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The paper deals with investigation of the processes of laser radiation transformation by biological crystals networks using the singular optics techniques. The results obtained showed a distinct correlation between the points of “characteristic” values of coordinate distributions of Mueller matrix (

Laser polarimetry [

all the variety of human BT can be represented by four main types—connective, muscular epithelial, and neural tissues;

structure of any BT type is regarded as a two-component amorphous-crystalline one;

the crystalline component or extracellular matrix is formed by the network of optically uniaxial birefringent protein (collagen, myosin, elastine, etc.) fibrils or biological crystals;

the process of transformation of laser radiation polarization state by biological crystal is characterized by Mueller

Here

A new approach to description of the BT laser images based on the analysis of coordinate distributions of polarization singularities became developed the above-mentioned statistical [

Investigation of laser images of the connective tissue layers revealed a developed network of polarization singularities [

It should be pointed out that singular approach is predominantly realized out of the analysis of the mechanisms of forming polarizationally heterogeneous laser images of BT by an extracellular matrix. Thus, development of laser polarimetry techniques based on determination of singular interconnections “object-field” in order to find new methods of diagnostics of transformation of the BT extracellular matrix orientation-phase structure connected with precancer changes of their physiological state is very important.

To solve such a problem, we should revert to the analysis of optical properties of biological crystals’ nets, comprehensively described by the Mueller matrix though within a singular approach.

The use of the fourth parameter of the Stokes vector appears to be a suitable and widely applied means of such singularities representation

According to analysis of (

As it can be seen, relations (

Considering expressions (

the values

the complete set of L-points (

Mueller-matrix analysis enables to perform the sampling of polarization singularities of the laser image, formed by biological crystals with orthogonally oriented (

“orthogonal”

“orthogonal”

Thus, measuring the coordinate distributions of the characteristic values (

Figure

Optical scheme of polarimeter, where 1: He-Ne laser; 2: collimator; 3: stationary quarter-wave plates; 5, 8: mechanically movable quarter-wave plates; 4, 9: polarizer and analyzer correspondingly; 6: object of investigation; 7: microobjective; 10: CCD camera; 11: personal computer.

The parallel (

The optical thin (the absorption coefficient

At the first stage the interconnections (

Figure

Networks of characteristic values

It can be seen from the data obtained that there is direct correlation between the coordinate (

Coordinate distributions of characteristic values of matrix elements

Analytically substantiated and experimentally proven interconnections between the matrix and polarization singularities were used as the basis for Mueller-matrix singular diagnostics of oncological changes of the tissues of women’s reproductive sphere.

Three groups of histological sections of the main tissue of skin derma—were used as the objects of investigation:

biopsy of the sound tissue of skin derma (type “A”—Figure

biopsy of the skin derma in precancer state (type “B”—Figure

biopsy of the skin derma in cancer state (type “C”—Figure

Polarization images of the skin derma “A” (a), “B” (b), and “C” (c)-types in coaxial polarizer and analyzer.

To determine the criteria of Mueller-matrix diagnostics of skin derma oncological state and differentiation of its severity degree the following technique was used:

coordinate networks of characteristic values of matrix elements

within the obtained sampling

distributions of the number of “orthogonal” singular

statistical moments of the 1st–4th orders of the obtained distributions of

Figures

Networks of characteristic values

Networks of characteristic values

Networks of characteristic values

Figure

Distributions of the amount of characteristic values

The comparative analysis of the data obtained shows that

coordinate distributions of the elements

total amount of

dependencies

distributions

The obtained results can be connected with the increase of birefringence (

In terms of physics, such morphological processes are manifested in the increase of probability of forming the

In the end, the comparative investigations of diagnostic efficiency of the potential of famous techniques of laser polarimetry

Table

Values

skin derma “A”-type (21 samples) | skin derma “B”-type (21 samples) | skin derma “C”-type (21 samples) | |||||||

_{44} | _{34} | _{24} | _{44} | _{34} | _{24} | _{44} | _{34} | _{24} | |

0,67 | 0,32 | 0,27 | 0,59 | 0,27 | 0,24 | 0,37 | 0,19 | 0,18 | |

0,51 | 0,29 | 0,26 | 0,57 | 0,23 | 0,21 | 0,28 | 0,21 | 0,17 | |

1,13 | 0,88 | 0,74 | 0,98 | 0,79 | 0,66 | 0,66 | 0,49 | 0,41 | |

3,15 | 2,11 | 2,27 | 2,84 | 1,79 | 1,87 | 1,57 | 1,07 | 1,12 | |

0.12 | 0.24 | 0.15 | 0.28 | 0.18 | 0.29 | ||||

0.16 | 0.31 | 0.19 | 0.38 | 0.23 | 0.4 | ||||

0.70 | 0.92 | 0.93 | 1.12 | 1.27 | 1.72 | ||||

1.71 | 2.19 | 2.01 | 3.13 | 3.41 | 4.01 | ||||

0,61 | 0,43 | 0,12 | 0,39 | 0,37 | 0,23 | 0,29 | 0,28 | 0,19 | |

0,75 | 0,82 | 0,15 | 0,36 | 0,69 | 0,46 | 0,31 | 0,55 | 0,23 | |

1,19 | 0,92 | 1,86 | 0,63 | 0,87 | 1,86 | 0,53 | 0,76 | 2,06 | |

1,99 | 2,31 | 2,32 | 1,01 | 2,07 | 8,45 | 0,8 | 1,87 | 2,91 |

It follows from the data presented that:

efficiency of laser polarimetry for diagnostics and differentiation of early oncological changes of skin derma tissue is insufficient—the difference between the values of statistical moments

the technique of polarization-correlation mapping is efficient for differentiation of optical properties of sound and oncologically changed skin derma tissue—skewness (

the technique of Mueller-matrix singular diagnostics is efficient for differentiation of optical properties of all types of samples—statistical moments of the 3rd and 4th orders of distributions

for distributions

Correlation between the coordinate locations of characteristic points of 2D elements of Mueller matrix of optically thin layer of biological tissue and the network of L- and C-points in its laser image is defined. The potentiality of Mueller-matrix sampling of polarization singularities formed by biological crystals with orthogonally oriented (