Abstract

This paper discusses simulation of speckle-field dynamics during coherent light scattering by a cement surface in the process of hydration. Cement particles are represented by the spheres whose sizes and reflection indices are changing during the hydration process. The study of intensity fluctuations of scattered coherent radiation is a suitable technique for the analysis of both fast and slow processes of mineral binder hydration and formation of polycrystalline structures in the process of hardening. The results of simulation are in good agreement with the experimental data.

© 2012 Optical Society of America

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References

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  1. V. F. Gorsky, Plugging Materials and Solutions (Chernivtsi Oblpolihrafvydav, Ukrainian, 2006).
  2. F. M. Lee, The Chemistry of Cement and Concrete, 3rd ed.(Edward Arnold, 1970).
  3. V. S. Ramachandran, Handbook of Analytical Techniques in Concrete (National Research Council of Canada, 2001).
  4. M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).
    [CrossRef]
  5. M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E1–63412E6 (2006).
    [CrossRef]
  6. M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle-field dynamics scattered by surface of concrete during congelation,” Proc. SPIE 6635, 66350E (2006).
    [CrossRef]
  7. O. V. Angelsky, S. G. Hanson, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology estimation of the degree of coherence of optical waves,” Opt. Express 17, 15623–15634 (2009).
    [CrossRef]
  8. O. V. Angelsky, P. V. Polyanskii, and S. G. Hanson, “Singular-optical coloring of regularly scattered white light,” Opt. Express 14, 7580–7586 (2006).
    [CrossRef]
  9. O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
    [CrossRef]
  10. M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
    [CrossRef]
  11. M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Optical correlation technique for cement particle size measurements,” Appl. Opt. 10, 459–469 (2010).
  12. M. Francon, La granularité laser (spekle) etses applications en optique (Institut d’Optique et Université de Paris, 1978).
  13. A. Ishimaru, Wave Propagation and Scattering in Random Media, Vols. 1, 2 (Academic, 1978).
  14. M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).
  15. E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49, 77–98 (1988).
    [CrossRef]
  16. J. Stam, “Multiple scattering as a diffusion process,” presented at the Eurographics Rendering Workshop (1995).
  17. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).
  18. J. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Institute of Physics, 1999).

2010

2009

O. V. Angelsky, S. G. Hanson, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology estimation of the degree of coherence of optical waves,” Opt. Express 17, 15623–15634 (2009).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

2006

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E1–63412E6 (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle-field dynamics scattered by surface of concrete during congelation,” Proc. SPIE 6635, 66350E (2006).
[CrossRef]

O. V. Angelsky, P. V. Polyanskii, and S. G. Hanson, “Singular-optical coloring of regularly scattered white light,” Opt. Express 14, 7580–7586 (2006).
[CrossRef]

2002

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

1988

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49, 77–98 (1988).
[CrossRef]

Akkermans, E.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49, 77–98 (1988).
[CrossRef]

Angelsky, O. V.

O. V. Angelsky, S. G. Hanson, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology estimation of the degree of coherence of optical waves,” Opt. Express 17, 15623–15634 (2009).
[CrossRef]

O. V. Angelsky, P. V. Polyanskii, and S. G. Hanson, “Singular-optical coloring of regularly scattered white light,” Opt. Express 14, 7580–7586 (2006).
[CrossRef]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).

Francon, M.

M. Francon, La granularité laser (spekle) etses applications en optique (Institut d’Optique et Université de Paris, 1978).

Gorodyns’ka, N. V.

Gorsky, M. P.

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Optical correlation technique for cement particle size measurements,” Appl. Opt. 10, 459–469 (2010).

O. V. Angelsky, S. G. Hanson, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology estimation of the degree of coherence of optical waves,” Opt. Express 17, 15623–15634 (2009).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle-field dynamics scattered by surface of concrete during congelation,” Proc. SPIE 6635, 66350E (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E1–63412E6 (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).
[CrossRef]

Gorsky, V. F.

V. F. Gorsky, Plugging Materials and Solutions (Chernivtsi Oblpolihrafvydav, Ukrainian, 2006).

Hanson, S. G.

O. V. Angelsky, S. G. Hanson, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology estimation of the degree of coherence of optical waves,” Opt. Express 17, 15623–15634 (2009).
[CrossRef]

O. V. Angelsky, P. V. Polyanskii, and S. G. Hanson, “Singular-optical coloring of regularly scattered white light,” Opt. Express 14, 7580–7586 (2006).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media, Vols. 1, 2 (Academic, 1978).

Lee, F. M.

F. M. Lee, The Chemistry of Cement and Concrete, 3rd ed.(Edward Arnold, 1970).

Maksimyak, A. P.

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Optical correlation technique for cement particle size measurements,” Appl. Opt. 10, 459–469 (2010).

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle-field dynamics scattered by surface of concrete during congelation,” Proc. SPIE 6635, 66350E (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E1–63412E6 (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).
[CrossRef]

Maksimyak, P. P.

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Optical correlation technique for cement particle size measurements,” Appl. Opt. 10, 459–469 (2010).

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle-field dynamics scattered by surface of concrete during congelation,” Proc. SPIE 6635, 66350E (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E1–63412E6 (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).
[CrossRef]

Maret, G.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49, 77–98 (1988).
[CrossRef]

Maynard, R.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49, 77–98 (1988).
[CrossRef]

Mokhun, A. I.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Mokhun, I. I.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).

Nye, J.

J. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Institute of Physics, 1999).

Polyanskii, P. V.

O. V. Angelsky, P. V. Polyanskii, and S. G. Hanson, “Singular-optical coloring of regularly scattered white light,” Opt. Express 14, 7580–7586 (2006).
[CrossRef]

Ramachandran, V. S.

V. S. Ramachandran, Handbook of Analytical Techniques in Concrete (National Research Council of Canada, 2001).

Soskin, M. S.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Stam, J.

J. Stam, “Multiple scattering as a diffusion process,” presented at the Eurographics Rendering Workshop (1995).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).

Wolf, P. E.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49, 77–98 (1988).
[CrossRef]

Zenkova, C. Yu.

Appl. Opt.

J. Phys. France

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. France 49, 77–98 (1988).
[CrossRef]

Opt. Express

O. V. Angelsky, S. G. Hanson, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology estimation of the degree of coherence of optical waves,” Opt. Express 17, 15623–15634 (2009).
[CrossRef]

O. V. Angelsky, P. V. Polyanskii, and S. G. Hanson, “Singular-optical coloring of regularly scattered white light,” Opt. Express 14, 7580–7586 (2006).
[CrossRef]

Phys. Rev. E

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Proc. SPIE

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6254, 244–247 (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle dynamic light-scattering in the process of cement hydration,” Proc. SPIE 6341, 63412E1–63412E6 (2006).
[CrossRef]

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Study of speckle-field dynamics scattered by surface of concrete during congelation,” Proc. SPIE 6635, 66350E (2006).
[CrossRef]

Ukr. J. Phys. Opt.

M. P. Gorsky, A. P. Maksimyak, and P. P. Maksimyak, “Studies of light backscattering at concrete during its hydration,” Ukr. J. Phys. Opt. 10, 134–149 (2009).
[CrossRef]

Other

M. Francon, La granularité laser (spekle) etses applications en optique (Institut d’Optique et Université de Paris, 1978).

A. Ishimaru, Wave Propagation and Scattering in Random Media, Vols. 1, 2 (Academic, 1978).

M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).

V. F. Gorsky, Plugging Materials and Solutions (Chernivtsi Oblpolihrafvydav, Ukrainian, 2006).

F. M. Lee, The Chemistry of Cement and Concrete, 3rd ed.(Edward Arnold, 1970).

V. S. Ramachandran, Handbook of Analytical Techniques in Concrete (National Research Council of Canada, 2001).

J. Stam, “Multiple scattering as a diffusion process,” presented at the Eurographics Rendering Workshop (1995).

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).

J. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Institute of Physics, 1999).

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Figures (13)

Fig. 1.
Fig. 1.

Schematic sketch of spherical particle location in simulation.

Fig. 2.
Fig. 2.

Cement particle distribution according to the Rayleigh law.

Fig. 3.
Fig. 3.

Illustration of rays reflected from the inner surface of spherical particles.

Fig. 4.
Fig. 4.

Illustration of rays inside a spherical particle. θi=input angle; θt=angle of refraction; n1 and n2=refractive indices of the environment and particle, respectively; Lin(d,θi)=dsin(θi)/2=distance from the axial beam; γ=the angle that determines the exit point of beam on the particle surface; L0(d,θi)=optical path to the surface of the particles; LL(d,θi)=half of the beam path inside the particle.

Fig. 5.
Fig. 5.

Dependence of probability density ρξ vs. n.

Fig. 6.
Fig. 6.

Relative change in particle size dend/dst during particle’s dissolution.

Fig. 7.
Fig. 7.

Relative change in particle size dend/dst during particle’s growth.

Fig. 8.
Fig. 8.

The change of mk during hydration.

Fig. 9.
Fig. 9.

Relative change in particle size dend/dst of newly formed particles during their growth.

Fig. 10.
Fig. 10.

Theoretical dependence of the normalized intensity of the speckle field scattered by the cement paste on hydration and hardening time.

Fig. 11.
Fig. 11.

Theoretical temporal dependence of the normalized time derivative of the speckle field’s intensity fluctuations under light scattering by the cement paste in the process of hydration and hardening.

Fig. 12.
Fig. 12.

Experimental setup.

Fig. 13.
Fig. 13.

Experimental temporal dependence of the normalized derivative of the speckle field’s intensity fluctuations under light scattering by the cement paste in the process of hydration and hardening: (a) wf=0.275, (b) wf=0.3, (c) wf=0.325. Dashed lines show the beginning and the end of hardening according to the Vicat apparatus.

Equations (15)

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

Lf(d,θi)=n1Lin(d,θi)+2n2LL(d,θi).
TR=2n1cosθin2cosθi+n1cosθtA
TR=2n1cosθin1cosθi+n2cosθtA
AR=n2cosθin1cosθtn2cosθi+n1cosθtA
AR=n1cosθin2cosθtn1cosθi+n2cosθtA,
Δφ=2πLLΔnλ.
Ei(r,t)=Ewicos(ωwtkr)r,
Ex(ξ,μ)=i,jR(i,j)xEwycos(ωwt+kr(i,j)+φ(i,j))r(i,j)
Ey(ξ,μ)=i,jR(i,j)yEwycos(ωwtkr(i,j)+φ(i,j)+Δφ(i,j))r(i,j),
I(ξ,μ)=I0m(i,j)(A(ξ,μ)2+B(ξ,μ)2+C(ξ,μ)2+D(ξ,μ)2),
A(ξ,μ)=i,jR(i,j)xcos(kr(i,j)+φ(i,j))r(i,j),
B(ξ,μ)=i,jR(i,j)ycos(kr(i,j)+φ(i,j)+Δφ(i,j)),r(i,j)
C(ξ,μ)=i,jR(i,j)xsin(kr(i,j)+φ(i,j))r(i,j),
D(ξ,μ)=i,jR(i,j)ysin(kr(i,j)+φ(i,j)+Δφ(i,j))r(i,j).
d(t)=dstexp((tτh)δ)+dend(1exp((tτh)δ)),

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