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

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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).

Original languageEnglish
Pages (from-to)494-507
Number of pages14
JournalOptoelectronics, Instrumentation and Data Processing
Issue number5
Publication statusPublished - 1 Sep 2017


  • diffraction
  • Fourier optics
  • light interference
  • spectra and images of 3D objects


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