Simulation and error analysis of non-null interferometry for measuring high-order aspheric surface parameter errors

2021 ◽  
Author(s):  
Yiming Liu ◽  
Xin Tao ◽  
Yao Hu ◽  
Qun Hao
Keyword(s):  
Error Analysis ◽  
High Order ◽  
Aspheric Surface ◽  
Surface Parameter

Design and Error Analysis of the Computer-Generated Helogram Used for Concave Aspheric Surface Testing

2012 ◽  
Vol 49 (11) ◽  
pp. 110902
Author(s):  
冯婕 Feng Jie ◽  
邓超 Deng Chao ◽  
邢廷文 Xing Tingwen
Keyword(s):  
Error Analysis ◽  
Aspheric Surface ◽  
Surface Testing

Error analysis of aspheric surface with reference datum

2015 ◽  
Vol 54 (21) ◽  
pp. 6543
Author(s):  
Yanglin Peng ◽  
Yifan Dai ◽  
Shanyong Chen ◽  
Ci Song ◽  
Feng Shi
Keyword(s):  
Error Analysis ◽  
Aspheric Surface

scholarly journals A High Accurate and Stable Legendre Transform Based on Block Partitioning and Butterfly Algorithm for NWP

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 966
Author(s):  
Fukang Yin ◽  
Jianping Wu ◽  
Junqiang Song ◽  
Jinhui Yang
Keyword(s):  
Computational Complexity ◽  
Error Analysis ◽  
Numerical Stability ◽  
High Order ◽  
Numerical Results ◽  
Computational Time ◽  
Legendre Transform ◽  
Practical Application ◽  
Block Partitioning ◽  
Very High

In this paper, we proposed a high accurate and stable Legendre transform algorithm, which can reduce the potential instability for a very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of the Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(Nlog2N /loglogN) in theory and O(Nlog3N) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.

Profile Measurement of Large Aspheric Optical Surface by Scanning Deflectometry with Rotatable Optical Devices - Error Analysis and Pre-Experiment-

2010 ◽  
Vol 447-448 ◽  
pp. 604-608 ◽  
Author(s):  
Mu Zheng Xiao ◽  
Satomi Jujo ◽  
Satoru Takahashi ◽  
Kiyoshi Takamasu
Keyword(s):  
Error Analysis ◽  
High Surface ◽  
Measuring Method ◽  
Optical Devices ◽  
Profile Measurement ◽  
Aspheric Surface ◽  
Optical Surface ◽  
Measuring Range ◽  
Angle Difference ◽  
Flat Mirror

Large aspheric mirrors with diameter over 300 millimeters with high surface accuracy are wildly used in many areas such as astronomical telescopes. Interferometers are widely used in profile measurement of optical flat and sphere. However, standard reference aspheric surface which is necessary for this method is difficult to make. Scanning defletometry based on ESAD (Extended Shear Angle Difference) is used to measure ultra-precise large near-flat and slight curved optical surface with the accuracy of sub-nanometer. However, it is not possible for it to measure aspheric surface because of the limitation of the measuring range of autocollimators. We proposed a new measuring method to scan the surface of a large aspheric optical surface using autocollimator with rotatable optical devices fixed on linear motion stage. To eliminate the influence of the pitching error of the scanning stage, we use two mirrors reflecting laser comes from autocollimator, which have the same effect with a pentaprism used in ESAD. To enlarge the measuring range of the autocollimator, we use a rotatable mirror to fit the changes of the slope of the mirror surface under measurement. The error analysis of the method is done. Measurement of an optical flat mirror and a sphere mirror with diameter of 50 mm and biggest slope of 6000 arc-second are done. The rotatable optical devices that we designed are proved effective on eliminating the pitching error of the moving stage.

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