Abstract

Objective speckles produced by two beams overlapping and interfering on a rough object surface contain information about the angle of incidence of the two beams, and how well they overlap. We obtain the autocovariance function for such a speckle pattern, and demonstrate how the information carried by the objective speckles can be used to probe the distance between the object and the observation plane. From a distance of 75 mm to a distance of 150 mm, and using an angle of 0.3 deg between the two incident beams, we can measure the actual distance with an uncertainty of better than ±0.1% of the full range. As long as the beams overlap at the object surface, the proposed method can measure distance with an uncertainty inversely proportional to the spot size at the object.

© 2012 Optical Society of America

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References

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  1. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).
  2. E. Archibold, J. M. Burch, and A. E. Ennos, “Recording of in-plane displacement by double-exposed speckle photography,” Opt. Acta 17, 883–898 (1970).
    [CrossRef]
  3. H. J. Tiziani, “A study of the use of laser speckle to measure small tilts of optically rough surface accuracy,” Opt. Commun. 5, 271–274 (1972).
    [CrossRef]
  4. I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
    [CrossRef]
  5. M. Sjödahl and I. Yamaguchi, “Strain and torque measurements on cylindrical object using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
    [CrossRef]
  6. C. T. Lant and J. P. Barranger, “Progress in high temperature speckle-shift strain measurement system,” in SEM Hologram Interferometry and Speckle Metrology (SEM, 1990), pp. 203–209.
  7. J. A. Leendertz, “Interferometric displacement measurement,” J. Phys. E 3, 214–218 (1970).
    [CrossRef]
  8. M. Sjödahl, “Some recent advances in electronic speckle photography,” Opt. Lasers Eng. 29, 125–144 (1998).
    [CrossRef]
  9. J. N. Butters, “Speckle pattern interferometry using video techniques,” J. Soc. Photo Opt. Instrum. Eng. 10, 5–9 (1971).
  10. O. J. Løkberg, Speckle Metrology (Dekker, 1993).
  11. I. Yamaguchi, “Theory and application of speckle displacement and decorrelation,” in Speckle MetrologyR. S. Sirohi, ed. (Dekker, 1993), pp. 1–39.
  12. Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Series in Optical Science (Springer, 2006).
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    [CrossRef]
  14. J. A. Leendertz, “Interferometric displacement measurement,” J. Phys. E 3, 214–218 (1970).
    [CrossRef]
  15. M. L. Jakobsen and S. G. Hanson, “Speckle dynamics for intensity-modulated illumination,” Appl. Opt. 47, 3674–3680 (2008).
    [CrossRef]
  16. H. T. Yura, B. Rose, and S. G. Hanson, “Dynamics laser speckle in complex ABCD optical systems,” J. Opt. Soc. Am. A 15, 1160–1166 (1998).
    [CrossRef]
  17. A. E. Siegman, Lasers (University Science, 1986).
  18. M. Sjödahl and L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993).
    [CrossRef]
  19. R. G. Dorsch, G. Haüsler, and J. M. Herrmann, “Laser triangulation: fundamental uncertainty in distance measurement,” Appl. Opt. 33, 1306–1314 (1994).
    [CrossRef]
  20. R. Baribeau and M. Rioux, “Influence of speckle on laser range finders,” Appl. Opt. 30, 2873–2878 (1991).
    [CrossRef]
  21. H.-L. Huang, W.-Y. Jywe, C.-H. Liu, L. Duan, and M.-S. Wang, “Development of a novel laser-based measuring system for the thread profile of ballscrew,” Opt. Lasers Eng. 48, 1012–1018 (2010).
    [CrossRef]

2010

H.-L. Huang, W.-Y. Jywe, C.-H. Liu, L. Duan, and M.-S. Wang, “Development of a novel laser-based measuring system for the thread profile of ballscrew,” Opt. Lasers Eng. 48, 1012–1018 (2010).
[CrossRef]

2008

2005

1998

M. Sjödahl, “Some recent advances in electronic speckle photography,” Opt. Lasers Eng. 29, 125–144 (1998).
[CrossRef]

H. T. Yura, B. Rose, and S. G. Hanson, “Dynamics laser speckle in complex ABCD optical systems,” J. Opt. Soc. Am. A 15, 1160–1166 (1998).
[CrossRef]

1996

M. Sjödahl and I. Yamaguchi, “Strain and torque measurements on cylindrical object using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
[CrossRef]

1994

1993

1991

1981

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

1972

H. J. Tiziani, “A study of the use of laser speckle to measure small tilts of optically rough surface accuracy,” Opt. Commun. 5, 271–274 (1972).
[CrossRef]

1971

J. N. Butters, “Speckle pattern interferometry using video techniques,” J. Soc. Photo Opt. Instrum. Eng. 10, 5–9 (1971).

1970

J. A. Leendertz, “Interferometric displacement measurement,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

E. Archibold, J. M. Burch, and A. E. Ennos, “Recording of in-plane displacement by double-exposed speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

J. A. Leendertz, “Interferometric displacement measurement,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

Aizu, Y.

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Series in Optical Science (Springer, 2006).

Archibold, E.

E. Archibold, J. M. Burch, and A. E. Ennos, “Recording of in-plane displacement by double-exposed speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Asakura, T.

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Series in Optical Science (Springer, 2006).

Baribeau, R.

Barranger, J. P.

C. T. Lant and J. P. Barranger, “Progress in high temperature speckle-shift strain measurement system,” in SEM Hologram Interferometry and Speckle Metrology (SEM, 1990), pp. 203–209.

Benckert, L. R.

Burch, J. M.

E. Archibold, J. M. Burch, and A. E. Ennos, “Recording of in-plane displacement by double-exposed speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Butters, J. N.

J. N. Butters, “Speckle pattern interferometry using video techniques,” J. Soc. Photo Opt. Instrum. Eng. 10, 5–9 (1971).

Dorsch, R. G.

Duan, L.

H.-L. Huang, W.-Y. Jywe, C.-H. Liu, L. Duan, and M.-S. Wang, “Development of a novel laser-based measuring system for the thread profile of ballscrew,” Opt. Lasers Eng. 48, 1012–1018 (2010).
[CrossRef]

Ennos, A. E.

E. Archibold, J. M. Burch, and A. E. Ennos, “Recording of in-plane displacement by double-exposed speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

Hanson, S. G.

Haüsler, G.

Herrmann, J. M.

Huang, H.-L.

H.-L. Huang, W.-Y. Jywe, C.-H. Liu, L. Duan, and M.-S. Wang, “Development of a novel laser-based measuring system for the thread profile of ballscrew,” Opt. Lasers Eng. 48, 1012–1018 (2010).
[CrossRef]

Jakobsen, M. L.

Jywe, W.-Y.

H.-L. Huang, W.-Y. Jywe, C.-H. Liu, L. Duan, and M.-S. Wang, “Development of a novel laser-based measuring system for the thread profile of ballscrew,” Opt. Lasers Eng. 48, 1012–1018 (2010).
[CrossRef]

Kamshillin, A. A.

Lant, C. T.

C. T. Lant and J. P. Barranger, “Progress in high temperature speckle-shift strain measurement system,” in SEM Hologram Interferometry and Speckle Metrology (SEM, 1990), pp. 203–209.

Leendertz, J. A.

J. A. Leendertz, “Interferometric displacement measurement,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

J. A. Leendertz, “Interferometric displacement measurement,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

Liu, C.-H.

H.-L. Huang, W.-Y. Jywe, C.-H. Liu, L. Duan, and M.-S. Wang, “Development of a novel laser-based measuring system for the thread profile of ballscrew,” Opt. Lasers Eng. 48, 1012–1018 (2010).
[CrossRef]

Løkberg, O. J.

O. J. Løkberg, Speckle Metrology (Dekker, 1993).

Nippolainen, E.

Rioux, M.

Rose, B.

Semenov, D. V.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Sjödahl, M.

M. Sjödahl, “Some recent advances in electronic speckle photography,” Opt. Lasers Eng. 29, 125–144 (1998).
[CrossRef]

M. Sjödahl and I. Yamaguchi, “Strain and torque measurements on cylindrical object using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
[CrossRef]

M. Sjödahl and L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993).
[CrossRef]

Tiziani, H. J.

H. J. Tiziani, “A study of the use of laser speckle to measure small tilts of optically rough surface accuracy,” Opt. Commun. 5, 271–274 (1972).
[CrossRef]

Wang, M.-S.

H.-L. Huang, W.-Y. Jywe, C.-H. Liu, L. Duan, and M.-S. Wang, “Development of a novel laser-based measuring system for the thread profile of ballscrew,” Opt. Lasers Eng. 48, 1012–1018 (2010).
[CrossRef]

Yamaguchi, I.

M. Sjödahl and I. Yamaguchi, “Strain and torque measurements on cylindrical object using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
[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, “Theory and application of speckle displacement and decorrelation,” in Speckle MetrologyR. S. Sirohi, ed. (Dekker, 1993), pp. 1–39.

Yura, H. T.

Appl. Opt.

J. Opt. Soc. Am. A

J. Phys. E

J. A. Leendertz, “Interferometric displacement measurement,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

J. A. Leendertz, “Interferometric displacement measurement,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

J. Soc. Photo Opt. Instrum. Eng.

J. N. Butters, “Speckle pattern interferometry using video techniques,” J. Soc. Photo Opt. Instrum. Eng. 10, 5–9 (1971).

Opt. Acta

E. Archibold, J. M. Burch, and A. E. Ennos, “Recording of in-plane displacement by double-exposed speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

Opt. Commun.

H. J. Tiziani, “A study of the use of laser speckle to measure small tilts of optically rough surface accuracy,” Opt. Commun. 5, 271–274 (1972).
[CrossRef]

Opt. Eng.

M. Sjödahl and I. Yamaguchi, “Strain and torque measurements on cylindrical object using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
[CrossRef]

Opt. Lasers Eng.

M. Sjödahl, “Some recent advances in electronic speckle photography,” Opt. Lasers Eng. 29, 125–144 (1998).
[CrossRef]

H.-L. Huang, W.-Y. Jywe, C.-H. Liu, L. Duan, and M.-S. Wang, “Development of a novel laser-based measuring system for the thread profile of ballscrew,” Opt. Lasers Eng. 48, 1012–1018 (2010).
[CrossRef]

Opt. Lett.

Other

A. E. Siegman, Lasers (University Science, 1986).

C. T. Lant and J. P. Barranger, “Progress in high temperature speckle-shift strain measurement system,” in SEM Hologram Interferometry and Speckle Metrology (SEM, 1990), pp. 203–209.

O. J. Løkberg, Speckle Metrology (Dekker, 1993).

I. Yamaguchi, “Theory and application of speckle displacement and decorrelation,” in Speckle MetrologyR. S. Sirohi, ed. (Dekker, 1993), pp. 1–39.

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Series in Optical Science (Springer, 2006).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

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Figures (8)

Fig. 1.
Fig. 1.

The figure illustrates the principle configuration of the coordinate systems, describing the fields. Further, the two beams illuminating the object are illustrated. The r-coordinate system is located in the object plane, while the p-coordinate system is located in the observation plane.

Fig. 2.
Fig. 2.

Autocovariance function (a) in Eq. (15) and the corresponding power spectral density function (b) in Eq. (16) are plotted as a function of Δp and f, respectively. The parameters for the plot are Λ=0mm, Λ/w=0, zθ/ρ=3.37, and (kΛ)/z=0.

Fig. 3.
Fig. 3.

The autocovariance function (a) in Eq. (17) and the power spectral density function (b) in Eq. (18) are plotted as a function of Δp and f, respectively. The parameters for the plots are Λ/w=6.2, z/R=0, zθ/ρ=3.37, and (kΛ)/z=8.2×105m1.

Fig. 4.
Fig. 4.

The schematic for testing the principle is illustrated here. By moving the aperture up or down, either two or any of the two individual beams can illuminate the object.

Fig. 5.
Fig. 5.

The obtained intensity distribution (a) contains two correlated speckle structures, which are produced by two Gaussian beams, overlapping partly on the object. Further, the spatial autocovariance function (b) of the intensity distribution (a) is illustrated as well. The length scales in (a) and (b) are the same.

Fig. 6.
Fig. 6.

The center distance between the self-correlation peak and one of the distance-correlation peaks in the autocovariance function is plotted as a function of distance between object and observation plane.

Fig. 7.
Fig. 7.

Maximum distance-correlation peak level relative to self-correlation peak level is plotted as a function of distance between object and observation plane.

Fig. 8.
Fig. 8.

The center distance and ratio of maximum correlation between the self-correlation peak and one of the distance-correlation peaks in the autocovariance function is plotted as a function of distance between object and observation plane. In this setup, the experimental parameters are θmeas=0.678deg, w=0.8mm.

Equations (23)

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Rcn(p1,p2)=I(p1)I(p2)I(p1)I(p2){[I(p1)2I(p1)2][I(p2)2I(p2)2]}1/2,
Rcn(p1,p2)=|Γ(p1,p2)|2Γ(p1,p1)Γ(p2,p2),
Γ(p1,p2)=U(p1)U*(p2),
U(p)=Sd2rU0(r)G(r,p),
G(r,p)=ik2πzexp(ik2z(r22r·p+p2)),
U0(r)=Ui(r)Ψ(r),
Ψ(r1)Ψ*(r2)=const.×δ(r1r2),
Γ0(r1,r2)=U0(r1)U0*(r2)Ui(r1)Ui*(r2)δ(r2r1),
Γ(p1,p2)=Sd2rUi(r)Ui*(r)G(r,p1)G*(r,p2).
Ui(r)=(2Pπw2)1/2exp((rΛ2ex)2(1w2+ik2R)+ik(rΛ2ex)·θex+iφ1)+(2Pπw2)1/2exp((r+Λ2ex)2(1w2+ik2R)ik(r+Λ2ex)·θex+iφ2),
Rcn(Δp)=Rc0(exp(Λ22w21ρ2((Δpx(2θΛR)z)2+Δpy2))+exp(Λ22w21ρ2((Δpx+(2θΛR)z)2+Δpy2))+2exp(1ρ2(Δpx2+Δpy2))cos(k2zΛΔpx))2,
Rc0=(2+2exp(Λ22w2z2ρ2(2θΛR)2))2.
GnAC(f)=Rcn(Δp)exp(2πiΔp·f)dΔp.
GnAC(f)=πρ22R0(2exp(π2ρ22(fx2+fy2))[1+exp(Λ2w2)cos(2π(ΛR2θ)zfx)]+exp(π2ρ22((fx+kΛ2πz)2+fy2))+exp(π2ρ22((fxkΛ2πz)2+fy2))+2exp(Λ2w22z2ρ2(ΛR2θ)2)exp(π2ρ22(fx2+fy2))+4exp(Λ22w2z22ρ2(ΛR2θ)2)×[exp(π2ρ22((fx+kΛ4πz)2+fy2))cos(πz(ΛR2θ)(fx+kΛ4πz))+exp(π2ρ22((fxkΛ4πz)2+fy2))cos(πz(ΛR2θ)(fxkΛ4πz))]),
Rcn(Δp)=R0(exp(1ρ2((Δpx2θz)2+Δpy2))+exp(1ρ2((Δpx+2θz)2+Δpy2))+2exp(1ρ2(Δpx2+Δpy2)))2,
GnAC(f)=πρ2R0exp(π2ρ22(fx2+fy2))(2+exp(8θ2z2ρ2)+[cos(4πθzfx)+4exp(4θ2z22ρ2)cos(2πθzfx)]).
Rcn(Δp)=exp(2ρ2(Δpx2+Δpy2))cos2(k2zΛΔpx),
GnAC(f)=πρ22R0(2exp(π2ρ22(fx2+fy2))+exp(π2ρ22((fx+kΛ2πz)2+fy2))+exp(π2ρ22((fxkΛ2πz)2+fy2))).
z=Δp2θΔzz(Δ(Δp)Δp)2+(Δθθ)2λθw,
z=zc(1±λ2θ|Δfx|),
ΔzzwΛ.
z=ΛCCD2tanθmeas|ΔpCCD|,
Δp=2θz(1+(zzw)(zzc)b2+(zzw)2).

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