Freeform surface of progressive addition lens represented by Zernike polynomials

2016 ◽  
Author(s):  
Yiyu Li ◽  
Risheng Xia ◽  
Jiaojie Chen ◽  
Haihua Feng ◽  
Yimin Yuan ◽  
...  
Keyword(s):  
Freeform Surface ◽  
Zernike Polynomials ◽  
Progressive Addition Lens

Fabrication and correction of freeform surface based on Zernike polynomials by slow tool servo

Optifab 2017 ◽  
2017 ◽  
Author(s):  
Yuan-Chieh Cheng ◽  
Ming-Ying Hsu ◽  
Wei-Jei Peng ◽  
Wei-Yao Hsu
Keyword(s):  
Freeform Surface ◽  
Zernike Polynomials ◽  
Slow Tool Servo

Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description

2012 ◽  
Vol 63 (1-4) ◽  
pp. 225-233 ◽  
Author(s):  
Wei-Yao Hsu ◽  
Yen-Liang Liu ◽  
Yuan-Chieh Cheng ◽  
Ching-Hsiang Kuo ◽  
Chun-Chieh Chen ◽  
...  
Keyword(s):  
Freeform Surface ◽  
B Spline ◽  
Ultra Precision ◽  
Progressive Addition Lens

scholarly journals Study on Design and Diamond Turning of Optical Freeform Surface for Progressive Addition Lenses

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Yi Wei ◽  
Peng Zhai ◽  
Xiaoyi Chen ◽  
Lei He
Keyword(s):  
Tool Path ◽  
Single Point ◽  
Optical Design ◽  
Tool Path Generation ◽  
Diamond Turning ◽  
Freeform Surface ◽  
Path Generation ◽  
Nose Radius ◽  
Angle Method ◽  
Progressive Addition Lens

Optical freeform surface components have attracted much attention due to their high degree of design freedom and small size. However, the design and processing difficulty of such components limit its wide application in optics industry. In recent years, diamond turning has been considered an efficient method for processing optical freeform surfaces, but the research on tool path generation of this processing method is not systematic. Progressive addition lens (PAL) is a typical optical freeform surface and is widely used to correct people’s vision problems. Firstly, this paper introduces a method of designing PAL. Then, an optimized tool path generation method for diamond turning of the optical freeform surface is proposed, the equal angle method is used to select the discrete points, and a tool nose radius compensation method suitable for both slow slide servo (SSS) and fast tool servo (FTS) is adopted. Finally, the turning experiment is carried out with a single point diamond lathe, and a PAL surface with a roughness of 0.087 μm was obtained. The power and astigmatism distributions were measured using a Rotlex freeform verifier to verify the rationality of the optical design.

Soft Twisting Pneumatic Actuators Enabled by Freeform Surface Design

2021 ◽  
pp. 1-1
Author(s):  
Feifei Chen ◽  
Yunpeng Miao ◽  
Guoying Gu ◽  
Xiangyang Zhu
Keyword(s):  
Freeform Surface ◽  
Surface Design ◽  
Pneumatic Actuators

scholarly journals Asymmetric Double Freeform Surface Lens for Integrated LED Automobile Headlamp

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 663
Author(s):  
Hui Zhang ◽  
Dengfei Liu ◽  
Yinwan Wei ◽  
Hong Wang
Keyword(s):  
Optical System ◽  
Design Method ◽  
Chromatic Dispersion ◽  
Electronic Devices ◽  
Color Temperature ◽  
Freeform Surface ◽  
United Nations Economic Commission ◽  
System A ◽  
Economic Commission ◽  
Key Points

We propose a design method of asymmetric double freeform surface lens for an integrated LED automobile headlamp and develop an integrated LED automobile optical system. A single asymmetric double freeform surface lens is designed to redistribute rays emitting from the light source for realizing both low and high beams. Moreover, a freeform surface reflector is used to improve the energy efficiency of high beams. The prism placed in the optical path can suppress chromatic dispersion on the edge of the target plane. Simulation and experimental results show that the illumination values and color temperature of the key points can fully meet the requirements of United Nations Economic Commission for Europe vehicle regulations (ECE) R112, 48, and 128. The volume of the whole optical system comprised of freeform surface elements is smaller than that of the low beam system of a traditional headlamp, resulting in saved space, in which other electronic devices can be installed for the safety of the driver, which indicates that the proposed method is practical in the field of automobile lighting.

On the circle polynomials of Zernike and related orthogonal sets

1954 ◽  
Vol 50 (1) ◽  
pp. 40-48 ◽  
Author(s):  
A. B. Bhatia ◽  
E. Wolf
Keyword(s):  
Unit Circle ◽  
Generating Functions ◽  
Legendre Polynomials ◽  
Phase Contrast ◽  
Diffraction Theory ◽  
Zernike Polynomials ◽  
Optical Aberrations ◽  
Orthogonal Set ◽  
Complete Orthogonal Set ◽  
Explicit Expressions

ABSTRACTThe paper is concerned with the construction of polynomials in two variables, which form a complete orthogonal set for the interior of the unit circle and which are ‘invariant in form’ with respect to rotations of axes about the origin of coordinates. It is found that though there exist an infinity of such sets there is only one set which in addition has certain simple properties strictly analogous to that of Legendre polynomials. This set is found to be identical with the set of the circle polynomials of Zernike which play an important part in the theory of phase contrast and in the Nijboer-Zernike diffraction theory of optical aberrations.The results make it possible to derive explicit expressions for the Zernike polynomials in a simple, systematic manner. The method employed may also be used to derive other orthogonal sets. One new set is investigated, and the generating functions for this set and for the Zernike polynomials are also given.

Sign in / Sign up

Export Citation Format

Share Document