The possibility of synthesising dual offset reflector systems to produce a prescribed far-field power pattern with no depolarisation is examined under the principles of geometrical optics. A formulation is developed based upon a model in which both source and antenna far fields are represented by Huygen's fields. Numerical implementation in general appears difficult but a useful special case emerges in which the reference axes of the Huygen's fields are parallel. Results for a contoured beam application reveal that a shaped dual offset system with no optical depolarisation is possible, and further analysis using physical optics suggests that extremely good axial ratios can be obtained.