# Review on Complete Mueller Matrix Optical Scanning Microscopy Imaging
## 1 Introduction  
Polarization-based imaging techniques are powerful approaches having the unique ability to produce specific contrasts for revealing hidden information [1]. Over the last few decades, it has shown its efficiency in multiple areas showcasing its particular sensitivity to the medium structure and orientation [2]. As follows, it has been referred to a wide range of experimental applications from astrophysics [3, 4], remote target detection [5, 6, 7, 8], and micro/nanorquelics in a turbid or highly scattering medium [9, 10, 11, 12, 13, 14]. Especially, Mueller matrix polarimetry is the most comprehensive method as it provides the full polarimetric response of a sample through its \(4\times 4\) Mueller matrix (MM). At least 16 intensity measurements, obtained by a set of 16 coding and decoding polarization states, must be performed to determine the 16 real independent element of the Mueller matrix \(m_{ij}\)[15]. Various methods were then developed based on either temporal, spatial, or spectral polarization coding and decoding [16]. For imaging microscopy applications, two approaches provide the complete Mueller matrix elements \(m_{ij}\)(x,y) to be measured across a sample in two dimensions. The first and most common approach incorporates the full-field imaging approach using a CCD or a CMOS camera including full-field polarization coding and decoding stages. Most wide-field Mueller imagers use dynamic polarization optics to modulate light polarization in the temporal domain. The methodology consists of a sequential acquisition of at least 16 polarization-resolved intensity images of the sample for reconstructing the complete Mueller matrix in just few seconds up to few minutes. For tracking any fast polarimetric changes, recent works have proposed a snapshot Mueller matrix microscope based on the simultaneous coding/decoding of the polarization states physically splitted in the plane of the sensor which is of great interest for biomedical diagnosis [17]. The idea is to couple a micro-polarizer array with a CCD or CMOS camera. Each pixel of the camera is linearly polarization encoded (\(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\) and \(135^{\circ}\)) and a group of four pixels gives a super pixel allowing the reconstruction of the four Stokes coefficients through afield-programmable gate array (FPGA) card in real-time [18]. Nowadays, since this passive technique does not require any sophisticated mathematical model or expansive optical features, it exists numerous commercial polarization-resolved camera, dedicated for remote sensing or widefield imaging [19; 20; 21]. However, the limitation of such a method is the need of taking into account the crosstalk between pixels and the loss of spatial resolution due to the definition of the super-pixels [22]. Another limitation is the difficulty to be implemented with other imaging modalities due to the space required for the polarimetric optical features. In an attempt to preserve the axial optical resolution through the illumination volume, the second approach consists in point-by-point scanning laser microscopy (SLM) of the sample. Particularly, this review article is dedicated to the description of the experimental advances in the field of complete MM in optical scanning microscope for imaging pixel-by-pixel the xy focal plane of the objective. This measurement method differs from using the scanning beam and is based on collecting the angular fingerprint of the sample as it is often proposed in polarization-resolved scatterometry [23]. In this review, we demonstrate the capability of this method for imaging localized contrasts based on the single optical and structural properties of the sample at the microscale. Commonly, the imaging of such small objects is made using fluorescence techniques showing an extraordinary capability of tracking localized molecules beyond the diffraction limit. Nevertheless, it requires the use of fluorophores and high light-dose that can alter the sample organization.