Abstract

The model of a Mueller matrix description of mechanisms of optical anisotropy typical for polycrystalline films of blood plasma—optical activity, birefringence, as well as linear and circular dichroism—is suggested. On this basis, the algorithms of reconstruction of parameters distribution (polarization plane rotations, phase shifts, coefficients of linear and circular dichroism) of the indicated types of anisotropy were found for different spectrally selective ranges. Within the statistical analysis of such distributions, the objective criteria of differentiation of films of blood plasma taken from healthy women and breast cancer patients were determined. From the point of view of probative medicine, the operational characteristics (sensitivity, specificity and accuracy) of the method of Mueller matrix reconstruction of optical anisotropy parameters were found, and its efficiency in diagnostics of breast cancer was demonstrated.

© 2014 Optical Society of America

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2013 (2)

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[CrossRef]

P. O. Angelsky, A. G. Ushenko, A. V. Dubolazov, M. I. Sidor, G. B. Bodnar, G. Koval, and L. Trifonyuk, “The singular approach for processing polarization-inhomogeneous laser images of blood plasma layers,” J. Opt. 15, 044030 (2013).
[CrossRef]

2012 (6)

Y. A. Ushenko, “Concerted spatial-frequency and polarization-phase filtering of laser images of polycrystalline networks of blood plasma smears,” J. Biomed. Opt. 17, 117005 (2012).
[CrossRef]

N. Ortega-Quijano, B. Haj-Ibrahim, E. García-Caurel, J. L. Arce-Diego, and R. Ossikovski, “Experimental validation of Mueller matrix differential decomposition,” Opt. Express 20, 1151–1163 (2012).
[CrossRef]

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Y. 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]

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photonics News 23, 25–29 (2012).
[CrossRef]

Y. A. Ushenko, A. V. Dubolazov, V. O. Balanetskaya, A. O. Karachevtsev, and V. A. Ushenko, “Wavelet-analysis of polarization maps of human blood plasma,” Opt. Spectrosc. 113, 332–343 (2012).
[CrossRef]

2011 (7)

Y. A. Ushenko, O. I. Olar, A. V. Dubolazov, V. O. Balanetskaya, V. P. Unguryan, N. I. Zabolotna, and B. P. Oleinichenko,“Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma,” Semicond. Phys., Quantum Electron. Optoelectron. 14, 98–105 (2011).

Y. A. Ushenko, Y. Y. Tomka, A. V. Dubolazov, and O. Y. Telenga, “Diagnostics of optical anisotropy changes in biological tissues using Müller matrix,” Quantum Electron. 41, 273–277 (2011).
[CrossRef]

Y. A. Ushenko, O. V. Dubolazov, and A. O. Karachevtsev, “Statistical structure of skin derma Mueller matrix images in the process of cancer changes,” Opt. Mem. Neural Netw. 20, 145–154 (2011).
[CrossRef]

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

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

N. Ortega-Quijano and J. L. Arce-Diego, “Mueller matrix differential decomposition,” Opt. Lett. 36, 1942–1944 (2011).
[CrossRef]

2010 (1)

O. V. Angelsky, Y. A. Ushenko, A. V. Dubolazov, and O. Y. Telenha, “The interconnection between the coordinate distribution of Mueller-matrixes images characteristic values of biological liquid crystals net and the pathological changes of human tissues,” Adv. Opt. Technol. 2010, 130659 (2010).

2009 (1)

G. P. Petrova, A. V. Boiko, K. V. Fedorova, I. A. Sergeeva, N. V. Sokol, and T. N. Tichonova, “Optical properties of solutions consisting of albumin and γ-globulin molecules in different ratio modeling blood serum,” Laser Phys. 19, 1303–1307 (2009).
[CrossRef]

2007 (1)

2006 (1)

S. N. Savenkov, V. V. Marienko, E. A. Oberemok, and O. I. Sydoruk, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 605–607 (2006).
[CrossRef]

2005 (2)

O. V. Angelsky, Y. Y. Tomka, A. G. Ushenko, Y. G. Ushenko, and Y. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for pre-clinical diagnostics of their pathological states,” J. Phys. D 38, 4227–4235 (2005).
[CrossRef]

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

2003 (1)

2002 (1)

2001 (4)

T. T. Tower and R. T. Tranquillo, “Alignment maps of tissues: II. fast harmonic analysis for imaging,” Biophys. J. 81, 2964–2971 (2001).
[CrossRef]

M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001).
[CrossRef]

T. T. Tower and R. T. Tranquillo, “Alignment maps of tissues: I. microscopic elliptical polarimetry,” Biophys. J. 81, 2954–2963 (2001).
[CrossRef]

J. M. Bueno and J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthal. Physiol. Opt. 21, 384–392 (2001).
[CrossRef]

2000 (1)

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3991, 210–216 (2000).
[CrossRef]

1999 (1)

O. V. Angel’skii, A. G. Ushenko, A. D. Archelyuk, 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]

1996 (1)

1986 (1)

1956 (1)

W. J. Waddell, “A simple ultraviolet spectrophotometric method for the determination of protein,” J. Lab. Clin. Med. 48, 311–314 (1956).

1951 (1)

A. R. Goldfarb, L. J. Saidel, and E. Mosovich, “The ultraviolet absorption spectra of proteins,” J. Biol. Chem. 193, 397–404 (1951).

Angel’skii, O. V.

O. V. Angel’skii, A. G. Ushenko, A. D. Archelyuk, 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]

Angelskii, P. O.

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[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, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photonics News 23, 25–29 (2012).
[CrossRef]

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Y. 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, Y. A. Ushenko, A. V. Dubolazov, and O. Y. Telenha, “The interconnection between the coordinate distribution of Mueller-matrixes images characteristic values of biological liquid crystals net and the pathological changes of human tissues,” Adv. Opt. Technol. 2010, 130659 (2010).

O. V. Angelsky, Y. Y. Tomka, A. G. Ushenko, Y. G. Ushenko, and Y. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for pre-clinical diagnostics of their pathological states,” J. Phys. D 38, 4227–4235 (2005).
[CrossRef]

Angelsky, P. O.

P. O. Angelsky, A. G. Ushenko, A. V. Dubolazov, M. I. Sidor, G. B. Bodnar, G. Koval, and L. Trifonyuk, “The singular approach for processing polarization-inhomogeneous laser images of blood plasma layers,” J. Opt. 15, 044030 (2013).
[CrossRef]

Arce-Diego, J. L.

Archelyuk, A. D.

O. V. Angel’skii, A. G. Ushenko, A. D. Archelyuk, 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]

Arvin, H.

Balanetskaya, V. O.

Y. A. Ushenko, A. V. Dubolazov, V. O. Balanetskaya, A. O. Karachevtsev, and V. A. Ushenko, “Wavelet-analysis of polarization maps of human blood plasma,” Opt. Spectrosc. 113, 332–343 (2012).
[CrossRef]

Y. A. Ushenko, O. I. Olar, A. V. Dubolazov, V. O. Balanetskaya, V. P. Unguryan, N. I. Zabolotna, and B. P. Oleinichenko,“Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma,” Semicond. Phys., Quantum Electron. Optoelectron. 14, 98–105 (2011).

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]

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Y. 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]

Bizer, L. I.

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[CrossRef]

Bodnar, G. B.

P. O. Angelsky, A. G. Ushenko, A. V. Dubolazov, M. I. Sidor, G. B. Bodnar, G. Koval, and L. Trifonyuk, “The singular approach for processing polarization-inhomogeneous laser images of blood plasma layers,” J. Opt. 15, 044030 (2013).
[CrossRef]

Boiko, A. V.

G. P. Petrova, A. V. Boiko, K. V. Fedorova, I. A. Sergeeva, N. V. Sokol, and T. N. Tichonova, “Optical properties of solutions consisting of albumin and γ-globulin molecules in different ratio modeling blood serum,” Laser Phys. 19, 1303–1307 (2009).
[CrossRef]

Bueno, J. M.

J. M. Bueno and F. Vargas-Martin, “Measurements of the corneal birefringence with a liquid-crystal imaging polariscope,” Appl. Opt. 41, 116–124 (2002).
[CrossRef]

J. M. Bueno and J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthal. Physiol. Opt. 21, 384–392 (2001).
[CrossRef]

Burke, P.

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3991, 210–216 (2000).
[CrossRef]

Burkovets, D. N.

O. V. Angel’skii, A. G. Ushenko, A. D. Archelyuk, 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]

Cassidy, L. D.

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

Chipman, R. A.

Davis, C. S.

C. S. Davis, Statistical Methods of the Analysis of Repeated Measurements (Springer-Verlag, 2002), p. 744.

De Martino, A.

Dubolazov, A. V.

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[CrossRef]

P. O. Angelsky, A. G. Ushenko, A. V. Dubolazov, M. I. Sidor, G. B. Bodnar, G. Koval, and L. Trifonyuk, “The singular approach for processing polarization-inhomogeneous laser images of blood plasma layers,” J. Opt. 15, 044030 (2013).
[CrossRef]

Y. A. Ushenko, A. V. Dubolazov, V. O. Balanetskaya, A. O. Karachevtsev, and V. A. Ushenko, “Wavelet-analysis of polarization maps of human blood plasma,” Opt. Spectrosc. 113, 332–343 (2012).
[CrossRef]

Y. A. Ushenko, Y. Y. Tomka, A. V. Dubolazov, and O. Y. Telenga, “Diagnostics of optical anisotropy changes in biological tissues using Müller matrix,” Quantum Electron. 41, 273–277 (2011).
[CrossRef]

Y. A. Ushenko, O. I. Olar, A. V. Dubolazov, V. O. Balanetskaya, V. P. Unguryan, N. I. Zabolotna, and B. P. Oleinichenko,“Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma,” Semicond. Phys., Quantum Electron. Optoelectron. 14, 98–105 (2011).

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

O. V. Angelsky, Y. A. Ushenko, A. V. Dubolazov, and O. Y. Telenha, “The interconnection between the coordinate distribution of Mueller-matrixes images characteristic values of biological liquid crystals net and the pathological changes of human tissues,” Adv. Opt. Technol. 2010, 130659 (2010).

Dubolazov, O. V.

Y. A. Ushenko, O. V. Dubolazov, and A. O. Karachevtsev, “Statistical structure of skin derma Mueller matrix images in the process of cancer changes,” Opt. Mem. Neural Netw. 20, 145–154 (2011).
[CrossRef]

Ermolenko, S. B.

O. V. Angel’skii, A. G. Ushenko, A. D. Archelyuk, 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]

Fedorova, K. V.

G. P. Petrova, A. V. Boiko, K. V. Fedorova, I. A. Sergeeva, N. V. Sokol, and T. N. Tichonova, “Optical properties of solutions consisting of albumin and γ-globulin molecules in different ratio modeling blood serum,” Laser Phys. 19, 1303–1307 (2009).
[CrossRef]

Felde, C. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photonics News 23, 25–29 (2012).
[CrossRef]

García-Caurel, E.

Goldfarb, A. R.

A. R. Goldfarb, L. J. Saidel, and E. Mosovich, “The ultraviolet absorption spectra of proteins,” J. Biol. Chem. 193, 397–404 (1951).

Guyot, S.

Haj-Ibrahim, B.

Hanson, S. G.

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. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Y. 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]

Hillman, L. W.

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3991, 210–216 (2000).
[CrossRef]

Istratyy, V. V.

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

Jaronski, J.

J. M. Bueno and J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthal. Physiol. Opt. 21, 384–392 (2001).
[CrossRef]

Karachevtsev, A. O.

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[CrossRef]

Y. A. Ushenko, A. V. Dubolazov, V. O. Balanetskaya, A. O. Karachevtsev, and V. A. Ushenko, “Wavelet-analysis of polarization maps of human blood plasma,” Opt. Spectrosc. 113, 332–343 (2012).
[CrossRef]

Y. A. Ushenko, O. V. Dubolazov, and A. O. Karachevtsev, “Statistical structure of skin derma Mueller matrix images in the process of cancer changes,” Opt. Mem. Neural Netw. 20, 145–154 (2011).
[CrossRef]

Koval, G.

P. O. Angelsky, A. G. Ushenko, A. V. Dubolazov, M. I. Sidor, G. B. Bodnar, G. Koval, and L. Trifonyuk, “The singular approach for processing polarization-inhomogeneous laser images of blood plasma layers,” J. Opt. 15, 044030 (2013).
[CrossRef]

Lompado, A.

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3991, 210–216 (2000).
[CrossRef]

Lu, S.

Maksimyak, A. P.

Maksimyak, P. P.

Marienko, V. V.

S. N. Savenkov, V. V. Marienko, E. A. Oberemok, and O. I. Sydoruk, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 605–607 (2006).
[CrossRef]

Mintser, O. P.

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[CrossRef]

Misevitch, I. Z.

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

Mokhun, I. I.

Mosovich, E.

A. R. Goldfarb, L. J. Saidel, and E. Mosovich, “The ultraviolet absorption spectra of proteins,” J. Biol. Chem. 193, 397–404 (1951).

Oberemok, E. A.

S. N. Savenkov, V. V. Marienko, E. A. Oberemok, and O. I. Sydoruk, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 605–607 (2006).
[CrossRef]

Olar, O. I.

Y. A. Ushenko, O. I. Olar, A. V. Dubolazov, V. O. Balanetskaya, V. P. Unguryan, N. I. Zabolotna, and B. P. Oleinichenko,“Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma,” Semicond. Phys., Quantum Electron. Optoelectron. 14, 98–105 (2011).

Oldenbourg, R.

Oleinichenko, B. P.

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[CrossRef]

Y. A. Ushenko, O. I. Olar, A. V. Dubolazov, V. O. Balanetskaya, V. P. Unguryan, N. I. Zabolotna, and B. P. Oleinichenko,“Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma,” Semicond. Phys., Quantum Electron. Optoelectron. 14, 98–105 (2011).

Ortega-Quijano, N.

Ossikovski, R.

Petrie, A.

A. Petrie and B. Sabin, Medical Statistics at a Glance (Blackwell, 2005), p. 157.

Petrova, G. P.

G. P. Petrova, A. V. Boiko, K. V. Fedorova, I. A. Sergeeva, N. V. Sokol, and T. N. Tichonova, “Optical properties of solutions consisting of albumin and γ-globulin molecules in different ratio modeling blood serum,” Laser Phys. 19, 1303–1307 (2009).
[CrossRef]

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, 2004) Vol. 1, pp. 93–138.

Polyanskii, P. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photonics News 23, 25–29 (2012).
[CrossRef]

Sabin, B.

A. Petrie and B. Sabin, Medical Statistics at a Glance (Blackwell, 2005), p. 157.

Saidel, L. J.

A. R. Goldfarb, L. J. Saidel, and E. Mosovich, “The ultraviolet absorption spectra of proteins,” J. Biol. Chem. 193, 397–404 (1951).

Savenkov, S. N.

S. N. Savenkov, V. V. Marienko, E. A. Oberemok, and O. I. Sydoruk, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 605–607 (2006).
[CrossRef]

Sergeeva, I. A.

G. P. Petrova, A. V. Boiko, K. V. Fedorova, I. A. Sergeeva, N. V. Sokol, and T. N. Tichonova, “Optical properties of solutions consisting of albumin and γ-globulin molecules in different ratio modeling blood serum,” Laser Phys. 19, 1303–1307 (2009).
[CrossRef]

Shribak, M.

Sidor, M. I.

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[CrossRef]

P. O. Angelsky, A. G. Ushenko, A. V. Dubolazov, M. I. Sidor, G. B. Bodnar, G. Koval, and L. Trifonyuk, “The singular approach for processing polarization-inhomogeneous laser images of blood plasma layers,” J. Opt. 15, 044030 (2013).
[CrossRef]

Smith, M. H.

M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001).
[CrossRef]

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3991, 210–216 (2000).
[CrossRef]

Sokol, N. V.

G. P. Petrova, A. V. Boiko, K. V. Fedorova, I. A. Sergeeva, N. V. Sokol, and T. N. Tichonova, “Optical properties of solutions consisting of albumin and γ-globulin molecules in different ratio modeling blood serum,” Laser Phys. 19, 1303–1307 (2009).
[CrossRef]

Sydoruk, O. I.

S. N. Savenkov, V. V. Marienko, E. A. Oberemok, and O. I. Sydoruk, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 605–607 (2006).
[CrossRef]

Tanner, E.

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3991, 210–216 (2000).
[CrossRef]

Telenga, O. I.

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

Telenga, O. Y.

Y. A. Ushenko, Y. Y. Tomka, A. V. Dubolazov, and O. Y. Telenga, “Diagnostics of optical anisotropy changes in biological tissues using Müller matrix,” Quantum Electron. 41, 273–277 (2011).
[CrossRef]

Telenha, O. Y.

O. V. Angelsky, Y. A. Ushenko, A. V. Dubolazov, and O. Y. Telenha, “The interconnection between the coordinate distribution of Mueller-matrixes images characteristic values of biological liquid crystals net and the pathological changes of human tissues,” Adv. Opt. Technol. 2010, 130659 (2010).

Tichonova, T. N.

G. P. Petrova, A. V. Boiko, K. V. Fedorova, I. A. Sergeeva, N. V. Sokol, and T. N. Tichonova, “Optical properties of solutions consisting of albumin and γ-globulin molecules in different ratio modeling blood serum,” Laser Phys. 19, 1303–1307 (2009).
[CrossRef]

Tomka, Y. Y.

Y. A. Ushenko, Y. Y. Tomka, A. V. Dubolazov, and O. Y. Telenga, “Diagnostics of optical anisotropy changes in biological tissues using Müller matrix,” Quantum Electron. 41, 273–277 (2011).
[CrossRef]

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

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

O. V. Angelsky, Y. Y. Tomka, A. G. Ushenko, Y. G. Ushenko, and Y. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for pre-clinical diagnostics of their pathological states,” J. Phys. D 38, 4227–4235 (2005).
[CrossRef]

Tower, T. T.

T. T. Tower and R. T. Tranquillo, “Alignment maps of tissues: I. microscopic elliptical polarimetry,” Biophys. J. 81, 2954–2963 (2001).
[CrossRef]

T. T. Tower and R. T. Tranquillo, “Alignment maps of tissues: II. fast harmonic analysis for imaging,” Biophys. J. 81, 2964–2971 (2001).
[CrossRef]

Tranquillo, R. T.

T. T. Tower and R. T. Tranquillo, “Alignment maps of tissues: II. fast harmonic analysis for imaging,” Biophys. J. 81, 2964–2971 (2001).
[CrossRef]

T. T. Tower and R. T. Tranquillo, “Alignment maps of tissues: I. microscopic elliptical polarimetry,” Biophys. J. 81, 2954–2963 (2001).
[CrossRef]

Trifonyuk, L.

P. O. Angelsky, A. G. Ushenko, A. V. Dubolazov, M. I. Sidor, G. B. Bodnar, G. Koval, and L. Trifonyuk, “The singular approach for processing polarization-inhomogeneous laser images of blood plasma layers,” J. Opt. 15, 044030 (2013).
[CrossRef]

Tyurin, A. V.

Unguryan, V. P.

Y. A. Ushenko, O. I. Olar, A. V. Dubolazov, V. O. Balanetskaya, V. P. Unguryan, N. I. Zabolotna, and B. P. Oleinichenko,“Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma,” Semicond. Phys., Quantum Electron. Optoelectron. 14, 98–105 (2011).

Ushenko, A. G.

P. O. Angelsky, A. G. Ushenko, A. V. Dubolazov, M. I. Sidor, G. B. Bodnar, G. Koval, and L. Trifonyuk, “The singular approach for processing polarization-inhomogeneous laser images of blood plasma layers,” J. Opt. 15, 044030 (2013).
[CrossRef]

O. V. Angelsky, Y. Y. Tomka, A. G. Ushenko, Y. G. Ushenko, and Y. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for pre-clinical diagnostics of their pathological states,” J. Phys. D 38, 4227–4235 (2005).
[CrossRef]

O. V. Angel’skii, A. G. Ushenko, A. D. Archelyuk, 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]

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, 2004) Vol. 1, pp. 93–138.

Ushenko, V. A.

Y. A. Ushenko, A. V. Dubolazov, V. O. Balanetskaya, A. O. Karachevtsev, and V. A. Ushenko, “Wavelet-analysis of polarization maps of human blood plasma,” Opt. Spectrosc. 113, 332–343 (2012).
[CrossRef]

Ushenko, Y. A.

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[CrossRef]

Y. A. Ushenko, “Concerted spatial-frequency and polarization-phase filtering of laser images of polycrystalline networks of blood plasma smears,” J. Biomed. Opt. 17, 117005 (2012).
[CrossRef]

Y. A. Ushenko, A. V. Dubolazov, V. O. Balanetskaya, A. O. Karachevtsev, and V. A. Ushenko, “Wavelet-analysis of polarization maps of human blood plasma,” Opt. Spectrosc. 113, 332–343 (2012).
[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]

Y. A. Ushenko, Y. Y. Tomka, A. V. Dubolazov, and O. Y. Telenga, “Diagnostics of optical anisotropy changes in biological tissues using Müller matrix,” Quantum Electron. 41, 273–277 (2011).
[CrossRef]

Y. A. Ushenko, O. I. Olar, A. V. Dubolazov, V. O. Balanetskaya, V. P. Unguryan, N. I. Zabolotna, and B. P. Oleinichenko,“Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma,” Semicond. Phys., Quantum Electron. Optoelectron. 14, 98–105 (2011).

Y. A. Ushenko, O. V. Dubolazov, and A. O. Karachevtsev, “Statistical structure of skin derma Mueller matrix images in the process of cancer changes,” Opt. Mem. Neural Netw. 20, 145–154 (2011).
[CrossRef]

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

O. V. Angelsky, Y. A. Ushenko, A. V. Dubolazov, and O. Y. Telenha, “The interconnection between the coordinate distribution of Mueller-matrixes images characteristic values of biological liquid crystals net and the pathological changes of human tissues,” Adv. Opt. Technol. 2010, 130659 (2010).

O. V. Angelsky, Y. Y. Tomka, A. G. Ushenko, Y. G. Ushenko, and Y. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for pre-clinical diagnostics of their pathological states,” J. Phys. D 38, 4227–4235 (2005).
[CrossRef]

Ushenko, Y. G.

O. V. Angelsky, Y. Y. Tomka, A. G. Ushenko, Y. G. Ushenko, and Y. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for pre-clinical diagnostics of their pathological states,” J. Phys. D 38, 4227–4235 (2005).
[CrossRef]

Ushenko, Y. O.

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

Vargas-Martin, F.

Waddell, W. J.

W. J. Waddell, “A simple ultraviolet spectrophotometric method for the determination of protein,” J. Lab. Clin. Med. 48, 311–314 (1956).

Zabolotna, N. I.

Y. A. Ushenko, O. I. Olar, A. V. Dubolazov, V. O. Balanetskaya, V. P. Unguryan, N. I. Zabolotna, and B. P. Oleinichenko,“Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma,” Semicond. Phys., Quantum Electron. Optoelectron. 14, 98–105 (2011).

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]

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Y. 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]

Adv. Opt. Technol. (1)

O. V. Angelsky, Y. A. Ushenko, A. V. Dubolazov, and O. Y. Telenha, “The interconnection between the coordinate distribution of Mueller-matrixes images characteristic values of biological liquid crystals net and the pathological changes of human tissues,” Adv. Opt. Technol. 2010, 130659 (2010).

Appl. Opt. (2)

Appl. Spectrosc. (1)

Biophys. J. (2)

T. T. Tower and R. T. Tranquillo, “Alignment maps of tissues: I. microscopic elliptical polarimetry,” Biophys. J. 81, 2954–2963 (2001).
[CrossRef]

T. T. Tower and R. T. Tranquillo, “Alignment maps of tissues: II. fast harmonic analysis for imaging,” Biophys. J. 81, 2964–2971 (2001).
[CrossRef]

J. Biol. Chem. (1)

A. R. Goldfarb, L. J. Saidel, and E. Mosovich, “The ultraviolet absorption spectra of proteins,” J. Biol. Chem. 193, 397–404 (1951).

J. Biomed. Opt. (2)

Y. A. Ushenko, “Concerted spatial-frequency and polarization-phase filtering of laser images of polycrystalline networks of blood plasma smears,” J. Biomed. Opt. 17, 117005 (2012).
[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]

J. Lab. Clin. Med. (1)

W. J. Waddell, “A simple ultraviolet spectrophotometric method for the determination of protein,” J. Lab. Clin. Med. 48, 311–314 (1956).

J. Opt. (1)

P. O. Angelsky, A. G. Ushenko, A. V. Dubolazov, M. I. Sidor, G. B. Bodnar, G. Koval, and L. Trifonyuk, “The singular approach for processing polarization-inhomogeneous laser images of blood plasma layers,” J. Opt. 15, 044030 (2013).
[CrossRef]

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

J. Phys. D (1)

O. V. Angelsky, Y. Y. Tomka, A. G. Ushenko, Y. G. Ushenko, and Y. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for pre-clinical diagnostics of their pathological states,” J. Phys. D 38, 4227–4235 (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]

Laser Phys. (1)

G. P. Petrova, A. V. Boiko, K. V. Fedorova, I. A. Sergeeva, N. V. Sokol, and T. N. Tichonova, “Optical properties of solutions consisting of albumin and γ-globulin molecules in different ratio modeling blood serum,” Laser Phys. 19, 1303–1307 (2009).
[CrossRef]

Ophthal. Physiol. Opt. (1)

J. M. Bueno and J. Jaronski, “Spatially resolved polarization properties for in vitro corneas,” Ophthal. Physiol. Opt. 21, 384–392 (2001).
[CrossRef]

Opt. Eng. (1)

Y. O. Ushenko, Y. Y. Tomka, I. Z. Misevitch, V. V. Istratyy, 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. (2)

Opt. Mem. Neural Netw. (1)

Y. A. Ushenko, O. V. Dubolazov, and A. O. Karachevtsev, “Statistical structure of skin derma Mueller matrix images in the process of cancer changes,” Opt. Mem. Neural Netw. 20, 145–154 (2011).
[CrossRef]

Opt. Photonics News (1)

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “The emerging field of correlation optics,” Opt. Photonics News 23, 25–29 (2012).
[CrossRef]

Opt. Spectrosc. (3)

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

Y. A. Ushenko, A. V. Dubolazov, V. O. Balanetskaya, A. O. Karachevtsev, and V. A. Ushenko, “Wavelet-analysis of polarization maps of human blood plasma,” Opt. Spectrosc. 113, 332–343 (2012).
[CrossRef]

Y. A. Ushenko, P. O. Angelskii, A. V. Dubolazov, A. O. Karachevtsev, M. I. Sidor, O. P. Mintser, B. P. Oleinichenko, and L. I. Bizer, “Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure,” Opt. Spectrosc. 115, 601–609 (2013).
[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]

Phys. Rev. E (1)

S. N. Savenkov, V. V. Marienko, E. A. Oberemok, and O. I. Sydoruk, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 605–607 (2006).
[CrossRef]

Proc. SPIE (2)

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3991, 210–216 (2000).
[CrossRef]

M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001).
[CrossRef]

Quantum Electron. (2)

O. V. Angel’skii, A. G. Ushenko, A. D. Archelyuk, 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]

Y. A. Ushenko, Y. Y. Tomka, A. V. Dubolazov, and O. Y. Telenga, “Diagnostics of optical anisotropy changes in biological tissues using Müller matrix,” Quantum Electron. 41, 273–277 (2011).
[CrossRef]

Semicond. Phys., Quantum Electron. Optoelectron. (1)

Y. A. Ushenko, O. I. Olar, A. V. Dubolazov, V. O. Balanetskaya, V. P. Unguryan, N. I. Zabolotna, and B. P. Oleinichenko,“Mueller-matrix diagnostics of optical properties inherent to polycrystalline networks of human blood plasma,” Semicond. Phys., Quantum Electron. Optoelectron. 14, 98–105 (2011).

Other (3)

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, 2004) Vol. 1, pp. 93–138.

C. S. Davis, Statistical Methods of the Analysis of Repeated Measurements (Springer-Verlag, 2002), p. 744.

A. Petrie and B. Sabin, Medical Statistics at a Glance (Blackwell, 2005), p. 157.

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Figures (6)

Fig. 1.
Fig. 1.

Optical scheme of polarimeter, where 1, is the He–Ne(Cd) laser; 2, is the collimator; 3, is the stationary quarter-wave plate; 5, 8 are the mechanically movable quarter-wave plates; 4, 9 are the polarizer and analyzer, respectively; 6, is the object of investigation; 7, is the polarization micro-objective; 10, is the CCD camera; 11, is the personal computer. Explanations are in the text.

Fig. 2.
Fig. 2.

Coordinate [(1), (3), (5), (7)] and probability [(2), (4), (6), (8)] distribution of phase shift δ, introduced by polycrystalline blood plasma films of a donor group [(1), (2), (5), (6)] and cancer group patients [(3), (4), (7), (8)].

Fig. 3.
Fig. 3.

Coordinate [(1), (3), (5), (7)] and probability [(2), (4), (6), (8)] distribution of rotation of polarization plane θ of polycrystalline blood plasma films of a donor group [(1), (2), (5), (6)] and cancer group patients [(3), (4), (7), (8)].

Fig. 4.
Fig. 4.

Coordinate [(1), (3), (5), (7)] and probability [(2), (4), (6), (8), (10), (12)] distribution of linear dichroism Δτ of polycrystalline blood plasma films of a donors group [(1), (2), (5), (6)] and cancer group patients [(3), (4), (7), (8)].

Fig. 5.
Fig. 5.

Coordinate [(1), (3), (5), (7)] and probability [(2), (4), (6), (8)] distribution of circular dichroism C of polycrystalline blood plasma films of a donors group [(1), (2), (5), (6)] and cancer group patients [(3), (4), (7), (8)].

Fig. 6.
Fig. 6.

Histograms of distributions N(Z¯i) of averaged values of statistical moments within the limits of both groups of blood plasma films.

Tables (2)

Tables Icon

Table 1. Average (Z¯i=1;2;3;4) and Standard Deviations (±σ) of Statistical Moments Zi=1;2;3;4 of Optical Anisotropy Distributions of Blood Plasma of Groups 1 and 2

Tables Icon

Table 2. Operational Characteristics of the Method of Mueller Matrix Reconstruction of Polycrystalline Structure of Blood Plasma Films

Equations (28)

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

{F}={Ω}{D}=f111×10000f22f23f240f32f33f340f42f43f44.
{Ω}=10000ω22ω2300ω32ω3300001,ωik={ω22=ω33=cos2θ;ω23=ω32=sin2θ,
{D}=10000d22d23d240d32d33d340d42d43d44,dik={d22=cos22ρ+sin22ρcosδ;d23=d32=cos2ρsin2ρ(1cosδ);d33=sin22ρ+cos22ρcosδ;d42=d24=sin2ρsinδ;d34=d43=cos2ρsinδ;d44=cosδ.
{M}=Πi=14{Mi}=M111×1M12M13M14M21M22M23M24M31M32M33M34M41M42M43M44.
{Φ}=100ϕ140ϕ220000ϕ330ϕ41001,ϕik={ϕ22=ϕ33=1C21+C2;ϕ14=ϕ41=±2C1+C2.
{Ψ}=1φ12φ130φ21φ22φ230φ31φ32φ330000φ44,φik={φ12=φ21=(1Δτ)cos2ρ;φ13=φ31=(1Δτ)sin2ρ;φ22=(1+Δτ)cos22ρ+2Δτsin22ρ;φ23=φ32=(1Δτ)sin2ρ;φ33=(1+Δτ)sin22ρ+2Δτcos22ρ;φ44=2Δτ.
{M}={Φ}{Ψ}{D}{Ω}.
{θ=f(Mik);δ=g(Mik);C=h(Mik);Δτ=u(Mik).
{M11(Θ)=const;M14(Θ)=const;M41(Θ)=const;M44(Θ)=const;{[M22+M33](Θ)ΣM22;33(Θ)=const;[M23M32](Θ)ΔM23;32(Θ)=const.
{θ=f*(M11;14;41;44,M22;33,ΔM23;32);δ=g*(M11;14;41;44,M22;33,ΔM23;32);C=h*(M11;14;41;44,M22;33,ΔM23;32);Δτ=u*(M11;14;41;44,M22;33,ΔM23;32)
δ,θΔτ,C.
{F(λ1)}={D}{Ω}=10000(d22ω22+d23ω32)(d22ω23+d23ω33)d240(d32ω22+d33ω32)(d32ω23+d33ω33)d340(d42ω22+d43ω32)(d42ω23+d43ω33)d44.
{δ=arccosf44(λ1);θ=0.5arctanΔf23;32(λ1)f22;33(λ1).
{F˜(λ1)}={Ω}{D}=10000(d22ω22+d32ω23)(d23ω22+d33ω23)(d24ω22+d34ω23)0(d22ω32+d32ω33)(d23ω32+d33ω33)(d24ω32+d34ω33)0d42d43d44.
C=h*(M11;14;41;44,M22;33,ΔM23;32);Δτ=u*(M11;14;41;44,M22;33,ΔM23;32)
{{M(λ2)}={Φ}{Ψ}{F};{M*(λ2)}={Ψ}{Φ}{F}.
{M14(λ2)=φ12f24+φ13f34+ϕ14φ44f44=ϕ14φ44f44;M41(λ2)=ϕ41;M44(λ2)=ϕ41φ12f24+ϕ41φ13f34+φ44f44=φ44f44.
Δτ=0.25M44(λ2)M44(λ1)×λ2λ1;
C=1+(1M41(λ2))0,5.
M41(λ2)=M14(λ2)M44(λ2).
{M14*(λ2)=ω22φ12f24+ω33φ13f34+ω14f44=ω14f44;M41*(λ2)=ω41φ44;M44*(λ2)=φ44f44.
Δτ=0.25M44*(λ2)M44*(λ1)×λ2λ1;
C=1+(1M41*(λ2)2τ0,5)0,5.
{f44(λ2)=(M14*(λ2)M44*(λ2)M41*(λ2))0.5}cos(λ1λ2arccos(f44(λ1)))=(M14*(λ2)M44*(λ2)M41*(λ2))0.5.
{Si=20;45;90;(λ1,λ2)=I00;45;90;+I900;45;90;;Si=20;45;90;(λ1,λ2)=I00;45;90;I900;45;90;;Si=30;45;90;(λ1,λ2)=I450;45;90;I1350;45;90;;Si=40;45;90;(λ1,λ2)=I0;45;90;I0;45;90;.
{M14(λ2)=S10.5(S10+S190);M41(λ2)=0.5(S40+S490);M44(λ1,λ2)=S40.5(S40+S490);M22;33(λ1)=M22+M33=0.5(S20S290)+S3450.5(S30+S390);ΔM23;32(λ1)=M23M32=S2450.5(S20+S290)0.5(S30S390).
Z1=1Pj=1Pqj;Z2=1Pj=1P(q)j2;Z3=1Z231Pj=1P(q)j3;Z4=1Z241Pj=1P(q)j4.
{δ(λ1)R(δ){Se(Z3;4)=81%82%;Sp(Z3;4)=77%81%;Ac(Z3;4)=79%82%};θ(λ1)R(θ){Se(Z3;4)=86%89%;Sp(Z3;4)=83%86%;Ac(Z3;4)=84%88%};Δτ(λ2)R(Δτ){Se(Z3;4)=91%95%;Sp(Z3;4)=88%92%;Ac(Z3;4)=90%93%};C(λ2)R(C){Se(Z2;3;4)=93%95%;Sp(Z3;4)=90%93%;Ac(Z2;3;4)=91%94%}.

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