## 1 Introduction  
The light scattering and absorption by non-spherical particles (such as ice crystals, dust aerosols, etc.) plays an important role in the atmospheric radiative transfer [1; 2; 3; 4]. However, because of the irregular shape of these particles, there is still considerable uncertainty in their scattering characteristics [5; 6; 7], which has become an important factor restricting the accuracy of atmospheric remote sensing [8; 9]. For polarized remote sensing, the effect of the \"non-spherical effect\" is much more remarkable since the polarization of diffuse light is very sensitive to the particles' shape [10; 11]. Therefore, how to obtain the scattering properties of these non-spherical particles accurately has become a hot issue in the field of atmospheric radiation [12; 13; 9; 14]. In order to simulate the light scattering by non-spherical particles, many scattering computational models were established [15; 16]. Typical models include the T-matrix method [17; 18], Discrete DipoleApproximation (DDA) [19; 20], Finite Difference Time Domain (FDTD) [21; 22], Pseudo-Spectral Time Domain (PSTD) [23; 24; 25], and Multi-Resolution Time Domain (MRTD) [26; 27]. DDA and FDTD can be applied to the light scattering calculation for particles with arbitrary shape; however, due to the limitation of their computational stability and complexity, it is a tough job for them to simulate the light scattering by particles with large sizes [15]. Although PSTD and MRTD can calculate the scattering properties of large particles, their scattering simulation processes are closely related to particle's orientation and incident light (propagation direction and polarization state). Namely, as long as any of these parameters changes, their scattering processes need to be re-simulated as well [15; 16]. Therefore, if the scattering properties of the particles with certain orientation distributions are needed to be calculated, the computational process should be repeated many times, which will be very time-consuming (DDA and FDTD also have the same problem). In contrast, the T-matrix method has a significant advantage over these models. Since the T-matrix is a complete dataset of scattering information which only depends on the refractive index, size, and shape of the particle, the scattering properties for arbitrary orientations can be calculated analytically once the T-matrix is obtained [28]. In the traditional T-matrix models, the T-matrix is calculated by the Extended Boundary Condition Method (EBCM, also known as the \"null-field method\") [29; 30]. Though these models are very efficient at calculating light scattering by particles with ideal morphologies, like spheres, spheroids, and cylinders [31; 18; 32], they generally have limited applicability to the irregularly shaped aerosol and ice crystal particles [15]. Besides, with the increase of particle size and refractive index, their calculation processes will become divergent. In the actual applications, many researchers have also found that the performance is highly doubtful if the non-spherical aerosol particles are taken as the spherical or spheroidal ones in a radiative transfer simulation [9; 33]. Considering the tremendous advantage of the T-matrix, many scholars have attempted to calculate the T-matrix by other methods, except the EBCM. For example, [PERSON] used the Separation of Variable Method (SVM) to calculate the T-matrix of spheroidal particles [34]. [PERSON] et al. applied the Discrete Dipole Approximation to calculate the T-matrix of the non-spherical particles [35], while [PERSON] et al. [36] tried to combine the DDA with the Point Matching Method (PMM) to calculate the T-matrix. However, similar to the DDA, most of these methods can only be applied to simulate the light scattering by small particles. In order to obtain the T-matrix of the particles with irregular shapes, [PERSON] and [PERSON] also applied the Invariant Imbedding (IIM) T-Matrix method to the light scattering calculation [31; 37; 38].