Abstract

Speckle photography can be used to monitor deformations of solid surfaces. Its measuring characteristics, such as range or lateral resolution, depend heavily on the optical recording and illumination setup. I show how, by the addition of two suitably perforated masks, the effective optical aperture of the system may vary from point to point of the surface, accordingly adapting the range and resolution to local requirements. Furthermore, by illuminating narrow areas, speckle size can be chosen independently from the optical aperture, thus lifting an important constraint on the choice of the latter. The technique, which I believe to be new, is described within the framework of digital defocused speckle photography under normal collimated illumination. Mutually limiting relations between the range of measurement and the spatial frequency resolution turn up both locally and when the whole surface under study is considered. They are deduced and discussed in detail. Finally, experimental results are presented.

© 2007 Optical Society of America

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References

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  1. T. Belendez, C. Neipp, and A. Belendez, "Large and small deflections of a cantilever beam," Cent. Eur. J. Phys. 23, 371-379 (2002).
  2. J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer Verlag, 1975).
    [CrossRef]
  3. R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge University Press, 1989).
  4. M. Sjödahl and L. R. Benckert, "Systematic and random errors in electronic speckle photography," Appl. Opt. 32, 7461-7471 (1994).
    [CrossRef]
  5. M. Sjödahl, "Accuracy in electronic speckle photography," Appl. Opt. 36, 2875-2883 (1997).
    [CrossRef] [PubMed]
  6. M. Sjödahl, "Some recent advances in electronic speckle photography," Opt. Lasers Eng. 29, 125-144 (1998).
    [CrossRef]
  7. H. Tiziani, "A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately," Opt. Commun. 5, 271-274 (1972).
    [CrossRef]
  8. H. Tiziani, "Vibration analysis and deformation measurement," in Speckle Metrology, R. K. Erf, ed. (Academic, 1978).
  9. P. K. Rastogi, "Techniques of displacement and deformation measurements in speckle metrology," in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, 1993).
  10. D. A. Gregory, "Basic physical principles of defocused speckle photography: a tilt topology inspection technique," Opt. Laser Technol. 8, 201-213 (1976).
    [CrossRef]
  11. D. A. Gregory, "Speckle scatter, affine geometry, and tilt topology," Opt. Commun. 20, 1-5 (1977).
    [CrossRef]
  12. D. A. Gregory, "Topological speckle and structural inspection," in Speckle Metrology, R. K. Erf, ed. (Academic, 1978).
  13. F. P. Chiang and R. M. Juang, "Laser speckle interferometry for plate bending problems," Appl. Opt. 15, 2199-2204 (1976).
    [CrossRef] [PubMed]
  14. A. E. Ennos and M. S. Virdee, "Laser speckle photography as an alternative to holographic interferometry fot measuring plate deformation," Opt. Eng. 21, 478-482 (1982).
  15. F. P. Chiang and R. M. Juang, "Vibration analysis of plate and shell by laser speckle interferometry," Opt. Acta 23, 997-1009 (1976).
    [CrossRef]
  16. H. Schwieger and J. Banken, "Speckle photography for deformation analysis of bent plates," Mater. Pruef 27, 153-156 (1985).
  17. M. Sjödahl, "Electronic speckle photography: measurement of in-plane strain fields through the use of defocused laser speckle," Appl. Opt. 34, 5799-5808 (1995).
    [CrossRef] [PubMed]
  18. M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacements using an improved digital correlation method," Comput. Vision 1, 133-139 (1983).
    [CrossRef]
  19. D. J. Chen, F. P. Chiang, Y. S. Tan, and H. D. Don, "Digital speckle-displacement measurement using a complex spectrum method," Appl. Opt. 32, 1839-1849 (1993).
    [CrossRef] [PubMed]
  20. M. Sjödahl and L. R. Benckert, "Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy," Appl. Opt. 1993; 32:2278-84.
    [CrossRef] [PubMed]
  21. D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, "Digital speckle correlation for strain measurement by image analysis," Exp. Mech. 34, 396-402 (2003).
    [CrossRef]
  22. G. Cloud, Optical Methods of Engineering Analysis (Cambridge University Press, 1998).

2003 (1)

D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, "Digital speckle correlation for strain measurement by image analysis," Exp. Mech. 34, 396-402 (2003).
[CrossRef]

2002 (1)

T. Belendez, C. Neipp, and A. Belendez, "Large and small deflections of a cantilever beam," Cent. Eur. J. Phys. 23, 371-379 (2002).

1998 (1)

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

1997 (1)

1995 (1)

1994 (1)

M. Sjödahl and L. R. Benckert, "Systematic and random errors in electronic speckle photography," Appl. Opt. 32, 7461-7471 (1994).
[CrossRef]

1993 (2)

1985 (1)

H. Schwieger and J. Banken, "Speckle photography for deformation analysis of bent plates," Mater. Pruef 27, 153-156 (1985).

1983 (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacements using an improved digital correlation method," Comput. Vision 1, 133-139 (1983).
[CrossRef]

1982 (1)

A. E. Ennos and M. S. Virdee, "Laser speckle photography as an alternative to holographic interferometry fot measuring plate deformation," Opt. Eng. 21, 478-482 (1982).

1977 (1)

D. A. Gregory, "Speckle scatter, affine geometry, and tilt topology," Opt. Commun. 20, 1-5 (1977).
[CrossRef]

1976 (3)

F. P. Chiang and R. M. Juang, "Laser speckle interferometry for plate bending problems," Appl. Opt. 15, 2199-2204 (1976).
[CrossRef] [PubMed]

D. A. Gregory, "Basic physical principles of defocused speckle photography: a tilt topology inspection technique," Opt. Laser Technol. 8, 201-213 (1976).
[CrossRef]

F. P. Chiang and R. M. Juang, "Vibration analysis of plate and shell by laser speckle interferometry," Opt. Acta 23, 997-1009 (1976).
[CrossRef]

1972 (1)

H. Tiziani, "A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately," Opt. Commun. 5, 271-274 (1972).
[CrossRef]

Appl. Opt. (6)

Cent. Eur. J. Phys. (1)

T. Belendez, C. Neipp, and A. Belendez, "Large and small deflections of a cantilever beam," Cent. Eur. J. Phys. 23, 371-379 (2002).

Comput. Vision (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacements using an improved digital correlation method," Comput. Vision 1, 133-139 (1983).
[CrossRef]

Exp. Mech. (1)

D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, "Digital speckle correlation for strain measurement by image analysis," Exp. Mech. 34, 396-402 (2003).
[CrossRef]

Mater. Pruef (1)

H. Schwieger and J. Banken, "Speckle photography for deformation analysis of bent plates," Mater. Pruef 27, 153-156 (1985).

Opt. Acta (1)

F. P. Chiang and R. M. Juang, "Vibration analysis of plate and shell by laser speckle interferometry," Opt. Acta 23, 997-1009 (1976).
[CrossRef]

Opt. Commun. (2)

H. Tiziani, "A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately," Opt. Commun. 5, 271-274 (1972).
[CrossRef]

D. A. Gregory, "Speckle scatter, affine geometry, and tilt topology," Opt. Commun. 20, 1-5 (1977).
[CrossRef]

Opt. Eng. (1)

A. E. Ennos and M. S. Virdee, "Laser speckle photography as an alternative to holographic interferometry fot measuring plate deformation," Opt. Eng. 21, 478-482 (1982).

Opt. Laser Technol. (1)

D. A. Gregory, "Basic physical principles of defocused speckle photography: a tilt topology inspection technique," Opt. Laser Technol. 8, 201-213 (1976).
[CrossRef]

Opt. Lasers Eng. (1)

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

Other (6)

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer Verlag, 1975).
[CrossRef]

R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge University Press, 1989).

D. A. Gregory, "Topological speckle and structural inspection," in Speckle Metrology, R. K. Erf, ed. (Academic, 1978).

H. Tiziani, "Vibration analysis and deformation measurement," in Speckle Metrology, R. K. Erf, ed. (Academic, 1978).

P. K. Rastogi, "Techniques of displacement and deformation measurements in speckle metrology," in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, 1993).

G. Cloud, Optical Methods of Engineering Analysis (Cambridge University Press, 1998).

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Figures (6)

Fig. 1
Fig. 1

DIDDSP setup for recording defocused specklegrams of a rough surface.

Fig. 2
Fig. 2

AADDSP setup, showing two suitably perforated masks to enhance measuring possibilities.

Fig. 3
Fig. 3

AADDSP uniaxial equivalent to make geometry simpler.

Fig. 4
Fig. 4

(a) Illumination mask (IM); (b) aperture mask (AM); (c) speckle circles at the recording plane.

Fig. 5
Fig. 5

Measuring range versus lateral resolution for DIDDSP and AADDSP.

Fig. 6
Fig. 6

(Color online) Example of theoretical tilt distribution (continuous) and its derivative (dotted) in the deflection of a cantilever plate.

Tables (1)

Tables Icon

Table 1 Simultaneous Tilt Measurement Experimental Results for Five Different Points on the Plate

Equations (46)

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s * 2 w ,
s = 1.22 λ f a m ,
a m 1.22 λ f s * .
b f = L d ,
d x = 2 f β ,
d y = 2 f α ,
s = 1.22 λ f D .
2 α > D d .
Γ = D 2 d .
Γ Δ = 1 2 d
D = 1.22 λ f s * ,
Γ = 1.22 f λ 2 d s * ,
Δ = 1.22 λ f s * .
c i 4 a i ,
s i = 1.22 λ f a i .
a = 1.22 λ f s * .
p c i b g i ,
g i = f c i m ,
p = n b f ,
m n .
m L ,
L m d 2 = f L 2 b ,
f 2 b ,
δ c = n δ d ,
δ c c 2 m ,
D 2 d δ c c 2 m = n m δ d 2 m c .
D c d m .
γ = c 2 m ,
γ d D 2 n m δ γ d ,
Γ = D 2 d ,
Δ 2 m d Γ n ,
Δ 2 d Γ ,
Δ = 2 d Γ .
m = n = d 2 .
L Δ = b 2 f Γ .
4 a < 2 γ m ,
a < 2.5   mm,
a 1.22 f λ 2 w 0.5   mm,
γ > 2.44 λ f w d .
γ δ d Γ ,
D = 2 d Γ .
γ 8 Γ D I ,
Δ 8 Δ D I ,
z ( x ) = ζ ( x 3 2 L 3 3 x 2 2 L 2 ) ,
z ( x ) = ζ ( 3 x 2 2 L 3 3 x L 2 ) ,
Ψ ( x ) = Δ ζ ( 3 x 2 2 L 3 3 x L 2 ) ,

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