Calculation of the object edge position after its projection in a spatially noninvariant coherent optical system

Specific features of half-plane image formation in a spatially noninvariant (aberration-free) coherent optical system of the 2F–2F telecentric type with a limited aperture of the projection objective (in the absence of the spatial frequency filter) are studied. The dependence of the light intensity behavior at a point corresponding to the half-plane edge in the image on the object position is found in an analytical form on the basis of approximating the Fresnel functions by analytical functions. As the half-plane approaches the boundary of the field of vision of the system determined by the objective aperture diameter, the light intensity is demonstrated to deviate significantly from that in the case of the axial position of the half-plane, which may lead to noticeable measurement errors in inspecting the geometric parameters of objects by the projection method in transmitted light.