We propose a new approach to the complete retrieval of a coherent field (amplitude and phase) using the same hardware configuration as a Shack-Hartmann sensor but with two modifications: first, we add a transversally shifted measurement to resolve ambiguities in the measured phase; and second, we employ factored form descent (FFD), an inverse algorithm for coherence retrieval, with a hard rank constraint. We verified the proposed approach using both numerical simulations and experiments.