[1] [1] K P Thompson, J P Rolland. Freeform optical surfaces: a revolution in imaging optical design [J]. Opt Pho News, 2012, 23(6): 30-35.

[2] [2] D Cheng, Y Wang, H Hua, et al.. Design of an optical see-through head-mounted display with a low F-number and large field of view using a freeform prism [J]. Appl Opt, 2009, 48(14): 2655-2668.

[3] [3] K Fuerschbach, J P Rolland, K P Thompson. A new family of optical systems employing φ-polynomial surfaces [J]. Opt Express, 2011, 19(22): 21919-21928.

[4] [4] R R Shannon, J C Wyant. Applied Optics and Optical Engineering VIII [M]. San Diego: Academic Press, 1980.

[5] [5] R J Noll. Zernike polynomials and atmospheric turbulence [J]. J Opt Soc Am, 1976, 66(3): 207-211.

[6] [6] G W Forbes. Characterizing the shape of freeform optics [J]. Opt Express, 2012, 20(3): 2483-2499.

[7] [7] O Cakmakci, Sophie Vo, H Foroosh, et al.. Application of radial basis functions to shape description in a dual-element off-axis magnifier [J]. Opt Lett, 2008, 33(11): 1237-1239.

[8] [8] J E Stacy. Asymmetric spline surfaces: characteristics and applications [J]. Appl Opt, 1984, 23(16): 2710-2714.

[9] [9] Li Yun, Xing Yanwen. Surface error of optical components extended with non-uniform rational B-spline surface [J]. Acta Optica Sinica, 2012, 32(7): 0722001.

[10] [10] G D Wassermann, E Wolf. On the theory of aplanatic aspheric systems [J]. Proc Phys Soc B, 1949, 62(1): 2-8.

[11] [11] Wang Chao, Zhang Xin, Qu Hemeng, et al.. Design of novel catadioptric elliptical dome optical system [J]. Acta Optica Sinica, 2012, 32(8): 0822002.

[12] [12] D Cheng, Y Wang, H Hua. Free form optical system design with differential equations [C]. SPIE, 2010, 7849: 78490Q.

[13] [13] R Winstion, W Zhang. Novel aplanatic designs [J]. Opt Lett, 2009, 34(19): 3018-3019.

[14] [14] J C Miano, P Benitez, L Wang, et al.. An application of the SMS method for imaging designs [J]. Opt Express, 2009, 17(26): 24036-24044.

[15] [15] Zhang Hang, Liang Xue, Yan Jinhua, et al.. Compound parabolic concentrator-simultaneout multiple surfaces design methods for LED collimators [J]. Acta Optica Sinica, 2012, 32(9): 0922004.

[16] [16] V N Chekal, Y I Chudakov, S E Shevtsov. The use of coordinate-measurement machines to optimize the technology of automatic shaping of optical surfaces [J]. J Opt Tech, 2008, 25(11): 755-759.

[17] [17] J E Greivenkamp, R O Gappinger. Design of a nonnull interferometer for aspheric wave fronts [J]. Appl Opt, 2004, 43(27): 5143-5151.

[18] [18] H Shen, R Zhu, Z Gao, et al.. Design and fabrication of computer-generated holograms for testing optical freeform surfaces [J]. Chin Opt Lett, 2013, 11(3): 032201.

[19] [19] Shen Hua, Li Jia, Zhu Rihong, et al.. Design of non-null interferometer based on point source array for testing freeform surface [J]. Acta Optica Sinica, 2013, 33(12): 1222003.

[20] [20] W H Southwell. Wave-front estimation from wave-front slope measurements [J]. J Opt Soc Am, 1980, 70(8): 998-1006.

[21] [21] M Ares, S Royo. Comparison of cubic B-spline and Zernike-fitting techniques in complex wavefront reconstruction [J]. Appl Opt, 2006, 45(27): 6954-6964.

[22] [22] 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.

[23] [23] I Kaya, K P Thompson, J P Rolland. Comparative assessment of freeform polynomials as optical surface descriptions [J]. Opt Express, 2012, 20(20): 22683-22691.

[24] [24] Wang Qingfeng, Cheng Dewen, Wang Yongtian. Description of free-form optical curved surface using two-variable orthogonal polynomials [J]. Acta Optica Sinica, 2012, 32(9): 0922002.

[25] [25] W Cheng, M Chen. Transformation and connection of subapertures in the multiaperture overlap-scanning technique for large optics tests [J]. Opt Eng, 1993, 32(8): 1947-1950.

[26] [26] H Wendland. Fast evaluation of radial basis functions: methods based on partition of unity [C]. Approximation Theory X: Wavelets, Splines, and Applications, 2002. 473-483.

[27] [27] H Wendland. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree [J]. Advances in computational Mathematics, 1995, 4(1): 389-396.

[28] [28] R Franke. A Critical Comparison of Some Methods for Interpolation of Scattered Data [R]. Naval Postgraduate School, Monterey, California, 1979.