# Applications of Mueller Matrix Polarimetry to Biological and Agricultural Diagnostics: A Review
## 2 Principles of Mueller Matrix Analysis
### 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].  
Figure 4: Combined PS-OCT and MMIP schematic.