Abstract

A new method for measuring the rotation angle of a cylinder is described, based on the speckle displacement detection caused by the cylinder surface rotation. It is shown that this method is effective for measuring the small rotation angle with high resolution. The accuracy, sensitivity, and resolution of this method are determined by the speckle size, detector pitch, and magnification of the speckle displacement. The configuration to obtain an accurate, sensitive, stable measuring system is discussed. The usefulness of this method is confirmed by experiments.

© 1983 Optical Society of America

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References

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  1. See, for example, J. C. Dainty, Ed., Laser Speckle and Related Phenomena (Springer, Berlin, 1975).
  2. G. Stavis, Instrum. Control Syst. 39, 99 (1966).
  3. H. Ogiwara, H. Ukita, Jpn. J. Appl. Phys. Suppl. 14-1, 307 (1975).
  4. S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
    [CrossRef]
  5. N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
    [CrossRef]
  6. J. Ohtsubo, Opt. Commun. 34, 147 (1980).
    [CrossRef]
  7. J. H. Churnside, H. T. Yura, Appl. Opt. 20, 3539 (1981).
    [CrossRef] [PubMed]
  8. A. Hayashi, Y. Kitagawa, Opt. Commun. 43, 161 (1982).
    [CrossRef]
  9. E. Ingelstam, S.-I. Ragnarsson, Vision Res. 12, 411 (1972).
    [CrossRef] [PubMed]
  10. L. H. Tanner, Appl. Opt. 13, 2026 (1974).
    [CrossRef] [PubMed]
  11. A. F. Fercher, H. Sprongl, Opt. Acta 22, 799 (1975).
    [CrossRef]
  12. J. L. McLaughlin, Appl. Opt. 18, 1042 (1979).
    [CrossRef] [PubMed]
  13. I. Yamaguchi, Jpn. J. Appl. Phys. 19, L133 (1980).
    [CrossRef]
  14. I. Yamaguchi, J. Phys. E 14, 1270 (1981).
    [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 370.

1982 (1)

A. Hayashi, Y. Kitagawa, Opt. Commun. 43, 161 (1982).
[CrossRef]

1981 (2)

1980 (3)

I. Yamaguchi, Jpn. J. Appl. Phys. 19, L133 (1980).
[CrossRef]

N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
[CrossRef]

J. Ohtsubo, Opt. Commun. 34, 147 (1980).
[CrossRef]

1979 (1)

1976 (1)

S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
[CrossRef]

1975 (2)

H. Ogiwara, H. Ukita, Jpn. J. Appl. Phys. Suppl. 14-1, 307 (1975).

A. F. Fercher, H. Sprongl, Opt. Acta 22, 799 (1975).
[CrossRef]

1974 (1)

1972 (1)

E. Ingelstam, S.-I. Ragnarsson, Vision Res. 12, 411 (1972).
[CrossRef] [PubMed]

1966 (1)

G. Stavis, Instrum. Control Syst. 39, 99 (1966).

Asakura, T.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 370.

Churnside, J. H.

Fercher, A. F.

A. F. Fercher, H. Sprongl, Opt. Acta 22, 799 (1975).
[CrossRef]

Hayashi, A.

A. Hayashi, Y. Kitagawa, Opt. Commun. 43, 161 (1982).
[CrossRef]

Ingelstam, E.

E. Ingelstam, S.-I. Ragnarsson, Vision Res. 12, 411 (1972).
[CrossRef] [PubMed]

Iwai, T.

Kitagawa, Y.

A. Hayashi, Y. Kitagawa, Opt. Commun. 43, 161 (1982).
[CrossRef]

Komatsu, S.

S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
[CrossRef]

McLaughlin, J. L.

Ogiwara, H.

H. Ogiwara, H. Ukita, Jpn. J. Appl. Phys. Suppl. 14-1, 307 (1975).

Ohtsubo, J.

J. Ohtsubo, Opt. Commun. 34, 147 (1980).
[CrossRef]

Ragnarsson, S.-I.

E. Ingelstam, S.-I. Ragnarsson, Vision Res. 12, 411 (1972).
[CrossRef] [PubMed]

Saito, H.

S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
[CrossRef]

Sprongl, H.

A. F. Fercher, H. Sprongl, Opt. Acta 22, 799 (1975).
[CrossRef]

Stavis, G.

G. Stavis, Instrum. Control Syst. 39, 99 (1966).

Takai, N.

Tanner, L. H.

Ukita, H.

H. Ogiwara, H. Ukita, Jpn. J. Appl. Phys. Suppl. 14-1, 307 (1975).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 370.

Yamaguchi, I.

I. Yamaguchi, J. Phys. E 14, 1270 (1981).
[CrossRef]

I. Yamaguchi, Jpn. J. Appl. Phys. 19, L133 (1980).
[CrossRef]

S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
[CrossRef]

Yura, H. T.

Appl. Opt. (3)

Instrum. Control Syst. (1)

G. Stavis, Instrum. Control Syst. 39, 99 (1966).

J. Opt. Soc. Am. (1)

J. Phys. E (1)

I. Yamaguchi, J. Phys. E 14, 1270 (1981).
[CrossRef]

Jpn. J. Appl. Phys. (2)

I. Yamaguchi, Jpn. J. Appl. Phys. 19, L133 (1980).
[CrossRef]

S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
[CrossRef]

Jpn. J. Appl. Phys. Suppl. (1)

H. Ogiwara, H. Ukita, Jpn. J. Appl. Phys. Suppl. 14-1, 307 (1975).

Opt. Acta (1)

A. F. Fercher, H. Sprongl, Opt. Acta 22, 799 (1975).
[CrossRef]

Opt. Commun. (2)

J. Ohtsubo, Opt. Commun. 34, 147 (1980).
[CrossRef]

A. Hayashi, Y. Kitagawa, Opt. Commun. 43, 161 (1982).
[CrossRef]

Vision Res. (1)

E. Ingelstam, S.-I. Ragnarsson, Vision Res. 12, 411 (1972).
[CrossRef] [PubMed]

Other (2)

See, for example, J. C. Dainty, Ed., Laser Speckle and Related Phenomena (Springer, Berlin, 1975).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 370.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the system for measuring the rotation angle of a cylinder using the speckle displacement caused by cylinder surface rotation.

Fig. 2
Fig. 2

Theoretical model to investigate the ratio of the speckle displacement magnification to the cylinder surface displacement: O, rotation axis; S, point light source position; Q, scattering position; P, observation point.

Fig. 3
Fig. 3

Magnification m as a function of the scattering position angle α for various values of light source distance ρ.

Fig. 4
Fig. 4

Experimental setup for measuring the rotation angle. The speckle displacement is measured by a vidicon camera, and the rotation angle as the standard is measured by a laser spot reflected by the plane mirror.

Fig. 5
Fig. 5

Cross-correlation function of the intensity distributions of speckles before and after the cylinder surface displacement. The speckle displacement can be determined by the peak position.

Fig. 6
Fig. 6

Magnification m in the direction when the angle of reflection equals the angle of incidence as a function of the illuminating beam angle γ for various values of the light source distance ρ.

Fig. 7
Fig. 7

Magnification m as a function of the observation angle β for various values of the scattering position angle α.

Fig. 8
Fig. 8

Speckle displacement D as a function of the rotation angle θ.

Equations (23)

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θ = D / ( mr ) .
s = λ R / ( π w ) ,
Δ θ = s / ( mr ) .
dD / d θ = mr ,
δ θ = p / ( mr ) .
h ( θ , ψ ) = A f ( φ θ ) exp { j 2 π λ [ l 1 ( φ ) + l 2 ( φ , ψ ) ] } d φ ,
l 1 ( φ ) = ζ + ξ φ + η φ 2 ,
l 2 ( φ , ψ ) = ζ + ξ ( ψ φ ) + η ( ψ φ ) 2 ,
h ( θ , ψ ) = A f ( φ ) exp { j 2 π λ [ l 1 ( φ ) + l 2 ( φ , ψ η + η η θ ) + χ ] } d φ = exp ( j 2 π λ χ ) h ( 0 , ψ η + η η θ ) ,
χ = η ( η + η ) η θ 2 + ( ξ + 2 η ψ + ξ η η ) θ .
| h ( θ , ψ ) | 2 = | h ( 0 , ψ η + η η θ ) | 2 .
Ω = ( 1 + η / η ) θ .
η = g ( r , ρ , α ) ,
η = g ( r , L , β α ) ,
g ( x , y , a ) = x ( x + y ) cos a 2 y 2 + 2 x ( x + y ) ( 1 cos a ) × [ 1 x ( x + y ) y 2 + 2 x ( x + y ) ( 1 cos a ) sin 2 a cos a ] .
m = ( 1 + L r ) [ 1 + g ( r , ρ , α ) g ( r , L , β α ) ] .
cos 1 r r + ρ α cos 1 r r + ρ ,
α cos 1 r r + L β α + cos 1 r r + L .
m = 2 ( 1 + L / r ) ,
m = ( 1 + L ρ + 2 L r ) .
α = γ + sin 1 [ ( 1 + ρ r ) sin γ ] ,
β = 2 α + γ sin 1 ( r + ρ r + L sin γ ) .
sin 1 r r + ρ γ sin 1 r r + ρ .

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