Although subspace-based direction-finding algorithms have been widely accepted as the most powerful method in estimating the source's directions-of-arrival, its derivation was based on the linear independence of the source's manifold vectors. An undesirable manifoldly ambiguous situation is said to occur when this condition is not satisfied. To minimize the presence of ambiguities, the recent work in [1] proposed a method to resolve ambiguities by placing medium substrates at the front-end of antenna elements, which results in the change of direction and the propagation delay. This effectively breaks down the linear dependence amongst the manifold vectors. In this paper, the use of planar substrates to resolve manifold ambiguities in a diversely-polarized antenna array system is investigated, where the actual causes of ambiguities are assessed from the differential geometry perspective. The criteria is provided to find the allocated placement positions and the total number of required substrates. © 2014 IEEE.