TY - JOUR

T1 - Fourier optics of constant-thickness three-dimensional objects on the basis of diffraction models

AU - Chugui, Yu V.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Results of investigations of diffraction phenomena on constant-thickness three-dimensional objects with flat inner surfaces (thick plates) are summarized on the basis of our constructive theory of their calculation as applied to dimensional inspection. It is based on diffraction models of 3D objects with the use of equivalent diaphragms (distributions), which allow the Kirchhoff–Fresnel approximation to be effectively used. In contrast to available rigorous and approximate methods, the present approach does not require cumbersome calculations; it is a clearly arranged method, which ensures sufficient accuracy for engineering applications. It is found that the fundamental diffraction parameter for 3D objects of constant thickness d is the critical diffraction angle θcr=λ/d at which the effect of three-dimensionality on the spectrum of the 3D object becomes appreciable. Calculated Fraunhofer diffraction patterns (spectra) and images of constant-thickness 3D objects with absolutely absorbing, absolutely reflecting, and gray internal faces are presented. It is demonstrated that selection of 3D object fragments can be performed by choosing an appropriate configuration of the wave illuminating the object (plane normal or inclined waves, spherical waves).

AB - Results of investigations of diffraction phenomena on constant-thickness three-dimensional objects with flat inner surfaces (thick plates) are summarized on the basis of our constructive theory of their calculation as applied to dimensional inspection. It is based on diffraction models of 3D objects with the use of equivalent diaphragms (distributions), which allow the Kirchhoff–Fresnel approximation to be effectively used. In contrast to available rigorous and approximate methods, the present approach does not require cumbersome calculations; it is a clearly arranged method, which ensures sufficient accuracy for engineering applications. It is found that the fundamental diffraction parameter for 3D objects of constant thickness d is the critical diffraction angle θcr=λ/d at which the effect of three-dimensionality on the spectrum of the 3D object becomes appreciable. Calculated Fraunhofer diffraction patterns (spectra) and images of constant-thickness 3D objects with absolutely absorbing, absolutely reflecting, and gray internal faces are presented. It is demonstrated that selection of 3D object fragments can be performed by choosing an appropriate configuration of the wave illuminating the object (plane normal or inclined waves, spherical waves).

KW - diffraction

KW - Fourier optics

KW - light interference

KW - spectra and images of 3D objects

KW - INSPECTION

KW - VOLUMETRIC BODIES

KW - FRAUNHOFER-DIFFRACTION

UR - http://www.scopus.com/inward/record.url?scp=85038076346&partnerID=8YFLogxK

U2 - 10.3103/S8756699017050090

DO - 10.3103/S8756699017050090

M3 - Article

AN - SCOPUS:85038076346

VL - 53

SP - 494

EP - 507

JO - Optoelectronics, Instrumentation and Data Processing

JF - Optoelectronics, Instrumentation and Data Processing

SN - 8756-6990

IS - 5

ER -