DIFFRACTION PHENOMENA ON AN EXTENDED ASYMMETRIC SLIT WITH ABSOLUTELY ABSORBING INNER FACES
Yu. V. Chugui1,2,3
1Technological Design Institute of Scientific Instrument Engineering, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia
3Novosibirsk State Technical University, Novosibirsk, Russia
Keywords: Fresnel and Fraunhofer diffraction, Fourier optics, spectra of extended objects, volumetric hole, optical dimensional inspection
Abstract
Based on the model of equivalent diagrams, the Fraunhofer diffraction patterns (spectra) of extended (in depth) asymmetric slit-type holes with absolutely absorbing inner faces and different input (D) and output (D1) apertures are calculated in the far field zone. The behavior of the spectrum of an extended object is studied analytically in the case of differences in apertures 2÷Dç =÷D1-Dç noticeably smaller than the size of the Fresnel zone dd = Öld (l is the light wavelength, and d is the hole depth). It is shown that, in the range of angles ÷qç<< qкр= Öl/d, the observed diffraction pattern of an extended object is equivalent to the diffraction of light by a flat slit (d=0) with an effective width Deff=D+D-qd /(Ö2p). On the basis of a constructive approximation of the Fresnel integral function, the features of light diffraction by volumetric holes, whose apertures differ significantly from each other: 2÷Dç>> dd, are studied analytically. Calculations have shown that, in the cases of expanding (D1> D) and narrowing (D1< D) apertures, the behavior of the minima of the observed diffraction patterns in the angle ranges ÷qç<÷qDç= ÷Dç/d differs only slightly from the equidistant behavior for a flat slit (d =0) with widths D and D1, respectively. The results obtained can be used in the development of optoelectronic systems for dimensional inspection of plates with holes.
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