 Tukaj, Viktor. Hvala, mene količnih in vsi. Veselim, da sem tukaj, da videlem vši sveti, in da sem tukaj izgleda tukaj rečen, da je tukaj, da je tukaj, polizacija, mikroskopija, tukaj medikalima in diagnostika. Nama je, ops, okej, nama je Yuri Ušenko, sem reprezentovat černjevci našeljne universitete v Ukraine. Tako, tudi bomo vse ležite, in v februji 2023 bomo vse laboretory eksperimentalne demonstracije, tudi vse, tako ki smo vse zelo zelo zelo izvizili in izvizili vse, o če so tega. Hvala lektu, in se so različili, z nej, nekaj, izdramatici in izveči, je tako čas. Vse lektu je pričan opravljen, povrčan, stoksvektor, muler matrix in vsega, in basičnih polerimetričnih laserov. V drugi leči smo vzoutovali nekaj basičnih modelov skriptičnih stručov in optičnih in zotropičnih biologičnih tihših. Na drugi leči smo vzoutovali vzoutovali metod in resursi in analizičnih vzoutovali vzoutovali vzoutovali vzoutovali biologičnih tihših polerizacijnih homogeničnih imagičnih. Na drugi leči smo vzoutovali te principali, metod polerizacijnih na prižaeh metod in repliščnih vzoutovali. Speli počkeli iz vseh našipa, vzoutovali私jih nalega. Na vseh tihših nekaj bilo najbolj vzoutovali se priživ center. A to je okreža. Poblada na St sounds, je to centra kaj vstala, všeč ga immersed. Poblada na st, tkoout, bi je dvisno od 1864 kot skela naprej ljubez in ozostrohenerja kot zliz in V tem vseh zelo iznosnje ovo Vršanje, ovo je vsi vseh ispravitv, vseh iznosnje ovo se vseh zelo iznosnje ovo všetih katerom. Vseh zelo iznosnje zelo iznosnje ovo všetih katerom. So let's start with an introduction and we are trying to formulate some basic concepts of what we will talk about. So the first concept is that why we are dealing with optical methods at all. So optical methods of diagnosis of biological objects itself and the visualization of the structure occupy now a leading positions, same to the high information contact and capacity also, and multi-functional capabilities. So you are, you will learn about the photometric methods, spectral methods, polarization itself methods, correlation methods, et cetera. What should be stated is that new scientific direction within optics at all is now formed, it called optics of biological tissues and fluids, and this direction is a rapidly developing thing. The main areas of basic research are the results of theoretical and experimental studies of photon transport from the very beginning in biological tissues and fluids. After that, separate direction in optics of biological tissues and fluids formed by polarimetric investigations. It should be stated that analysis of polarization characteristics of the scattered radiation allow us to obtain additional quantitatively new results on morphological and physiological state of biological tissues. A new step, you may be know about it, lies in the development of methods of optical diagnostics of biological tissues. It deals with the fluorescent techniques and the analysis of polarization state of these fluorescence techniques. So-called laser fluorescence polarimetry or laser after fluorescence polarimetry. Let's start with the light. You know that the light, it's a electromagnetic wave. The electric vector oscillates in, here you can see in X plane, magnetic vector oscillates in Y plane. And the number of, the wave propagation is along to Z axis. In optics, we deals mostly with electric field itself, because magnetic field is some other very wide research area of research. So let's consider the electric vector here, this one. So here you can see it yellow. It can be decomposed on a two orthogonal projection, here sub X and here sub Y. This is, these are two plane waves. You can see the equations of these fields here. It's X component of our electric vector oscillation and Y component of our electricity vector oscillation. It differs by these amplitudes, and here the initial phase is also presented. So, you know, the omega is angular frequency, K is a wave number. And this is a very important thing that a phase, initial phase. The initial phase, yes, it's a time from the beginning of oscillation. As you can see in this figure, what is the initial phase? Zero, zero, yes, exactly zero. But a little bit later, we will discuss it very precisely. So what kind of parameters do we, or can we use in order to make some diagnosis or make some quantification of, for example, scattered light due to this representation. Amplitude can be used for some evaluation. Yes, maybe frequency also phase, including the initial phase. And force parameters, I'd like to present, it's a polarization. Who knows about polarization, what does it mean? Yeah, exactly. It's a trajectory of the tip of this vector when we see, like here. So, about the polarization and the importance of these parameters and the possible realization of diagnostical methods. So, it is, as Bill was said, it's an important property of electromagnetic waves. For example, in communication, completely polarized waves are used. In radio astronomy, unpolarized component exist. And the technique to analyze the polarization known as polarimetry, when it deals with the laser radiation called laser polarimetry. The complete polarization types of electromagnetic waves are the following, it's three types. Linear polarization, circular polarization and the most common type is elliptical polarization. Due to the radiostromical sources they may possess random polarization, also known as unpolarized waves, and the partial polarization. It's a sum or mixture of completely polarized and completely unpolarized radiation. So, it's a very complex situation, so we are not talking about it. So, we will, this lecture we will deal with the classical complete polarization types. Let's start with the graphical representation and the so-called polarization ellipse. So, as we just talking, so the polarization is a trajectory of the tip of electricity vector here when we are looking in this direction. So, when we analyze these two orthogonal components of the electricity vector and do some algebra, it can be done by itself. So, we can obtain these equations. Where's, yeah, sine, cosine and so on. This is a well-known equation of the ellipse. Let's start with the parameters which these ellipse can be characterized. First one is the size of a minor axis. Minor axis, semi-minor axis. The size of major axis here and semi-major axis also oftenly used. The third very important parameter is orientation, so-called tilt angle or ademos of elliptical polarization between this direction x and semi-major axis. The fourth important parameter is the actual ratio, so-called ellipticity of polarization. Is the angle between, let me see, yeah, between the length of the minor to the length of the major axis here. It can be plus or minus, yeah? This is ellipticity angle, very important parameters. Also it can be used as a diagnostical parameter, it's a sense, clockwise or anti-clockwise. So, you know, this electricity vector we obtain ellipse, it's sensing clockwise or anti-clockwise, while wave is distributed forward. On this slide you can see the most easy and the most conventional type of polarization oftenly used in different investigations, it's a linear polarization. It should be stated that any form of complete polarization resulting from a coherent source can be analyzed using the polarization ellipse. For example, or this one, yeah, these two projections, so if there is no amplitude in y, this one is equal to zero. So there is only one component exists, it's x vertical, yeah? If we can return one slide, so when you here place y, yeah? Or x is zero, so we will obtain simple like this oscillation. So in this direction, in x direction, in x plane, here's a propagation direction. It's like the projection of this oscillation on this plane will be linear. Or if there is no amplitude in x component, there is only one component exists, it's y component, yeah? This one. Or this oscillation, it always said it's a linear polarization with azimus is equal to zero here with azimus is equal to 90 degrees. For example, for the plus minus 45 degrees azimus, the phase difference between of these two oscillations or these two orthogonal projection of our electricity vector should be zero or pi for plus and for minus. And the ratio between these amplitudes, they must be equal. So they are equal and the resulting oscillation we can obtain here is plus 45 degrees azimus or minus 45 degrees azimus. So let's start with another case. So it should be noted that linear and this one's circular polarization, it's a boundary states of the most common elliptical polarization. So if we have our well-known two projections, yeah? And if the phase difference initial, yeah, this delta is plus minus 90 degrees and we have this ratio of equality between of these two components, then this ratio is equal to cosine and this ratio is equal to sine and we get the equation of a circle itself, yeah, with a clockwise or anti counterclockwise, your rotation. And this wave is said to be circularly polarized. Yeah, you can see it here. There's a procedure of adding of these two orthogonal components and if we will look here in this direction, we will see circle. Here you can see the procedure of adding of these two components. So we call the phase difference plus minus 90 degrees and this shift is equal to quarter wave between of these two oscillations and when you will do summarization of this vector and this vector and after that this and this, the tip of your summarized vector will be rotating. Here this is. Okay, let's continue with elliptical polarization. So in the most common case, in the most common case, the magnitudes of e, x and e, y are not equal and there is exist a phase difference between the two. In this case, the tip of the electricity vector describes an ellipse and the wave is said to be elliptically polarized. Here you can see these two oscillations, these two projections. The amplitude is not equal between each other and there is some phase shift, not zero and not 90 degree. Okay, and in this case in this direction we will see ellipse. Due to the ratio between of these magnitudes and the value of this phase shift, the rotation could be clockwise or anti-clockwise. Here you can see it. So linear and circular polarization when we can add it gives us elliptical polarization and you should know that any wave may be written as a superposition of the two polarization. Let's see some interesting program. You can download it freely through the Internet. It's called Emanim. So if you have a linear polarization, this one if we have another linear polarization this two wave what should we obtain when we add one to another? Who can? Yes. Exactly. We will obtain also linear wave but in this direction the blue one. Okay, another interesting question. What should we do if these two waves or a projection of one wave will be left and right circular. We obtain exactly because the amplitudes are equal and the phase difference are the same zero. So let's try to show axis only. This blue one and these two vectors are rotating. Let's continue with as we said a few minutes ago that elliptical polarization is the sum of linear and the circular one. Let's check. Yeah, this one, yes. Yes, you can see it. And what we will obtain for example we talked about when the amplitudes of two oscillations are not equal and there is some phase difference between of them. So we should obtain we have to obtain the elliptical polarization. Let's try the amplitude of this one. We make smaller and a little bit phase difference for the second wave. This one the phase difference is very sensitive for a difference. This all I said was about the sensitivity of the ratio between of amplitudes and the phase difference between of two oscillations. So in another wave polarization is very sensitive to any disturbances in these ratios. So the first conclusion so it this tool is very sensitive to the any changes in for example in biological objects. But we should know how to use these changes in polarization in order to make some diagnosis or something like that. So let's start with the stocks parameters. This model experiment you saw it's only calculation. But how one can measure directly from the intensity measurements this polarization and said that this one is linear this one is circular this one is even partly polarized this one is elliptical. So in early 18 52 George Gabriel stocks took a very different approach and discovered that polarization can be described in terms of observables using an experimental identification or definition. So cause the polarization ellipse itself is only valid for a given instant of times. This ellipse is a function of time. With time this ellipse will change. To get the stocks parameters firstly one to time average integral over time and a little bit of algebra also. And one can obtain this equation. So here you see the time in this x y. Here we deal now only with amplitudes without time. And these two parameters this one, this, this and this one also he called own parameters the first one it's a sum of amplitudes of these two orthogonal oscillations the second one is the difference between of them. The third one and the first one it's a this kind of combinations with a phase with initial phase also. Okay, let's return the polarization ellipse itself. And how stocks parameters can be described in geometrical terms. Here we are. This is normalized stocks parameters a little bit later about this. The first element is unity in any cases because it's a whole intensity we can divide all the elements on this intensity and obtain this one will be unity. The second one is a combination of cosines where here we are with azimus and this one is what is this ellipticity or vice versa this one azimus this one ellipticity thanks a lot. Okay, the third one and the fourth one because it deals with for example elliptical polarization and we can measure the fourth stocks vector parameters immediately just after that we will obtain the value of ellipticity of our polarization or our wave. The stocks parameters after that can be arranged in the stocks vector. It's not the real vector it's something like in from the matrix calculation so we have a matrix in different dimension and we have a vector it's a matrix with one dimension is unity. So this one is stocks vector this first element is a total intensity of light. The second one how we can measure the second one we should just measure just adjust our analyzer analyzer on the output of our system with angle zero and measure this intensity from a ccd camera from a photo diode from all you want measure respectively just turn out this polarizer analyzer at angle 90 degree and measure this intensity and calculate in matlab as I saw where many people where many scientists are in charge in matlab in very closely charged. The second one this one is a difference between these two components intensity so this one is a measurable quantity just intensity what about the force parameters it's a little bit it's a little bit I can say harder because here we should make this intensity of right circular component and left circular component so in this measurement we should add the so called optical compensator namely a quarter wave plate before the analyzer and adjust analyzer on these angles here and here and also just divide between of them stocks vector elements for a linearly polarization or a linearly polarized wave is the following because we have only this one is unity this one and this one is not equal to zero and the force one is absolutely zero differences between of linearly polarized with azimus of zero and 90 degree is only this one will be unity this one will be minus unity and so on for a circular polarization situation when we have a fully polarized and circular polarized wave the second and third elements are absolutely zero and the force one is non zero for a fully polarized light this equation is in charge here it's divide for example if we deal with a partly polarized light so here will be less not equal but less we just talking about stocks vector so we deal with a field optical field polarization state of this field and so on we can obtain even topological distribution of different polarization when we use a CCD camera and as a detector but what about object what object did this perturbation in polarization states so together with stocks if light is represented by stocks vectors optical components as then should be described with a Miller matrices in such a way this is a description of output light this one is stocks vector of input light in order to do this mathematical operation this one converted to this one we have to use this four matrix called Miller matrix when all these elements connected with an optical property of our object itself so for example for very simple case this one input light output light rhombus some lens and some triangles from different types of glasses this one element one two and three so the transformation of light can be described with this simple equation but this Miller matrices should be written in reverse way you know this is a main formula connected this one also connected with the transformation of polarization and even non-polarized light we can use this as it was said by professor kalve we have to use some formalism we have to invent some formalism in order to predict what is optical properties of object with measured this stocks vector we measure stocks vector of the output after the object we know stocks vector as an input signal for example it's linearly polarized with edimus zero degree and after that we can calculate Miller matrix when different elements different it will be said a little bit later connected with some properties of object it can be bifringens, dichroism and so on absorption so briefly on the basis of laser polarimetry so every polarization microscope allows us to invent for example crystalline objects yes but not everyone give us a possibility to measure all the stocks vector elements in order to calculate Miller matrix so we deal with Miller polarimetry so it can be it can be constructed on the base of conventional polarization microscope but it can be separately collected with necessary optical elements you will see it next Thursday here in order to measure briefly describe laser source it may be not a laser source but wideband source and after that you should use for example some narrowband interferometric filter in order to get some wavelengths you want but laser it's more simple this is a collimator in order to create a collimated beam with needed collimation ratio this one is a first quarter wave plate the task of this plate is only to create a circularly polarized wave cause the laser here for example it can be diode laser yes it linearly polarized and when we after that by means of this polarizer or do some changes in illumination in polarization of illumination beam the intensity will decrease yes and some position so in order to overcome this problem we use this quarter wave plate for example if you have a laser with a circular polarization on the output so ok no problem but this is more flexible system this one this plate put it here provides a condition of circular polarization for the object in order to calculate the force stocks vector parameters object can be slice of histological section it can be dried biological fluid it can be something but this one is for if you want to deal with a reflection mode you only put this part of this setup needed angle and you measure all the same the procedure is the same against quarter wave plate analyzer ccd camera and the processing unit can be so in order to obtain system distribution of azimus and ellipticity of polarization for example it's a so called polarization maps using ccd camera you should only measure minimal and maximal intensity here by means of rotating analyzer 9 it can be done with for example step engines this two arrays minimal and maximal and after that calculate these angles for corresponding angles of this analyzer for this minimal array and after that simply calculate the polarization azimus by subtracting pi divided by 2 and the ellipticity of this ratio of minimal intensity to maximal intensity so it can be done automatically and some automatical polyrimeters exists but not with the ccd camera but for a single beam is only photodiode so let's talk about basics of model description of structure and optical of biological tissues what does it mean optical anisotropy because every biological object almost every except of fat tissue is anisotropic object so optical anisotropy is a difference in the optical properties of a medium as a function of the direction of propagation of optical radiation in the medium and of the state of polarization of the radiation so one can separate amplitude anisotropy so called dichroism and phase anisotropy called bifringence what about amplitude anisotropy so crystals and the biological tissue is a polycrystalline structure may similarly show absorption which depends upon polarization so for different polarization states of illuminating beams absorption will be different one can see the linear dichroism and the circular dichroism linear dichroism it's a dependence of absorption for a linear polarization circular dichroism it's a depending on absorption of circular polarization what about bifringence asymmetry in crystal structures causes two different refractive indices and opposite polarization follow different paths through the crystal one can show the linear bifringence and the circular bifringence or so called optical activity so let's start with some animations just look at the phenomenon we start with linear bifringence and linear dichroism what about linear dichroism you can see that oscillation absorption of red oscillation is much more than for example for the green one it depends on the azimus of polarization what can we obtain this yellow one cube it's a object our medium what we will obtain on the what we can measure on the output of this object cause this too is only projection of the whole polarization yeah so we will obtain something like this strange curve what about circular dichroism so you see also that the green oscillation is not absorbing but the red one is and the output total polarization yeah oscillation on the output of this object will be as follows so we are talking about it's not really in a crystal this one we have some cause any state of polarization any state of polarization can be represented by combination of two or linear one or circular one so in the crystal it can be ordinary extraordinary and this dependence in absorption is evidence ok, what about let's start with linear biafringens this is my so we have these two oscillations on the input and one of them for one of these oscillations the refraction index is a bit higher you can see 1.05 and 1.00 so if I choose the similar refraction index is the situation we were talking about we were talking about in the previous lecture and only just a change a little change in refraction index will lead to creation of elliptical polarization on the output of this object so we can we can we should something do with this in our experiments we should know what we are measuring and what is the process in object brings these changes ok so briefly here you can see a soft tissue structure it's a transmission electron microscope in the skin dermis and this is the model cause every tissue most of them muscular and derma and so on connected with the very first element in this it's a glitzine and predominantly amino acids it forms the tropical again the tropical again forms the collagen fibers and the collagen fibers form fiber bundle so biological tissue reveal self similar fractal structure as a result of growth processes here and the very very fresh publications about multi fractal light scattering in tissues proof this theory in optics express and optics letters here you can see also this one it's fibers collagen fibers and this one also but in this direction ok let's start with the algorithm of mirror matrix modeling of biological layer anisotropy as we can discuss bit later so there are following mechanisms phase anisotropy and amplitude anisotropy divided to optical activity or circular biofringence and linear biofringence circular dichraism and linear dichraism what parameters can we measure we can measure in for this process polarization plane rotation angle sigma and the corresponding partial for this sigma we can measure phase difference phase shift between the orthogonal component of amplitude delta and this partial matrix operator index of circular and linear dichraisms and the corresponding partial mirror matrices this one is mirror matrix M of generalized optical anisotropy of our biological optics this one we measure in our experiments but we should know the influence of this partial mirror matrices corresponding to the different optical activities in this object in order to for example to diagnose the cancer changes on very early stages and so on cause cancer changes on early stage connected with optical activity of molecules so and we can decompose this mirror matrix we should know the processes of the composing of this mirror matrix in order to define these algorithms separately ok just a bit of matrix algebra for circular linear biofringence for circular and linear dichraisms here you can see it these parameters here row this one row is a fibril in the tissue in every point delta it's a phase shift that this fibril brings between of orthogonal component of polarization here the values of absorption so the generalized mirror matrix is as follows this is normalized mirror matrix that's where this element is 0 is unity what about the experiment experiment proof this situation for the skeletal muscle tissue or skeletal muscle you can see this whole mirror matrix this mirror matrix images and no one of this mirror matrix images is not 0 cause it tell us about the presence of whole four processes in biofringences and dichraisms in one tissue at one time but what is the information content of mirror matrix element of all this one how we can decode we can measure this but how we can decode all of these images in order to obtain some necessary information so due to the modeling and so on this one of elements it's a first line this line is connected with mechanisms of optical and isotropic absorption the second and the third line of this mirror matrix is connected with a phase modulation of laser radiation on the background of optical and isotropic absorption so the mechanism presented simultaneously in these elements the last line it's a complex information about superposition of mechanisms of linear biofringence and dichraisms but in several papers about the decomposition of mirror matrices and so on of Lu Chipman and other scientists one can divide some mirror matrix invariance this one and this one are connected only with a with a very high precision connected only with the mechanisms of anisotropic absorption this one m44 connected directly with the phase of linear biofringence and this one delta m is a combination of elements this one difference and the other elements difference between it connected with a tangence of two sigma circular biofringence so how much time? 30 minutes so this is quite microscopic images in polarization microscope of different type of tissue you can see it for example tissue with ordered and disordered structure here you can see this order it's a myocardium tissue in coaxial and crossed polarizer analyzer so you can see that in crossed polarizer analyzer here we can see optical activity light changed polarizationally changed and comes through the analyzer the same for a brain tissue in coaxial and crossed polarizer analyzer this one it's a photographer, ccd image of benin tumor adenoma of prostate gland tissue in coaxial and crossed polarizer analyzer this one is a tissue with benin and malignant formation so pre-cancer malignant formation of cancer of cervix uteri adenoma adenocarcinoma this one is my favorite this one is a blood plasma crystallite blood plasma in coaxial and crossed polarizer analyzer it's a so-called biological fluid and this one is a synovial fluid of a joint with rheumatoid arthritis in coaxial and crossed polarizer analyzer so we deal not only with some soft images we deal with pretty nice images so let's start about what can we do after the obtaining of this pre-cancer matrix elements what is the procedure of processing of these images because image is not a diagnosis and if it is possible to make some objective evaluation, not subjective because you know about the final diagnosis it's a histochemical methods when some very clever man or woman looking in the microscope and said, this is cancer this is not cancer and this one, I don't know exactly but maybe you can see and you see yes, it's maybe cancer okay, the third one, the fourth one and so on so we try to elaborate some objective mechanisms of evaluation so we deal with statistic analysis we have four statistical moments so-called mean value or average standard deviation or dispersion coefficient of skewness and coefficient of kurtosis for example, if we have some what does it mean, will mean value you know, yes, it's a formula standard deviation, it's a disturbances between mean value what is the skewness, skewness it's some like a tilt from left side to right side this is normal distribution, yeah, Gaussian this one with positive skewness this one with negative skewness okay here we have for example, this one is a Gaussian distribution this one is with higher kurtosis this one is with lower kurtosis but the mean value is the same you know this is very sensitive moment this one and this especially kurtosis you get some two images this equal mean value it's quite the same but due to calculation of these higher order moments you can evaluate some differences between of them it can be very small the second one it's a well known correlation analysis and autocorrelation analysis so you know this formula yes, it's a autocorrelation, it's a correlation of signal with itself what can we do with this for example, in order to diagnose so any okay any azimutically asymmetric distribution can be evaluated by correlation analysis in perpendicular direction x and y based on this we use the following methodology of autocorrelation processing for the distribution of values q q it can be stocks vector element millermatrix element and so on your signal here we have two different correlation function half width here you can see it's quite the same, but not the same and this asymmetric coefficient is this divided pmax on pmin this one pmax on pmin gives us evaluation for example we can compare between almost the same image almost the same two images for example with malign information and with normal the half width of the autocorrelation function plays main role okay we have told about fractality of biological tissue also we can calculate the power spectrum density of our images here it's a model image for example for stocks vector of bifringent cylinders this one is two dimensional autocorrelation function and this one is power spectrum density okay fractal analysis is based on the calculation of logarithmic dependencies of power spectra of values q and further mention dependencies are approximated by the least square method in curves f due to the form of this curve this one it doesn't don't show on here but this one it's approximation curve so the distribution is a fractal distribution is a fractal when there is only one stable inclination angle exists within two, three decades of sizes changes distribution a multi fractal when there is several stables inclination angles exist and the distribution are random when there is no stable inclination angles one can use this approach independently of statistic and autocorrelation okay we called these approaches statistic correlation and fractal we call it multifunctional laser polarimetry because not only one parameters are evaluated and described and several parameters can be simultaneously described and when one method is not very good for evaluations, the second one will be much better for example because also this one I want to keep in mind all the data and parameters q presented in previous lecture measured in previous lecture need to be quantitatively analyzed this is the message okay the last one yeah 20 minutes, okay it's more time to the question maybe so principles and methods of polarization and Mueller matrix mapping finally, here this is a Mueller polarimeter so called Stokes polarimeter whatever you want we don't speak about the procedure of measurement of Mueller matrix Stokes vector, yes, but Mueller matrix no the illumination conditions it's a linear polarization with azimus 0 45 degree 90 degree and right circular polarization analysis with respect to azimus analyzer is 0, 45 90 and 135 or it can be minus 45 yeah it's the same and right and left circular using this plate here this is procedure what we will do next Thursday for example, first step set transmission plane of analyzer with angles 0 and 90 degree here measured intensity of zero component here measured intensity of the 90 degree this is a calculation here we can obtain first Stokes vector element and the second one the second step 45 and 135 the analyzer 9 measure two distributions and calculate the third Stokes vector parameters normalized on the first and the third step is measure consist of measuring the fourth Stokes vector parameters and we obtain this one similarly, one can calculate other Stokes vectors for another illumination condition cause here so let the problem beam will be linearly polarized with azimus 0 degree here the whole algorithm this is Stokes vector calculation this is Miller matrix calculation using these Stokes vectors elements and this is the calculation of polarization parameters or so called polarization maps azimus and electricity polarization for azimus polarization you should divide the third Stokes vector element on the second one and do these rectangles the electricity parameters it depends on the fourth Stokes vector parameters here we can see the measured experimentally measured and analyzed three approach Miller matrix invariance optical and isotropy parameters for linear bifringens you can see it here this is a histogram of this distribution and this is a power spectrum of this distribution this is a circular bifringens namely optical activity is analogously situation if you could see here that this one is more regular than this one cause this power spectrum is more linear than this one so even just take a look on this picture this one is linear for Miller matrix elements for linear and circular bifringens with a necessary evaluation of this and here the last table for this is a possibilities of multifunctional polarimetry for evaluation of these Miller matrix elements this is calculated for statistic moments these two and the first statistic moment for the autocorrelation function and this one D is a standard deviation of power spectrum for two groups of patients pre-cancer and cancer states so and you could see that prostat cancer and you could see that here this is a balanced accuracy of the diagnosis these diagnostical methods and this balanced accuracy is on the level of 90 80 75 percent it's quite higher it's near the gold standard due to the histochemical methods thank you for your attention and all the participants are kindly invited to attend correlation optics conference in Chernivtsi in September and this year you could refer this website so thank you once more