Abstract

Laser speckle decorrelation has previously been applied to measure the mean powder size of bulk powder beds and the roughness of porous rocks. The angular decorrelation rate of laser speckle from bulk powder beds correlates strongly with the mean powder size. However it was found that the angular decorrelation rates of transparent powders were much higher than those of opaque or dyed powders of the same size distribution. The accuracy of size measurements could be severely compromised if transparency effects were not compensated. Monte Carlo modelling of remitted photon path lengths in a powder bed suggests and experimental data supports that diffuse reflectance data may be used to correct for transparency effects on angular decorrelation rate data.

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References

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  1. D. L�ger, E. Mathieu and J.C. Perrin, "Optical surface roughness determination using speckle correlation technique," Appl. Opt., 14, 4, 872-877 (1975).
    [CrossRef] [PubMed]
  2. D. L�ger and J.C. Perrin, "Real-time measurement of surface roughness by correlation of speckle patterns," J. Opt. Soc. Am., 66, 11, 1210-1217, (1976).
    [CrossRef]
  3. H. Nitta and T. Asakura, "Method for measuring mean particle size of the bulk powder using speckle patterns," Appl. Opt., 30, 33, 4854-4958 (1991).
    [CrossRef] [PubMed]
  4. N.A. Russo and E.E. Sicre, "Real time measurement of surface roughness through Young's fringes modulated speckle," Appl. Opt., 31, 22, 4334-4336 (1992).
    [CrossRef] [PubMed]
  5. M. Lehman, J.A. Pomarico and R.D. Torroba, "Digital speckle pattern interferometry applied to a surface roughness study," Opt. Eng., 34, 4, 1148-1152 (1995).
    [CrossRef]
  6. N.A. Russo, N.A. Bolognini, E.E. Sicre and M. Garavaglia, "Surface roughness measurement through speckle method," Int. J. Optoelectron., 5, 5, 389-395 (1990).
  7. M.A. Rebollo, E.N. Hogert, J. Albano, C.A. Raffo and N.G. Gagglio, "Correlation between roughness and porosity in rocks," Opt. Laser Tech., 28, 1, 21-23 (1996).
    [CrossRef]
  8. Spectralon Reflectance Material from LabSphere, Inc. North Sutton, NH, USA http://www.labsphere.com/
  9. Garnet from Barton Mines Company, Lake George, NY, USA http://www.barton.com/
  10. Ballotini� impact beads from Potters Industries Inc. Valley Forge, PA, USA http:// www.pottersbeads.com/
  11. Labtechnics laboratory test sieves. (Conforming to Australian Standard AS1142 and British Standard BS410), sizes 20, 25, 32, 38, 45, 53, 63, 75, 90, 106, 125, 150, 180, 212, 250 �m.
  12. G. Kort�m , Reflectance Spectroscopy, (Springer-Verlag, New York, 1969).
    [CrossRef]
  13. M. Ohl�dal, "Comparison of the two dimensional Fraunhofer and the two-dimensional Fresnel approximations in the analysis of surface roughness by angle speckle correlation. I. Theory," J. Mod. Opt., 38, 11, 2115-2135, (1991).
    [CrossRef]
  14. M. Ohl�dal, "Comparison of the two dimensional Fraunhofer and the two-dimensional Fresnel approximations in the analysis of surface roughness by angle speckle correlation. II. Experimental results," J. Mod. Opt., 42, 10, 2081-2094, (1995).
    [CrossRef]
  15. F.P. Quinti�n, M.A. Rebollo and N.G. Gaggioli, "Diffusion of light transmitted from rough surfaces", J. Mod. Opt., 44, 3, 447-460, (1997).
    [CrossRef]

Other (15)

D. L�ger, E. Mathieu and J.C. Perrin, "Optical surface roughness determination using speckle correlation technique," Appl. Opt., 14, 4, 872-877 (1975).
[CrossRef] [PubMed]

D. L�ger and J.C. Perrin, "Real-time measurement of surface roughness by correlation of speckle patterns," J. Opt. Soc. Am., 66, 11, 1210-1217, (1976).
[CrossRef]

H. Nitta and T. Asakura, "Method for measuring mean particle size of the bulk powder using speckle patterns," Appl. Opt., 30, 33, 4854-4958 (1991).
[CrossRef] [PubMed]

N.A. Russo and E.E. Sicre, "Real time measurement of surface roughness through Young's fringes modulated speckle," Appl. Opt., 31, 22, 4334-4336 (1992).
[CrossRef] [PubMed]

M. Lehman, J.A. Pomarico and R.D. Torroba, "Digital speckle pattern interferometry applied to a surface roughness study," Opt. Eng., 34, 4, 1148-1152 (1995).
[CrossRef]

N.A. Russo, N.A. Bolognini, E.E. Sicre and M. Garavaglia, "Surface roughness measurement through speckle method," Int. J. Optoelectron., 5, 5, 389-395 (1990).

M.A. Rebollo, E.N. Hogert, J. Albano, C.A. Raffo and N.G. Gagglio, "Correlation between roughness and porosity in rocks," Opt. Laser Tech., 28, 1, 21-23 (1996).
[CrossRef]

Spectralon Reflectance Material from LabSphere, Inc. North Sutton, NH, USA http://www.labsphere.com/

Garnet from Barton Mines Company, Lake George, NY, USA http://www.barton.com/

Ballotini� impact beads from Potters Industries Inc. Valley Forge, PA, USA http:// www.pottersbeads.com/

Labtechnics laboratory test sieves. (Conforming to Australian Standard AS1142 and British Standard BS410), sizes 20, 25, 32, 38, 45, 53, 63, 75, 90, 106, 125, 150, 180, 212, 250 �m.

G. Kort�m , Reflectance Spectroscopy, (Springer-Verlag, New York, 1969).
[CrossRef]

M. Ohl�dal, "Comparison of the two dimensional Fraunhofer and the two-dimensional Fresnel approximations in the analysis of surface roughness by angle speckle correlation. I. Theory," J. Mod. Opt., 38, 11, 2115-2135, (1991).
[CrossRef]

M. Ohl�dal, "Comparison of the two dimensional Fraunhofer and the two-dimensional Fresnel approximations in the analysis of surface roughness by angle speckle correlation. II. Experimental results," J. Mod. Opt., 42, 10, 2081-2094, (1995).
[CrossRef]

F.P. Quinti�n, M.A. Rebollo and N.G. Gaggioli, "Diffusion of light transmitted from rough surfaces", J. Mod. Opt., 44, 3, 447-460, (1997).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram of experimental set-up used to make speckle measurements. The bed-CCD spacing was 185mm.

Fig. 2.
Fig. 2.

Decorrelation rate as a function of particle size for calcite and silicon carbide.

Fig. 3.
Fig. 3.

Cross-correlation versus incremental tilt angle for mixtures of clear and dyed ballotini. The percentage of purple ballotini in each mixture is shown by weight.

Fig. 4.
Fig. 4.

Cross-correlation versus incremental tilt angle for coloured and transparent powders of the same nominal size.

Fig. 5.
Fig. 5.

MC Calculated mean path lengths of remitted photons in powder beds versus the KM function of the absorption to scatter ratio.

Fig. 6.
Fig. 6.

Experimental data on decorrelation rate and KM function of dyed ballotini of various sizes demonstrated similar parallel line behaviour to the Monte Carlo calculations.

Fig. 7.
Fig. 7.

Decorrelation versus sin(θ1) for opaque and transparent powders. Note that the fitted regressions are each forced through zero to hi-light the dependency of the decorrelation technique on the transparency of the material studied.

Tables (2)

Tables Icon

Table 1. Regression fits of Eq. 4. to Monte Carlo data of Fig. 5.

Tables Icon

Table 2. Regression fits of Eq. 4. To the experimental data of Fig. 6.

Equations (5)

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V ( δ θ ) e ( σ · 2 π · sin ( θ 1 ) · δ θ λ ) 2
C 0 , n ( A 0 · A n ) 1 2 .
K S ( 1 R ) 2 2 · R
y = a · x b
n e ( K S ) · p

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