Automatic dimensional inspection of 3D articles with high resolution and productivity is an urgent problem for industry and science. Using optical inspection methods, it is essential to take into account the influence of 3D bodies' extension on their Fraunhofer diffraction pattern and images. This influence strongly depends on the configuration of illumination, which therefore is fundamentally important. The previously suggested constructive method, based on the model of equivalent diaphragms, for calculation of diffraction phenomena by 3D bodies of constant thickness was developed for inclined plane and spherical illuminating waves. The equations describing the spatial spectra of a volumetric asymmetric edge and a 3D slit under plane inclined wave illumination have been obtained in analytical form. It was shown that the cross-selection of front and back faces of the volumetric slit occurs in the case of inclined illumination. The solution for diffraction phenomena by a volumetric slit under spherical wave illumination has been represented. In this case the simultaneous selection of either front or back faces of the 3D slit takes place. The obtained results can be applied for investigation of formation and high-frequency filtering images of 3D bodies of constant thickness.