δ φ , X + X ¯ ) } ] d φ .
L A ( φ ) = [ ( L s cos θ s + R R cos φ ) 2 + ( L s sin θ s R sin φ ) 2 ] 1 / 2 ,
L B ( φ , X ) = [ ( X cos θ 0 + L 0 sin θ 0 R sin φ ) 2 + ( X sin θ 0 + L 0 cos θ 0 + R R cos φ ) 2 ] 1 / 2 .
L A ( φ ) = L s + R [ cos θ s ( 1 cos φ ) + sin θ s sin φ ] + R 2 L s ( 1 cos φ ) ,
L B ( φ , X ) = L 0 R [ cos ( φ θ 0 ) cos θ 0 ] R X L 0 [ sin ( φ θ 0 ) + sin θ 0 ] + X 2 + 2 R 2 ( 1 cos φ ) 2 L 0 .
U 1 ( X ) U 2 * ( X + X ¯ ) = R 2 I 0 ( φ R ) I 0 [ ( φ + Δ φ ) R ] exp [ i k { R sin φ × [ X ¯ L 0 cos θ 0 + X ¯ Δ φ L 0 sin θ 0 Δ φ ( cos θ s + cos θ 0 + R L s + R L 0 X L 0 sin θ 0 ) ] R cos φ [ X ¯ L 0 sin θ 0 X ¯ Δ φ L 0 cos θ 0 Δ φ ( sin θ s + sin θ 0 + X L 0 cos θ 0 ) ] } ] d φ ,
sin φ sin ( φ + Δ φ ) Δ φ cos φ cos φ cos ( φ + Δ φ ) Δ φ sin φ .
X ¯ = L 0 Δ φ ( cos θ 0 + Δ φ sin θ 0 ) ( cos θ s + cos θ 0 + R L s + R L 0 X sin θ 0 L 0 ) A X .
A X = L 0 Δ φ [ 1 + cos θ s + R ( 1 L s + 1 L 0 ) ] ,
σ A X Δ φ = L 0 [ 1 + cos θ s + R ( 1 L s + 1 L 0 ) ] ,
Δ I 1 ( X ) Δ I 2 ( X + A X ) [ Δ I 1 ( X ) ] 2 = { I 0 ( φ R ) I 0 [ ( φ + Δ φ ) R ] d φ } 2 [ I 0 ( φ R ) d φ ] 2 ,

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