Necessary and Sufficient Conditions for Thin Phase Imagery

A thin phase structure is rendered visible when the optical image-forming system produces interference between the direct light and the diffracted light. The condition required to relate explicitly some uniquely identifiable terms of the coherent transfer function of the optical system with the image irradiance variations associated with the interference terms is derived. This treatment is employed firstly to establish the necessary and sufficient conditions for rendering visible a thin phase structure, and secondly to define a unique effective transfer function to map the object's thin phase structure into image irradiance terms. Thus, thin phase imagery is represented by a linear filtering process as previously suggested by Menzel. Finally, the equivalence between Menzel's phase contrast function and the effective transfer function is indicated, as well as the advantages of employing the present symmetry-based approach.