## 2 Materials and Methods  
### Data Collection  
The detection of remote objects and collection of the data to be used in their classification is achieved by using the complete MM polarimeter described in Ref. [9]. The measurements were performed under conditions close to backscattering, with a small angle (\(\approx\)9\({}^{\circ}\)) between the illumination and detection arms of the setup [9]. The polarimetric database used in the present work contains the MMEs of the objects/materials listed in Table 1.  
The four-component Stokes vector, \(\vec{S}\), describes the state of polarization of any light beam, no matter whether it is fully or partially polarized and coherent or not [10]. Its components are real parameters, which can be expressed as quadratic forms of the electric field amplitudes corresponding to different polarizations, either linear or circular. An arbitrary light scattering process can be described by the relation \[\vec{S}_{o}=\widehat{M}\vec{S}_{i} \tag{1}\]  
where \(\vec{S}_{i}\) and \(\vec{S}_{o}\) are the Stokes vectors of the incident and outgoing beams, respectively, and \(\widehat{M}\) stands for the Mueller matrix, which contains information regarding the polarizing/depolarizing properties of the sample. In general, it requires 16 independent measurements made with a polarimetric setup to determine the full MM. Under backscattering conditions, it has certain symmetry properties, which reduce the number of independent MMEs to 10 or even to 9 if it is considered normalized by the element \(M_{00}\) as it usually is the case [6]. Nevertheless, it can be useful to retain some redundancy, which can compensate for measurement errors. The information received from the polarimeter is processed to obtain the Mueller matrix elements, at a given AoI (denoted by \(\alpha\)) (The angle of incidence is known in laboratory measurements, while it can be determined using the triangulation method employing the parallax effect in non-laboratory situations. It can strongly influence the state of polarization of the backscattered light, especially for grazing incidence [11]). The polarimetric measurement matrix principle followed to calculate any Mueller matrix was described in detail elsewhere [10]. Summarizing the method, according to Equation (1) one needs to relate the input and output Stokes vectors, which are determined by the polarization state generator (PSG) and polarization state analyzer (PSA). Therefore, combining different PSG and PSA configurations, the matrix of intensities measured by the camera, \(\widehat{B}\), can be written as  
\[\widehat{B}=\widehat{A}\widehat{M}\widehat{G}\,, \tag{2}\]  
where the columns in the matrix \(\widehat{G}\) correspond to the Stokes vectors generated by the PSG and \(\widehat{A}\) is a matrix whose rows contain the different configurations used by the PSA. The Mueller matrix is calculated by selecting one of the relevant PSG-PSA configuration combinations, measuring the respective intensity and then solving Equation (2) at each pixel. It yields a map such as that shown in Figure 1.  
Complete Mueller-Stokes polarimetry requires at least 16 measurements per data point which is difficult in a non-laboratory scenario. If we abdicate measuring the retardance, the number of measurements per data point can be reduced. By using only linear polarizations, the device has the potential to be more compact, affordable, and faster compared to a complete polarimeter. Two particular cases of interest are explored in this work:  
1. Only two linear polarizations (horizontal and vertical) are used in both PSG and PSA; four measurements per data point are performed yielding the MMEs \(M_{00}\), \(M_{01}\), \(M_{10}\), and \(M_{11}\). 2. Multiple angles are used for the linear polarizers in both PSG and PSA, so that at least nine measurements per data point are performed resulting in the MMEs listed in (i) plus \(M_{02}\ldots M_{22}\).