  Spatial light modulators are widely used to perform modulations of different
properties of the electromagnetic field. In this work, a simple optimization
method for general double-pass setups was developed. It takes into account the
involved polarizing elements and displays, and a numerical simulation based on
an exhaustive search routine finds the optimal optical axes orientation of the
polarizing elements for the desired modulation. By simultaneously considering
both impingements, we are able to take full advantage of the modulation
capabilities of the chosen spatial light modulators. In particular, different
polarization modulations and complex amplitude modulations were studied for
twisted nematic liquid crystal displays and passive linear optical elements.
Examples for different optimization criteria are shown and compared with
experimental results, supporting the feasibility of this approach. This method
offers the possibility of independent modulation of two properties of the input
light state, outperforming the use of a single screen.
