# Applications of Mueller Matrix Polarimetry to Biological and Agricultural Diagnostics: A Review
## 2 Principles of Mueller Matrix Analysis
### 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. Figure 2: Simplified scheme of an MM scatterometer. 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].