An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials
Zernike circular polynomials (ZCP) play a significant role in optics engineering. The symbolic expressions for ZCP are valuable for theoretic analysis and engineering designs. However, there are still two problems which remain open: firstly, there is a lack of sufficient mathematical formulas of the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10144301/ |
| _version_ | 1797804073804627968 |
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| author | Hong-Yan Zhang Yu Zhou Fu-Yun Li |
| author_facet | Hong-Yan Zhang Yu Zhou Fu-Yun Li |
| author_sort | Hong-Yan Zhang |
| collection | DOAJ |
| description | Zernike circular polynomials (ZCP) play a significant role in optics engineering. The symbolic expressions for ZCP are valuable for theoretic analysis and engineering designs. However, there are still two problems which remain open: firstly, there is a lack of sufficient mathematical formulas of the ZCP for optics designers; secondly the formulas for inter-conversion of Noll’s single index and Born-Wolf’s double indices of ZCP are neither uniquely determinate nor satisfactory. An automatic method for generating symbolic expressions for ZCP is proposed based on five essential factors: the new theorems for converting the single/double indices of the ZCP, the robust and effective numeric algorithms for computing key parameters of ZCP, the symbolic algorithms for generating mathematical expressions of ZCP, and meta-programming & LATEX programming for generating the table of ZCP. The theorems, method, algorithms and system architecture proposed are beneficial to both optics design process, optics software, computer-output typesetting in publishing industry as well as STEM education. |
| first_indexed | 2024-03-13T05:30:40Z |
| format | Article |
| id | doaj.art-99afafc8a39a4be6b16fe8d0b4838f37 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-13T05:30:40Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-99afafc8a39a4be6b16fe8d0b4838f372023-06-14T23:00:27ZengIEEEIEEE Access2169-35362023-01-0111564815649310.1109/ACCESS.2023.328302810144301An Automatic Method for Generating Symbolic Expressions of Zernike Circular PolynomialsHong-Yan Zhang0https://orcid.org/0000-0002-4400-9133Yu Zhou1https://orcid.org/0000-0002-8481-1796Fu-Yun Li2School of Information Science and Technology, Hainan Normal University, Haikou, ChinaSchool of Information Science and Technology, Hainan Normal University, Haikou, ChinaSchool of Information Science and Technology, Hainan Normal University, Haikou, ChinaZernike circular polynomials (ZCP) play a significant role in optics engineering. The symbolic expressions for ZCP are valuable for theoretic analysis and engineering designs. However, there are still two problems which remain open: firstly, there is a lack of sufficient mathematical formulas of the ZCP for optics designers; secondly the formulas for inter-conversion of Noll’s single index and Born-Wolf’s double indices of ZCP are neither uniquely determinate nor satisfactory. An automatic method for generating symbolic expressions for ZCP is proposed based on five essential factors: the new theorems for converting the single/double indices of the ZCP, the robust and effective numeric algorithms for computing key parameters of ZCP, the symbolic algorithms for generating mathematical expressions of ZCP, and meta-programming & LATEX programming for generating the table of ZCP. The theorems, method, algorithms and system architecture proposed are beneficial to both optics design process, optics software, computer-output typesetting in publishing industry as well as STEM education.https://ieeexplore.ieee.org/document/10144301/Zernike circular polynomialsymbolic computationmathematical tablecomputer-output typesettingLATEX programmingSTEM education |
| spellingShingle | Hong-Yan Zhang Yu Zhou Fu-Yun Li An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials IEEE Access Zernike circular polynomial symbolic computation mathematical table computer-output typesetting LATEX programming STEM education |
| title | An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials |
| title_full | An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials |
| title_fullStr | An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials |
| title_full_unstemmed | An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials |
| title_short | An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials |
| title_sort | automatic method for generating symbolic expressions of zernike circular polynomials |
| topic | Zernike circular polynomial symbolic computation mathematical table computer-output typesetting LATEX programming STEM education |
| url | https://ieeexplore.ieee.org/document/10144301/ |
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