[1] 文 亮. 分数傅里叶变换及其应用［D］. 重庆; 重庆大学, 2008: 18-33.

    Wen Liang. Fractional Fourier transform and its application［D］. Chongqing: Chongqing University, 2008: 18-33.

[2] 张 岩, 顾本源, 杨国桢. 光学分数傅里叶变换及其应用［J］. 物理, 1999, 28(8): 484-490.

    Zhang Yan, Gu Benyuan,Yang Guozhen. Optical fractional Fourier transform and its applications［J］. Physics, 1999, 28(8): 484-490.

[3] 苏显渝, 李继陶, 曹益平, 等. 信息光学［M］. 2版. 北京: 科学出版社, 2012: 271-278.

    Su Xianyu, Li Jitao, Cao Yiping, et al. Information optics［M］. 2nd ed. Beijing: Science Press, 2012: 271-278.

[4] Mendlovic D, Ozaktas H M. Fractional Fourier transforms and their optical implementation: Ⅰ［J］. Journal of the Optical Society of America A, 1993, 10(9): 1875-1881.

[5] Ozaktas H M, Mendlovic D. Fourier transforms of fractional order and their optical interpretation［J］. Journal of the Optics Society of America A, 1993, 101(3): 163-169.

[6] Lohmann A W. Image rotation, Wigner rotation, and the fractional Fourier transform［J］. Journal of the Optical Society of America A, 1993, 10(10): 2181-2186.

[7] 吴 平. 分数傅里叶变换的应用研究［J］. 学术动态, 2005, 11(3): 17-21.

[8] 吴 平, 李 波, 陈天禄, 等. 分数傅里叶变换面上余弦-高斯光束的变换特性［J］. 强激光与粒子束, 2005, 17(12): 1787-1790.

    Wu Ping, Li Bo, Chen Tianlu, et al. Transformation properties of a cosine-Gaussian beam in fractional Fourier transform plane［J］. High Power Laser and Particle Beams, 2005, 17(12): 1787-1790.

[9] 吴 平, 吕百达, 陈天禄. 光束分数傅里叶变换的Wigner分布函数分析方法［J］. 物理学报, 2005, 54(2): 658-664.

    Wu Ping, Lü Baida, Chen Tianlu. Fractional Fourier transform of beams in the use of the Wigner distribution function method［J］. Acta Physica Sinica, 2005, 54(2): 658-664.

[10] 陈森会, 张廷蓉, 冯小芳. 分数傅里叶变换面上厄米-拉盖尔-高斯光束的变换特性［J］. 中国激光, 2009, 36(2): 374-378.

    Chen Senhui, Zhang Tingrong, Feng Xiaofang. Transformation properties of Hermite-Laguerre-Gaussian beam in fractional Fourier transform plane［J］. Chinese J Lasers, 2009, 36(2): 374-378.

[11] 陈森会, 张廷蓉. 1维线阵离轴高斯光束的分数傅里叶变换［J］. 强激光与粒子束, 2009, 21(2): 190-194.

    Chen Senhui, Zhang Tingrong. Fractional Fourier transform for incoherent one-dimensional off-axis Gaussian beams［J］. High Power Laser and Particle Beams, 2009, 21(2): 190-194.

[12] 陈森会, 张廷蓉, 黄永超, 等. 高斯-谢尔模型光束在有色差的分数傅里叶变换系统中的光谱特性［J］. 光学学报, 2011, 31(1): 0107001.

    Chen Senhui, Zhang Tingrong, Huang Yongchao, et al. Spectrum properties of Gaussian-Shell mode beam in the Chromatics aberrated fractional Fourier transforms system［J］. Acta Optica Sinica, 2011, 31(1): 0107001.

[13] 陈天禄, 吴 平. 双曲余弦-高斯光束的分数傅里叶变换特性研究［J］. 中国激光, 2005, 32(7): 908-912.

    Chen Tianlu, Wu Ping. Fractional Fourier transforms for cosh-Gaussian beams［J］. Chinese J Lasers, 2005, 32（7）: 908-912.

[14] 杨 磊, 夏 军, 张晓兵, 等. 基于多平面全息成像的三维显示［J］. 中国激光, 2014, 41(2): 0209017.

    Yang Lei, Xia Jun, Zhang Xiaobing, et al. Three-dimensional display by holographic imaging on multiple focal planes［J］. Chinese J Lasers, 2014, 41(2): 0209017.

[15] 孔德照, 沈学举, 赵 燕, 等. 基于计算全息和随机相位编码的三维信息的加密与显示［J］. 激光与光电子学进展, 2015, 52(10): 100902.

    Kong Dezhao, Shen Xueju, Zhao Yan, et al. Encryption and display of three-dimensional information based computer generated hologram and random phase encoding［J］. Laser & Optoelectronics Progress, 2015, 52(10): 100902.

[16] Siegman A E. Analysis of laser beam quality degradation caused by quartic phase aberrations［J］. Applied Optics, 1993, 32(30): 5893-5901.

[17] 赵道木, 毛海丹. 带透镜球差的分数傅立叶变换［J］. 光电子·激光, 2004, 15(6): 724-730.

    Zhao Daomu, Mao Haidan. Fractional Fourier transform with spherically aberrated lens［J］. Journal of Optoelectronics·Laser, 2004, 15(6): 724-730.

[18] 季小玲, 吕百达. 球差透镜对高斯光束质量的影响［J］. 中国激光, 2001, 28(4): 347-350.

    Ji Xiaoling, Lü Baida. Effect of the spherically aberrated lens on beam quality［J］. Chinese J Lasers, 2001, 28(4): 347-350.

[19] 季小玲, 吕百达. 高斯光束通过球差透镜的聚焦特性［J］. 激光技术, 2001, 25(2): 150-153.

    Ji Xiaoling, Lü Baida. Focusing property of Gaussian beams through a spherical aberrant lens［J］. Laser Technology, 2001, 25(2): 150-153.

[20] 王庆峰, 王喜庆, 黄 庆. 球差透镜对余弦高斯光束聚焦特性的影响［J］. 激光杂志, 2006, 27(4): 41-42.

    Wang Qingfeng, Wang Xiqing, Huang Qing. Effect of the spherically aberrated lens on the property of cosine-Gaussian［J］. Laser Journal, 2006, 27(4): 41-42.

[21] 蒲继雄. 利用球差透镜获得超衍射极限聚焦［J］. 中国激光, 1999, 26(6): 542-546.

    Pu Jixiong. Lenses with spherical aberration for generating subdiffraction-limited focusing［J］. Chinese J Lasers, 1999, 26(6): 542-546.

[22] Chen J R, Yan J L. Study on spherical aberration of imaging system constructed by fractional Fourier transform［C］. SPIE, 2008, 6034: 60341U.

[23] Mao H D, Zhao D M, Jing F, et al. Propagation characteristics of the kurtosis parameters of flat-topped beams passing through fractional Fourier transformation systems with a spherically aberrated lens［J］. Journal of Optics A, 2004, 6（6）: 640-650.

[24] 毛海丹, 叶 腾. 带球差的分数傅立叶变换系统的传输特性研究［J］. 杭州电子科技大学学报, 2008, 28(4): 88-91.

    Mao Haidan, Ye Teng. Studies on the fractional Fourier transform with spherically aberrated lenses［J］. Journal of Hangzhou Dianzi University, 2008, 28(4): 88-91.

[25] 孙 川, 何艳林, 吴逢铁. 双环透镜聚焦平行光产生局域空心光束［J］. 光学学报, 2015, 35(12): 1208001.

    Sun Chuan, He Yanlin, Wu Fengtie. Bottle beam generation with a double ring lens by focusing parallel light［J］. Acta Optica Sinica, 2015, 35(12): 1208001.

[26] 王绍民, 林 强, 江晓清. 余弦-高斯光束［J］. 光子学报, 1999, 28(4): 367-370.

    Wang Shaomin, Lin Qiang, Jiang Xiaoqing. Cosine-Gauss beam［J］. Acta Photonica Sinica, 1999, 28(4): 367-370.

[27] 李艳桃, 张廷蓉, 张伟林, 等. 余弦高斯光束在单轴晶体中垂直于光轴的传输［J］. 四川师范大学学报(自然科学版), 2013, 36(6): 893-901.

    Li Yantao, Zhang Tingrong, Zhang Weilin, et al. Propagation of cosine-Gaussian beams in uniaxial crystals orthogonal to the optical axis［J］. Journal of Sichuan Normal University (Natural Science), 2013, 36(6): 893-901.

[28] 宋宏远, 张廷蓉, 陈森会, 等. 余弦高斯光束在梯度折射率介质中的传输特性［J］. 强激光与粒子束, 2011, 23(4): 890-894.

    Song Hongyuan, Zhang Tingrong, Chen Senhui, et al. Propagation properties of cosine-Gaussian beams in gradient-index medium［J］. High Power Laser and Particle Beams, 2011, 23(4): 890-894.

[29] 包建勤, 张廷蓉, 霍雅洁. 余弦高斯光束通过左手平板材料的传输特性［J］. 光电子·激光, 2013, 24(6): 1231-1237.

    Bao Jianqin, Zhang Tingrong, Huo Yajie. Propagation properties of cosine-Gaussian beam through a left-handed material slab［J］. Journal of Optoelectronics·Laser, 2013, 24(6): 1231-1237.

[30] 王喜庆, 柯尊平, 吕百达. 余弦高斯光束的传输特性［J］. 激光技术, 2001, 25(2): 121-125.

    Wang Xiqing, Ke Zunping, Lü Baida. Propagation properties of cosine-Gaussian beams［J］. Laser Technology, 2001, 25(2): 121-125.

[31] 张以谟, 张红霞, 贾大功. 应用光学［M］. 北京: 电子工业出版社, 2015: 170-176.

[32] 刘竹琴, 徐 红. 单色球差的实验研究［J］. 延安大学学报(自然科学版), 2005, 24（2）: 39-40.

    Liu Zhuqin, Xu Hong. Experimental study on solid colored spherical aberration［J］. Journal of Yan′an University (Natural Science Edition), 2005, 24（2）: 39-40.