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We show that there are number of ways to transform an arbitrary polarizationstate to another with just two quarter wave plates (QWP). We have verified thisgeometrically using the trajectories of the initial and final polarizationstates corresponding to all the fast axis orientations of a QWP on the Poincaresphere. The exact analytical expression for the locus of polarization stateshas also been given that describes the trajectory. An analytical treatment ofthe equations obtained through matrix operations corresponding to thetransformation supports the geometrical representation. This knowledge can beused to obtain the Mueller matrix by just using quarter wave plates which hasbeen shown experimentally by exploiting projections of the output states on theinput states.

A polarization gadget with two quarter wave plates: Application to Mueller Polarimetry