Description of Free-form Optical Curved Surface Using Two-Variable Orthogonal Polynomials

Wang Qingfeng; Cheng Dewen; Wang Yongtian

doi:10.3788/aos201232.0922002

[1] Fan Xinlong, Guan Chunlin, Rao Changhui. Wave-front fitting capability analysis of 1.8 m telescope′s adaptive secondary mirror［J］. Acta Optica Sinica, 2011, 31(8): 0822002

[2] Chen Xu, Yuan Wenquan, Feng Yutao. Study of the error of the reference lens in absolute spherical testing and the thermal deformation model establishment［J］. Acta Optica Sinica, 2011, 31(2): 0212002

[3] Peng Xiang, Yin Yongkai, Liu Xiaoli et al.. Phase-aided three-dimensional imaging and metrology［J］. Acta Optica Sinica, 2011, 31(9): 189～201

[4] Qingfeng Wang, Qican Zhang, Yuankun Liu. Three-dimensional measurement of object in water by tracking phase value［J］. Acta Optica Sinica, 2009, 31(6): 1570～1576

[5] P. A. Coronato, R. C. Juergens. Transferring FEA results to optics codes with Zernikes: a review of techniques［C］. SPIE, 2003, 5176: 1～8

[6] R. C. Juergens, P. A. Coronato. Improved method for transfer of FEA results to optical codes［C］. SPIE, 2003, 5174: 105～115

[7] G. W. Forbes. Shape specification for axially symmetric optical surfaces［J］. Opt. Express, 2007, 15(8): 5218～5226

[8] G. W. Forbes. Robust and fast computation for the polynomials of optics［J］. Opt. Express, 2010, 18(13): 13851～13862

[9] G. W. Forbes. Characterizing the shape of freeform optics［J］. Opt. Express, 2012, 20(3): 2483～2499

[10] K. Fuerschbach, J. P. Rolland, K. P. Thompson. A new family of optical systems employing -polynomial surfaces［J］. Opt. Express, 2011, 19(22): 21919～21928

[11] D. Cheng, Y. Wang, H. Hua. Free form optical system design with differential equations［C］. SPIE, 2010, 7849: 78490Q

[12] C. Minano Juan, Benitez Pablo, Lin Wang. An application of the SMS method for imaging designs［J］. Opt. Express, 2009, 17(26): 24036～24044

[13] F. Liu, B. M. Robinson, P. J. Reardon et al.. Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials［J］. Opt. Engng., 2011, 50(4): 43608～43609

[14] V. N. Mahajan, G. Dai. Orthonormal polynomials in wavefront analysis: analytical solution［J］. J. Opt. Soc. Am. A, 2007, 24(9): 2994～3016

[15] V. N. Mahajan. Zernike annular polynomials and optical aberrations of systems with annular pupils［J］. Appl. Opt., 1994, 33(34): 8125～8127

[16] V. N. Mahajan. Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils［J］. Appl. Opt., 2010, 49(36): 6924～6929

[17] G. W. Forbes. Manufacturability estimates for optical aspheres［J］. Opt. Express, 2011, 19(10): 9923～9941

[18] F. Greg. Better ways to specify aspheric shapes can facilitate design, fabrication and testing alike［C］. Optical Society of America, 2010. JMA1

[19] P. T. Kevin, F. Florian, P. R. Jannick et al.. The Forbes polynomial: a more predictable surface for fabricators［C］. Optical Society of America, 2010. O7uA6

[20] B. Ma, L. Li, K. P. Thompson et al.. Applying slope constrained Q-type aspheres to develop higher performance lenses［J］. Opt. Express, 2011, 19(22): 21174～21179

[21] E. W. Weisstein. Gram-Schmidt Orthonormalization［Z］. 2012From MathWorld--A Wolfram Web Resource

[22] C. F. Dunkl, Y. Xu. Orthogonal Polynomials of Several Variables［M］. Cambrihge: Cambridge University Press, 2003. 30～57

[23] I. Kaya, K. P. Thompson, J. P. Rolland. Edge clustered fitting grids for φ-polynomial characterization of freeform optical surfaces［J］. Opt. Express, 2011, 19(27): 26962～26974

[24] Synopsys. Code V Reference Manual［Z］. 2011

[25] Liu Jianfeng, Long Funian, Zhang Wei. Frequency domain analysis of surface figure fitting based on Zernike polynomials［J］. Acta Optica Sinica, 2005, 25(8): 1062～1066

CLP Journals