Abstract

The optical model of polycrystalline networks of histological sections of rectum wall is suggested. The results of investigating the interrelation between the values of statistical (statistical moments of the 1st–4th order) and correlation (cross correlation coefficients) parameters are presented. Such parameters characterize the coordinate distributions of the fourth parameter of the Stokes vector of Fourier transforms of laser images of myometrium tissues. The diagnostic criteria of myometrium pathologies are determined.

© 2012 Optical Society of America

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  1. L. E. Preuss and A. E. Profio, “Optical properties of mammalian tissue: introduction by the feature editors,” Appl. Opt. 28, 2207–2207 (1989).
    [CrossRef]
  2. W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum. Electron. 26, 2166–2185 (1990).
    [CrossRef]
  3. S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).
  4. O. V. Angelsky, Tomka, Yu. Ya, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states,” J. Phys. D: Appl. Phys. 38, 4227–4235 (2005).
    [CrossRef]
  5. A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).
  6. O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, and Ye. G. Ushenko, “Polarization singularities of the object field of skin surface,” J. Phys. D 39, 3547–3558 (2006).
    [CrossRef]
  7. A. G. Ushenko, “Polarization structure of biospeckles and the depolarization of laser radiation,” Opt. Spectrosc. 89, 597–600 (2000).
    [CrossRef]
  8. A. G. Ushenko, “Polarization contrast enhancement of images of biological tissues under the conditions of multiple scattering,” Opt. Spectrosc. 91, 937–940 (2001).
    [CrossRef]
  9. O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Scattering of laser radiation by multifractal biological structures,” Opt. Spectrosc. 88, 444–447 (2000).
    [CrossRef]
  10. V. Pishak, A. Ushenko, P. Gryhoryshyn, S. Yermolenko, V. Rudeychuk, and O. Pishak, “Study of polarization structure of biospeckle fields in cross linked tissues of human organism: 1. Vector structure of skin biospeckles,” Proc. SPIE 3317, 418–424 (1997).
    [CrossRef]
  11. A. G. Ushenko, “Laser probing of biological tissues and the polarization selection of their images,” Opt. Spectrosc. 91, 932–936 (2001).
    [CrossRef]
  12. S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
    [CrossRef]
  13. A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
    [CrossRef]
  14. O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, D. N. Burkovets, and Yu. A. Ushenko, “Laser polarimetry of pathological changes in biotissues,” Opt. Spectrosc. 89, 973–978 (2000).
    [CrossRef]
  15. O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in bio tissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).
  16. S. H. Guminetskiy, A. G. Ushenko, I. P. Polyanskiy, A. V. Motrych, and F. V. Grynchuk, “The optical method of the investigation of peritonitis progressing process,” Proc. SPIE 7008, 700827 (2008).
    [CrossRef]
  17. M. R. Ostermeyer, D. V. Stephens, L. Wang, and S. L. Jacques, “Nearfield polarization effects on light propagation in random media,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 20–26.
  18. P. Bruscaglioni, G. Zaccanti, and Q. Wei, “Transmission of a pulsed polarized light beam through thick turbid media: numerical results,” Appl. Opt. 32, 6142–6150 (1993).
    [CrossRef]
  19. V. Sankaran, M. J. Everett, D. J. Maitland, and J. T. Walsh, “Comparison of polarized-light propagation in biological tissue and phantoms,” Opt. Lett. 24, 1044–1046 (1999).
    [CrossRef]
  20. M. C. Pierce, J. Strasswimmer, B. Hyle Park, B. Cense, and J. F. de Boer, “Birefringence measurements in human skin using polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9, 287–291 (2004).
    [CrossRef]
  21. J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22, 934–936 (1997).
    [CrossRef]
  22. C. E. Saxer, J. F. de Boer, B. H. Park, Y. Zhao, Z. Chen, and J. S. Nelson, “High-speed fiber based polarization-sensitive optical coherence tomography of in vivo human skin,” Opt. Lett. 25, 1355–1357 (2000).
    [CrossRef]
  23. J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” Biomed. Opt. 7, 359–371 (2002).
    [CrossRef]
  24. Y. Yasuno, S. Makita, Y. Sutoh, M. Itoh, and T. Yatagai, “Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography,” Opt. Lett. 27, 1803–1805 (2002).
    [CrossRef]
  25. A. G. Ushenko, “Polarization structure of biospeckles and the depolarization of laser radiation,” Opt. Spectrosc. 89, 597–600 (2000).
    [CrossRef]
  26. A. G. Ushenko, “Polarization correlometry of angular structure in the microrelief pattern of rough surfaces,” Opt. Spectrosc. 92, 227–229 (2002).
    [CrossRef]
  27. O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
    [CrossRef]
  28. O. V. Angelsky, M. P. Gorsky, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and Yu C. Zenkova, “Investigation of optical currents in coherent and partially coherent vector fields,” Opt. Express 19, 660–672 (2011).
    [CrossRef]
  29. O. V. Angelsky, S. G. Hanson, Yu C. 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]

2011

2010

A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).

2009

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

O. V. Angelsky, S. G. Hanson, Yu C. 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]

2008

A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
[CrossRef]

S. H. Guminetskiy, A. G. Ushenko, I. P. Polyanskiy, A. V. Motrych, and F. V. Grynchuk, “The optical method of the investigation of peritonitis progressing process,” Proc. SPIE 7008, 700827 (2008).
[CrossRef]

2006

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, and Ye. G. Ushenko, “Polarization singularities of the object field of skin surface,” J. Phys. D 39, 3547–3558 (2006).
[CrossRef]

2005

O. V. Angelsky, Tomka, Yu. Ya, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states,” J. Phys. D: Appl. Phys. 38, 4227–4235 (2005).
[CrossRef]

2004

M. C. Pierce, J. Strasswimmer, B. Hyle Park, B. Cense, and J. F. de Boer, “Birefringence measurements in human skin using polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9, 287–291 (2004).
[CrossRef]

2002

A. G. Ushenko, “Polarization correlometry of angular structure in the microrelief pattern of rough surfaces,” Opt. Spectrosc. 92, 227–229 (2002).
[CrossRef]

Y. Yasuno, S. Makita, Y. Sutoh, M. Itoh, and T. Yatagai, “Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography,” Opt. Lett. 27, 1803–1805 (2002).
[CrossRef]

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” Biomed. Opt. 7, 359–371 (2002).
[CrossRef]

2001

A. G. Ushenko, “Laser probing of biological tissues and the polarization selection of their images,” Opt. Spectrosc. 91, 932–936 (2001).
[CrossRef]

A. G. Ushenko, “Polarization contrast enhancement of images of biological tissues under the conditions of multiple scattering,” Opt. Spectrosc. 91, 937–940 (2001).
[CrossRef]

2000

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Scattering of laser radiation by multifractal biological structures,” Opt. Spectrosc. 88, 444–447 (2000).
[CrossRef]

A. G. Ushenko, “Polarization structure of biospeckles and the depolarization of laser radiation,” Opt. Spectrosc. 89, 597–600 (2000).
[CrossRef]

A. G. Ushenko, “Polarization structure of biospeckles and the depolarization of laser radiation,” Opt. Spectrosc. 89, 597–600 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, D. N. Burkovets, and Yu. A. Ushenko, “Laser polarimetry of pathological changes in biotissues,” Opt. Spectrosc. 89, 973–978 (2000).
[CrossRef]

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in bio tissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

C. E. Saxer, J. F. de Boer, B. H. Park, Y. Zhao, Z. Chen, and J. S. Nelson, “High-speed fiber based polarization-sensitive optical coherence tomography of in vivo human skin,” Opt. Lett. 25, 1355–1357 (2000).
[CrossRef]

1999

V. Sankaran, M. J. Everett, D. J. Maitland, and J. T. Walsh, “Comparison of polarized-light propagation in biological tissue and phantoms,” Opt. Lett. 24, 1044–1046 (1999).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

1997

V. Pishak, A. Ushenko, P. Gryhoryshyn, S. Yermolenko, V. Rudeychuk, and O. Pishak, “Study of polarization structure of biospeckle fields in cross linked tissues of human organism: 1. Vector structure of skin biospeckles,” Proc. SPIE 3317, 418–424 (1997).
[CrossRef]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22, 934–936 (1997).
[CrossRef]

1993

1990

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum. Electron. 26, 2166–2185 (1990).
[CrossRef]

1989

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

L. E. Preuss and A. E. Profio, “Optical properties of mammalian tissue: introduction by the feature editors,” Appl. Opt. 28, 2207–2207 (1989).
[CrossRef]

Angel’skii, O. V.

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Scattering of laser radiation by multifractal biological structures,” Opt. Spectrosc. 88, 444–447 (2000).
[CrossRef]

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in bio tissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, D. N. Burkovets, and Yu. A. Ushenko, “Laser polarimetry of pathological changes in biotissues,” Opt. Spectrosc. 89, 973–978 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Angelsky, O. V.

O. V. Angelsky, M. P. Gorsky, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and Yu C. Zenkova, “Investigation of optical currents in coherent and partially coherent vector fields,” Opt. Express 19, 660–672 (2011).
[CrossRef]

O. V. Angelsky, S. G. Hanson, Yu C. 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, A. G. Ushenko, Yu. A. Ushenko, and Ye. G. Ushenko, “Polarization singularities of the object field of skin surface,” J. Phys. D 39, 3547–3558 (2006).
[CrossRef]

O. V. Angelsky, Tomka, Yu. Ya, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states,” J. Phys. D: Appl. Phys. 38, 4227–4235 (2005).
[CrossRef]

Arkhelyuk, A. D.

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, D. N. Burkovets, and Yu. A. Ushenko, “Laser polarimetry of pathological changes in biotissues,” Opt. Spectrosc. 89, 973–978 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Scattering of laser radiation by multifractal biological structures,” Opt. Spectrosc. 88, 444–447 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Arkhelyuk, O. D.

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in bio tissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

Bachyns’ka, I.

A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).

Bruscaglioni, P.

Burkovets, D. N.

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, D. N. Burkovets, and Yu. A. Ushenko, “Laser polarimetry of pathological changes in biotissues,” Opt. Spectrosc. 89, 973–978 (2000).
[CrossRef]

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in bio tissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Scattering of laser radiation by multifractal biological structures,” Opt. Spectrosc. 88, 444–447 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Cense, B.

M. C. Pierce, J. Strasswimmer, B. Hyle Park, B. Cense, and J. F. de Boer, “Birefringence measurements in human skin using polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9, 287–291 (2004).
[CrossRef]

Chen, Z.

Cheong, W.-F.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum. Electron. 26, 2166–2185 (1990).
[CrossRef]

de Boer, J. F.

M. C. Pierce, J. Strasswimmer, B. Hyle Park, B. Cense, and J. F. de Boer, “Birefringence measurements in human skin using polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9, 287–291 (2004).
[CrossRef]

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” Biomed. Opt. 7, 359–371 (2002).
[CrossRef]

C. E. Saxer, J. F. de Boer, B. H. Park, Y. Zhao, Z. Chen, and J. S. Nelson, “High-speed fiber based polarization-sensitive optical coherence tomography of in vivo human skin,” Opt. Lett. 25, 1355–1357 (2000).
[CrossRef]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22, 934–936 (1997).
[CrossRef]

Ermolenko, S. B.

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Scattering of laser radiation by multifractal biological structures,” Opt. Spectrosc. 88, 444–447 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, D. N. Burkovets, and Yu. A. Ushenko, “Laser polarimetry of pathological changes in biotissues,” Opt. Spectrosc. 89, 973–978 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Everett, M. J.

Gavrila, C.

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

Gorodyns’ka, N. V.

Gorsky, M. P.

Goudail, F.

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

Gruia, I.

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
[CrossRef]

Gryhoryshyn, P.

V. Pishak, A. Ushenko, P. Gryhoryshyn, S. Yermolenko, V. Rudeychuk, and O. Pishak, “Study of polarization structure of biospeckle fields in cross linked tissues of human organism: 1. Vector structure of skin biospeckles,” Proc. SPIE 3317, 418–424 (1997).
[CrossRef]

Grynchuk, F. V.

S. H. Guminetskiy, A. G. Ushenko, I. P. Polyanskiy, A. V. Motrych, and F. V. Grynchuk, “The optical method of the investigation of peritonitis progressing process,” Proc. SPIE 7008, 700827 (2008).
[CrossRef]

Guminetskiy, S. H.

S. H. Guminetskiy, A. G. Ushenko, I. P. Polyanskiy, A. V. Motrych, and F. V. Grynchuk, “The optical method of the investigation of peritonitis progressing process,” Proc. SPIE 7008, 700827 (2008).
[CrossRef]

Guminetsky, S.

A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
[CrossRef]

Hanson, S. G.

Hyle Park, B.

M. C. Pierce, J. Strasswimmer, B. Hyle Park, B. Cense, and J. F. de Boer, “Birefringence measurements in human skin using polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9, 287–291 (2004).
[CrossRef]

Istratiy, V.

A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).

Itoh, M.

Ivashko, P.

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

Jacques, S. L.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

M. R. Ostermeyer, D. V. Stephens, L. Wang, and S. L. Jacques, “Nearfield polarization effects on light propagation in random media,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 20–26.

Keijzer, M.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

Maitland, D. J.

Makita, S.

Maksimyak, A. P.

Maksimyak, P. P.

Mikhailova, A.

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

Milner, T. E.

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” Biomed. Opt. 7, 359–371 (2002).
[CrossRef]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22, 934–936 (1997).
[CrossRef]

Misevich, I. Z.

A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).

Moiysuk, T. G.

A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).

Motrych, A. V.

S. H. Guminetskiy, A. G. Ushenko, I. P. Polyanskiy, A. V. Motrych, and F. V. Grynchuk, “The optical method of the investigation of peritonitis progressing process,” Proc. SPIE 7008, 700827 (2008).
[CrossRef]

Nelson, J. S.

Numan, O. K.

A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).

Ostermeyer, M. R.

M. R. Ostermeyer, D. V. Stephens, L. Wang, and S. L. Jacques, “Nearfield polarization effects on light propagation in random media,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 20–26.

Park, B. H.

Peresunko, A. P.

A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).

Pierce, M. C.

M. C. Pierce, J. Strasswimmer, B. Hyle Park, B. Cense, and J. F. de Boer, “Birefringence measurements in human skin using polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9, 287–291 (2004).
[CrossRef]

Pishak, O.

V. Pishak, A. Ushenko, P. Gryhoryshyn, S. Yermolenko, V. Rudeychuk, and O. Pishak, “Study of polarization structure of biospeckle fields in cross linked tissues of human organism: 1. Vector structure of skin biospeckles,” Proc. SPIE 3317, 418–424 (1997).
[CrossRef]

Pishak, V.

V. Pishak, A. Ushenko, P. Gryhoryshyn, S. Yermolenko, V. Rudeychuk, and O. Pishak, “Study of polarization structure of biospeckle fields in cross linked tissues of human organism: 1. Vector structure of skin biospeckles,” Proc. SPIE 3317, 418–424 (1997).
[CrossRef]

Polyanskiy, I. P.

S. H. Guminetskiy, A. G. Ushenko, I. P. Polyanskiy, A. V. Motrych, and F. V. Grynchuk, “The optical method of the investigation of peritonitis progressing process,” Proc. SPIE 7008, 700827 (2008).
[CrossRef]

Prahl, S. A.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum. Electron. 26, 2166–2185 (1990).
[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

Preuss, L. E.

Profio, A. E.

Prydij, A.

A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
[CrossRef]

Rudeychuk, V.

V. Pishak, A. Ushenko, P. Gryhoryshyn, S. Yermolenko, V. Rudeychuk, and O. Pishak, “Study of polarization structure of biospeckle fields in cross linked tissues of human organism: 1. Vector structure of skin biospeckles,” Proc. SPIE 3317, 418–424 (1997).
[CrossRef]

Sankaran, V.

Saxer, C. E.

Stephens, D. V.

M. R. Ostermeyer, D. V. Stephens, L. Wang, and S. L. Jacques, “Nearfield polarization effects on light propagation in random media,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 20–26.

Strasswimmer, J.

M. C. Pierce, J. Strasswimmer, B. Hyle Park, B. Cense, and J. F. de Boer, “Birefringence measurements in human skin using polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9, 287–291 (2004).
[CrossRef]

Sutoh, Y.

Toma, O.

A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
[CrossRef]

Tomka,

O. V. Angelsky, Tomka, Yu. Ya, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states,” J. Phys. D: Appl. Phys. 38, 4227–4235 (2005).
[CrossRef]

Ushenko, A.

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
[CrossRef]

V. Pishak, A. Ushenko, P. Gryhoryshyn, S. Yermolenko, V. Rudeychuk, and O. Pishak, “Study of polarization structure of biospeckle fields in cross linked tissues of human organism: 1. Vector structure of skin biospeckles,” Proc. SPIE 3317, 418–424 (1997).
[CrossRef]

Ushenko, A. G.

A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).

S. H. Guminetskiy, A. G. Ushenko, I. P. Polyanskiy, A. V. Motrych, and F. V. Grynchuk, “The optical method of the investigation of peritonitis progressing process,” Proc. SPIE 7008, 700827 (2008).
[CrossRef]

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, and Ye. G. Ushenko, “Polarization singularities of the object field of skin surface,” J. Phys. D 39, 3547–3558 (2006).
[CrossRef]

O. V. Angelsky, Tomka, Yu. Ya, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states,” J. Phys. D: Appl. Phys. 38, 4227–4235 (2005).
[CrossRef]

A. G. Ushenko, “Polarization correlometry of angular structure in the microrelief pattern of rough surfaces,” Opt. Spectrosc. 92, 227–229 (2002).
[CrossRef]

A. G. Ushenko, “Polarization contrast enhancement of images of biological tissues under the conditions of multiple scattering,” Opt. Spectrosc. 91, 937–940 (2001).
[CrossRef]

A. G. Ushenko, “Laser probing of biological tissues and the polarization selection of their images,” Opt. Spectrosc. 91, 932–936 (2001).
[CrossRef]

A. G. Ushenko, “Polarization structure of biospeckles and the depolarization of laser radiation,” Opt. Spectrosc. 89, 597–600 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, D. N. Burkovets, and Yu. A. Ushenko, “Laser polarimetry of pathological changes in biotissues,” Opt. Spectrosc. 89, 973–978 (2000).
[CrossRef]

A. G. Ushenko, “Polarization structure of biospeckles and the depolarization of laser radiation,” Opt. Spectrosc. 89, 597–600 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Scattering of laser radiation by multifractal biological structures,” Opt. Spectrosc. 88, 444–447 (2000).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Ushenko, O. G.

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in bio tissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

Ushenko, Ye. G.

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, and Ye. G. Ushenko, “Polarization singularities of the object field of skin surface,” J. Phys. D 39, 3547–3558 (2006).
[CrossRef]

O. V. Angelsky, Tomka, Yu. Ya, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states,” J. Phys. D: Appl. Phys. 38, 4227–4235 (2005).
[CrossRef]

Ushenko, Yu. A.

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, and Ye. G. Ushenko, “Polarization singularities of the object field of skin surface,” J. Phys. D 39, 3547–3558 (2006).
[CrossRef]

O. V. Angelsky, Tomka, Yu. Ya, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states,” J. Phys. D: Appl. Phys. 38, 4227–4235 (2005).
[CrossRef]

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in bio tissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, D. N. Burkovets, and Yu. A. Ushenko, “Laser polarimetry of pathological changes in biotissues,” Opt. Spectrosc. 89, 973–978 (2000).
[CrossRef]

van Gemert, M. J. C.

Vladychenko, K.

A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
[CrossRef]

Walsh, J. T.

Wang, L.

M. R. Ostermeyer, D. V. Stephens, L. Wang, and S. L. Jacques, “Nearfield polarization effects on light propagation in random media,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 20–26.

Wei, Q.

Welch, A. J.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum. Electron. 26, 2166–2185 (1990).
[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

Ya, Yu.

O. V. Angelsky, Tomka, Yu. Ya, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states,” J. Phys. D: Appl. Phys. 38, 4227–4235 (2005).
[CrossRef]

Yasuno, Y.

Yatagai, T.

Yermolenko, S.

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
[CrossRef]

V. Pishak, A. Ushenko, P. Gryhoryshyn, S. Yermolenko, V. Rudeychuk, and O. Pishak, “Study of polarization structure of biospeckle fields in cross linked tissues of human organism: 1. Vector structure of skin biospeckles,” Proc. SPIE 3317, 418–424 (1997).
[CrossRef]

Zaccanti, G.

Zenkova, Yu C.

Zhao, Y.

Zimnyakov, D.

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

Adv. Opt. Tech.

A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns’ka, A. P. Peresunko, O. K. Numan, and T. G. Moiysuk, “Evolution of statistic moments of 2D- distributions of biological liquid crystal netmueller matrix elements in the process of their birefringent structure changes,” Adv. Opt. Tech. 2010, 423145 (2010).

Appl. Opt.

Biomed. Opt.

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” Biomed. Opt. 7, 359–371 (2002).
[CrossRef]

IEEE J. Quantum. Electron.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum. Electron. 26, 2166–2185 (1990).
[CrossRef]

J. Biomed. Opt.

M. C. Pierce, J. Strasswimmer, B. Hyle Park, B. Cense, and J. F. de Boer, “Birefringence measurements in human skin using polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9, 287–291 (2004).
[CrossRef]

J. Phys. D

O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, and Ye. G. Ushenko, “Polarization singularities of the object field of skin surface,” J. Phys. D 39, 3547–3558 (2006).
[CrossRef]

J. Phys. D: Appl. Phys.

O. V. Angelsky, Tomka, Yu. Ya, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states,” J. Phys. D: Appl. Phys. 38, 4227–4235 (2005).
[CrossRef]

Laser Phys.

O. V. Angel’skii, O. G. Ushenko, D. N. Burkovets, O. D. Arkhelyuk, and Yu. A. Ushenko, “Polarization-correlation studies of multifractal structures in bio tissues and diagnostics of their pathologic changes,” Laser Phys. 10, 1136–1142 (2000).

Opt. Express

Opt. Lett.

Opt. Spectrosc.

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, D. N. Burkovets, and Yu. A. Ushenko, “Laser polarimetry of pathological changes in biotissues,” Opt. Spectrosc. 89, 973–978 (2000).
[CrossRef]

A. G. Ushenko, “Polarization structure of biospeckles and the depolarization of laser radiation,” Opt. Spectrosc. 89, 597–600 (2000).
[CrossRef]

A. G. Ushenko, “Polarization correlometry of angular structure in the microrelief pattern of rough surfaces,” Opt. Spectrosc. 92, 227–229 (2002).
[CrossRef]

A. G. Ushenko, “Polarization structure of biospeckles and the depolarization of laser radiation,” Opt. Spectrosc. 89, 597–600 (2000).
[CrossRef]

A. G. Ushenko, “Polarization contrast enhancement of images of biological tissues under the conditions of multiple scattering,” Opt. Spectrosc. 91, 937–940 (2001).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Scattering of laser radiation by multifractal biological structures,” Opt. Spectrosc. 88, 444–447 (2000).
[CrossRef]

A. G. Ushenko, “Laser probing of biological tissues and the polarization selection of their images,” Opt. Spectrosc. 91, 932–936 (2001).
[CrossRef]

Proc. SPIE

S. Yermolenko, A. Ushenko, P. Ivashko, F. Goudail, I. Gruia, C. Gavrila, D. Zimnyakov, and A. Mikhailova, “Spectropolarimetry of cancer change of biotissues,” Proc. SPIE 7388, 73881D (2009).
[CrossRef]

A. Ushenko, S. Yermolenko, A. Prydij, S. Guminetsky, I. Gruia, O. Toma, and K. Vladychenko, “Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues,” Proc. SPIE 7008, 70082C (2008).
[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

V. Pishak, A. Ushenko, P. Gryhoryshyn, S. Yermolenko, V. Rudeychuk, and O. Pishak, “Study of polarization structure of biospeckle fields in cross linked tissues of human organism: 1. Vector structure of skin biospeckles,” Proc. SPIE 3317, 418–424 (1997).
[CrossRef]

S. H. Guminetskiy, A. G. Ushenko, I. P. Polyanskiy, A. V. Motrych, and F. V. Grynchuk, “The optical method of the investigation of peritonitis progressing process,” Proc. SPIE 7008, 700827 (2008).
[CrossRef]

Quantum Electron.

O. V. Angel’skii, A. G. Ushenko, A. D. Arkhelyuk, S. B. Ermolenko, and D. N. Burkovets, “Structure of matrices for the transformation of laser radiation by biofractals,” Quantum Electron. 29, 1074–1077 (1999).
[CrossRef]

Other

M. R. Ostermeyer, D. V. Stephens, L. Wang, and S. L. Jacques, “Nearfield polarization effects on light propagation in random media,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 20–26.

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Figures (5)

Fig. 1.
Fig. 1.

Polarization images of myometrium histological sections of group A (a) and group B (b).

Fig. 2.
Fig. 2.

An optical diagram of Fourier–Stokes polarimeter, where 1 —He-Ne laser, 2—a collimator; 3—a stationary quarter-wave plate; 4, 8—a polarizer and analyzer respectively; 5, 9—mechanically mobile quarter-wave plates; 6—an object of investigation; 7—a polarization microobjective; 10—CCD camera; 11—a personal computer.

Fig. 3.
Fig. 3.

Coordinate structure and histogram of values distribution of the 4th parameter of Stokes vector scattered by histological section of group A [(a), (c)] (Media 4) and B [(b), (d)] in Fourier plane (Media 5).

Fig. 4.
Fig. 4.

Autocorrelation functions of S4(m*×n*) distribution—group A (Media 6).

Fig. 5.
Fig. 5.

Autocorrelation functions of S4(m*×n*) distribution—group B (Media 7).

Tables (2)

Tables Icon

Table 1. Statistical Moments of the 1st–4th Orders of Fourier Spectrum S4

Tables Icon

Table 2. Correlation Moments of the 1st–4th Orders of Fourier Spectrum S4(m*×n*)

Equations (12)

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

{R}=r11r12r21r22=exp(iτl){cos2ξ+sin2ξexp(iψ);cosξsinξ[1exp(iψ)];cosξsinξ[1exp(iψ)];sin2ξ+cos2ξexp(iψ);}.
U={R}U0=([cos2ξ+sin2ξexp(iψ)]U0x+cosξsinξ[1exp(iψ)]U0ycosξsinξ[1exp(iψ)]U0x+[sin2ξ+cos2ξexp(iψ)]U0y)=(UxUyexp(iφxy)).
Ux(m*,n*)=Aiλf+Ex(m,n)exp[i2πλf(nn*+mm*)dndm];
Uy(m*,n*)=Aiλf+Ey(m,n)exp[i2πλf(nn*+mm*)dndm].
Δ(ν)=Ux(m*)+Uy(m*)Ux(n*)+Uy(n*),
S1(m*,n*)=UxUx*+UyUy*;S2(m*,n*)=UxUx*UyUy*;S3(m*,n*)=UxUy*UyUx*;S4(m*,n*)=i(UyUx*UxUy*),
K(Δνx)=1(νmax)xj=1NSk(νx)Sk(νxjΔνx);
K(Δνy)=1(νmax)yj=1MSk(νy)Sk(νyjΔνy).
dQ1=R1(K(Δνy))/R1(K(Δνx));dQ2=R2(K(Δνy))/R2(K(Δνx));dQ3=R3(K(Δνy))/R3(K(Δνx));dQ4=R4(K(Δνy))/R4(K(Δνx)),
S={1;(I0I90/I0+I90);(I45I135/I0+I90);(II/I0+I90).}.
((S4)11(S4)1n..(S4)m1(S4)mn)
(K(S4)11K(S4)1n..K(S4)m1K(S4)mn)Kx(S4)and(K(S4)11K(S4)1nK(S4)m1K(S4)mn)Ky(S4)

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