Abstract

High-accuracy, noncontact measurements of in-plane strain fields have been performed through the use of an electronic-speckle-photography system. The strain fields are extracted from the displacement of defocused laser speckle in a telecentric imaging system. Two different illumination configurations have been suggested, both of which use four illumination directions. Both configurations produce results of an accuracy according to MeL, where M is the demagnification of the telecentric imaging system, e is the random error in the speckle-displacement fields, and ΔL is the magnitude of the defocusing distance. The maximum defocusing distance possible was found to be restricted by the spatial resolution, especially at high magnifications. In experiments on a semicircularly and a rectangularly notched aluminum sheet, the principal strain field around the notch was measured with a random error in the strain field of less than 10 μstrain (μm/m).

© 1995 Optical Society of America

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References

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  1. D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth splinelike finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
    [CrossRef]
  2. M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
    [CrossRef]
  3. M. Sjödahl, “Strain-field measurements using electronic speckle photography: a comparison,” in Recent Advances in Experimental Mechanics, J. F. Silva Gomes, F. B. Branco, F. Martins de Brito, J. G. Saravia, M. Lurdes Eusébio, J. Sousa Cirne, A. Correia da Cruz, eds. (Balkema, Rotterdam, The Netherlands, 1994).
  4. Y. Y. Hung, “A speckle-shearing interferometer: a tool for measuring derivatives of surface displacements,” Opt. Commun. 11, 132–135 (1974).
    [CrossRef]
  5. Y. Y. Hung, “Displacement and strain measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, Boca Raton, Fla., 1978), pp. 51–71.
  6. I. Yamaguchi, “A laser-speckle strain gauge,” J. Phys. E 14, 1270–1273 (1981).
    [CrossRef]
  7. K. A. Stetson, “Miscellaneous topics in speckle metrology,” in Speckle Metrology, R. K. Erf, ed. (Academic, Boca Raton, Fla., 1978), pp. 295–320.
  8. M. Sjödahl, L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993).
    [CrossRef] [PubMed]
  9. M. Sjödahl, L. R. Benckert, “Systematic and random errors in electronic speckle photography,” Appl. Opt. 33, 7461–7471 (1994).
    [CrossRef] [PubMed]
  10. M. Sjödahl, “Electronic speckle photography: increased accuracy by nonintegral pixel shifting,” Appl. Opt. 33, 6667–6673 (1994).
    [CrossRef] [PubMed]
  11. M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital-correlation method,” Image Vision Comput. 1, 133–139 (1983).
    [CrossRef]
  12. T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
    [CrossRef]
  13. H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using the Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
    [CrossRef]
  14. P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
    [CrossRef]
  15. D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
    [CrossRef] [PubMed]
  16. S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–1301 (1992).
    [CrossRef]
  17. I. Yamaguchi, S. Noh, “Deformation measurement by 2-D speckle correlation,” in Cryogenic Optical Systems and Instruments V, R. K. Melugin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1756, 106–118 (1992).
  18. C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
    [CrossRef]
  19. H. T. Huang, H. E. Fiedler, J. J. Wang, “Limitation and improvement of PIV Part II: Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).
  20. M. Sjödahl, “Calculation of speckle displacement, decorrelation, and object-point location in imaging systems,” Appl. Opt. (to be published).
  21. D. W. Li, F. P. Chiang, “Decorrelation functions in laser speckle photography,” J. Opt. Soc. Am. A 3, 1023–1031 (1986).
    [CrossRef]

1994 (2)

1993 (4)

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

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
[CrossRef] [PubMed]

H. T. Huang, H. E. Fiedler, J. J. Wang, “Limitation and improvement of PIV Part II: Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

1992 (1)

S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–1301 (1992).
[CrossRef]

1991 (2)

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

1989 (1)

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using the Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

1986 (1)

1985 (1)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

1983 (1)

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

1981 (1)

I. Yamaguchi, “A laser-speckle strain gauge,” J. Phys. E 14, 1270–1273 (1981).
[CrossRef]

1979 (1)

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth splinelike finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

1974 (1)

Y. Y. Hung, “A speckle-shearing interferometer: a tool for measuring derivatives of surface displacements,” Opt. Commun. 11, 132–135 (1974).
[CrossRef]

Benckert, L. R.

Bruck, H. A.

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using the Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

Chae, T. A.

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

Chao, Y. J.

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

Chen, D. J.

Chiang, F. P.

Chu, T. C.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

Don, H. S.

Fiedler, H. E.

H. T. Huang, H. E. Fiedler, J. J. Wang, “Limitation and improvement of PIV Part II: Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

Gharib, M.

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

Huang, H. T.

H. T. Huang, H. E. Fiedler, J. J. Wang, “Limitation and improvement of PIV Part II: Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

Hung, Y. Y.

Y. Y. Hung, “A speckle-shearing interferometer: a tool for measuring derivatives of surface displacements,” Opt. Commun. 11, 132–135 (1974).
[CrossRef]

Y. Y. Hung, “Displacement and strain measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, Boca Raton, Fla., 1978), pp. 51–71.

Li, D. W.

Luo, P. F.

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

McNeill, S. R.

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using the Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

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

Noh, S.

S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–1301 (1992).
[CrossRef]

I. Yamaguchi, S. Noh, “Deformation measurement by 2-D speckle correlation,” in Cryogenic Optical Systems and Instruments V, R. K. Melugin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1756, 106–118 (1992).

Peters, W. H.

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using the Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

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

Ranson, W. F.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

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

Rowlands, R. E.

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth splinelike finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

Segalman, D. J.

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth splinelike finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

Sjödahl, M.

M. Sjödahl, L. R. Benckert, “Systematic and random errors in electronic speckle photography,” Appl. Opt. 33, 7461–7471 (1994).
[CrossRef] [PubMed]

M. Sjödahl, “Electronic speckle photography: increased accuracy by nonintegral pixel shifting,” Appl. Opt. 33, 6667–6673 (1994).
[CrossRef] [PubMed]

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

M. Sjödahl, “Strain-field measurements using electronic speckle photography: a comparison,” in Recent Advances in Experimental Mechanics, J. F. Silva Gomes, F. B. Branco, F. Martins de Brito, J. G. Saravia, M. Lurdes Eusébio, J. Sousa Cirne, A. Correia da Cruz, eds. (Balkema, Rotterdam, The Netherlands, 1994).

M. Sjödahl, “Calculation of speckle displacement, decorrelation, and object-point location in imaging systems,” Appl. Opt. (to be published).

Stetson, K. A.

K. A. Stetson, “Miscellaneous topics in speckle metrology,” in Speckle Metrology, R. K. Erf, ed. (Academic, Boca Raton, Fla., 1978), pp. 295–320.

Sutton, M. A.

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using the Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

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

Tan, Y. S.

Turner, J. L.

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

Wang, J. J.

H. T. Huang, H. E. Fiedler, J. J. Wang, “Limitation and improvement of PIV Part II: Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

Willert, C. E.

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

Wolters, W. J.

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

Woyak, D. B.

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth splinelike finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

Yamaguchi, I.

S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–1301 (1992).
[CrossRef]

I. Yamaguchi, “A laser-speckle strain gauge,” J. Phys. E 14, 1270–1273 (1981).
[CrossRef]

I. Yamaguchi, S. Noh, “Deformation measurement by 2-D speckle correlation,” in Cryogenic Optical Systems and Instruments V, R. K. Melugin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1756, 106–118 (1992).

Appl. Opt. (4)

Exp. Fluids (2)

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

H. T. Huang, H. E. Fiedler, J. J. Wang, “Limitation and improvement of PIV Part II: Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

Exp. Mech. (5)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using the Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

D. J. Segalman, D. B. Woyak, R. E. Rowlands, “Smooth splinelike finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech. 19, 429–437 (1979).
[CrossRef]

M. A. Sutton, J. L. Turner, H. A. Bruck, T. A. Chae, “Full-field representation of sampled surface deformation for displacement and strain analysis,” Exp. Mech. 31, 168–177 (1991).
[CrossRef]

Image Vision Comput. (1)

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

J. Opt. Soc. Am. A (1)

J. Phys. E (1)

I. Yamaguchi, “A laser-speckle strain gauge,” J. Phys. E 14, 1270–1273 (1981).
[CrossRef]

Jpn. J. Appl. Phys. (1)

S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–1301 (1992).
[CrossRef]

Opt. Commun. (1)

Y. Y. Hung, “A speckle-shearing interferometer: a tool for measuring derivatives of surface displacements,” Opt. Commun. 11, 132–135 (1974).
[CrossRef]

Other (5)

Y. Y. Hung, “Displacement and strain measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, Boca Raton, Fla., 1978), pp. 51–71.

M. Sjödahl, “Strain-field measurements using electronic speckle photography: a comparison,” in Recent Advances in Experimental Mechanics, J. F. Silva Gomes, F. B. Branco, F. Martins de Brito, J. G. Saravia, M. Lurdes Eusébio, J. Sousa Cirne, A. Correia da Cruz, eds. (Balkema, Rotterdam, The Netherlands, 1994).

I. Yamaguchi, S. Noh, “Deformation measurement by 2-D speckle correlation,” in Cryogenic Optical Systems and Instruments V, R. K. Melugin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1756, 106–118 (1992).

M. Sjödahl, “Calculation of speckle displacement, decorrelation, and object-point location in imaging systems,” Appl. Opt. (to be published).

K. A. Stetson, “Miscellaneous topics in speckle metrology,” in Speckle Metrology, R. K. Erf, ed. (Academic, Boca Raton, Fla., 1978), pp. 295–320.

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Figures (5)

Fig. 1
Fig. 1

Telecentric imaging system.

Fig. 2
Fig. 2

Definitions used in the analysis.

Fig. 3
Fig. 3

Setup used in the experiments. The electronic speckle-photography system seen to the right side of the figure consists of a CCD camera, a personal computer (PC), and a monitor. Numbers 1–4 refer to the illumination directions.

Fig. 4
Fig. 4

Diagram of the test area and results from a tensile test of a sheet of aluminum that has a semicircular notch. The numbers on the horizontal and vertical axes define the resulting matrix positions. (a) The measured area of 14.5 mm × 14.5 mm showing the notch (R2). (b) The shape of the principal strain field. The maximum strain component is equal to 347 μstrain. (c) Contour plot of the inner 14 × 14 elements of the principal strain field that is mainly parallel to the pulling direction seen in (b). The value labels in the figure are in μstrain. (d) Contour plot of the inner 14 × 14 elements of the principal strain field that is mainly perpendicular to the pulling direction seen in (b). The value labels in the figure are in μstrain.

Fig. 5
Fig. 5

Diagram of the test area and results from a tensile test of a sheet of aluminum with a rectangular notch. The numbers on the horizontal and vertical axes define the resulting matrix positions. (a) The measured area of 5.8 mm × 5.8 mm showing the notch. (b) Shape of the principal strain field. The maximum strain component is equal to 1014 μstrain. (c) Contour plot of the inner 14 × 14 elements of the principal strain field that is mainly parallel to the pulling direction seen in (b). The value labels in the figure are in μstrain. (d) Contour plot of the inner 14 × 14 elements of the principal strain field that is mainly perpendicular to the pulling direction seen in (b). The value labels in the figure are in μstrain.

Tables (2)

Tables Icon

Table 1 Parameters Defined in Figs. 1 and 2 and Eq. (13) and Used in the Tensile-Test Experiments on Sheet Aluminum

Tables Icon

Table 2 Results from the Tensile-Test Experiments Listed in Table 1

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

A X = a x M - Δ L M [ ɛ x x l s x + ɛ x y l s y - Ω y ( 1 + l s z ) + Ω z l s y ] ,
A Y = a y M - Δ L M [ ɛ x y l s x + ɛ y y l s y + Ω x ( 1 + l s z ) - Ω z l s x ] ,
M A = Ha ,
ɛ x x = M ( A X - - A X + ) 2 Δ L l s x | l s y = 0 ,
ɛ x y - Ω z = M ( A Y - - A Y + ) 2 Δ L l s x | l s y = 0 ,
ɛ y y = M ( A Y - - A Y + ) 2 Δ L l s y | l s x = 0 ,
ɛ x y + Ω z = M ( A X - - A X + ) 2 Δ L l s y | l s x = 0.
ɛ x y = M 4 Δ L [ A X - - A X + l s y | l s x = 0 + A Y - - A Y + l s x | l s y = 0 ] ,
γ = [ ( θ - sin θ ) / π ] 2 ,
θ = 2 cos - 1 ( d r D ) ,
A ξ = f 1 [ a x L 0 + ɛ x x l s x + ɛ x y l s y - Ω y ( 1 + l s z ) + Ω z l s y ] ,
A Ψ = f 1 [ a y L 0 + ɛ x y l s x + ɛ y y l s y + Ω x ( 1 + l s z ) - Ω z l s x ] ,
max δ X , δ Y λ L 2 2 D ,
F eff 16 × 10 - 6 M f 2 λ f 1 ,
δ = [ f 2 ( M + 1 ) - f 1 ] Δ L F eff f 1 ( M + 1 - f 1 / f 2 ) ,
Δ L S N F eff M f 1 ( M + 1 - f 1 / f 2 ) 512 [ f 2 ( M + 1 ) - f 1 ] ,
ρ = δ / ( M 5.8 ) ,
γ = i = 0 m - 1 j = 0 m - 1 [ I 1 ( i , j ) - I ] [ I 2 ( i , j ) - I ] { i = 0 m - 1 j = 0 m - 1 [ I 1 ( i , j ) - I ] 2 i = 0 m - 1 j = 0 m - 1 [ I 2 ( i , j ) - I ] 2 } 1 / 2 ,
e 512 s ɛ Δ L M ( 5.8 × 10 6 ) ,

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