Peculiarities of high-frequency filtering (contouring) of images of symmetric thick (extended along the optical axis) edge are investigated in analytical form by the Kirchhoff–Fresnel approximation. They are based on a model of equivalent diaphragms (transparencies) earlier proposed by the authors [J. Opt. Soc. Am. 71, 483 (1981)]. Expressions for the fields in special cases of perfect absorption and reflection are derived. For the case of slight volumetric effects, a structure of the contoured images of the front and back faces is shown to be similar to a structure of the contoured image of the plane edge. But the influence of the extension causes a shift of the basic minimum position proportional to the size of the Fresnel zone. When volumetric effects are significant, the profile of the filtered image of the front face has a single maximum (instead of a double one). Here the structure of the filtered image of the back face depends to a great extent on the reflection properties of the inner surface, changing from the form with a double maximum to the form with a single one. There is agreement between theoretical and experimental results.
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