# Applications of Mueller Matrix Polarimetry to Biological and Agricultural Diagnostics: A Review
## 2 Principles of Mueller Matrix Analysis
### 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.  
Figure 3: General scheme of a single-beam scanning MM spectropolarimeter. A dual-rotating retarder polarimeter configured to measure the MM in the spectral range from 3 to 12 \(\upmu\)m 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 dichroism (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 dichroism in the measurement of polarization spectra. To solve this problem, the occurrence of artifacts can be combatted by equipping the circular dichroism (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, \(\alpha\)-silica, liquid crystals, beetle cuticles and films of cellulose nanocrystals.