# Review on Complete Mueller Matrix Optical Scanning Microscopy Imaging
## 2 Mueller Matrix Optical Scanning Architecture  
Any MM polarimeters are composed of two optical modules aiming to encode/decode the polarization states after interaction with the medium. First, the Polarization States Generator (PSG) encodes the polarization states from the incoming light source (emitted by a lamp or a laser diode), as described by the Stokes vector \(\vec{S_{in}}=[S_{0},S_{1},S_{2},S_{3}]^{in}\), where \(S_{0}\) is the total transmitted light, \(S_{1}\), \(S_{2}\) and \(S_{3}\) are related to the linear horizontal/vertical, \(+45^{\circ}/-45^{\circ}\) and circular right/left polarization states. Their combinations provide valuable information increasing the information available, such as the Degree Of Linear Polarization (DOLP), and Circular (DOCP) [24]. Then, after the sample, the transformation of the polarized light is decoded by the Polarization States Analyzer (PSA) giving the output Stokes vector as \(\vec{S_{out}}=[S_{0},S_{1},S_{2},S_{3}]^{out}\) and collected by a photodetector. In the literature, the mix of the PSA and the detector part is also referred to as the Polarization States Detector (PSD). The MM, noted M, describes how the polarization state of the input light changes upon interaction with the sample by  
\[\vec{S_{out}}=[M]\vec{S_{in}}, \tag{1}\]  
where \(\vec{S_{in}}\) and \(\vec{S_{out}}\) are the input and output Stokes vectors. Since the imaging contrasts erase from the only linear optical response of the medium with the polarized light, there is no need of using high power laser source or extremely sensitive photodetectors, which decreased drastically the cost and the complexity of polarization-resolved techniques. The main challenge for implementing this technique in an SLM configuration is to adapt a proper methodology for encoding/decoding the polarization states in a way to retrieve the full MM pixel-by-pixel. Additionally, the critical issue for extracting the accurate MM is the calibration of the full optical system. It has to count on the polarization state inaccuracy from the PSG and PSA errors combined with the polarimetric artifacts because of the multiple interaction with the optical features composing the microscope (lenses and mirrors). In SLM, the specimen is scanned by a diffraction limited spot of a laser light after reflection in galvanometric mirrors. Then, the light is transmitted or reflected by the in-focus illuminated volume element (voxel) of the specimen and is focused onto a photodetector. For MM SLM, the lateral resolution is approaching the diffraction limitation given by the objective numerical aperture express as  
\[R_{lateral}=\frac{\lambda}{2\cdot NA} \tag{2}\]  
We present the different configuration available from such a technique Figure 1.  
Usually the calibration steps consist in measuring the polarimetric contributions independently of the sample of (1) the PSG and PSA blocks and (2) the optical microscope features fingerprints. First, the PSG and PSA could be calibrated separately using dedicated methods according to its architecture. Studying the conditioning of the measurement matrix have been used by several authors to optimize the polarimeter performance. Particularly, if a simple set of rotated polarizers and waveplate are used for encoding the polarization states, a simple model such as Eigenvalue Calibration Method (ECM) [25; 26; 27] have been proven to be robust and versatile enough. In this way, the trace of the matrices measured using simple reference sample at specific orientation gives a Condition Number (CN) that resumes the robustness against noise propagation through the whole system. If the PSG and PSA are more complex to model, for instance by using electro optics devices  
Figure 1: Block diagram for implementing a general Mueller matrix (MM )polarimeter into a scanning laser microscopy (SLM) architecture (**a**) in transmission and (**b**) in confocal reflection configuration. PSG: polarization states generator. Obj: microscope objective. GS: galvanometric scanner. TL: tube lens. S: sample. BS: beamsplitter.