On elliptic trigonometric form of the Zernike system and polar limits

Atakishiyev Natig M.; Pogosyan George S.; Bernardo Wolf Kurt; Yakhno Alexander

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On elliptic trigonometric form of the Zernike system and polar limits

机译：关于Zernike系统和极性限制的椭圆三角形式

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摘要

The Zernike system provides orthogonal polynomial solution bases on the unit disk that separate in coordinates that are generically elliptic. This is a superintegrable system whose optical realization is a scalar wavefield on the plane of a circular pupil. Here we describe the solution set in the trigonometric form of elliptic coordinates expressed in terms of special functions, and examine closely the two limits where the explicit form of the wavefunctions in elliptic coordinates reduce to wavefunctions in polar coordinates.

机译：Zernike系统在单位盘上提供正交多项式溶液基础，其在彼此椭圆形分开的坐标上。这是一种超纬度系统，其光学实现是圆形瞳孔平面上的标量波形。在这里，我们描述了在特殊功能方面表达的椭圆坐标的三角形式的解决方案，并且仔细检查了椭圆坐标中的波力的显式形式的两个限制，从极性坐标中减少到波力源。

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来源
《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2019年第4期|共13页
作者
Atakishiyev Natig M.; Pogosyan George S.; Bernardo Wolf Kurt; Yakhno Alexander;
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作者单位

Univ Nacl Autonoma Mexico Inst Matemat Cuernavaca Morelos Mexico;

Univ Guadalajara Ctr Univ Ciencias Exactas &

Ingn Dept Matemat Guadalajara Jalisco Mexico;

Univ Nacl Autonoma Mexico Inst Ciencias Fis Cuernavaca Morelos Mexico;

Univ Guadalajara Ctr Univ Ciencias Exactas &

Ingn Dept Matemat Guadalajara Jalisco Mexico;

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原文格式 PDF
正文语种 eng
中图分类物理学;
关键词
Zernike system; separation of variables; elliptic trigonometric coordinates; limits to polar spherical coordinates;

机译：Zernike System;变量的分离;椭圆三角坐标;极限北极球形坐标;

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1. On elliptic trigonometric form of the Zernike system and polar limits [J] . Atakishiyev Natig M., Pogosyan George S., Bernardo Wolf Kurt, Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2019,第4期

机译：关于Zernike系统和极性限制的椭圆三角形式
2. Modular Transformation and Twist Between Trigonometric Limits of sl(n) Elliptic R-Matrix [J] . 无理论物理通讯：英文版 . 2001,第002期

机译：sl（n）椭圆R矩阵的三角极限之间的模转换和扭曲
3. Application of the Elliptical Trigonometry in industrial electronic systems with analyzing, modeling and simulating two functions Elliptic Mar and Elliptic Jes-x [J] . CLAUDE BAYEH WSEAS Transactions on Circuits and Systems . 2010,第7a9期

机译：椭圆三角函数在工业电子系统中的应用，通过分析，建模和仿真两个函数Elliptic Mar和Elliptic Jes-x
4. A survey on the application of the Elliptical Trigonometry in industrial electronic systems using controlled waveforms with modeling and simulating of two functions Elliptic Mar and Elliptic Jes-x [C] . CLAUDE BAYEH Latest trends on circuits, systems and signals . 2010

机译：椭圆三角法在工业电子系统中的应用研究-使用受控波形并建模和仿真两个函数Elliptic Mar和Elliptic Jes-x
5. Imaging performance of elliptical-boundary varifocal mirrors in active optical systems. [D] . Lukes, Sarah Jane. 2015

机译：主动光学系统中椭圆边界变焦镜的成像性能。
6. An Enhanced Biometric-Based Authentication Scheme for Telecare Medicine Information Systems Using Elliptic Curve Cryptosystem [O] . Yanrong Lu, Lixiang Li, Haipeng Peng, -1

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7. Modular transformation and twist between trigonometric limits of $sl(n)$ elliptic R-matrix [O] . Yang, W. -L., Zhen, Y. 2001

机译：模块化转换和$ sl（n）$的三角限制之间的扭曲椭圆R矩阵

On elliptic trigonometric form of the Zernike system and polar limits

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