Abstract

We present a low-cost optical design for the detection of speckle translation, which can provide measures of in-plane translation or the rotation of a solid structure. A nonspecular target surface is illuminated with coherent light. The scattered light is propagated through an optical arrangement that has been particularly designed for the type of mechanical measurand for which the sensor is intended. The dynamics of the speckle field that arise from the target surface are projected onto a lenticular array, constituting a narrow spatial bandpass filter for the speckle spectrum. The filter provides access to the full phase information of the temporal quasi-sinusoidal intensity output; thus differential arrangements of photodetectors can provide suppression of low-frequency oscillations and higher harmonics, and the direction of the speckle translation can be determined. The spatial filter of the sensor is characterized, and the precision of the sensor when it is integrated with an electronic zero-crossing-detection processor is investigated. The best measurement accuracy obtained at constant velocity is 1% at 1.6-mm translation; the relative standard deviation decreases with the square root of the distance traveled.

© 2004 Optical Society of America

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References

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  1. T. Asakura, N. Takai, “Dynamic laser speckles and their application to velocity measurements of a diffuse object,” Appl. Phys. 25, 179–194 (1981).
    [CrossRef]
  2. Y. Aizu, T. Asakura, “Principle and development of spatial filter velocimetry,” Appl. Phys. B 43, 209–224 (1987).
    [CrossRef]
  3. B. E. A. Saleh, “Speckle correlation measurement of the velocity of a small rotating rough surface,” Appl. Opt. 14, 2344–2346 (1975).
    [CrossRef] [PubMed]
  4. B. Rose, H. Imam, S. G. Hanson, H. T. Yura, R. S. Hansen, “Laser-speckle angular-displacement sensor: theoretical and experimental study,” Appl. Opt. 37, 2119–2129 (1998).
    [CrossRef]
  5. J. T. Ator, “Image velocity sensing by optical correlation,” Appl. Opt. 5, 1325–1331 (1966).
    [CrossRef] [PubMed]
  6. T. Ushizaka, T. Asakura, “Measurements of flow velocity in a microscopic region using a transmission grating,” Appl. Opt. 22, 1870–1874 (1983).
    [CrossRef] [PubMed]
  7. Y. Aizu, T. Ushizaka, T. Asakura, “Measurements of the flow velocity in a microscopic region using a transmission grating: elimination of directional ambiguity,” Appl. Opt. 24, 636–640 (1985).
    [CrossRef]
  8. T. Ushizaka, Y. Aizu, T. Asakura, “Measurements of velocity using a lenticular grating,” Appl. Phys. B 39, 97–106 (1986).
    [CrossRef]
  9. U. Schnell, J. Piot, R. Dändliker, “Detection of movement with laser speckle patterns: statistical properties,” J. Opt. Soc. Am. A 15, 207–216 (1998).
    [CrossRef]
  10. H. T. Yura, B. Rose, S. G. Hanson, “Dynamic laser speckle in complex ABCD optical systems,” J. Opt. Soc. Am. A 15, 1160–1166 (1998).
    [CrossRef]
  11. H. T. Yura, S. G. Hanson, “Optical beam propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987).
    [CrossRef]
  12. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 4–29.

1998 (3)

1987 (2)

H. T. Yura, S. G. Hanson, “Optical beam propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987).
[CrossRef]

Y. Aizu, T. Asakura, “Principle and development of spatial filter velocimetry,” Appl. Phys. B 43, 209–224 (1987).
[CrossRef]

1986 (1)

T. Ushizaka, Y. Aizu, T. Asakura, “Measurements of velocity using a lenticular grating,” Appl. Phys. B 39, 97–106 (1986).
[CrossRef]

1985 (1)

1983 (1)

1981 (1)

T. Asakura, N. Takai, “Dynamic laser speckles and their application to velocity measurements of a diffuse object,” Appl. Phys. 25, 179–194 (1981).
[CrossRef]

1975 (1)

1966 (1)

Aizu, Y.

Y. Aizu, T. Asakura, “Principle and development of spatial filter velocimetry,” Appl. Phys. B 43, 209–224 (1987).
[CrossRef]

T. Ushizaka, Y. Aizu, T. Asakura, “Measurements of velocity using a lenticular grating,” Appl. Phys. B 39, 97–106 (1986).
[CrossRef]

Y. Aizu, T. Ushizaka, T. Asakura, “Measurements of the flow velocity in a microscopic region using a transmission grating: elimination of directional ambiguity,” Appl. Opt. 24, 636–640 (1985).
[CrossRef]

Asakura, T.

Y. Aizu, T. Asakura, “Principle and development of spatial filter velocimetry,” Appl. Phys. B 43, 209–224 (1987).
[CrossRef]

T. Ushizaka, Y. Aizu, T. Asakura, “Measurements of velocity using a lenticular grating,” Appl. Phys. B 39, 97–106 (1986).
[CrossRef]

Y. Aizu, T. Ushizaka, T. Asakura, “Measurements of the flow velocity in a microscopic region using a transmission grating: elimination of directional ambiguity,” Appl. Opt. 24, 636–640 (1985).
[CrossRef]

T. Ushizaka, T. Asakura, “Measurements of flow velocity in a microscopic region using a transmission grating,” Appl. Opt. 22, 1870–1874 (1983).
[CrossRef] [PubMed]

T. Asakura, N. Takai, “Dynamic laser speckles and their application to velocity measurements of a diffuse object,” Appl. Phys. 25, 179–194 (1981).
[CrossRef]

Ator, J. T.

Dändliker, R.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 4–29.

Hansen, R. S.

Hanson, S. G.

Imam, H.

Piot, J.

Rose, B.

Saleh, B. E. A.

Schnell, U.

Takai, N.

T. Asakura, N. Takai, “Dynamic laser speckles and their application to velocity measurements of a diffuse object,” Appl. Phys. 25, 179–194 (1981).
[CrossRef]

Ushizaka, T.

Yura, H. T.

Appl. Opt. (5)

Appl. Phys. (1)

T. Asakura, N. Takai, “Dynamic laser speckles and their application to velocity measurements of a diffuse object,” Appl. Phys. 25, 179–194 (1981).
[CrossRef]

Appl. Phys. B (2)

Y. Aizu, T. Asakura, “Principle and development of spatial filter velocimetry,” Appl. Phys. B 43, 209–224 (1987).
[CrossRef]

T. Ushizaka, Y. Aizu, T. Asakura, “Measurements of velocity using a lenticular grating,” Appl. Phys. B 39, 97–106 (1986).
[CrossRef]

J. Opt. Soc. Am. A (3)

Other (2)

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 4–29.

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Figures (12)

Fig. 1
Fig. 1

Schematic of an optical sensor with an imaging configuration for detection of one-dimensional in-plane translation of an object.

Fig. 2
Fig. 2

Schematic of the mixing of wavelets at the detector plane when a spatially coherent, plane optical wave enters the sensor.

Fig. 3
Fig. 3

Schematic of the detector arrangement imaged onto the input plane of the sensor.

Fig. 4
Fig. 4

Logarithmic power spectrum of the spatial filter.

Fig. 5
Fig. 5

Top and middle, signals from the two detectors; trace D, the corresponding differential signal. The detector signals are ac coupled.

Fig. 6
Fig. 6

Ensemble-averaged power spectra at relative aperture sizes (A f ) of 0.0075 (top) and 0.020 (bottom). The detector signals are ac coupled.

Fig. 8
Fig. 8

Ensemble-averaged (16 samples) power spectra of dc-coupled signals. When entrance aperture A s is removed, the aperture of spherical lens L2 destroys the desired suppression of the low-frequency variations.

Fig. 7
Fig. 7

Power in several harmonics relative to power of the fundamental order plotted versus relative aperture (A f ) size.

Fig. 9
Fig. 9

Theoretical and experimental relative widths (FWHM) of the fundamental spectral peak plotted versus number of illuminated lenslets, determined by the size of entrance aperture A s .

Fig. 10
Fig. 10

Average number of counts for 1.6-mm travels plotted versus the level of relative hysteresis at various sizes of entrance aperture A s for the sensor.

Fig. 11
Fig. 11

Relative standard deviation of counts (Fig. 10) plotted versus the level of relative hysteresis for various sizes of entrance aperture A s .

Fig. 12
Fig. 12

Relative uncertainty for the 1.6-mm-step measurements plotted versus the number of illuminated lenslets. The third-order regression is applied to Fig. 11 plotted with a logarithmic axis for the relative hysteresis.

Equations (27)

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|γΔp; τ|=exp-Ai-2Brkrs22υτ2+Δp-Ar+2Bikrs2vτ2ρ02,
ρ0=8|B|2k2rs2+4kImBA*+rc2|A|2+4|B|2k2rs4+4 ImBA*krs21/2.
β=KbKb2+Kt2-1/2,
Kt=Ar+2Bikrs2,
Kb=Ai-2Brkrs2.
Δp=Ar+2Bikrs2ντ.
ws<2M34rs.
M12=f2/f1
Λu=M12Λ12.
ρ0=4f4krs32f32k2Af4+2rs2Af21/2.
Δpx=-f4f3-16f3f4k2Af2rs2υxτ,
Λfr,n=λ cosθi+θi+n/22 sinθi-θi+n/2λf2Λ1n,
λf2/Λ1wd,
it=Ispx, tssnx,
PSξ, t=|Sspξ, tSsnξ|2,
ssnx=scombxswinxsunitxsdetx.
PSξ, t=|Sspξ, t|2|ScombξSwinξ|2|Sunitξ|2|Sdetξ|2.
|ScombSwinξ|2=m=-sinc2wwinξ-mΛ1.
|Sunitξ|2=1-cosΛ1φξ.
φ=2π ΛuΛ1M12.
|Sdetξ|2=sinc2wdξM12.
ξ0=Afλf4=4πρ05Λ1.
NA2Λ12f1f2d12+f1Narray-2,
f0=ΔpxυxτυxΛ1=7.5×104 m-1υx.
|Swinξ|2=sinc2wwinξ.
ΔwFWHMw=2.78πNarray.
Δs=LΔx1/2σΔxNarray;

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