# Review on Complete Mueller Matrix Optical Scanning Microscopy Imaging
## 2 Mueller Matrix Optical Scanning Architecture
### Spectral Domain Encoding/Decoding
At this early stage, the device was developed in a non-imaging transmission configuration but recently upgraded for SLM polarization-resolved SHG [64]. The acquisition rate of this approach is limited by only the spectrometer performances that can be high (hundred of MHz). Then, inspired by OCT technology, the technique has been upgraded by using a wavelength-swept laser source, high order retarders, and a single-channel detector [65]. The device uses a wavelength-swept source (SS) laser instead of the broad spectrum source and a photodiode instead of the spectrometer, which results in a much simpler optical setup as shown in Figure 3a. For instance, the PSG and the PSA composed of simple polarization features (linear polarizers and retarder slices) have been compacted in mechanical blocks with centimeter dimensions [31, 66]. A single-point Mueller matrix is measured at the rate of the SS, which could be hundreds of kHz. This compactness allows for straightforward implementation on a commercial scanning microscope and has been upgraded in transmission into a commercial SLM already use for performing TPEF and SHG imaging [31]. In this work experiment, the fundamental thickness e was chosen to generate six modulations at the frequency f0. This rather large spectral analysis window could be reduced by using thicker retarders but at the expense of the number of samples per channeled spectrum. The channeled intensity spectrum \(I(v,t)\) is modulated by the polarimetric fingerprint of the sample and can be expressed as  
\[I(v,t)=\sum_{k=0}^{n}\left[a_{k,t}\cdot cos\left(k\frac{2\pi\Delta ne}{c}v \right)+b_{k,t}\cdot sin\left(k\frac{2\pi\Delta ne}{c}v\right)\right] \tag{4}\]  
where \(a_{k,t}\) and \(b_{k,t}\) are linear combinations of Mueller matrix elements \(m_{ij}\). In the configuration resumed Figure 3b, the sum stops at n = 12 leading to 12 Fourier amplitudes in real and imaginary part, giving finally 25 values used to retrieved the 16 Mueller elements simultaneously. The same philosophy has been proposed also in a multimodal approach for label-free cancer cervix study [67] by coupling MM wide field imaging with optical scanning OCT. Despite the extraordinary advantage offers by the speed of this technique, an important assumption is that the sample is achromatic within the excitation wavelength range. Additionally, the modeling of the instruments assumed that all the linear retarders used do not present any diattanuation or depolarization. Thus, a precise validation of the polarimetric properties of the sample should be done in the working spectral range. Finally, thanks to the high speed rate and the spectral information that give access to numerous measurable quantities at the same time, this method has been successfully proposed for real-time imaging through an endoscopic approach [66]. The main issue of endoscopic technique polarization-resolved is decoupling at any time the signatures of the sample from the optical fiber polarization transformation. We have summarized the typical performances reached by the methods presented in this section in Table 1. Additionally, we have reported the acquisition speed for the 16 MM images in Figure 4.  
Figure 3: (**a**) Block diagram of a MM SLM based on the spectral encoding/decoding of the polarization states from Reference [31]. (**b**) Schematic presenting the extraction of the MM images of the measured intensities images in the spectral approach. PSG: polarization states generator. PSA: polarization states analyzer. Reti: retarder. Obj: microscope objective. GS: galvanometric scanner. TL: tube lens. S: sample. PMT: photomultiplier tube.