Applications of Mueller Matrix Polarimetry to Biological and Agricultural Diagnostics: A Review

Abstract

The review contains a systematization of the main approaches to the practical implementation of Mueller matrix polarimetry and the prospects for its application in biology and agriculture. The most typical optical layouts for measuring the Mueller matrix of various objects, such as disperse systems, tissues and surface structures, are discussed. Mueller matrix measurements, being integrated into standard schemes of conventional optical methods, such as scatterometry, optical coherence tomography, fluorimetry, spectrophotometry and reflectometry, can significantly expand their capabilities in the characterization of biological systems and bioorganic materials. Additionally, microwave Mueller matrix polarimetry can be used for monitoring soil conditions and crop growth. The proposed systematization is aimed at outlining the conceptual directions for the development of non-invasive diagnostic tools based on measuring the Mueller matrix, primarily with a focus on biological research and agricultural practice.

1. Introduction

For the last several decades, non-destructive methods for studying biological systems and bioorganic materials have been increasingly used to analyze the composition of drugs, the structure of biological tissues, the microbiology of food products, the concentration of soils, the content of complex organic substances in water and soil and so on. However, the physical characteristics of many biological and food samples are inherently difficult to measure using traditional contact procedures due to the fact that samples can be sticky, very viscous or contain particles of different sizes and shapes. Consequently, there exists a need to develop reliable, multi-functional, automated sensors which are capable of rapidly and continuously monitoring the state of the system under test. This review is intended to help those involved in the development of sensing and analytical equipment for biological and agricultural tasks to find general information about the use of Mueller matrix polarimetry in characterizing bioorganic systems and materials.

In order to carry out non-destructive diagnostics, various optical methods based on the detection of transmitted or scattered light are used [1,2,3,4,5]. However, conventional optical instruments usually measure only the light intensity without taking into account changes in the polarization state of the light. Techniques that also detect polarization changes can provide additional information about the investigated medium and improve measurement accuracy. The Mueller matrix (4 × 4) most fully describes the interaction of an arbitrary object with fully or partially polarized electromagnetic radiation; therefore, the existing polarimetric methods can be generalized by the Mueller matrix formalism, and that generalization is termed Mueller matrix polarimetry (MMP) [6,7,8,9,10,11,12,13]. In the case of a scattering medium, a light scattering matrix (LSM), defined in the sense of the Mueller matrix (MM), is directly influenced by the physical characteristics of the scatterers and is very sensitive to the optical properties, shape and size distribution of scattering particles [3,4,5,14,15,16,17,18]. Thus, it is possible to obtain these characteristics by solving the inverse scattering problem. For example, when their size exceeds the wavelength of light, it becomes possible to determine whether they are separate monolithic particles or aggregates of particles smaller than the wavelength. Elucidation of the features of the angular and spectral dependences of matrix elements for various kinds of dispersed system, taking into account the aggregation of particles in the dispersed phase, makes it possible to develop a method for retrieving the parameters of the microphysical structure of the investigated dispersed system from the measured values of the Mueller matrix elements. More specifically, we can determine the number, size of particles and their state of aggregation.

MMP has recently begun to find wide application in many fields of science and technology, including physical chemistry, geophysics, biomedicine and pharmacology, technological control, environmental monitoring and agriculture. Non-destructive diagnostic methods based on the measurement of the Mueller matrix elements are widely used to obtain information on the properties of colloidal solutions and suspensions, rough surfaces of materials, nanoparticle coatings and composite materials, which can be multilayer systems of discrete scattering particles, as well as to study microbiological systems and biological tissues. These methods are relatively inexpensive to implement and can be easily automated, allowing quick results in laboratory research, industry or the field. So, technologies based on MMP are already being developed for non-destructive analysis in biology, biomedicine and agriculture.

There are quite a few thorough reviews describing the current state of MMP for biomedical applications [19,20,21,22,23,24,25]. However, when covering the principles of MM measurements, error analysis, optimization, calibration and, importantly, approaches to extracting practical information from the measured Mueller matrices, they mainly focused on the diagnostics of biological tissues.

Our review aims to fill a gap in the available MMP reviews by focusing on MM-based detection and characterization of microbiological entities, bioorganic solutions and dispersions, films and bulk materials. Additionally, we want to draw attention to the ability of the MM to respond to biomolecular orientation, aggregation and assembly with nanoparticles, which need to be tracked in biotechnology. Another basic goal of this review is to outline promising directions for the development of MMP devices for agriculture, including the control of the quality and composition of agricultural materials and food and monitoring crop vegetation and soil conditions.

Further, we present some examples of MMP applications. For instance, MMP was used to analyze blood for the presence of dengue virus [26]. MMP provides an efficient method for imaging localized structures, in particular for distinguishing the type of collagen organization [27]. In addition, MMP was employed to monitor changes in myocardial tissues and perform non-invasive measurement of glucose levels [28]. MMP, in combination with other various methods of quantitative analysis, can provide ample opportunities for the visualization of biological tissues; for example, it can distinguish between cancerous and healthy tissues, while being a cheaper method for the diagnostics of tissues before and after surgery, as shown in [29,30]. MMP can be successfully applied when tracking colonies of microorganisms [31]. The imaging contrasts of MM-derived parameters media can be used to characterize the anisotropic and isotropic structures of tissues [32]. It was confirmed that optical coherence tomography (OCT) supplemented with MMP can record polarization contrast images of any biological sample, in particular, soft tissues [33]. A combination of OCT and MMP was used in a novel device for measuring the anisotropy and bulk properties of tissue [34].

Optical diagnostic methods, including those based on MMP, have some agricultural applications. For example, these methods are used for diagnostics of dairy products [35,36,37,38,39]. The size distributions of fat droplets and casein aggregates were reconstructed from the block-diagonal elements of a scattering matrix of milk samples diluted by volume with water [36]. Using the size histograms, fat content and protein and the protein-to-fat ratio were estimated. MMP is capable of characterizing and authenticating vegetable oils [40,41]. MM imaging polarimetry can serve as a non-contact method for meat quality control [42]. MM spectropolarimetry around the absorption band of chlorophyll can be used for the non-destructive study of the molecular architecture of plant photosynthesis, which can be applied to vegetation monitoring [43].

In addition, MMP is suitable for determining the microphysical parameters of soils and soil suspensions. The ability of MMP to characterize soil suspensions was assessed with the aim to implement MMP as a unit for measuring the disperse composition in a robotic system for converting soil into a stable, high-performance, organic, chemical bioreactor for more controlled biomolecular interaction of nanoparticles and their adsorption by biological and mineral media [44]. A semi-empirical model of the averaged differential MM for microwave backscattering from bare soil surfaces in terms of moisture content and surface roughness was proposed in [45]. Measurements of polarized scattering of a carbon dioxide laser radiation from sandy soil enabled the retrieval of information about the dielectric constants and size of sand particles [46].

It is also worth noting the studies of protein solutions [47,48]. Using laser ellipsometry, organic molecular films formed at the interface of solids as a result of adsorption of a protein solution were studied in [47]. The results of a correlative experiment that was carried out to compare the interaction of human serum albumin and immunoglobulin G with sodium dodecyl sulfonate using polarized synchronous light scattering were in good agreement with dynamic light scattering measurements [48].

The works devoted to the metrological aspects of MMP, in particular, the calibration of MM polarimeters and the quantification of MMP results to determine the properties of biological samples, are valuable for the practical utilization of MMP [49,50,51,52,53,54,55,56].

It is important to note that MMP is no longer limited to only exploratory studies with unique laboratory instruments, and, at present, ready-to-use equipment for MMP is quite accessible and well described for customers. Commercial MMP systems supplied with a wide range of analysis software for specific applications provide easy-to-understand data for various MMP-related research and industries [57,58].

The cited references demonstrate the widespread use of MMP methods. Our review describes the foundations of Mueller matrix polarimetry and the ways of integrating it into existing schemes of optical diagnostics with an explanation of the corresponding restrictions and also analyzes specific examples of and prospects for the application of MMP methods in biology and agriculture.

2. Principles of Mueller Matrix Analysis

The Mueller matrix $M$ describes the transformation of the Stokes vector $\overrightarrow{S}$, which represents the state of light polarization due to the interaction of light with an object. The components of the Stokes vector that are called the Stokes parameters can be expressed in terms of the intensities of the basic polarized components of the light wave as follows:

$$\overrightarrow{S}=\left[\begin{array}{c}I\\ Q\\ U\\ V\end{array}\right]=\left[\begin{array}{c}{I}_x+I_y\\ I_x-I_y\\ I_{45°}-I_{-45°}\\ I_R-I_L\end{array}\right],$$

(1)

where $I, Q, U \mathrm{and} V$ are the Stokes parameters, $I_x, I_y \mathrm{and} I_{\pm 45°}$ are the intensities of linearly polarized components oriented along the corresponding directions ($x, y, \pm 45°)$ and $I_{R,L}$ are the intensities of right and left circular polarized components.

$${\overrightarrow{S}}_{out}=M {\overrightarrow{S}}_{in},$$

(2)

$$M=\left[\begin{array}{cc}\begin{array}{cc}{M}_{11}& M_{12}\\ M_{21}& M_{22}\end{array}& \begin{array}{cc}{M}_{13}& M_{14}\\ M_{23}& M_{24}\end{array}\\ \begin{array}{cc}{M}_{31}& M_{32}\\ M_{41}& M_{42}\end{array}& \begin{array}{cc}{M}_{33}& M_{34}\\ M_{43}& M_{44}\end{array}\end{array}\right],$$

(3)

For more details on the algebraic aspects of the Mueller–Stokes formalism, see [59,60].

In the case of dispersed media, the light scattering matrix (LSM) defined as the Mueller matrix (MM) contains the most complete information on particles scattering light that is available for static scattering. The LSM elements, being functions of the scattering angle, also depend on the wavelength of the probe radiation, optical properties and size distribution of the dispersed entities [3,4,5,14,15,16,17,18,61]. In the particular case of spherical particles, it has a block-diagonal structure:

$$M=\left[\begin{array}{cc}\begin{array}{cc}{M}_{11}& M_{12}\\ M_{21}& M_{22}\end{array}& \begin{array}{cc}0 & 0\\ 0 & 0\end{array}\\ \begin{array}{cc}0 & 0\\ 0 & 0\end{array}& \begin{array}{cc}{M}_{33}& M_{34}\\ M_{43}& M_{44}\end{array}\end{array}\right],$$

(4)

where $M_{11}=M_{22}$, $M_{12}=M_{21}$, $M_{34}=-M_{43}$ and $M_{33}=M_{44}$. The physical meaning of the element $M_{11}\left(\theta \right)$ is the scattering indicatrix, that is, the angular distribution of the scattered light intensity ($\theta$ is the scattering angle).

For example, the $M_{34}$ element normalized to $M_{11}$ or $M_{33}$ is sensitive to changes in the morphological properties of bacterial colonies during growth [16,62], while the normalized $M_{14}$ element is sensitive to changes in the structure of chiral polymers, such as DNA [16,63,64].

To better understand how the angular variations are related to the properties of the medium, numerical modeling of the angular-resolved radiation transfer problem was considered in [65]. It was found that light is anisotropically reflected from all media encountered in practice, and that the angular changes depend on the absorption and transmission of the medium, as well as on the angular distribution of the incident light.

Particle diagnostics using the MM are carried out, in fact, by the mathematical processing of its elements measured for scattering, absorption and emission of light in accordance with the selected structural model of the investigated medium or sample in order to extract the values of its microphysical parameters [4]. The simplest structural model is a collection of spherical particles. However, particles can be both solid elements and clusters of such particles, as well as have different shapes and sizes, to which the MM is also sensitive [5]. Various mathematical approaches are used to solve the inverse problem from the MM. Most often, it is decompositions of directly measured MM [11,13,20,60], in particular, using group theory [66] or stochastic simulations by the Monte Carlo method [67,68,69,70]. Monte Carlo simulations of MMs for multiple scattering media are very important in interpreting MMs measured for turbid media such as biological tissues [23,71].

It is worth dwelling on some details of the MM polar decomposition method [20,60]. Lu and Chipman proposed a procedure for decomposing a MM into a successive product of three basis matrices [72].

$$M\equiv M_{11}\left[\begin{array}{cc}1& {\overrightarrow{D}}^T\\ \overrightarrow{P}& m\end{array}\right]=M_{\Delta }{M}_R{M}_D,$$

(5)

The original matrix $M$ is partitioned into the polarizance vector $\overrightarrow{P}$, the diattenuation vector $\overrightarrow{D}$:

$$\overrightarrow{P}\equiv \frac{1}{M_{11}}{\left[\begin{array}{ccc}{M}_{21}& M_{31}& M_{41}\end{array}\right]}^T, \overrightarrow{D}\equiv \frac{1}{M_{11}}{\left[\begin{array}{ccc}{M}_{12}& M_{13}& M_{14}\end{array}\right]}^T$$

(6)

and 3 × 3 submatrix $m$:

$$m\equiv \frac{1}{M_{11}}\left[\begin{array}{ccc}{M}_{22}& M_{23}& M_{24}\\ M_{32}& M_{33}& M_{34}\\ M_{42}& M_{43}& M_{44}\end{array}\right].$$

(7)

The matrices $M_{\Delta }$, $M_R$ and $M_D$ have the following form:

$$M_D=M_{11}\left[\begin{array}{cc}1& {\overrightarrow{D}}^T\\ \overrightarrow{D}& m_D\end{array}\right], M_R=\left[\begin{array}{cc}1& {\overrightarrow{0}}^T\\ \overrightarrow{0}& m_R\end{array}\right], M_{\Delta }=\left[\begin{array}{cc}1& {\overrightarrow{0}}^T\\ {\overrightarrow{P}}_{\Delta }& m_{\Delta }\end{array}\right].$$

(8)

A set of polarimetric parameters that are related to the intrinsic properties of the tissue can be derived from this representation of the MM. These parameters are considered to be as follows [20]:

Depolarization:

$$\Delta =1-\frac{\left|\mathrm{Tr}\left(M_{\Delta }\right)-1\right|}{3},$$

(9)

Diattenuation:

$$d=\frac{1}{M\left(1,1\right)}\sqrt{M{\left(1,2\right)}^2+M{\left(1,3\right)}^2+M{\left(1,4\right)}^2},$$

(10)

Total retardance:

$$R={\cos }^{-1}\left\{\frac{\mathrm{Tr}\left(M_R\right)}{2}-1\right\},$$

(11)

Linear retardance:

$$\delta ={\cos }^{-1}\left\{\sqrt{{\left[M_R\left(2,2\right)+M_R\left(3,3\right)\right]}^2+{\left[M_R\left(3,2\right)-M_R\left(2,3\right)\right]}^2}-1\right\},$$

(12)

Optical rotation:

$$\psi ={\tan }^{-1}\left\{\frac{M_R\left(3,2\right)-M_R\left(2,3\right)}{M_R\left(2,2\right)+M_R\left(3,3\right)}\right\}$$

(13)

Such a representation of the MM and the parameters thus defined are especially informative in tissue diagnostics.

For light transmitted through a homogeneous, anisotropic material, the polarization effects are described by a set of eight parameters with a clear physical interpretation: circular dichroism ($CD$), circular birefringence ($CB$), horizontal linear dichroism ($LD$), 45° linear dichroism (${LD}^{\prime }$), horizontal linear birefringence ($LB$), 45° linear birefringence (${LB}^{\prime }$), isotropic retardation ($\eta$) and isotropic amplitude absorption ($\kappa$). In terms of these parameters, the MM of a non-depolarizing sample can be written as a matrix exponent [8]:

$$M=e^L, L=\left[\begin{array}{cc}\begin{array}{cc}-\kappa & -LD\\ -LD& -\kappa \end{array}& \begin{array}{cc}-{LD}^{\prime }& CD\\ CB& {LB}^{\prime }\end{array}\\ \begin{array}{cc}-{LD}^{\prime }& -CB\\ CD& -{LB}^{\prime }\end{array}& \begin{array}{cc}-\kappa & -LB\\ LB& -\kappa \end{array}\end{array}\right],$$

(14)

If an anisotropic material is only transversely homogeneous, then the differential expansion of the MM can be applied to analyze the evolution of its polarization properties along the direction of light propagation [60].

In the context of the diagnostics of organic substances, the results of comparing three approaches to determine the parameters of optical chirality [12]—direct evaluation from the MM elements, differential decomposition of the MM and electromagnetic modeling using Tellegen’s constitutive relations—may be of interest.

The operation principle of the polarimetric devices measuring the MM (MM polarimeters) can be illustrated by a general block diagram (Figure 1).

In general, an MM polarimeter consists of a light source (LS), a polarization state generator (PSG), a test sample cuvette (S), a polarization state analyzer (PSA) and a photodetector (PD). Light sources can vary depending on the purpose of the polarimetric instrument and the accuracy of the measurements, from broadband lamps and super luminescent diodes [12,73,74,75] to lasers [14,61], including tunable lasers [76]. A polarization state generator (PSG) is a transmissive optical system that allows the generation of any arbitrary polarization state (generally elliptical) and is used to convert the polarization of source radiation which is not initially polarized or has constant polarization into a set of polarized light states that is required for measuring the Mueller matrix of an arbitrary object. They can have different designs; the most common PSG in polarimetric instruments consists of a combination of phase modulators, phase plates and a linear polarizer [14,15,74,75,76]. Note that PSGs based on liquid crystals are very promising [74,77], since they are compact and have no moving parts. On the basis of full Poincaré beams, which represent all possible completely polarized states of polarization in their cross-section and can be generated by focusing a laser beam on the front face of a uniaxial crystal, it is possible to implement a parallel-type PSG [78].

After the PSG, the polarization state of the radiation is changed (time-modulated). Two ways are possible here:

• Polarization is modulated continuously or pulse-modulated (periodically, as a rule);
• Polarization sequentially passes a fixed, discrete set of time-constant states.

In the first case, the Stokes vector of radiation, after passing through the PSG to be incident on the object, has the form:

$$S_i=y_i\left(t\right), i=1\dots 4$$

(15)

where $y_i\left(t\right)$ are known time functions determined by the modulation method. The Stokes vector at the output of the object is expressed as follows:

$$S_i^{*}\left(t\right)={\displaystyle \sum }_{k=1}^4{M}_{ik}{S}_k={\displaystyle \sum }_{k=1}^4{M}_{ik}{y}_k\left(t\right), i=1\dots 4$$

(16)

where $M$ is the MM of the object.

If the functions $y_i\left(t\right)$ are linearly independent, then the matrix elements $M_{ik}$ can be obtained as the corresponding coefficients of the expansions of the measured Stokes vector components $S_i^{*}$ in these functions.

In the second case, it is necessary to set at least four discrete polarization states of the input radiation, which are described by linearly independent Stokes vectors ${\overrightarrow{S}}^{\left(j\right)}$ ($j=1\dots 4$). Having measured the four corresponding output Stokes vectors ${\overrightarrow{S}}^{*\left(j\right)}$ ($j=1\dots 4$), we obtain a system of 16 linear algebraic equations:

$$S_i^{*\left(j\right)}={\displaystyle \sum }_{k=1}^4{M}_{ik}{S}_k^{\left(j\right)}, i,j=1\dots 4$$

(17)

The solution of this system gives the values of all 16 elements of the Muller matrix of the object.

Similar to a PSG, a PSA is also a combination of phase optical elements (phase modulators, phase plates) and a linear polarizer, which serves to measure the components of the Stokes vector of radiation coming out of an object. For instance, a PSA using a certain set of relative azimuthal orientations of a linear polarizer together with a quarter-wave plate enables complete Stokes vector measurements. Actually, this PSA successively implements particular cases of a linear polarizer oriented at 0°, 90° and ±45° and a circular polarizer.

For spectroscopic measurements of the MM, it is attractive to use polarimeters with four photoelastic modulators, two each in the PSG and PSA, since modulators of this type are easily adjusted to different wavelengths [79]. Having no moving parts, they perform relatively fast MM measurements, which, additionally, can be made with spatial resolution.

Error analysis of a MM polarimeter carried out in [49] provided a basis for the calibration procedure in order to correct angular misalignments and compensate for retardance errors and, thus, obtain accurate values of the Mueller matrix elements.

It is worth noting that the sample type—biological tissue, solid surface or aqueous suspension, etc.—determines the scheme for receiving light after interaction with the sample (S). Radiation scattered or reflected from the sample can be detected either directly or using a collecting and directing optical system. For example, weakly scattering samples can be placed in immersion cuvettes. In many cases, it is convenient to use standard spectroscopic plane-parallel cells, which require operation together with lenses. Lenses can be moved to focus light from different areas of the sample. The photodetector (PD) is used in conjunction with a signal acquisition system to interface with a computer to determine the MM based on digital signal processing algorithms.

The block diagram (Figure 1) shows that the measurement of the Mueller matrix of an object requires the introduction of polarimetric blocks PSG and PSA into the optical system before and after the object. The next section shows general schemes of the most common optical instruments (scatterometers, OCT systems, transmission or fluorescence spectrometers, ellipsometers) used to study various types of bioorganic systems, which, when supplemented with polarimetric elements, enable the measurement of the complete Mueller matrix.

3. Basic Schemes for Using Mueller Matrix Polarimetry in Optical Diagnostics of Biological and Bioorganic Systems

Optical methods of non-destructive diagnostics can be divided into four groups. The first group includes methods based on measuring the angular distribution of light scattered by a sample (scatterometers) and the polarization features of the scattered light. The second group is imaging systems for densely structured objects, such as biological tissues, in particular those which detect backscattered light from a narrow layer in depth through low coherence interferometry; this is called optical coherence tomography (OCT). The third group includes spectrophotometers that measure the dependence of the transmission/absorption of light by a sample of the light wavelength, that is, spectral methods. The fourth group is devoted to fluorescence spectrometers separately. Considering the literary sources, the schematic features of all these groups and the conditions for their use are analyzed below. To these techniques, the general principle of modifying the optical design by surrounding the studied sample with polarimetric blocks (PSG and PSA) can be applied in order to expand measurement capabilities from light intensity alone to the complete Mueller matrix.

3.1. Mueller Matrix Scatterometry

Scatterometry is a non-destructive diagnostic method based on the measurement of light scattered by a sample. This method measures the intensity of the light scattered by the sample. The advantages of this method lie in the relative simplicity and the flexibility in the choice of the light sources and photodetectors; both a monochromatic laser with various wavelengths and broadband lamps can be used.

Measurement of the angular dependence of the scattered light intensity can be, in principle, used to determine the size and number of particles contained in the sample if all these particles are the same and separate (in the absence of aggregation). However, intensity measurement at one light wavelength is unable to give complete information on the dispersed composition of the sample. There exist two ways of solving this problem:

• Use of multi-wavelength sources. This method is called multi-wavelength scatterometry;
• Use of MM measurements. Such a method is called polarimetric scatterometry or MM scatterometry (MMS).

Performed for a set of different wavelengths, MMS (spectroscopic MMS) is able to provide the most complete information about the scattering medium. The introduction of additional, polarimetric, optical elements into the scatterometer layout (Figure 2) allows the modulation and analysis of the light polarization in order to determine the MM [15,61,80]. Further, using the measured angular dependences of the MM, it is possible to solve the inverse scattering problem, which can provide comprehensive information about the distribution, quantity and size of particles contained in the sample. Therefore, the use of polarimetric scatterometry in applied research, including for technological control, biomedicine and agriculture, looks quite promising.

Scatterometers measuring a wide range of light scattering angles can have a goniometric design where the receiving arm makes angular movements (Figure 2).

Alternatively, fixed array photodetectors can be used to measure the angular distribution of the scattered light. To enhance the scattering intensity, a cylindrical cuvette, where the sample cell is surrounded by an immersion liquid, is often used.

An MM scatterometer similar to that shown in Figure 2 was used in experiments with aqueous NaCl solutions to observe the presence of stochastic clusters consisting of air nanobubbles [80]. Using this setup, MM measurements of immunoglobulin dispersions in water and aqueous solution of ethanol revealed aggregation of immunoglobulin molecules and allowed the determination of the fractal dimension of immunoglobulin aggregates [81]. MMS also allows the determination of the shape and size of biological cells, such as B cells [61], and microbiological entities [16,62,82].

Note that, to determine the properties of turbid media, for example, the concentration of particles, turbidimetry, is routinely used. This technique measures the light intensity at a certain wavelength passed through a cuvette containing dispersion. In this method, it is convenient that any photometer or spectrophotometer is suitable for measurements. The disadvantage is low accuracy; as a result of which, this method should be used only in cases where other methods do not give satisfactory results. A similar method called nephelometry differs from turbidimetry in that the scattered light flux is measured. This method requires that the suspended particles are insoluble and do not sediment. Turbidimetry and nephelometry can also be used in combination with MMP. In this case, they are classified as polarimetric scatterometry.

It has been shown that the method of tomographic Mueller scatterometry (TMS) collects more scattering information than conventional reflectometry, providing better sensitivity and measurement accuracy [83]. This method was specially developed for use in metrology down to the scale of tens of nanometers as a fast, inexpensive and non-destructive metrology method which is very useful for sustainable nanoproduction. TMS uses a double rotating compensator configuration and illuminates the nanostructure sequentially under plane-wave test conditions with different illumination directions. The polarized scattering along each observation direction is measured so as to determine the corresponding MMs.

3.2. Transmission Mueller Matrix Spectropolarimetry

Spectroscopic methods of analysis are based on the ability of atoms and molecules of a substance to differently emit, absorb or scatter electromagnetic radiation depending on the wavelength. The main advantages of spectroscopy are as follows:

• High sensitivity and accuracy;
• High measurement speed;
• Multicomponent analysis;
• Universality—components of interest can be defined in a variety of objects.

Spectrophotometry explores the spectral properties of the electromagnetic radiation reflected or transmitted by the material using a special device (photometer) that measures the intensity at different wavelengths. The most common spectrophotometers are near-infrared (IR), visible and ultraviolet (UV), albeit microwave and X-ray spectrophotometers also exist. Spectrophotometers are distinguished as single-beam and double-beam. The single-beam spectrophotometer measures the relative intensity of the light beam before and after the introduction of the studied sample. A dual-beam spectrophotometer compares the intensity between two light paths, one of which is directed to the sample under study, the other to the reference. In addition, spectrophotometers can be subdivided into scanning and array. The scanning spectrophotometer uses one detector and a movable dispersive element, while the array spectrophotometer uses an array of detectors and a stationary dispersive element. The combination of spectrophotometry with Mueller matrix polarimetry enables the measurement of optical anisotropy spectra, which provide additional information on the configuration of complex organic molecules and, for example, the secondary structure of biopolymers. Such combined systems are called spectropolarimeters. A possible layout using a single-beam scanning spectrophotometer is shown in Figure 3.

A dual-rotating retarder polarimeter configured to measure the MM in the spectral range from 3 to 12 µm is an effective tool for characterizing transmissive bulk materials [84]. A setup for MM measurements in terahertz time-domain spectroscopy was proposed in [85].

In bioorganic research, spectropolarimetry with incomplete polarization measurements is commonly used, that is, not the entire MM, but, specifically, the circular dichronism (CD) is measured. Compared to MM spectropolarimetry, CD spectropolarimetry has some disadvantages in the form of artifacts arising due to macroscopic anisotropy (such as linear birefringence) and linear dichronism in the measurement of polarization spectra. To solve this problem, the occurrence of artifacts can be combatted by equipping the circular dichronism (CD) spectropolarimeter with additional software, a step controller, an analyzer and a specially designed solid-state holder for the samples under study with the ability to rotate [86]. A new scheme for a CD spectropolarimeter, which eliminates the above-mentioned problem, was developed in [73].

Spectroscopic measurements of the transmission MM in the spectral range of 210–1690 nm were used for the study of chiral phenomena in [12]. Three approaches to determining the chirality parameters were discussed. In the first approach, applicable in the absence of linear polarization effects, circular birefringence and circular dichroism were estimated directly from the MM elements. The second method used differential expansion, which allows the unambiguous separation of the chirality parameters from linear anisotropic parameters, as well as from depolarization, provided that the sample is homogeneous along the optical path. Finally, electromagnetic modeling using Tellegen’s constitutive relations was presented. The latter method also allows for structural effects. Three methods for quantifying optical chirality were demonstrated for selected materials, including sugar solutions, α-silica, liquid crystals, beetle cuticles and films of cellulose nanocrystals. Note that, in the study described above, spectroellipsometry means the same as spectropolarimetry, since the Mueller matrix spectra were measured for transmission, not reflection, as is customary when the term spectroellipsometry is used.

The cited studies show that the elements of the MM have specific spectral dependences, which suggests that MM spectropolarimetry provides significantly more information about the investigated substance than conventional spectrophotometry without polarization measurements or MMP at one wavelength.

3.3. Mueller Matrix Imaging Polarimetry and Optical Coherence Tomography

MM imaging polarimetry (MMIP) consists of measuring spatially dependent polarization properties of samples in the form of 2D patterns of MM elements, generally with the aid of matrix photodetectors such as CCD cameras [22,87,88]. Depending on the properties of the sample and the structures to be studied inside it, MM images can be recorded in transmission [87] and reflection [88] or backscatter configurations [22,33]. Thin tissue sections can be visualized using transmission MM microscopy, and, for bulk tissue samples, backscatter observation is most suitable. MMIP can provide essential details of tissue microstructure [22], cell functions and interactions between cellular structures [88].

Optical coherence tomography (OCT) refers to a class of optical imaging techniques used to obtain micrometer-resolution 2D and 3D images of optically scattering media, such as biological tissues. This method is based on interferometry with a short coherence length, typically realized in the near-infrared range (NIR, 800–1300 nm). Unlike classical laser interferometry with a long coherence length, in OCT, interference occurs within a few micrometers due to the use of light sources with a wide bandwidth. Time-domain optical coherence tomography is based on the interference of low-coherence probing optical radiation, backscattered from the inhomogeneities of the medium and reflected from the reference mirror. In OCT, the coherence condition for the reference and backscattered light can be met within a thin layer of the sample. By adjusting the path delay for the reference beam, it is possible to scan through the depth of the sample and, thus, obtain a volumetric image.

The use of polarimetry with OCT does not necessarily imply the measurements of the Mueller matrix. Thus, two approaches: polarization-sensitive OCT (PS-OCT) and Mueller matrix OCT (MM-OCT) were compared in [89]. These approaches perform somewhat different tasks: for example, PS-OCT enables one to obtain detailed images of the sample under study, while MM-OCT enables one to examine its properties. For the measurement of Jones or Mueller matrices, a multichannel PS-OCT with dynamic calibration and improved by using a fiber-optic system was developed in [90].

The key advantages of OCT are as follows:

• Real-time images of subsurface objects with a resolution close to microscopic;
• Instant, direct visualization of tissue morphology;
• No need for preliminary sample preparation;
• Non-invasiveness;
• Absence of ionizing radiation.

Comprehensive information about the optical properties of tissue can be obtained by integrating MMIP and PS-OCT. Figure 4 shows a combined PS-OCT and MMIP proposed in [34].

Using the setup in Figure 4, cross-sectional images of local tissue birefringence, which are provided by PS-OCT, can be supplemented with the bulk properties of tissue measured by the MMIP system.

Note that polarimetric elements (polarizers together with waveplates) can be installed in the probing arm, as well as in the reference arms of the standard OCT scheme, so that the combinations of polarization states needed to determine the complete MM can be set in both arms. Thus, not only tissue features, such as optical anisotropy, but also the complete MM can be imaged, which is the purpose of MM-OCT [89].

The quality of MM images is important for further sample quantification, which necessitates the calibration and quality assessment of the resulting MM [56].

3.4. Mueller Matrix Fluorimetry

Fluorimetry is a highly sensitive method based on measuring the intensity of fluorescence, that is, the ability of a substance to emit light when absorbing external electromagnetic radiation, mostly at a wavelength longer than that of the absorbed radiation. This method has a high sensitivity. However, this leads to the main disadvantage of the method; because of the high sensitivity, fluorimetry detects not only the substance of interest but also all possible impurities that cause background radiation. Consequently, cleaning requirements increase, and sample preparation becomes more difficult. It is also worth noting that not all substances are fluorophores; thus, fluorimetry has certain limits of applicability.

The sources of fluorescence excitation in substances can be different, but, as a rule, ultraviolet radiation sources (UV, 10–400 nm) are used. According to the method of isolating fluorescent radiation from the incident radiation, two main groups of fluorometric devices are distinguished: filter fluorometers using optical filters and spectrofluorometers using monochromators. The detectors used in fluorimeters can be either single-channel (the intensity of only one wavelength is measured) or multichannel (the intensity of all wavelengths is measured simultaneously); in schemes with multichannel detectors, filters and monochromators can be excluded.

The principles underlying the use of fluorescence polarization to study protein–protein and protein–DNA interactions are outlined in [91]. The polarization properties of fluorescence contain potentially valuable information on the chemical composition, molecular structure and orientation and local environment of fluorescent elements. A method that combines both fluorimetry and polarimetry can be appropriately designated as fluoripolarimetry. The method is a very powerful diagnostic tool that is quite simple and inexpensive.

It is worth noting that hybrid supramolecular materials have been studied using a combined method that combines spectral fluorometry and MMP [92]. Spectroscopic fluorescence MMP, together with inverse analysis, made it possible to determine the organization and orientation of achiral fluorescent dye molecules around a supramolecular nanotube and, thus, confirmed its promise for the characterization of complex hybrid materials.

A typical layout of a polarimetric fluorescence spectrometer involving MM measurement is shown in Figure 5.

Note that, when using a wavelength tunable source to excite fluorescence, all polarimetric elements making up the PSG and PSA must be achromatic. Such an instrument can be termed an MM spectrofluorimeter.

MM fluorescence spectroscopy has been used to identify precancerous tissue areas [50,51].

From the above, we can conclude that, within its applicability limits, which are quite wide, fluoripolarimetry is a no less powerful method than spectropolarimetry, since it is based on a similar principle, that is, the measurement of the spectral dependences of the MM elements through the use of polarimetric elements.

3.5. Reflection Mueller Matrix Ellipsometry

Ellipsometry is a highly sensitive method for determining the optical parameters of reflecting samples based on the relative change, as a result of reflection, in the amplitudes and phases of the components of the electric field of an electromagnetic wave, parallel and transverse to the plane of incidence. Simultaneous measurement of the amplitude and phase changes of an electromagnetic wave, expressed by the so-called ellipsometric parameters Ψ and Δ [93], for example, allows precise determination of both the thickness and optical constants of the film material on the surface. Ellipsometry generalized to obtain the full MM (MM ellipsometry) provides a higher stability of determining the material optical properties in the case of diffusely reflecting samples than ellipsometry measuring only two ellipsometric parameters [94]. A general scheme of an MM ellipsometer is shown in Figure 6.

Spectral ellipsometers (spectroellipsometers) have significant capabilities in the characterization of organic molecular structures and biological systems on a solid substrate. For example, MM spectroscopic ellipsometry was used to study the polarization and depolarization properties of chiral films [95]. As a light source, lamps of various types, LEDs and lasers are employed in different spectral regions. Multi-laser ellipsometers have the potential to be well conditioned [96]. In spectroellipsometers, optical monochromators and filters can be used in analogy with other spectral methods [94].

Spectroellipsometry in the IR range is relevant for the analysis of multicomponent organic materials with characteristic IR absorption lines. The reflected Mueller matrix elements can be measured in a spectral range of 9–11 µm using an IR spectroellipsometer based on a tunable CO₂ laser [76]. To work with thick samples, an attenuated total reflection (ATR) device in combination with achromatic polarimetric elements can be installed into a standard Fourier-transform infrared (FTIR) spectrometer to measure the reflection MM of bulk materials in the spectral range from 3 to 14 μm [97]. A scheme of an ATR-FTIR spectrometer for measuring the IR spectra of MM elements of the sample placed on the ATR surface is shown in Figure 7.

An IR laser or FTIR MM spectroellipsometers are suitable for the complex analysis of organic bulk materials, films and liquids [98,99,100].

The performance of an ellipsometer can be improved by particular technical solutions. Multichannel ellipsometry is increasingly used [101,102,103,104]. For example, a coupled-phase polarization modulator, together with a multichannel polarimeter, allows Mueller matrix measurements without choppers and lock-in amplifiers [105]. Polarization modulation using photoelastic modulators (PEM) can provide a high measurement speed and sensitivity [106].

4. Applications of MMP to Biology and Agriculture

The considered examples of MMP implementation show that MMP is a powerful tool for non-invasive diagnostics of bioorganic systems, especially in combination with other optical techniques, significantly expanding their capabilities. The above review of MMP installations allows us to systematize optical methods supplemented by MM measurements into groups depending on:

• Geometry of the sample—volumetric (MM scatterometry, MM spectrophotometry, MM fluorometry) and surface (MM-OCT and MM ellipsometry);
• Properties of incoming radiation—spectral (spectrophotometry and spectroscopic MM scatterometry, MM fluorometry and MM ellipsometry) and non-spectral (MM-OCT and single-wavelength MM scatterometry, MM fluorometry and MM ellipsometry);
• Received information—visual (MM-OCT and other methods of polarization-sensitive imaging) and structural (all methods that measure the MM with subsequent retrieval of the microphysical parameters of the sample using inverse analysis);
• Operating conditions—stationary and mobile.

Table 1. Main types of biological and agricultural sample and MMP methods for their characterization.

Sample Type	Methods	Sample Properties	References
Organic materials and molecular systems	MM ellipsometry and Transmission MMP	Complex refractive index, film thickness,	[93,97]
		Anisotropy, orientation of polymer molecules and fibers	[8,94,95,107,108,109,110,111]
	MM scatterometry, Transmission MMP and MM fluorometry	Structure and size of molecular aggregates	[64,81]
		Chirality, molecular structure and orientation	[8,12,91,92,112]
	MM IR spectroscopy	Spectral properties, composition	[97,98,99,100]
Cell and microbiological systems	MM scatterometry	Size and shape of cells and microorganisms,	[16,61,62,82,113]
		structural changes in DNA	[16,63,64]
	MM imaging polarimetry	Distinguishing colonies	[31]
Tissues	MM-OCT and MM imaging polarimetry, MM fluorometry	Optical polarization properties,	[20,32,33,34]
		microstructural characteristics,	[27,54]
		cell properties,	[56,88]
		pathology detection,	[24,25,28,29,30,50,114]
		microbial contamination	[26]
Milk	MM scatterometry	Size distribution,	[35,36]
		fat and protein content
Vegetable oils	Transmission MMP	Optical polarization properties,	[40,41]
		authenticity
Meat	MM imaging polarimetry	Freshness assessment	[42]
Plants	MM spectopolarimetry Microwave MMP	Chlorophyll organization	[43]
		Vegetation	[70,115,116]
Soils	MM scatterometry	Particle size and optical properties	[46]
	Microwave MMP	Moisture content, surface roughness	[45]

contains brief information on MMP methods applicable to the characterization of the main types of biological and agricultural sample and the resulting properties.

The prospects for the application of the MMP-supplemented methods described above to biology, biomedicine and agriculture are discussed below. Based on the material studied, we can point out the main research areas where MMP is increasingly used. Aiming to counter the lack of generalized information on using MMP in agriculture, we have schematically illustrated the main agricultural applications of MMP by a block diagram in Figure 8.

4.1. Studying the Structure of Organic Materials

MMP can be a useful tool for studying various materials in order to assess the quality of products made from them and, subsequently, detect defects. An experimental procedure using MMP, which enables studying foams, was described in [117]. The use of MM spectroscopic ellipsometry to study the anisotropy of materials, in particular, polyethylene terephthalate (PET) was proposed in [94]; this method proved to be successful in obtaining additional information about the anisotropy of materials. MMP was used to study films of chiral nanocrystalline cellulose [95] and to measure the anisotropy and orientation of liquid crystals [107]. Strain-induced birefringence shows linear relationships with both strain and orientation of chain segments. MM scatterometry was used to compare the polarization properties of white fabric and white wood [108]. Linear and circular birefringence, as well as circular dichroism in chiral nanocellulose films obtained by self-assembly of cellulose nanocrystals, were estimated using MMP [109]. Optical chirality parameters were determined from MM measured for organic materials such as sugar solutions and liquid crystals [12]. The MM-based measurement of the intensity difference between right and left circular polarizations in light scattered from an optically active medium is sensitive to the molecular conformation of complex biopolymers [63].

MMP can be used to quantify the anisotropy of plant fibers by the MM differential decomposition [110]. Measuring the topology of polymer fiber scaffolds by MMP is of considerable interest for tissue engineering [111]. It has been shown that the MM responds to the orientation of the fibers and their mechanical properties, which confirms the accuracy of the MMP method is sufficient for evaluating fiber structures.

Tomographic Mueller scatterometry (TMS) can visualize the topology of structures down to tens of nanometers in size, which is promising for non-destructive testing in nano-manufacturing [83].

IR laser spectroellipsometry [76] and polarimetric FTIR spectroscopy [97,98,99,100] aiming to measure the Mueller matrix of liquid and solid organic materials would be suitable, in particular, for complex analysis of fodders to determine fat, protein, fiber, ash or grain gluten content.

MMP is very important in studying protein systems. For example, the fractal structure of protein aggregates can be determined from the light scattering matrix [81]. Additionally, fluorescence polarization measurements [91], especially in the form of the Mueller matrix [92], provide information on molecular orientation and mobility and the processes that modulate them, including receptor–ligand interactions, protein–protein and protein–nucleic acid interactions, proteolysis and fluidity membranes [118].

4.2. Microbiological Research

MMP is relevant for the detection of viruses and microorganisms. For example, MMP was used to analyze blood for the presence of the dengue virus [19]. It was found that blood samples with dengue fever virus have a higher depolarization factor than normal samples, which, hypothetically, could allow the detection of this virus in the early stages of infection. Changes in the growth of rod-shaped bacteria were studied using polarimetric scatterometry [62]. The block-diagonal elements of MM are sensitive to the size and shape of microbiological entities, as shown in the example of microalgae in [113]. Quantitative parameters for distinguishing between different bacterial colonies can be acquired from MM images using the MM polar decomposition method, frequency distribution histograms and the central moment analysis method [31]. Water-polarized reflectance was investigated to retrieve the properties of oceanic constituents (suspended organic matter and phytoplankton), primarily their concentration and biomass [119].

4.3. Biological Tissues

The concepts and applications of tissue MMP were concisely reviewed in [20]. Inverse analysis of MMs based on scattering theory and MM polar decomposition was considered. Several medium-specific polarimetric parameters that are practical for recognizing tissue structures and their changes can be derived from the polar decomposition of MM: diattenuation, depolarization (linear, circular and total), linear retardance (and its orientation) and optical rotation.

MMP increases the quality of visualization of biological tissues and, in particular, makes it possible to distinguish between cancerous and healthy tissues, while being, at the same time, a cheaper method for analysis of tissues before and after surgery [29,30].

Microscopic imaging based on MM-derived parameters related to depolarization and retardance proved to be effective in assessing the polarization properties and structural features of biological tissues and were helpful for diagnosing pathological tissue samples [32]. In particular, measuring the retardance and depolarization of thin biopsies by MMP can be used to quantify human liver fibrosis [116]. MMP was tested as a non-invasive method for the characterization of various dermatological diseases [24,25]. The depolarization and retardance were shown to be important polarization metrics, indicating changes in the fibrous structure of skin tissues. OCT integrated with MMP can record tissue anisotropies and is capable of measuring the polarization contrast of any biological sample, in particular, soft tissue samples [33]. MM-based polarization imaging was used for quantitative digital screening of polycrystalline structures of biological tissues in vitro [54]. It was shown that the spatial distributions of the phase of light and optical anisotropy of scattering, which are inherent in myocardial fibrillar networks at different stages of necrosis, can be effectively used as a quantitative marker of the stages of myosin fibril degradation. The use of MM calculus facilitates the calibration of fiber-optic PS-OCT to quantitatively measure the birefringence and optical axis orientation of tissues [55].

Monte Carlo simulations showed the possibility of determining the glucose concentration in turbid media using MMs [69]. Similar studies showed that linear polarization and total intensity are more sensitive to increased glucose concentration in backscatter than in forward scatter in highly turbid environments, indicating that backscatter geometry may be preferable for potential glucose detection in biomedical diagnostics. At the same time, comparative measurements with optically inactive glycerol showed that the refractive index matching effect, rather than the chiral nature of the solute, dominates the observed optical rotation caused by glucose in a highly turbid medium [112]. By multi-region segmentation of polarized light images, a radiofrequency-ablated lesion in myocardial tissue was quantified [120].

MM measurements for fluorescence and elastic scattering in the backward direction were used to study connective tissue regions of human cervical tissue [50,51]. Fluorescence linear and circular diattenuation, together with fluorescence linear and circular polarizance, were used as parameters derived from experimental MM. Significant differences were found between precancerous and normal tissues in the fluorescence polarimetric parameters—fluorescence linear diattenuation and linear polarizance—and in the diattenuation of the elastic scattering. These parameters are much lower at higher stages of precancer, which is explained by the loss of the anisotropic orientation of the molecular structures of collagens in precancerous connective tissues. A weaker, circular diattenuation arises from the presence of chiral moiety in collagen. The progression of precancer is accompanied by the destruction of collagen cross-links, which leads to loss of anisotropic organization and reduction of the diattenuation. It was concluded that it is possible to use fluorescence linear diattenuation and linear polarizance as new diagnostic parameters for detecting precancer.

It can be summarized that, although the MM contains rich, microstructural information about tissues, such information is difficult to obtain directly from the MM elements. To solve this problem, several methods have been proposed for transforming the MM elements into various groups of derived parameters that have a clearer physical and structural meaning [50,51,52,53,54].

The capabilities of polarimetric diagnostics can be tested on model tissue-like samples. The MM of soybean oil, which has a high degree of tissue-like properties, was studied [40].

4.4. Milk Composition Analysis and Food Quality Control

Among the needs of agriculture, milk quality control is of great importance. Information on the quantitative content of milk components (fat, proteins, lactose, somatic cells, progesterone, amino acids, etc.) is the basis for assessing milk quality and monitoring the nutritional balance and clinical condition of cows. In particular, the content of fat and protein is considered the main criterion for determining the market value of milk. Rapid analysis of milk composition is necessary for a prompt response to deviations in the parameters of the physiological state of animals and for timely correction of food rations if milk yield decreases. Additionally, milk analysis is an important part of the medical diagnostics which concern human milk for newborns [39]. Rapid milk testing can be performed by optical methods [35,36,37,38,39], among which MMP-based ones [35,36] are capable of multicomponent analysis. Using a setup which is actually an MM scatterometer, an empirical dependence of the MM elements of diluted milk on the amount of fat particles was obtained [35]. By solving the inverse problem for MM measurements, the distributions of fat and casein particles are retrieved; thereby, both fat and casein content in milk can be determined simultaneously from MM [36]. The ability of MMP to authenticate olive oil by linear dichroism and optical rotation of the circular birefringence retrieved from the MM of oil samples was revealed [41]. Changes in the depolarization of fresh and aged meat samples over time are clearly visible on MM polarimetric images and can serve as quantitative indicators for the non-invasive assessment of meat freshness [42].

4.5. Characterization of Soils and Fodders and Vegetation Monitoring

MMP finds application in the characterization of bulk materials such as soils and fodders. An MMP setup can be implemented as a unit for measuring the disperse composition in a robotic system that transforms soils into a stable, high-performance, organic, chemical bioreactor to better control the biomolecular interaction of nanoparticles and their adsorption by biological and mineral media [44]. MMs of microwave backscatter from bare soils are used to determine moisture content and surface irregularities [45]. Polarized IR laser scattering from sandy soil proved to be effective enough for evaluating the optical properties of sand particles and their size [46]. Information about vegetation properties can be obtained from the MM of vegetation-covered surfaces measured in bistatic scatter geometry by polarimetric radars [115,116]. Vegetation biomass can be derived from microwave polarized scattering returns using neural networks which are trained with vegetation scattering models [70]. The IR spectra of the MM elements measured for organic polymer films showed the presence of characteristic spectral lines in the block-diagonal elements of MM [98,99], which reveals the potential of IR MM spectroellipsometers for the analysis of organic compounds in soils and fodders.

4.6. Further Development of MMP Diagnostics Using Fiber Optics

Methods of non-destructive optical diagnostics, including those based on MMP, are constantly being developed. Fiber-optic devices have a special place in modern MMP instruments. To measure the MM, a multichannel PS-OCT with dynamic calibration improved by the use of a fiber-optic system was developed [90]. In the design of MMP devices, it is important to know the intrinsic polarization characteristics of the fiber-optic systems used. A virtual, generalized MM method for the characterization of a fiber-optic system with polarization-dependent elements and amplification was proposed [121]. This method allows obtaining data on polarization mode dispersion with high resolution and reduced noise level. An approach to measuring the MM for an optical fiber system with both birefringence and polarization-dependent loss or gain was tested [122]. Design examples of Mueller polarimetric endoscope and fiber Mueller polarimeter were described in [123].

5. Conclusions

From the review, it can be concluded that the introduction of MMP into conventional optical methods significantly increases their capabilities for more accurate and reliable diagnostics of biological and bioorganic systems, including those related to agriculture. Existing MMP implementations are able to characterize organic and microbiological dispersions, surface structures and biological tissues by obtaining polarization contrast images and the microphysical properties (particle size distribution, fractal and anisotropic properties) from measured MMs. In addition, MMP has the potential to analyze the content of organic constituents in agricultural materials and products (milk and beverages, fodders, etc.) and monitoring soil properties and vegetation. From the MM, it is possible to derive material-specific parameters that can serve as indicators of the quality of agricultural products. Thus, we can consider MMP to be an effective diagnostic tool in biological and agricultural studies.

Polarimetric optical elements allowing the measurement of the complete MM can be integrated into any standard optical spectrometer layout without rebuilding the signal registration system. The use of modern optical technologies, such as fiber optics, can further enhance the capabilities of MMP methods owing to flexible sensing system and noise reduction.