# Review on Complete Mueller Matrix Optical Scanning Microscopy Imaging
## 2 Mueller Matrix Optical Scanning Architecture
### Spectral Domain Encoding/Decoding  
The previous techniques are based on acquiring a set of a sequentially generated polarization resolved images and recombined them in a post data process for recovering the full MM image, although this approach is not suitable for any dynamic characterization of the sample limiting the use of such a technique for in vivo microscopy imaging. Indeed, the MM polarimeter should be able of acquiring the full MM in the pixel dwell time by mean in few microseconds and requires a very fast intensity modulation of the polarized light. For wide field imaging, the solution has been found by using multiple electro-optics devices in series such as Photoelastic Modulators (PEMs) or PC triggered with the camera frame rate via a data acquisition (DAQ) board [53]. Briefly, the method is based on the analysis of the time-variation of the intensity induced by the electro-optics effect. Thus, the detected signal is a channeled spectrum represented in the Fourier domain by complex modulation amplitudes at numerous frequencies. A 50 MHz FPGA counts the edges of each PEM modulation signal and locks when a unique phase between all the four PEMs is occurring within a short time in a nanosecond timescale. Then, the FPGA sends a trigger to the CCD to gate the signal in 0.5 us, giving a full image acquisition took in approximately 20 ms. Another approach consisting in dealing directly with the Fourier transform of such modulated signal where the complex amplitudes are linear combinations of the MM elements [54]. In this method, the common approach is to choose different PEMs with separated working frequencies. This kind of optical device is composed of a passive crystal subjected to periodic mechanical stress, resulting in a time-varying birefringence due to the photoelastic effect [28, 55]. In numerous earlier works, polarization-resolved setups used one PEM with an LP oriented orthogonally as a PSG for measuring the differential circular polarized intensities [33, 36, 56]. Coupled with a lock-in detection at the reference frequency of the PEM, the passive setup was able to provide few elements of the MM in order of tens of kHz. In order to speed up the acquisition rate and the number of elements, common solutions proposed to add another PEM in the PSA synchronized with the first one [57]. In recent works, this technique upgraded such a measurement by dealing with 3 and 4 PEMs [58]. The main advantage brought by adding multiple PEMs is that all the elements of the MM can be retrieved without any mechanical moving part. Thus, this experimental approach has been proven to be of interest for studying ultrafast conformational changes in biopolymers [59, 60]. For such a technique, the acquisition speed has reached 100 us (10 kHz repetition rate), very close to the pixel dwell time from any GS. Even if the speed for acquiring the full MM image is fast, a new method for fast polarization encoding has recently emerged and is based on spectral coding of polarization (channeled spectropolarimeters) by using passive elements such as birefringent plates [61]. The principle is the parallelization of polarization states in the spectral domain so that the polarimetric response of a sample can be calculated when using a single-channel spectrum I(\(v\)), where \(v\) is the optical frequency. Each channeled spectrum I(\(v\)) is periodic and is composed of discrete frequencies from 0 to 12.f0 that are integer multiples of the fundamental one f0. This last one depends on both the thickness e and birefringence \(\Delta\)n of the retarders by the relation f0 \(\Delta\)ne/c, where c is the celerity of light in vacuum. Such polarimeters have the potential to perform polarimetric scanning microscopy thanks to their speed provided that the thickness ratio of the retarders is well-chosen [62]. The first experimental snapshot Mueller polarimeter based on spectral coding of polarization using a broad spectrum source (superluminescent diode), thick retarder plates, and a CCD-based spectrometer [63].