Fresnel diffraction from the edge of a transparent plate in the general case

Fresnel diffraction from the edge of a transparent plate with arbitrary orientation of its surfaces is formulated in transmission mode. It is shown theoretically and evaluated experimentally that the thickness of a plate and the angles between its surfaces, near the edge, can be determined accurately. This allows us to construct a quantitative 3D image of the plate edge. It is also illustrated that the recorded diffraction pattern of a plate edge can be regarded as a hologram produced by the interference of two diffracted waves: one passing above the plate and the other transmitting through the plate near the edge. Thus, the hologram makes it possible to reconstruct the plate's edge as a 3D image, and the approach can be utilized in constructing 3D images of phase objects and in quantitative phase microscopy.