TY - JOUR

T1 - Diffraction Phenomena on Extended Asymmetric Slit with Absolutely Absorbing Inner Faces

AU - Chugui, Yu V.

N1 - Funding Information: The work was supported by the Ministry of Science and Higher Education of the Russian Federation (project no. AAAA-A17-117121270018-3). Publisher Copyright: © 2022, >Allerton Press, Inc.

PY - 2022/2

Y1 - 2022/2

N2 - Fraunhofer diffraction patterns (spectra) of extended (in depth) asymmetric slit holes with absolutely absorbing inner faces and with different input (D) and output (D1) apertures are calculated in the far field based on the model of equivalent diaphragms. The behavior of the spectrum of an extended object is studied analytically in the case of aperture differences (Formula Presented.) that are noticeably smaller than the size of the Fresnel zone (Formula Presented.) is the light wavelength and d is the hole depth). It is shown that in the range of angles (Formula Presented.) the observed diffraction pattern of an extended object is equivalent to the diffraction of light on a flat slit (d=0) with an effective width (Formula Presented.). Based on a constructive approximation of the integral Fresnel function, the features of light diffraction on volumetric holes with noticeably different apertures are studied analytically: (Formula Presented.). Calculations show that in the cases of expanding ((Formula Presented.)) and narrowing ((Formula Presented.)) apertures, the behavior of the minima of the observed diffraction patterns in the ranges of angles (Formula Presented.) differs little from the equidistant behavior for a flat slit (d=0) of width D and D1, respectfully. The results can be used in the development of optoelectronic systems for dimensional inspection of perforated plates.

AB - Fraunhofer diffraction patterns (spectra) of extended (in depth) asymmetric slit holes with absolutely absorbing inner faces and with different input (D) and output (D1) apertures are calculated in the far field based on the model of equivalent diaphragms. The behavior of the spectrum of an extended object is studied analytically in the case of aperture differences (Formula Presented.) that are noticeably smaller than the size of the Fresnel zone (Formula Presented.) is the light wavelength and d is the hole depth). It is shown that in the range of angles (Formula Presented.) the observed diffraction pattern of an extended object is equivalent to the diffraction of light on a flat slit (d=0) with an effective width (Formula Presented.). Based on a constructive approximation of the integral Fresnel function, the features of light diffraction on volumetric holes with noticeably different apertures are studied analytically: (Formula Presented.). Calculations show that in the cases of expanding ((Formula Presented.)) and narrowing ((Formula Presented.)) apertures, the behavior of the minima of the observed diffraction patterns in the ranges of angles (Formula Presented.) differs little from the equidistant behavior for a flat slit (d=0) of width D and D1, respectfully. The results can be used in the development of optoelectronic systems for dimensional inspection of perforated plates.

KW - Fourier optics

KW - Fresnel and Fraunhofer diffraction

KW - optical dimensional inspection

KW - spectra of extended objects

KW - volumetric hole

UR - http://www.scopus.com/inward/record.url?scp=85133907131&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0e01b658-dcc7-3695-9b01-5ffab5d0b909/

U2 - 10.3103/S8756699022010022

DO - 10.3103/S8756699022010022

M3 - Article

AN - SCOPUS:85133907131

VL - 58

SP - 43

EP - 54

JO - Optoelectronics, Instrumentation and Data Processing

JF - Optoelectronics, Instrumentation and Data Processing

SN - 8756-6990

IS - 1

ER -