The structure of the backscattering phase matrix for hexagonal ice crystals is studied. The architecture and content of a data bank for interpreting the experimentally measured backscattering matrices of crystalline clouds are described. The beam splitting method is used for calculation of the data bank elements. Integral optical characteristics of the backscattering light are analyzed. Backscattering matrices of crystalline clouds obtained with the Stratosfera 1M lidar are compared with model matrices calculated with the use of the data bank. The close agreement between the model and measured matrices is demonstrated.