FORMATION OF IMAGES OF AN ASYMMETRIC ABSOLUTELY REFLECTIVE EDGE OF A 3D-OBJECT IN COHERENT LIGHT
Yu. V. Chugui1,2,3
1Technological Design Institute of Scientific Instrument Engineering, Siberian Branch, Russian Acadaemy of Sciences, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia
3Novosibirsk State Technical University, Novosibirsk, Russia
Keywords: Fresnel and Fraunhofer diffraction, Fourier optics, spatial filtering, images and spectra of 3D-objects, volumetric edge, 3D-inspection
Abstract
Specific features of the formation of images of an asymmetric edge of a 3D-object with an absolutely reflective internal surface are analytically investigated from the viewpoint of dimensional inspection. Formulas are derived for calculating fields in images of object faces in ideal and diffraction-limited systems depending on the magnitude of the object bevel с , phase shift ϕ of the wave reflected from the inner surface of the object, and angular aperture 2θ0 of the coherent projecting optical system. For metallic 3D-objects (ϕ = π) the value of the field in the image of the back face at a point x1 = c, corresponding to the position of its boundary is found to be negligible if the depth of focus of the system is much smaller than the object thickness. For object bevels с much smaller than the size of the Fresnel zone δd ~ √λd(λ is the light wavelength, and d is the object thickness) and greater than the depth of focus ∆z, the displacement of the intensity profile in the image of the front face is proportional to c/δd and depends on the angle ϕ. With large bevels, when c >> δd and Δz >> d, the displacement of the front face boundary is inversely proportional to c/δd. These displacements can lead to systematic errors of measuring the boundary positions of the 3D-object and should be taken into account in precision dimensional inspection.
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