An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1
Based on the importance of spherical harmonics and their applicability in many physical problems, this research aimed to study the diffraction pattern of light by a circular aperture starting from the first Rayleigh–Sommerfeld diffraction equation and to expand the polar radius of a point on the sur...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Optics |
| Online Access: | http://dx.doi.org/10.1155/2020/3057674 |
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| _version_ | 1832565892812111872 |
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| author | Mahmoud Ahmad Najah Kabalan Samar Omran |
| author_facet | Mahmoud Ahmad Najah Kabalan Samar Omran |
| author_sort | Mahmoud Ahmad |
| collection | DOAJ |
| description | Based on the importance of spherical harmonics and their applicability in many physical problems, this research aimed to study the diffraction pattern of light by a circular aperture starting from the first Rayleigh–Sommerfeld diffraction equation and to expand the polar radius of a point on the surface of the circular aperture based on spherical harmonics. We depended on this theoretical framework in our paper. We calculated the optical intensity compounds C00,C10,C11,C1−1 for n=0,1,m=−1,0,1. We studied the intensity distributions in three special cases (along the optical axis, at the geometrical focal plane, and along the boundary of the geometrical shadow). We presented numerical comparative examples to illustrate the variation of the intensity versus a ratio (Z/A is the ratio of the distance between the circular aperture and the observation plane to a radius of the circular aperture), and we used Maple program to represent these results. We noticed that the expansion we made using spherical harmonic analysis led to an increase in the number of fringes bright enough to be visible to the naked eye. We then concluded with a brief discussion of the results. |
| format | Article |
| id | doaj-art-e13b9a65aeaf493188b69a3b76578832 |
| institution | Kabale University |
| issn | 1687-9384 1687-9392 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Optics |
| spelling | doaj-art-e13b9a65aeaf493188b69a3b765788322025-02-03T01:06:22ZengWileyInternational Journal of Optics1687-93841687-93922020-01-01202010.1155/2020/30576743057674An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1Mahmoud Ahmad0Najah Kabalan1Samar Omran2Department of Physics, Faculty of Science, Tishreen University, Lattakia, SyriaDepartment of Physics, Faculty of Science, Tishreen University, Lattakia, SyriaDepartment of Physics, Faculty of Science, Tishreen University, Lattakia, SyriaBased on the importance of spherical harmonics and their applicability in many physical problems, this research aimed to study the diffraction pattern of light by a circular aperture starting from the first Rayleigh–Sommerfeld diffraction equation and to expand the polar radius of a point on the surface of the circular aperture based on spherical harmonics. We depended on this theoretical framework in our paper. We calculated the optical intensity compounds C00,C10,C11,C1−1 for n=0,1,m=−1,0,1. We studied the intensity distributions in three special cases (along the optical axis, at the geometrical focal plane, and along the boundary of the geometrical shadow). We presented numerical comparative examples to illustrate the variation of the intensity versus a ratio (Z/A is the ratio of the distance between the circular aperture and the observation plane to a radius of the circular aperture), and we used Maple program to represent these results. We noticed that the expansion we made using spherical harmonic analysis led to an increase in the number of fringes bright enough to be visible to the naked eye. We then concluded with a brief discussion of the results.http://dx.doi.org/10.1155/2020/3057674 |
| spellingShingle | Mahmoud Ahmad Najah Kabalan Samar Omran An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1 International Journal of Optics |
| title | An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1 |
| title_full | An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1 |
| title_fullStr | An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1 |
| title_full_unstemmed | An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1 |
| title_short | An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1 |
| title_sort | analytical study of the diffraction of light by a circular aperture using spherical harmonics for n≤1 |
| url | http://dx.doi.org/10.1155/2020/3057674 |
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