Abstract

A method to reconstruct weakly anisotropic inhomogeneous dielectric tensors inside a transparent medium is proposed. The mathematical theory of integral geometry is cast into a workable framework that allows the full determination of dielectric tensor fields by scalar Radon inversions of the polarization transformation data obtained from six planar tomographic scanning cycles. Furthermore, a careful derivation of the usual equations of integrated photoelasticity in terms of heuristic length scales of the material inhomogeneity and anisotropy is provided, resulting in a self-contained account about the reconstruction of arbitrary three-dimensional, weakly anisotropic dielectric tensor fields.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Lassas, G. Uhlmann, “On determining a Riemannian manifold from the Dirichlet-to-Neumann map,” Ann. Sci. Ec. Normale Super. 34, 771–787 (2001).
  2. P. Ola, L. Päivärinta, E. Somersalo, “An inverse boundary value problem in electrodynamics,” Duke Math. J. 70, 617–653 (1993).
    [CrossRef]
  3. M. Joshi, S. McDowall, “Total determination of material parameters from electromagnetic boundary information,” Pac. J. Math. 193, 107–129 (2000).
    [CrossRef]
  4. Y. A. Kravtsov, “‘Quasi-isotropic’ approximation of geometric optics,” Dokl. Akad. Nauk SSSR 183, 74–76 (1968).
  5. Y. A. Kravtsov, Y. I. Orlov, Geometric Optics of Inhomogeneous Media (Nauka, Moscow, 1980).
  6. A. A. Fuki, Y. A. Kravtsov, O. N. Naida, Geometrical Optics of Weakly Anisotropic Media (Gordon & Breach, Amsterdam, 1998).
  7. V. A. Sharafutdinov, Integral Geometry of Tensor Fields (VSP, Zeist, The Netherlands, 1994).
  8. M. M. Frocht, Photoelasticity (Wiley, New York, 1948), Vols. 1 and 2.
  9. E. G. Coker, L. N. G. Filon, Photo-Elasticity, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1957).
  10. P. S. Theocaris, E. E. Gdoutos, Matrix Theory of Photoelasticity, Vol. 11 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1979).
    [CrossRef]
  11. H. T. Jessop, F. C. Harris, Photoelasticity (Cleaver-Hume, London, 1949).
  12. A. W. Hendry, Photoelastic Analysis (Pergamon, Oxford, UK, 1966).
  13. H. K. Aben, “Optical phenomena in photoelastic models by the rotation of principal axes,” Exp. Mech. 6, 13–22 (1966).
    [CrossRef]
  14. H. Aben, Integrated Photoelasticity (McGraw-Hill, New York, 1979).
  15. H. K. Aben, J. I. Josepson, K.-J. E. Kell, “The case of weak birefringence in integrated photoelasticity,” Opt. Lasers Eng. 11, 145–157 (1989).
    [CrossRef]
  16. H. Aben, C. Guillemet, Photoelasticity of Glass (Springer-Verlag, Berlin, 1993).
  17. H. Aben, A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221 (1997).
    [CrossRef]
  18. M. Davin, “Sur la composition des petites biréfringences subies par un rayon traversant un modèle photoélastique faiblement contraint,” C.R. Seances Acad. Sci. Ser. A 269, 1227–1229 (1969).
  19. H. Aben, S. Idnurm, A. Puro, “Integrated photoelasticity in case of weak birefringence,” in Proceedings of the 9th International Conference on Experimental Mechanics (ICEM, Copenhagen, 1990), Vol. 2, pp. 867–875.
  20. H. Aben, S. Idnurm, J. Josepson, K.-J. Kell, A. Puro, “Optical tomography of the stress tensor field,” in Analytical Methods for Optical Tomography, G. G. Levin, ed., Proc. SPIE1843, 220–229 (1991).
    [CrossRef]
  21. H. Aben, A. Errapart, L. Ainola, J. Anton, “Photoelastic tomography in linear approximation,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics, 2003 (available on CD-ROM).
  22. Y. A. Andrienko, M. S. Dubovikov, “Optical tomography of tensor fields: the general case,” J. Opt. Soc. Am. A 11, 1628–1631 (1994).
    [CrossRef]
  23. Y. A. Andrienko, M. S. Dubovikov, A. D. Gladun, “Optical tomography of a birefringent medium,” J. Opt. Soc. Am. A 9, 1761–1764 (1992).
    [CrossRef]
  24. Y. A. Andrienko, M. S. Dubovikov, A. D. Gladun, “Optical tensor field tomography: the Kerr effect and axisymmetric integrated photoelasticity,” J. Opt. Soc. Am. A 9, 1765–1768 (1992).
    [CrossRef]
  25. M. L. L. Wijerathne, K. Oguni, M. Hori, “Tensor field tomography based on 3D photoelasticity,” Mech. Mater. 34, 533–545 (2002).
    [CrossRef]
  26. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
  27. G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart & Winston, New York, 1975).
  28. A. Sommerfeld, Optics, Lectures on Theoretical Physics, 1st ed. (Academic, New York, 1954), Vol. 4.
  29. R. W. Ditchburn, Light, 3rd ed. (Academic, London, 1976).
  30. R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1973).
  31. H. Poincaré, Théorie mathématique de la lumiére (Carré Naud, Paris, 1892).
  32. H. Hammer, “Characteristic parameters in integrated photoelasticity: an application of Poincaré’s equivalence theorem,” J. Mod. Opt. 51, 597–618 (2004).
  33. D. Schupp, “Optical tensor field tomography for the determination of 3D stress in photoelastic materials,” in 1st World Congress on Industrial Process Tomography (Buxton, Greater Manchester, UK, 1999), pp. 494–501.
  34. D. Schupp, “Optische Tensortomographie zur Bestimmung räumlicher Spannungsverteilungen,” Tech. Mess. 66, 54–60 (1999).
    [CrossRef]
  35. S. Helgason, The Radon Transform (Birkhäuser, Basel, 1980).
  36. F. Natterer, The Mathematics of Computerized Tomography (Wiley–Teubner, Stuttgart, Germany, 1986).

2004 (1)

H. Hammer, “Characteristic parameters in integrated photoelasticity: an application of Poincaré’s equivalence theorem,” J. Mod. Opt. 51, 597–618 (2004).

2002 (1)

M. L. L. Wijerathne, K. Oguni, M. Hori, “Tensor field tomography based on 3D photoelasticity,” Mech. Mater. 34, 533–545 (2002).
[CrossRef]

2001 (1)

M. Lassas, G. Uhlmann, “On determining a Riemannian manifold from the Dirichlet-to-Neumann map,” Ann. Sci. Ec. Normale Super. 34, 771–787 (2001).

2000 (1)

M. Joshi, S. McDowall, “Total determination of material parameters from electromagnetic boundary information,” Pac. J. Math. 193, 107–129 (2000).
[CrossRef]

1999 (1)

D. Schupp, “Optische Tensortomographie zur Bestimmung räumlicher Spannungsverteilungen,” Tech. Mess. 66, 54–60 (1999).
[CrossRef]

1997 (1)

H. Aben, A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221 (1997).
[CrossRef]

1994 (1)

1993 (1)

P. Ola, L. Päivärinta, E. Somersalo, “An inverse boundary value problem in electrodynamics,” Duke Math. J. 70, 617–653 (1993).
[CrossRef]

1992 (2)

1989 (1)

H. K. Aben, J. I. Josepson, K.-J. E. Kell, “The case of weak birefringence in integrated photoelasticity,” Opt. Lasers Eng. 11, 145–157 (1989).
[CrossRef]

1969 (1)

M. Davin, “Sur la composition des petites biréfringences subies par un rayon traversant un modèle photoélastique faiblement contraint,” C.R. Seances Acad. Sci. Ser. A 269, 1227–1229 (1969).

1968 (1)

Y. A. Kravtsov, “‘Quasi-isotropic’ approximation of geometric optics,” Dokl. Akad. Nauk SSSR 183, 74–76 (1968).

1966 (1)

H. K. Aben, “Optical phenomena in photoelastic models by the rotation of principal axes,” Exp. Mech. 6, 13–22 (1966).
[CrossRef]

Aben, H.

H. Aben, A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221 (1997).
[CrossRef]

H. Aben, S. Idnurm, A. Puro, “Integrated photoelasticity in case of weak birefringence,” in Proceedings of the 9th International Conference on Experimental Mechanics (ICEM, Copenhagen, 1990), Vol. 2, pp. 867–875.

H. Aben, A. Errapart, L. Ainola, J. Anton, “Photoelastic tomography in linear approximation,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics, 2003 (available on CD-ROM).

H. Aben, Integrated Photoelasticity (McGraw-Hill, New York, 1979).

H. Aben, C. Guillemet, Photoelasticity of Glass (Springer-Verlag, Berlin, 1993).

H. Aben, S. Idnurm, J. Josepson, K.-J. Kell, A. Puro, “Optical tomography of the stress tensor field,” in Analytical Methods for Optical Tomography, G. G. Levin, ed., Proc. SPIE1843, 220–229 (1991).
[CrossRef]

Aben, H. K.

H. K. Aben, J. I. Josepson, K.-J. E. Kell, “The case of weak birefringence in integrated photoelasticity,” Opt. Lasers Eng. 11, 145–157 (1989).
[CrossRef]

H. K. Aben, “Optical phenomena in photoelastic models by the rotation of principal axes,” Exp. Mech. 6, 13–22 (1966).
[CrossRef]

Ainola, L.

H. Aben, A. Errapart, L. Ainola, J. Anton, “Photoelastic tomography in linear approximation,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics, 2003 (available on CD-ROM).

Andrienko, Y. A.

Anton, J.

H. Aben, A. Errapart, L. Ainola, J. Anton, “Photoelastic tomography in linear approximation,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics, 2003 (available on CD-ROM).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Coker, E. G.

E. G. Coker, L. N. G. Filon, Photo-Elasticity, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1957).

Davin, M.

M. Davin, “Sur la composition des petites biréfringences subies par un rayon traversant un modèle photoélastique faiblement contraint,” C.R. Seances Acad. Sci. Ser. A 269, 1227–1229 (1969).

Ditchburn, R. W.

R. W. Ditchburn, Light, 3rd ed. (Academic, London, 1976).

Dubovikov, M. S.

Errapart, A.

H. Aben, A. Errapart, L. Ainola, J. Anton, “Photoelastic tomography in linear approximation,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics, 2003 (available on CD-ROM).

Filon, L. N. G.

E. G. Coker, L. N. G. Filon, Photo-Elasticity, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1957).

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart & Winston, New York, 1975).

Frocht, M. M.

M. M. Frocht, Photoelasticity (Wiley, New York, 1948), Vols. 1 and 2.

Fuki, A. A.

A. A. Fuki, Y. A. Kravtsov, O. N. Naida, Geometrical Optics of Weakly Anisotropic Media (Gordon & Breach, Amsterdam, 1998).

Gdoutos, E. E.

P. S. Theocaris, E. E. Gdoutos, Matrix Theory of Photoelasticity, Vol. 11 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1979).
[CrossRef]

Gladun, A. D.

Guillemet, C.

H. Aben, C. Guillemet, Photoelasticity of Glass (Springer-Verlag, Berlin, 1993).

Hammer, H.

H. Hammer, “Characteristic parameters in integrated photoelasticity: an application of Poincaré’s equivalence theorem,” J. Mod. Opt. 51, 597–618 (2004).

Harris, F. C.

H. T. Jessop, F. C. Harris, Photoelasticity (Cleaver-Hume, London, 1949).

Helgason, S.

S. Helgason, The Radon Transform (Birkhäuser, Basel, 1980).

Hendry, A. W.

A. W. Hendry, Photoelastic Analysis (Pergamon, Oxford, UK, 1966).

Hori, M.

M. L. L. Wijerathne, K. Oguni, M. Hori, “Tensor field tomography based on 3D photoelasticity,” Mech. Mater. 34, 533–545 (2002).
[CrossRef]

Idnurm, S.

H. Aben, S. Idnurm, A. Puro, “Integrated photoelasticity in case of weak birefringence,” in Proceedings of the 9th International Conference on Experimental Mechanics (ICEM, Copenhagen, 1990), Vol. 2, pp. 867–875.

H. Aben, S. Idnurm, J. Josepson, K.-J. Kell, A. Puro, “Optical tomography of the stress tensor field,” in Analytical Methods for Optical Tomography, G. G. Levin, ed., Proc. SPIE1843, 220–229 (1991).
[CrossRef]

Jessop, H. T.

H. T. Jessop, F. C. Harris, Photoelasticity (Cleaver-Hume, London, 1949).

Josepson, J.

H. Aben, S. Idnurm, J. Josepson, K.-J. Kell, A. Puro, “Optical tomography of the stress tensor field,” in Analytical Methods for Optical Tomography, G. G. Levin, ed., Proc. SPIE1843, 220–229 (1991).
[CrossRef]

Josepson, J. I.

H. K. Aben, J. I. Josepson, K.-J. E. Kell, “The case of weak birefringence in integrated photoelasticity,” Opt. Lasers Eng. 11, 145–157 (1989).
[CrossRef]

Joshi, M.

M. Joshi, S. McDowall, “Total determination of material parameters from electromagnetic boundary information,” Pac. J. Math. 193, 107–129 (2000).
[CrossRef]

Kell, K.-J.

H. Aben, S. Idnurm, J. Josepson, K.-J. Kell, A. Puro, “Optical tomography of the stress tensor field,” in Analytical Methods for Optical Tomography, G. G. Levin, ed., Proc. SPIE1843, 220–229 (1991).
[CrossRef]

Kell, K.-J. E.

H. K. Aben, J. I. Josepson, K.-J. E. Kell, “The case of weak birefringence in integrated photoelasticity,” Opt. Lasers Eng. 11, 145–157 (1989).
[CrossRef]

Kravtsov, Y. A.

Y. A. Kravtsov, “‘Quasi-isotropic’ approximation of geometric optics,” Dokl. Akad. Nauk SSSR 183, 74–76 (1968).

A. A. Fuki, Y. A. Kravtsov, O. N. Naida, Geometrical Optics of Weakly Anisotropic Media (Gordon & Breach, Amsterdam, 1998).

Y. A. Kravtsov, Y. I. Orlov, Geometric Optics of Inhomogeneous Media (Nauka, Moscow, 1980).

Lassas, M.

M. Lassas, G. Uhlmann, “On determining a Riemannian manifold from the Dirichlet-to-Neumann map,” Ann. Sci. Ec. Normale Super. 34, 771–787 (2001).

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1973).

McDowall, S.

M. Joshi, S. McDowall, “Total determination of material parameters from electromagnetic boundary information,” Pac. J. Math. 193, 107–129 (2000).
[CrossRef]

Naida, O. N.

A. A. Fuki, Y. A. Kravtsov, O. N. Naida, Geometrical Optics of Weakly Anisotropic Media (Gordon & Breach, Amsterdam, 1998).

Natterer, F.

F. Natterer, The Mathematics of Computerized Tomography (Wiley–Teubner, Stuttgart, Germany, 1986).

Oguni, K.

M. L. L. Wijerathne, K. Oguni, M. Hori, “Tensor field tomography based on 3D photoelasticity,” Mech. Mater. 34, 533–545 (2002).
[CrossRef]

Ola, P.

P. Ola, L. Päivärinta, E. Somersalo, “An inverse boundary value problem in electrodynamics,” Duke Math. J. 70, 617–653 (1993).
[CrossRef]

Orlov, Y. I.

Y. A. Kravtsov, Y. I. Orlov, Geometric Optics of Inhomogeneous Media (Nauka, Moscow, 1980).

Päivärinta, L.

P. Ola, L. Päivärinta, E. Somersalo, “An inverse boundary value problem in electrodynamics,” Duke Math. J. 70, 617–653 (1993).
[CrossRef]

Poincaré, H.

H. Poincaré, Théorie mathématique de la lumiére (Carré Naud, Paris, 1892).

Puro, A.

H. Aben, A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221 (1997).
[CrossRef]

H. Aben, S. Idnurm, A. Puro, “Integrated photoelasticity in case of weak birefringence,” in Proceedings of the 9th International Conference on Experimental Mechanics (ICEM, Copenhagen, 1990), Vol. 2, pp. 867–875.

H. Aben, S. Idnurm, J. Josepson, K.-J. Kell, A. Puro, “Optical tomography of the stress tensor field,” in Analytical Methods for Optical Tomography, G. G. Levin, ed., Proc. SPIE1843, 220–229 (1991).
[CrossRef]

Schupp, D.

D. Schupp, “Optische Tensortomographie zur Bestimmung räumlicher Spannungsverteilungen,” Tech. Mess. 66, 54–60 (1999).
[CrossRef]

D. Schupp, “Optical tensor field tomography for the determination of 3D stress in photoelastic materials,” in 1st World Congress on Industrial Process Tomography (Buxton, Greater Manchester, UK, 1999), pp. 494–501.

Sharafutdinov, V. A.

V. A. Sharafutdinov, Integral Geometry of Tensor Fields (VSP, Zeist, The Netherlands, 1994).

Somersalo, E.

P. Ola, L. Päivärinta, E. Somersalo, “An inverse boundary value problem in electrodynamics,” Duke Math. J. 70, 617–653 (1993).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, Optics, Lectures on Theoretical Physics, 1st ed. (Academic, New York, 1954), Vol. 4.

Theocaris, P. S.

P. S. Theocaris, E. E. Gdoutos, Matrix Theory of Photoelasticity, Vol. 11 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1979).
[CrossRef]

Uhlmann, G.

M. Lassas, G. Uhlmann, “On determining a Riemannian manifold from the Dirichlet-to-Neumann map,” Ann. Sci. Ec. Normale Super. 34, 771–787 (2001).

Wijerathne, M. L. L.

M. L. L. Wijerathne, K. Oguni, M. Hori, “Tensor field tomography based on 3D photoelasticity,” Mech. Mater. 34, 533–545 (2002).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Ann. Sci. Ec. Normale Super. (1)

M. Lassas, G. Uhlmann, “On determining a Riemannian manifold from the Dirichlet-to-Neumann map,” Ann. Sci. Ec. Normale Super. 34, 771–787 (2001).

C.R. Seances Acad. Sci. Ser. A (1)

M. Davin, “Sur la composition des petites biréfringences subies par un rayon traversant un modèle photoélastique faiblement contraint,” C.R. Seances Acad. Sci. Ser. A 269, 1227–1229 (1969).

Dokl. Akad. Nauk SSSR (1)

Y. A. Kravtsov, “‘Quasi-isotropic’ approximation of geometric optics,” Dokl. Akad. Nauk SSSR 183, 74–76 (1968).

Duke Math. J. (1)

P. Ola, L. Päivärinta, E. Somersalo, “An inverse boundary value problem in electrodynamics,” Duke Math. J. 70, 617–653 (1993).
[CrossRef]

Exp. Mech. (1)

H. K. Aben, “Optical phenomena in photoelastic models by the rotation of principal axes,” Exp. Mech. 6, 13–22 (1966).
[CrossRef]

Inverse Probl. (1)

H. Aben, A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221 (1997).
[CrossRef]

J. Mod. Opt. (1)

H. Hammer, “Characteristic parameters in integrated photoelasticity: an application of Poincaré’s equivalence theorem,” J. Mod. Opt. 51, 597–618 (2004).

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

Mech. Mater. (1)

M. L. L. Wijerathne, K. Oguni, M. Hori, “Tensor field tomography based on 3D photoelasticity,” Mech. Mater. 34, 533–545 (2002).
[CrossRef]

Opt. Lasers Eng. (1)

H. K. Aben, J. I. Josepson, K.-J. E. Kell, “The case of weak birefringence in integrated photoelasticity,” Opt. Lasers Eng. 11, 145–157 (1989).
[CrossRef]

Pac. J. Math. (1)

M. Joshi, S. McDowall, “Total determination of material parameters from electromagnetic boundary information,” Pac. J. Math. 193, 107–129 (2000).
[CrossRef]

Tech. Mess. (1)

D. Schupp, “Optische Tensortomographie zur Bestimmung räumlicher Spannungsverteilungen,” Tech. Mess. 66, 54–60 (1999).
[CrossRef]

Other (22)

S. Helgason, The Radon Transform (Birkhäuser, Basel, 1980).

F. Natterer, The Mathematics of Computerized Tomography (Wiley–Teubner, Stuttgart, Germany, 1986).

H. Aben, C. Guillemet, Photoelasticity of Glass (Springer-Verlag, Berlin, 1993).

D. Schupp, “Optical tensor field tomography for the determination of 3D stress in photoelastic materials,” in 1st World Congress on Industrial Process Tomography (Buxton, Greater Manchester, UK, 1999), pp. 494–501.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart & Winston, New York, 1975).

A. Sommerfeld, Optics, Lectures on Theoretical Physics, 1st ed. (Academic, New York, 1954), Vol. 4.

R. W. Ditchburn, Light, 3rd ed. (Academic, London, 1976).

R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1973).

H. Poincaré, Théorie mathématique de la lumiére (Carré Naud, Paris, 1892).

H. Aben, Integrated Photoelasticity (McGraw-Hill, New York, 1979).

H. Aben, S. Idnurm, A. Puro, “Integrated photoelasticity in case of weak birefringence,” in Proceedings of the 9th International Conference on Experimental Mechanics (ICEM, Copenhagen, 1990), Vol. 2, pp. 867–875.

H. Aben, S. Idnurm, J. Josepson, K.-J. Kell, A. Puro, “Optical tomography of the stress tensor field,” in Analytical Methods for Optical Tomography, G. G. Levin, ed., Proc. SPIE1843, 220–229 (1991).
[CrossRef]

H. Aben, A. Errapart, L. Ainola, J. Anton, “Photoelastic tomography in linear approximation,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics, 2003 (available on CD-ROM).

Y. A. Kravtsov, Y. I. Orlov, Geometric Optics of Inhomogeneous Media (Nauka, Moscow, 1980).

A. A. Fuki, Y. A. Kravtsov, O. N. Naida, Geometrical Optics of Weakly Anisotropic Media (Gordon & Breach, Amsterdam, 1998).

V. A. Sharafutdinov, Integral Geometry of Tensor Fields (VSP, Zeist, The Netherlands, 1994).

M. M. Frocht, Photoelasticity (Wiley, New York, 1948), Vols. 1 and 2.

E. G. Coker, L. N. G. Filon, Photo-Elasticity, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1957).

P. S. Theocaris, E. E. Gdoutos, Matrix Theory of Photoelasticity, Vol. 11 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1979).
[CrossRef]

H. T. Jessop, F. C. Harris, Photoelasticity (Cleaver-Hume, London, 1949).

A. W. Hendry, Photoelastic Analysis (Pergamon, Oxford, UK, 1966).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Reconstruction of the anisotropy tensor (8a) gives valuable information about the internal structure of the object, even if the average dielectric constant ϵ [Eq. (1)] is not known: (a) cylindrical bar axially loaded, (b) oblique intersection, (c) original tensor component Aηη, (d) reconstruction with 254×254 pixels and 36 scans.

Equations (33)

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

=1vol B Bd3x13tr -,
l0|κ tr -(x)||tr -(x)|,
lp|κep(x)||ep(x)|.
lp,l0λ¯
Eˆ(x, t)=E(x)exp[iϕ(x)-iωt],
α=maxλ¯l0, λ¯lp.
α1.
Aij=ij-δij,
βmaxAij,
β/α1.
E(x, t)=E(x)exp(ikx-iωt)
k=ωu,u=1μ0,λ=2πk.
κDOλlpD,κEOλlp+βE.
β1.
k×(k×E)+ω2μ0-E-i[×(k×E)+k×(×E)]-×(×E)=0.
××EOλlp2E;
κ×(κ×E)-ik [×(κ×E)+κ×(×E)]+μ0u2-E=0,
OλlpE
ddzE1E2=iπλA11A12A21A22E1E2,
E1(z)E2(z)=U(z, z0)E1(z0)E2(z0),
ddzU(z, z0)=iπλA(z)U(z, z0),U(z0, z0)=12=1001.
U(z, z0)=12+iπλ z0zdz1A(z1)U(z1, z0),
U(z, z0)=12+iπλ z0zdz1A(z1)+iπλ2 z0zdz1A(z1) z0z1dz2A(z2)+.
U(z, z0)=12+iπλ z0zdz1A(z1).
U=S(Δ, θ, δ)exp(iΦ),S(Δ, θ, δ)SU(2),
Re(exp(iΦ)S11)=Re(exp(iΦ)S22)=1,Re(exp(iΦ)S12)=Re(exp(iΦ)S21)=0.
Uξξ(t, t0)Uξη(t, t0)Uηξ(t, t0)Uηη(t, t0)=1001+iπλt0zdt1Aξξ(t1)Aξη(t1)Aηξ(t1)Aηη(t1).
 dt1Aηη(t1)=[Uηη(+,-)-1]λiπ,
η1=e1,η2=e2,η3=e3,
η12=e1+e22,η23=e2+e32,η31=e3+e12.
A11,A22,A33
A(η12, η12)=12(A11+A22)+A12,
ij=(Aij+δij);

Metrics