TY - JOUR

T1 - Calculating the Images of a Volume Asymmetric Ideally Absorbing Edge of an Object in Coherent Light

AU - Chugui, Yu V.

N1 - Funding Information: The work is supported by the Ministry of Science and Higher Education of the Russian Federation (state registration no. AAAA-A17-117121270018-3). Publisher Copyright: © 2020, Allerton Press, Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020/11

Y1 - 2020/11

N2 - The peculiarities of image formation of a volume asymmetric ideally absorbing edge, the main fragment of extended (in depth) plates of constant thickness, in diffraction limited projection system are analytically studied with application to the size inspection of 3D objects. The structures and profiles of intensities in the images of the front and rear faces of object are investigated at small and large apertures of the optical system for different relations between the object bevel c, the size of the Fresnel zone (Formula presented.) is the wavelength of light and d is the object thickness), and angular aperture of the optical system 2θ0. In the case when the bevel c « δd, at large focal depth of the system the intensity profile is displaced in the image of the 3D edge in linear proportion to the Fresnel zone and to the bevel size. It is analytically demonstrated that, for large bevels (c » δd) and small apertures of the system in the plane conjugating with the front face, a sharp image of either the front face (the rear face is shadowed) or the rear face (the front face is shadowed by the rear face) is observed. The formulas for the image profile of the rear face are obtained and studied in the case of significant volume effects, when the focal depth of the system is far smaller than the object thickness. The calculation results are in good agreement with the results of computer modeling.

AB - The peculiarities of image formation of a volume asymmetric ideally absorbing edge, the main fragment of extended (in depth) plates of constant thickness, in diffraction limited projection system are analytically studied with application to the size inspection of 3D objects. The structures and profiles of intensities in the images of the front and rear faces of object are investigated at small and large apertures of the optical system for different relations between the object bevel c, the size of the Fresnel zone (Formula presented.) is the wavelength of light and d is the object thickness), and angular aperture of the optical system 2θ0. In the case when the bevel c « δd, at large focal depth of the system the intensity profile is displaced in the image of the 3D edge in linear proportion to the Fresnel zone and to the bevel size. It is analytically demonstrated that, for large bevels (c » δd) and small apertures of the system in the plane conjugating with the front face, a sharp image of either the front face (the rear face is shadowed) or the rear face (the front face is shadowed by the rear face) is observed. The formulas for the image profile of the rear face are obtained and studied in the case of significant volume effects, when the focal depth of the system is far smaller than the object thickness. The calculation results are in good agreement with the results of computer modeling.

KW - 3D size inspection

KW - Fourier optics

KW - Fraunhofer diffraction

KW - Fresnel diffraction

KW - images and spectra of 3D objects

KW - spatial filtering

KW - volumetric edge

UR - http://www.scopus.com/inward/record.url?scp=85104026467&partnerID=8YFLogxK

U2 - 10.3103/S8756699020060060

DO - 10.3103/S8756699020060060

M3 - Article

AN - SCOPUS:85104026467

VL - 56

SP - 623

EP - 633

JO - Optoelectronics, Instrumentation and Data Processing

JF - Optoelectronics, Instrumentation and Data Processing

SN - 8756-6990

IS - 6

ER -