**2. Liquid Crystal on Silicon displays characterization and optimization methodology**

In this section, we propose a characterization-optimization method, based on a combination of the Mueller-Stokes (M-S) formalism (Parke, 1949) and the Jones formalism (Jones, 1941), which is able to predict and optimize the intensity and the phase response of LCoS displays. The characterization of the LCoS display is conducted as a function of the addressed gray level (which is related to the applied voltages), by experimentally calibrating its corresponding Mueller matrices, which are able to describe depolarizing samples. In this situation, the intensity response of the LCoS display can be predicted but since Mueller matrices are calculated from intensity measurements, no information about the phase modulation response is obtained. As Jones matrices contain the required phase information, a conversion from Mueller matrices to Jones matrices is applied. To perform a proper conversion, a polar decomposition (Lu & Chipman, 1996; Foldyna et al., 2009) of the experimentally obtained Mueller matrices is carried on.

Once the intensity and phase response of the LCoS display can be predicted, an optimization procedure is applied, in order to get the desired LCoS display behaviour, i.e. to work as amplitude-only modulator or as phase-only modulator. In next subsections, the characterization and optimization methodology is described in detail and some results are provided.
