Modeling ophthalmic surfaces using Zernike, Bessel and Chebyshev type functions

被引：2

作者：

Rodrigues, M. M. ^{[4
]}

Rosa, A. ^{[1
,2
,3
]}

Vieira, N. ^{[4
]}

Murta, J. N. ^{[1
,2
,3
]}

机构：

[1] Ctr Hosp & Univ Coimbra, Ophthalmol Unit, Coimbra, Portugal

[2] Ctr Cirurg Coimbra, Coimbra, Portugal

[3] Univ Coimbra, Fac Med, Coimbra, Portugal

[4] Univ Aveiro, Dept Math, CIDMA Ctr Res & Dev Math & Applicat, Campus Univ Santiago, P-3810193 Aveiro, Portugal

来源：

32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32) | 2019年 / 1194卷

关键词：

ABERRATION;

D O I：

10.1088/1742-6596/1194/1/012093

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper the application of Zernike, Bessel and Chebyshev functions is studied and the results are compared when modeling ophthalmic surfaces in visual optics. The total RMS error is presented when addressing capability of these functions in fitting with different surfaces. It is shown that Chebyshev polynomials could be appropriate alternatives of the Zernike polynomials to represent complete anterior corneal surfaces.

引用

页数：7

共 50 条

[1] Extraction of wideband response using Bessel-Chebyshev functions
Koh, J
Kim, T
Lee, W
Sarkar, TK
[J]. IEICE TRANSACTIONS ON COMMUNICATIONS, 2002, E85B (10) : 2263 - 2272
[2] Zernike vs. Bessel circular functions in visual optics
Trevino, Juan P.
Gomez-Correa, Jesus E.
Iskander, D. Robert
Chavez-Cerda, Sabino
[J]. OPHTHALMIC AND PHYSIOLOGICAL OPTICS, 2013, 33 (04) : 394 - 402
[3] CLENSHAW,CW - CHEBYSHEV SERIES FOR BESSEL FUNCTIONS OF FRACTIONAL ORDER
GOLDSTEI.M
[J]. MATHEMATICS OF COMPUTATION, 1967, 21 (99) : 509 - &
[4] Optimal modeling of corneal surfaces with Zernike polynomials
Iskander, DR
Collins, MJ
Davis, B
[J]. IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, 2001, 48 (01) : 87 - 95
[5] CHEBYSHEV SERIES EXPANSIONS FOR MODIFIED BESSEL FUNCTIONS OF LARGE ORDER AND ARGUMENT
LUKE, YL
[J]. SIAM REVIEW, 1974, 16 (01) : 131 - 131
[6] The limitation of Bessel functions for ICME modeling
Russell, CT
Mulligan, T
[J]. SOLAR WIND TEN, PROCEEDINGS, 2003, 679 : 125 - 128
[7] EXTENSION OF HUYGENS TYPE INEQUALITIES FOR BESSEL AND MODIFIED BESSEL FUNCTIONS
Mehrez, Khaled
[J]. COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2019, 34 (03): : 799 - 809
[8] Jordan type inequalities involving the Bessel and modified Bessel functions
Zhu, Ling
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (02) : 724 - 736
[9] Laguerre-type Bessel functions
Cesarano, C
Germano, B
Ricci, PE
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2005, 16 (04) : 315 - 322
[10] Redheffer type bounds for Bessel and modified Bessel functions of the first kind
Baricz, Arpad
Mehrez, Khaled
[J]. AEQUATIONES MATHEMATICAE, 2018, 92 (03) : 425 - 439

← 1 2 3 4 5 →