We already implemented an imaging polarimeter able to capture at high-speed the full information about linear polarization of a monochromatic light beam (namely its first three Stokes parameters). The polarizing element was a single ferroelectric liquid crystal cell, acting as a half-wave plate (therefore as a polarization rotator) at its design wavelength. In this paper, we report the improvement of our system in order to grab the full Stokes information, including the fourth Stokes parameter. The procedure consists in two operations. First, optimally controlling our polarization component with an additional fourth voltage level. Second, shifting the wavelength operation in order to get benefit of the device chromatic behavior: away from its design wavelength, the device does not behave as a half-wave plate any longer, and with proper level control, the system matrix of our polarization state analyzer (consisting of the liquid crystal cell and of a fixed linear polarizer) can reach rank 4. Therefore, elliptical polarization can be fully analyzed, as it could be with a nematic liquid crystal device, but at a much higher frame rate. Results of operation at 200 fps are provided.