IMAGE FORMATION FOR AN EXTENDED SLIT HOLE OF A SYMMETRICAL TYPE WITH ABSOLUTELY ABSORBING INTERNAL FACES IN COHERENT LIGHT
Yu. V. Chugui
Technological Design Institute of Scientific Instrument Engineering, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
Keywords: Fresnel and Fraunhofer diffraction, Fourier optics, spectra of extended objects, volumetric slit hole, optical dimensional inspection
Abstract
The features of imaging faces of extended (in depth) slit holes of constant thickness d of symmetrical type (with equal input and output apertures D) with absolutely absorbing internal faces are investigated. The calculations are based on an optical-physical model of diffraction phenomena on extended absolutely absorbing objects using equivalent slit-type transparencies. The structures of images of such objects formed in ideal and diffraction-limited systems are studied. It is shown that the image profiles of the front and back faces of the extended slit hole largely depend on a parameter Nθ0 equal to the ratio of the critical diffraction angle θcr = √ λ/d to the half angular size θ0 of the aperture filter, as well as on the ratio of the slit aperture D to the size of the Fresnel zone δd = √ λd. It is shown that, when Nθ0 >> 1, there is a displacement of the object boundaries, which is determined both by the interaction of diffraction pictures of two edges for the case of a flat slit (d = 0) and by the influence of secondary diffraction of light on the back face of the extended object. At D >> √λd, the boundaries are found to be mainly shifted due to secondary diffraction of light, which leads to a systematic error of measuring the aperture D equal to εd = 0,22 δd . The features of the formation of diffraction-limited images of the back face with strong volumetric effects (Nθ0 << 1) are investigated.
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