TY - JOUR

T1 - Forming Images of an Asymmetric Absolutely Reflective Edge of a 3D Object in Coherent Light

AU - Chugui, Yu V.

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

PY - 2021/5

Y1 - 2021/5

N2 - In an analytical form, the features of the image formation of the faces of a three-dimensional asymmetric edge of an object with an absolutely reflective inner surface are studied in relation to the dimensional inspection. Formulas are obtained for calculating the fields in images of object faces in ideal and diffraction-limited systems, depending on the value of the object’s bevel c, the phase shift (Formula presented.) of the wave reflected from the inner surface of the object, and the angular aperture (Formula presented.) of the coherent optical image formation and filtering system. It is found that for metallic three-dimensional (3D) objects (Formula presented.), the field value in the image of the back face at the point (Formula presented.) corresponding to the position of its boundary is negligible when the depth of focus of the system is much less than the thickness of the object. It is shown that at c bevels of the object, much smaller than the Fresnel zone (Formula presented.) ((Formula presented.)is the wavelength of light, and d is the thickness of the object) and greater than the depth of focus (Formula presented.), the shift of the intensity profile in the image of the front face is proportional to (Formula presented.) and depends on the phase (Formula presented.). For large bevels, when (Formula presented.) and (Formula presented.), the active face is the back one and the displacement of the back face boundary is inversely proportional to the value of (Formula presented.). These offsets can lead to systematic errors in the measurement of the position of the boundaries of the 3D-object faces, and they must be taken into account during precision dimensional inspection.

AB - In an analytical form, the features of the image formation of the faces of a three-dimensional asymmetric edge of an object with an absolutely reflective inner surface are studied in relation to the dimensional inspection. Formulas are obtained for calculating the fields in images of object faces in ideal and diffraction-limited systems, depending on the value of the object’s bevel c, the phase shift (Formula presented.) of the wave reflected from the inner surface of the object, and the angular aperture (Formula presented.) of the coherent optical image formation and filtering system. It is found that for metallic three-dimensional (3D) objects (Formula presented.), the field value in the image of the back face at the point (Formula presented.) corresponding to the position of its boundary is negligible when the depth of focus of the system is much less than the thickness of the object. It is shown that at c bevels of the object, much smaller than the Fresnel zone (Formula presented.) ((Formula presented.)is the wavelength of light, and d is the thickness of the object) and greater than the depth of focus (Formula presented.), the shift of the intensity profile in the image of the front face is proportional to (Formula presented.) and depends on the phase (Formula presented.). For large bevels, when (Formula presented.) and (Formula presented.), the active face is the back one and the displacement of the back face boundary is inversely proportional to the value of (Formula presented.). These offsets can lead to systematic errors in the measurement of the position of the boundaries of the 3D-object faces, and they must be taken into account during precision dimensional inspection.

KW - 3D dimensional inspection

KW - Fourier optics

KW - Fresnel and Fraunhofer diffraction

KW - images and spectra of 3D objects

KW - spatial filtering

KW - volumetric edge

UR - http://www.scopus.com/inward/record.url?scp=85118127203&partnerID=8YFLogxK

U2 - 10.3103/S8756699021030080

DO - 10.3103/S8756699021030080

M3 - Article

AN - SCOPUS:85118127203

VL - 57

SP - 311

EP - 322

JO - Optoelectronics, Instrumentation and Data Processing

JF - Optoelectronics, Instrumentation and Data Processing

SN - 8756-6990

IS - 3

ER -