A New Algorithm for Solving the Best-Fit Sphere of Optical Aspherical Surface

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To solve the best-fit sphere (BFS) accurately is one of the technological keys for the generating and testing of optical aspherical surfaces. This paper presents a new algorithm for solving the BFS of aspherical surfaces to suppress some deficiencies in the existing BFS algorithms. In the proposed approach, a BFS is constructed, which passes through both sides of endpoints in the section of the aspherical surfaces, the center of the BFS is shifted along the x-axis, and its radius of curvature is automatically computed. The variable step size method is proposed to speed up the convergence of the iteration. Through numerically solving the BFS of conic and cubic surface, the advantages of the proposed approach are verified. The results show that the proposed approach is of rapid convergence, and high accuracy; it is not only suitable for the conic surface, but also for higher order aspheres. The obtained asphericity and material removal function is more suitable for the machining and test.

Info:

Periodical:

Advanced Materials Research (Volumes 418-420)

Edited by:

Xianghua Liu, Zhengyi Jiang and Jingtao Han

Pages:

1472-1477

Citation:

J. Q. Lin et al., "A New Algorithm for Solving the Best-Fit Sphere of Optical Aspherical Surface", Advanced Materials Research, Vols. 418-420, pp. 1472-1477, 2012

Online since:

December 2011

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Price:

$38.00

[1] J.H. Burge J.R. Angel and B. Cuerden: Lightweight mirror technology using a thin facesheet with active rigid support , (Proceedings of SPIE, Vol3356: 690-701, 1998).

[2] H.B. Cheng Y.P. Feng F.C. Song, et al,Calculation of the best-fit sphere aimed at least material removal ,. Transaction of Beijing Institute of Technology, Vol 28(5): 418-421+425, (2008).

[3] G .J. Dong, C.X. Han., S. Dong,Solution for best fitting spherical curvature radius and asphericity of off-axis aspherics of optical aspheric surface component ,. Key Engineering Materials, 364-366: 499-503,(2008).

DOI: https://doi.org/10.4028/www.scientific.net/kem.364-366.499

[4] X. Zhao , L.P. Song, Q. Kong, et al, Resolving of the best-fit sphere and the material removal in off-axis asphere fabrications ,. Acta Optica Sinica, (29): 61-64,(2009).

[5] H.B. Cheng Y.W. Wang, Z.J. Feng , Methods to determine best fit sphere for large off-axis aspheric lenses ,. Journal of Tsinghua University, 44(8): 1040-1042+1046,(2004).

[6] H.L. Liu D.G. Sha, Q. Hao, Q.D. Zhu, A method for calculating asphericity of high-order optical aspheric surface ,. Opto-Electronic Engineering, 31(6),(2004).

[7] E. Garbusi,C. Pruss,J. Liesener: New technique for flexible and rapid measurement of precision aspheres , (The International Society for Optical Engineering, 6616(1). 2007).

DOI: https://doi.org/10.1117/12.727898

[8] L. Yang,Advanced optical manufacturing technologies,. Beijing: Science Press, 46,(2001).

[9] D.G. Sha, S.X. Quan, Q.D. Zhu, et al,An optical asphericity definition and its accurate caculation ,. Aata Photonica Sinica, 24(1), (1995).

[10] C.M. Zeng, J. C. Yu, Aspherical grads method for calculating best fitting sphere of ultra-thin mirror and finite element analysis,. Optical Technique, 34(3): 323-327,(2008).

[11] Q.D. Wang, J.C. Yu,X.J. Zhang, Z.Y. Zhang , Solution for best fitting spherical curvature radius and asphericity of off-axis aspherics ,. Opto-Electronic Engineering, 27(3): 16-19,(2000).

DOI: https://doi.org/10.4028/0-87849-458-8.499