We have developed ellipsometry lidar and measured aerosol and ice-cloud characteristics. To measure a full normalized backscattering phase matrix (NBSPM) composed of nine elements, we have designed an optical system with three kinds of transmission and three kinds of reception, composed of λ/2 waveplate, λ/4 waveplate and empty optic. To find systematic optical errors, we used clean day middle-altitude (4-6km) lidar signals for which the aerosol's concentration was small and its orientation chaotic. After calibrating our lidar system, we have calculated NBSPM elements scattered from an aerosol and from an ice cloud. In the case of an aerosol, we found that the off-diagonal values m12,...,m34 of the NBSPM are smaller than those for a cirrus cloud. Also, the off-diagonal values of the NBSPM from a cirrus cloud depend on atmospheric conditions.