Abstract

This article presents the theoretical background of an azimuthally stable method of Jones-matrix mapping of histological sections of a uterine wall biopsy on the basis of spatial-frequency selection of the mechanisms of linear and circular birefringence. The diagnostic application of a new correlation parameter—a complex degree of mutual anisotropy—is analytically substantiated. The method of measuring coordinate distributions of a complex degree of mutual anisotropy with further spatial filtration of their high- and low-frequency components is developed. The interconnections of such distributions with linear and circular birefringence parameters of the uterine-wall-endometrium histological sections are found. The comparative results of measuring the coordinate distributions of a complex degree of mutual anisotropy formed by fibrillar networks of myosin and collagen fibrils of uterus wall tissue of different pathological states—pre-cancer (dysplasia) and cancer (adenocarcinoma)—are shown. The values and ranges of change of the statistical (moments of the first to fourth orders) parameters of complex degree of mutual-anisotropy coordinate distributions are studied. The objective criteria of diagnosing the pathology and differentiation of its severity degree are determined.

© 2014 Optical Society of America

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  1. V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed., Vol. PM166 of SPIE Press Monographs (SPIE, 2007).
  2. X. Wang, G. Yao, and L.-H. Wang, “Monte Carlo model and single-scattering approximation of polarized light propagation in turbid media containing glucose,” Appl. Opt. 41, 792–801 (2002).
    [CrossRef]
  3. X. Wang and L.-H. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
    [CrossRef]
  4. A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
    [CrossRef]
  5. O. V. Angelsky, A. Ya. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Yu. Zenkova, and A. V. Tyurin, “Circular motion of particles suspended in a Gaussian beam with circular polarization validates the spin part of the internal energy flow,” Opt. Express 20, 11351–11356 (2012).
    [CrossRef]
  6. Yu. A. Ushenko, “Statistical structure of polarization-inhomogeneous images of biotissues with different morphological structures,” Ukr. J. Phys. Opt. 6, 63–70 (2005).
    [CrossRef]
  7. O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, Yu. A. Ushenko, R. Jozwicki, and K. Patorski, “Automatic polarimetric system for early medical diagnosis by biotissue testing,” Opt. Appl. 32, 603–612 (2002).
  8. A. G. Ushenko and V. P. Pishak, “Laser polarimetry of biological tissue: principles and applications,” in Handbook of Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental and Material Science, V. V. Tuchin, ed. (Kluwer Academic Publishers, 2004), Vol. 1, pp. 93–138.
  9. O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, V. P. Pishak, and A. P. Peresunko, “Statistical, correlation and topological approaches in diagnostics of the structure and physiological state of birefringent biological tissues,” in Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (CRC Press, 2010), pp. 283–322.
  10. Y. A. Ushenko, T. M. Boychuk, V. T. Bachynsky, and O. P. Mincer, “Diagnostics of structure and physiological state of birefringent biological tissues: statistical, correlation and topological approaches,” in Handbook of Coherent-Domain Optical Methods (Springer, 2013), pp. 107–148.
  11. Y. A. Ushenko, “Investigation of formation and interrelations of polarization singular structure and Mueller-matrix images of biological tissues and diagnostics of their cancer changes,” J. Biomed. Opt. 16, 066006 (2011).
    [CrossRef]
  12. Yu. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
    [CrossRef]
  13. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” Pure Appl. Opt. 7, 941–951 (1998).
    [CrossRef]
  14. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
    [CrossRef]
  15. J. Tervo, T. Setala, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11, 1137–1143 (2003).
    [CrossRef]
  16. J. Ellis and A. Dogariu, “Complex degree of mutual polarization,” Opt. Lett. 29, 536–538 (2004).
    [CrossRef]
  17. O. V. Angelsky, A. G. Ushenko, and Y. G. Ushenko, “Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state,” J. Biomed. Opt. 10, 060502 (2005).
    [CrossRef]
  18. Y. O. Ushenko, Y. Ya. Tomka, I. Z. Misevitch, V. V. Istratiy, and O. I. Telenga, “Complex degree of mutual anisotropy of biological liquid crystals nets,” Opt. Eng. 50, 039001 (2011).
    [CrossRef]
  19. Yu. A. Ushenko, Yu. Ya. Tomka, and A. V. Dubolazov, “Complex degree of mutual anisotropy of extracellular matrix of biological tissues,” Opt. Spectrosc. 110, 814–819 (2011).
    [CrossRef]
  20. A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, 1975).
  21. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1975), pp. 9–75.
  22. L. D. Cassidy, “Basic concepts of statistical analysis for surgical research,” J. Surg. Res. 128, 199–206 (2005).
    [CrossRef]
  23. C. S. Davis, Statistical Methods of the Analysis of Repeated Measurements (Springer-Verlag, 2002).
  24. A. Petrie and B. Sabin, Medical Statistics at a Glance (Blackwell, 2005).

2012 (2)

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

O. V. Angelsky, A. Ya. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Yu. Zenkova, and A. V. Tyurin, “Circular motion of particles suspended in a Gaussian beam with circular polarization validates the spin part of the internal energy flow,” Opt. Express 20, 11351–11356 (2012).
[CrossRef]

2011 (3)

Y. A. Ushenko, “Investigation of formation and interrelations of polarization singular structure and Mueller-matrix images of biological tissues and diagnostics of their cancer changes,” J. Biomed. Opt. 16, 066006 (2011).
[CrossRef]

Y. O. Ushenko, Y. Ya. Tomka, I. Z. Misevitch, V. V. Istratiy, and O. I. Telenga, “Complex degree of mutual anisotropy of biological liquid crystals nets,” Opt. Eng. 50, 039001 (2011).
[CrossRef]

Yu. A. Ushenko, Yu. Ya. Tomka, and A. V. Dubolazov, “Complex degree of mutual anisotropy of extracellular matrix of biological tissues,” Opt. Spectrosc. 110, 814–819 (2011).
[CrossRef]

2010 (1)

Yu. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

2005 (3)

Yu. A. Ushenko, “Statistical structure of polarization-inhomogeneous images of biotissues with different morphological structures,” Ukr. J. Phys. Opt. 6, 63–70 (2005).
[CrossRef]

L. D. Cassidy, “Basic concepts of statistical analysis for surgical research,” J. Surg. Res. 128, 199–206 (2005).
[CrossRef]

O. V. Angelsky, A. G. Ushenko, and Y. G. Ushenko, “Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state,” J. Biomed. Opt. 10, 060502 (2005).
[CrossRef]

2004 (1)

2003 (2)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

J. Tervo, T. Setala, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11, 1137–1143 (2003).
[CrossRef]

2002 (3)

O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, Yu. A. Ushenko, R. Jozwicki, and K. Patorski, “Automatic polarimetric system for early medical diagnosis by biotissue testing,” Opt. Appl. 32, 603–612 (2002).

X. Wang, G. Yao, and L.-H. Wang, “Monte Carlo model and single-scattering approximation of polarized light propagation in turbid media containing glucose,” Appl. Opt. 41, 792–801 (2002).
[CrossRef]

X. Wang and L.-H. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

1998 (1)

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Angelsky, O. V.

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

O. V. Angelsky, A. Ya. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Yu. Zenkova, and A. V. Tyurin, “Circular motion of particles suspended in a Gaussian beam with circular polarization validates the spin part of the internal energy flow,” Opt. Express 20, 11351–11356 (2012).
[CrossRef]

O. V. Angelsky, A. G. Ushenko, and Y. G. Ushenko, “Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state,” J. Biomed. Opt. 10, 060502 (2005).
[CrossRef]

O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, Yu. A. Ushenko, R. Jozwicki, and K. Patorski, “Automatic polarimetric system for early medical diagnosis by biotissue testing,” Opt. Appl. 32, 603–612 (2002).

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, V. P. Pishak, and A. P. Peresunko, “Statistical, correlation and topological approaches in diagnostics of the structure and physiological state of birefringent biological tissues,” in Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (CRC Press, 2010), pp. 283–322.

Bachynsky, V. T.

Y. A. Ushenko, T. M. Boychuk, V. T. Bachynsky, and O. P. Mincer, “Diagnostics of structure and physiological state of birefringent biological tissues: statistical, correlation and topological approaches,” in Handbook of Coherent-Domain Optical Methods (Springer, 2013), pp. 107–148.

Baku, B. A.

Yu. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

Bekshaev, A. Y.

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

Bekshaev, A. Ya.

Borghi, R.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Boychuk, T. M.

Y. A. Ushenko, T. M. Boychuk, V. T. Bachynsky, and O. P. Mincer, “Diagnostics of structure and physiological state of birefringent biological tissues: statistical, correlation and topological approaches,” in Handbook of Coherent-Domain Optical Methods (Springer, 2013), pp. 107–148.

Burch, J. M.

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, 1975).

Burkovets, D. N.

O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, Yu. A. Ushenko, R. Jozwicki, and K. Patorski, “Automatic polarimetric system for early medical diagnosis by biotissue testing,” Opt. Appl. 32, 603–612 (2002).

Cassidy, L. D.

L. D. Cassidy, “Basic concepts of statistical analysis for surgical research,” J. Surg. Res. 128, 199–206 (2005).
[CrossRef]

Davis, C. S.

C. S. Davis, Statistical Methods of the Analysis of Repeated Measurements (Springer-Verlag, 2002).

Dogariu, A.

Dubolazov, A. V.

Yu. A. Ushenko, Yu. Ya. Tomka, and A. V. Dubolazov, “Complex degree of mutual anisotropy of extracellular matrix of biological tissues,” Opt. Spectrosc. 110, 814–819 (2011).
[CrossRef]

Ellis, J.

Friberg, A.

Gerrard, A.

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, 1975).

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1975), pp. 9–75.

Gori, F.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Guattari, G.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Hanson, S. G.

O. V. Angelsky, A. Ya. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Yu. Zenkova, and A. V. Tyurin, “Circular motion of particles suspended in a Gaussian beam with circular polarization validates the spin part of the internal energy flow,” Opt. Express 20, 11351–11356 (2012).
[CrossRef]

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

Istratiy, V. V.

Y. O. Ushenko, Y. Ya. Tomka, I. Z. Misevitch, V. V. Istratiy, and O. I. Telenga, “Complex degree of mutual anisotropy of biological liquid crystals nets,” Opt. Eng. 50, 039001 (2011).
[CrossRef]

Jozwicki, R.

O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, Yu. A. Ushenko, R. Jozwicki, and K. Patorski, “Automatic polarimetric system for early medical diagnosis by biotissue testing,” Opt. Appl. 32, 603–612 (2002).

Maksimyak, A. P.

Maksimyak, P. P.

Mincer, O. P.

Y. A. Ushenko, T. M. Boychuk, V. T. Bachynsky, and O. P. Mincer, “Diagnostics of structure and physiological state of birefringent biological tissues: statistical, correlation and topological approaches,” in Handbook of Coherent-Domain Optical Methods (Springer, 2013), pp. 107–148.

Misevitch, I. Z.

Y. O. Ushenko, Y. Ya. Tomka, I. Z. Misevitch, V. V. Istratiy, and O. I. Telenga, “Complex degree of mutual anisotropy of biological liquid crystals nets,” Opt. Eng. 50, 039001 (2011).
[CrossRef]

Mokhun, I. I.

Patorski, K.

O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, Yu. A. Ushenko, R. Jozwicki, and K. Patorski, “Automatic polarimetric system for early medical diagnosis by biotissue testing,” Opt. Appl. 32, 603–612 (2002).

Peresunko, A. P.

Yu. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, V. P. Pishak, and A. P. Peresunko, “Statistical, correlation and topological approaches in diagnostics of the structure and physiological state of birefringent biological tissues,” in Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (CRC Press, 2010), pp. 283–322.

Petrie, A.

A. Petrie and B. Sabin, Medical Statistics at a Glance (Blackwell, 2005).

Pishak, V. P.

A. G. Ushenko and V. P. Pishak, “Laser polarimetry of biological tissue: principles and applications,” in Handbook of Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental and Material Science, V. V. Tuchin, ed. (Kluwer Academic Publishers, 2004), Vol. 1, pp. 93–138.

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, V. P. Pishak, and A. P. Peresunko, “Statistical, correlation and topological approaches in diagnostics of the structure and physiological state of birefringent biological tissues,” in Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (CRC Press, 2010), pp. 283–322.

Sabin, B.

A. Petrie and B. Sabin, Medical Statistics at a Glance (Blackwell, 2005).

Santarsiero, M.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Setala, T.

Telenga, O. I.

Y. O. Ushenko, Y. Ya. Tomka, I. Z. Misevitch, V. V. Istratiy, and O. I. Telenga, “Complex degree of mutual anisotropy of biological liquid crystals nets,” Opt. Eng. 50, 039001 (2011).
[CrossRef]

Tervo, J.

Tomka, Y. Ya.

Y. O. Ushenko, Y. Ya. Tomka, I. Z. Misevitch, V. V. Istratiy, and O. I. Telenga, “Complex degree of mutual anisotropy of biological liquid crystals nets,” Opt. Eng. 50, 039001 (2011).
[CrossRef]

Tomka, Yu. Ya.

Yu. A. Ushenko, Yu. Ya. Tomka, and A. V. Dubolazov, “Complex degree of mutual anisotropy of extracellular matrix of biological tissues,” Opt. Spectrosc. 110, 814–819 (2011).
[CrossRef]

Tuchin, V. V.

V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed., Vol. PM166 of SPIE Press Monographs (SPIE, 2007).

Tyurin, A. V.

Ushenko, A. G.

O. V. Angelsky, A. G. Ushenko, and Y. G. Ushenko, “Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state,” J. Biomed. Opt. 10, 060502 (2005).
[CrossRef]

O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, Yu. A. Ushenko, R. Jozwicki, and K. Patorski, “Automatic polarimetric system for early medical diagnosis by biotissue testing,” Opt. Appl. 32, 603–612 (2002).

A. G. Ushenko and V. P. Pishak, “Laser polarimetry of biological tissue: principles and applications,” in Handbook of Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental and Material Science, V. V. Tuchin, ed. (Kluwer Academic Publishers, 2004), Vol. 1, pp. 93–138.

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, V. P. Pishak, and A. P. Peresunko, “Statistical, correlation and topological approaches in diagnostics of the structure and physiological state of birefringent biological tissues,” in Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (CRC Press, 2010), pp. 283–322.

Ushenko, Y. A.

Y. A. Ushenko, “Investigation of formation and interrelations of polarization singular structure and Mueller-matrix images of biological tissues and diagnostics of their cancer changes,” J. Biomed. Opt. 16, 066006 (2011).
[CrossRef]

Y. A. Ushenko, T. M. Boychuk, V. T. Bachynsky, and O. P. Mincer, “Diagnostics of structure and physiological state of birefringent biological tissues: statistical, correlation and topological approaches,” in Handbook of Coherent-Domain Optical Methods (Springer, 2013), pp. 107–148.

Ushenko, Y. G.

O. V. Angelsky, A. G. Ushenko, and Y. G. Ushenko, “Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state,” J. Biomed. Opt. 10, 060502 (2005).
[CrossRef]

Ushenko, Y. O.

Y. O. Ushenko, Y. Ya. Tomka, I. Z. Misevitch, V. V. Istratiy, and O. I. Telenga, “Complex degree of mutual anisotropy of biological liquid crystals nets,” Opt. Eng. 50, 039001 (2011).
[CrossRef]

Ushenko, Yu. A.

Yu. A. Ushenko, Yu. Ya. Tomka, and A. V. Dubolazov, “Complex degree of mutual anisotropy of extracellular matrix of biological tissues,” Opt. Spectrosc. 110, 814–819 (2011).
[CrossRef]

Yu. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

Yu. A. Ushenko, “Statistical structure of polarization-inhomogeneous images of biotissues with different morphological structures,” Ukr. J. Phys. Opt. 6, 63–70 (2005).
[CrossRef]

O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, Yu. A. Ushenko, R. Jozwicki, and K. Patorski, “Automatic polarimetric system for early medical diagnosis by biotissue testing,” Opt. Appl. 32, 603–612 (2002).

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, V. P. Pishak, and A. P. Peresunko, “Statistical, correlation and topological approaches in diagnostics of the structure and physiological state of birefringent biological tissues,” in Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (CRC Press, 2010), pp. 283–322.

Vicalvi, S.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Wang, L.-H.

X. Wang, G. Yao, and L.-H. Wang, “Monte Carlo model and single-scattering approximation of polarized light propagation in turbid media containing glucose,” Appl. Opt. 41, 792–801 (2002).
[CrossRef]

X. Wang and L.-H. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

Wang, X.

X. Wang and L.-H. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

X. Wang, G. Yao, and L.-H. Wang, “Monte Carlo model and single-scattering approximation of polarized light propagation in turbid media containing glucose,” Appl. Opt. 41, 792–801 (2002).
[CrossRef]

Wolf, E.

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

Yao, G.

Zenkova, C. Y.

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

Zenkova, C. Yu.

Adv. Opt. Technol. (1)

Yu. A. Ushenko, A. P. Peresunko, and B. A. Baku, “A new method of Mueller-matrix diagnostics and differentiation of early oncological changes of the skin derma,” Adv. Opt. Technol. 2010, 952423 (2010).
[CrossRef]

Appl. Opt. (1)

J. Biomed. Opt. (3)

X. Wang and L.-H. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

Y. A. Ushenko, “Investigation of formation and interrelations of polarization singular structure and Mueller-matrix images of biological tissues and diagnostics of their cancer changes,” J. Biomed. Opt. 16, 066006 (2011).
[CrossRef]

O. V. Angelsky, A. G. Ushenko, and Y. G. Ushenko, “Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state,” J. Biomed. Opt. 10, 060502 (2005).
[CrossRef]

J. Surg. Res. (1)

L. D. Cassidy, “Basic concepts of statistical analysis for surgical research,” J. Surg. Res. 128, 199–206 (2005).
[CrossRef]

Opt. Appl. (1)

O. V. Angelsky, A. G. Ushenko, D. N. Burkovets, Yu. A. Ushenko, R. Jozwicki, and K. Patorski, “Automatic polarimetric system for early medical diagnosis by biotissue testing,” Opt. Appl. 32, 603–612 (2002).

Opt. Eng. (1)

Y. O. Ushenko, Y. Ya. Tomka, I. Z. Misevitch, V. V. Istratiy, and O. I. Telenga, “Complex degree of mutual anisotropy of biological liquid crystals nets,” Opt. Eng. 50, 039001 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Spectrosc. (1)

Yu. A. Ushenko, Yu. Ya. Tomka, and A. V. Dubolazov, “Complex degree of mutual anisotropy of extracellular matrix of biological tissues,” Opt. Spectrosc. 110, 814–819 (2011).
[CrossRef]

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

Phys. Rev. A (1)

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86, 023847 (2012).
[CrossRef]

Pure Appl. Opt. (1)

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” Pure Appl. Opt. 7, 941–951 (1998).
[CrossRef]

Ukr. J. Phys. Opt. (1)

Yu. A. Ushenko, “Statistical structure of polarization-inhomogeneous images of biotissues with different morphological structures,” Ukr. J. Phys. Opt. 6, 63–70 (2005).
[CrossRef]

Other (8)

A. G. Ushenko and V. P. Pishak, “Laser polarimetry of biological tissue: principles and applications,” in Handbook of Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental and Material Science, V. V. Tuchin, ed. (Kluwer Academic Publishers, 2004), Vol. 1, pp. 93–138.

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, V. P. Pishak, and A. P. Peresunko, “Statistical, correlation and topological approaches in diagnostics of the structure and physiological state of birefringent biological tissues,” in Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (CRC Press, 2010), pp. 283–322.

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Figures (4)

Fig. 1.
Fig. 1.

Optical scheme of a Stokes polarimeter with the use of spatial-frequency filtration. 1, He–Ne laser; 2, collimator; 3, stationary quarter-wave plate; 5 and 10, mechanically movable quarter-wave plates; 4 and 11, polarizer and analyzer, respectively; 6, object of investigation; 7 and 9, polarization micro-objectives; 8, low-frequency and high-frequency filters; 12, CCD camera; and 13, personal computer.

Fig. 2.
Fig. 2.

Coordinate structures [(1), (3), (5), (7), (9), and (11)] and histograms [(2), (4), (6), (8), (10), and (12)] of CDMA distributions of linear birefringence of histological sections of a biopsy of uterine-wall tissue of group 1 [(1), (2), (5), (6), (9), and (10)] and group 2 [(3), (4), (7), (8), (11), and (12)].

Fig. 3.
Fig. 3.

Coordinate structures [(1), (3), (5), (7), (9), and (11)] and histograms [(2), (4), (6), (8), (10), and (12)] of CDMA distributions of circular birefringence of histological sections of a biopsy of uterine-wall tissue of group 1 [(1), (2), (5), (6), (9), and (10)] and group 2 [(3), (4), (7), (8), (11), and (12)].

Fig. 4.
Fig. 4.

Histograms of distributions of average values of Z¯i=1;2;3;4 statistical moments of the first to fourth orders, characterizing the correlation maps of linear Wρ,δ and circular Wθ birefringence of histological sections of biopsy of uterine-wall tissue.

Tables (2)

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Table 1. Parameters of Statistical Structure of CDMA Coordinate Distributions

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Table 2. Operational Characteristics of the Method of Jones-Matrix Mapping of Optical Anisotropy of Histological Sections of Biopsy of Uterine Wall

Equations (29)

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K(r,τ)=Ux(r,τ)Ex*(r,τ)Ux(r,τ)Uy*(r,τ)Ux*(r,τ)Uy(r,τ)Uy(r,τ)Uy*(r,τ),
P(r)=14|[Ux(r,τ)Ux*(r,τ)Uy(r,τ)Uy*(r,τ)Ux(r,τ)Uy*(r,τ)Uy(r,τ)Ux*(r,τ)]|[Ux(r,τ)Ux*(r,τ)+Uy(r,τ)Uy*(r,τ)]2.
J=Ux(r1,τ)Ux*(r2,τ)Ux*(r1,τ)Ux(r2,τ)Ux(r1,τ)Ux*(r2,τ)+Ux*(r1,τ)Ux(r2,τ).
{K(r,τ)}{Φ(r1,r2,τ)}.
Ux(r,τ)Ux*(r,τ)Ux(r,τ)Uy*(r,τ)Uy(r,τ)Ux*(r,τ)Uy(r,τ)Uy*(r,τ)Ux(r1,τ)Ux*(r2,τ)Ux(r1,τ)Uy*(r2,τ)Uy(r1,τ)Ux*(r2,τ)Uy(r1,τ)Uy*(r2,τ).
V(r1,r2,τ)=4ν12+ν22+ν32I(r1,τ)I(r2,τ),
ν1=Ux(r1,τ)Ux*(r2,τ)Uy(r1,τ)Uy*(r2,τ)2,ν2=Ux(r1,τ)Uy*(r2,τ)+Uy(r1,τ)Ux*(r2,τ)2,ν3=iUx(r1,τ)Uy*(r2,τ)Uy(r1,τ)Ux*(r2,τ)2.
V(r1,r2)=(Ux(r1)Ux*(r2)+Uy(r1)Uy*(r2))2I(r1)I(r2).
Re{V}V˜(r1,r2)={Ux(r1)Ux(r2)Uy(r1)Uy(r2)cos[φ(r1)φ(r2)]}2I(r1)I(r2),
{D}={Q}{A},
{Q}=[sin2ρ+cos2ρexp(iδ)][sinρcosρ(1exp(iδ))][sinρcosρ(1exp(iδ))][cos2ρ+sin2ρexp(iδ)],
{A}=cosθsinθsinθcosθ,
(Ux(r)Uy(r))=12d11(r)d12(r)d21(r)d22(r)(1i)=12(d11(r)+id12(r)d21(r)+id22(r)).
{Ux(r)=f(ρ,δ,θ);Uy(r)=g(ρ,δ,θ).
V(Ux(r1,r2)Uy(r1,r2))W(f(dik(r1,r2))g(dik(r1,r2))).
W(r1,r2)={d11(r1,r2)+d12(r1,r2)+d21(r1,r2)+d22(r1,r2)}2I(r1)I(r2).
{d11(r1,r2)=d11(r1)d11(r2);d12(r1,r2)=d12(r1)d12(r2);d21(r1,r2)=d21(r1)d21(r2);d22(r1,r2)=d22(r1)d22(r2),
{U^(ρ,δ,ν,μ)=R(Δν,Δμ)U(ν,μ);U˙(θ,ν,μ)=R1(Δν,Δμ)U(ν,μ).
W(ρ,δ,r1,r2){q11(r1,r2)+q12(r1,r2)+q21(r1,r2)+q22(r1,r2)}2I(r1)I(r2),
W(θ,r1,r2){a11(r1,r2)+a12(r1,r2)+a21(r1,r2)+a22(r1,r2)}2I(r1)I(r2).
{D}=R11(r)expΘ11(r)R12(r)expΘ12(r)R21(r)expΘ21(r)R22(r)expΘ22(r).
{R11=I00;R12=I900;R21=I090;R22=I9090.
θ11θ12=0,5arcsin(2I0R110,5R120,5R11R12)A,
θ22θ21=0,5arcsin(2I90R220,5R210,5R22R21)B.
θ11θ21=0,5arccos(2I045R110,5R120,5R11R12)C,
θ22θ12=0,5arccos(2I9045R220,5R210,5R22R21)D.
{Θ11=0.5(3CA3BD);Θ12=0,5(3C3A3BD);Θ21=0,5(CA3BD);Θ22=0,5(CABD).
{H(Δν,Δμ)dik(m×n)qik(m×n);H1(Δν,Δμ)dik(m×n)aik(m×n).
Z1=1Pj=1Pqj,Z2=1Pj=1P(qZ1)j2,Z3=1Z231Pj=1P(q)j3,Z4=1Z241Pj=1P(q)j4.

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