For a given transmission polarization, the four-element Stokes vector captures all of the information inherent to the dual-polarized backscattered signals. Stokes parameters are linear combinations of the like-polarized power, the cross-polarized power, and the cross product between the complex image amplitudes in the two receive channels. Most so-called dual-polarized synthetic aperture radar (SAR) systems provide only the like- and cross-product images, ignoring the cross product. In so doing, potentially valuable information is thrown away. For most dual-polarized SARs, data sufficient to generate the Stokes parameters can be generated with small marginal cost. A practical and sufficient output data format would be a mapping of the (complex) cross product between the two channels, as well as their respective images