An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials

被引：1

作者：

Zhang, Hong-Yan ^{[1
]}

Zhou, Yu ^{[1
]}

Li, Fu-Yun ^{[1
]}

机构：

[1] Hainan Normal Univ, Sch Informat Sci & Technol, Haikou 571158, Peoples R China

来源：

IEEE ACCESS | 2023年 / 11卷

基金：

海南省自然科学基金; 中国国家自然科学基金;

关键词：

Zernike circular polynomial; symbolic computation; mathematical table; computer-output typesetting; LATEX programming; STEM education; SYSTEMS;

D O I：

10.1109/ACCESS.2023.3283028

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：56481 / 56493

页数：13

共 19 条

[11]

Mahajan V.N., 2013, Optical Imaging and Aberrations, Part III: Wavefront Analysis

[12] ZERNIKE ANNULAR POLYNOMIALS FOR IMAGING-SYSTEMS WITH ANNULAR PUPILS [J].

MAHAJAN, VN .

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, 1981, 71 (01) :75-85

[13]

Malacara D., 2007, OPTICAL SHOP TESTING, Vthird

[14] ZERNIKE POLYNOMIALS AND ATMOSPHERIC-TURBULENCE [J].

NOLL, RJ .

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, 1976, 66 (03) :207-211

[15] Recursive formula to compute Zernike radial polynomials [J].

Shakibaei, Barmak Honarvar ;

Paramesran, Raveendran .

OPTICS LETTERS, 2013, 38 (14) :2487-2489

[16]

Wyant JamesC., ZERNIKE POLYNOMIALS

[17]

ZEMAX Development Corporation, 2008, EMAX OPT DES PROGR U

[18]

Zhang HY, 2024, Arxiv, DOI arXiv:2212.02495

[19]

Zhang S., 1996, COMPUTATION SPECIAL

← 1 2 →