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基于Dini级数展开, 导出了p(>0) 阶准离散Hankel变换(the pth-order quasi-discrete Hankel transform based on Dini series expansion, pDQDHT)算法, 并给出了该算法在光束传输中的应用. 通过不同输入函数分别对pDQDHT算法进行测试及光束通过透镜传输的应用实例, 结果表明: pDQDHT算法不仅精度高于现有的Hankel变换算法, 可以进行多次正、逆变换, 能广泛应用于光束分步传输问题, 而且执行速度也与一般的快速Hankel变换算法相当.
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关键词:
- Dini级数展开 /
- 高阶Hankel变换 /
- 光束传输
Based on Dini series expansion, p(>0) order quasi discrete Hankel transform (pDQDHT) algorithm is deduced. The application of this algorithm in beam propagation is presented. pDQDHT algorithm is tested with various input functions and used in beam propagation through lens. Experimental results show that the pDQDHT algorithm possesses a high accuracy compared with existing Hankel transformation algorithms. The pDQDHT algorithm can be transformed forwardly and inversely and widely used in beam distribution of transmission. The implementing speed is comparable to that of general fast Hankel transform algorithm.-
Keywords:
- Dini series expansion /
- high-order Hankel transform /
- beam propagation
[1] Du G H 1988 Acta Phys. Sin. 37 769 (in Chinese) [杜功焕 1988 37 769]
[2] Yan C C, Xue G G, Liu C, Gao S M 2005 Acta Phys. Sin. 54 3058 (in Chinese) [闰长春, 薛国刚, 刘诚, 高淑梅 2005 54 3058]
[3] Yang X J, Zang W P, Tian J G, Liu Z B, Zhou W Y, Zhang C P, Zhang G Y 2005 Acta Phys. Sin. 54 2735 (in Chinese) [杨新江, 臧维平, 田建国, 刘智波, 周文远, 张春平, 张光寅 2005 54 2735]
[4] Chen G B, Wang H N, Yao J J, Han Z Y, Yang S W 2009 Acta Phys. Sin. 58 1608 (in Chinese) [陈桂波, 汪宏年, 姚敬金, 韩子夜, 杨守文 2009 58 1608]
[5] Siegman E 1977 Opt. Lett. 1 13
[6] Agrawal G P 1981 Opt. Lett. 6 171
[7] Magni V, Cerulle G, De Silvestri S 1992 J. Opt. Soc. Am. A 9 2031
[8] Agnesi A, Reali G C, Patrini G, Tomaselli A 1993 J. Opt. Soc. Am. A 10 1872
[9] Ferrari J A 1995 J. Opt. Soc. Am. A 12 1812
[10] Ferrari J A, Perciante D, Dubra A 1999 J. Opt. Soc. Am. A 16 2581
[11] Perciante C D 2004 J. Opt. Soc. Am. A 2 1911
[12] Markham J, Conchello A J 2003 J. Opt. Soc. Am. A 20 621
[13] Knockaert L 2000 IEEE Trans. Signal Process. 48 1695
[14] Liu Q H, Zhang Z Q 1999 Appl. Opt. 38 6705
[15] Cerjan C 2007 J. Opt. Soc. Am. A 24 1609
[16] Yu L, Huang M, Chen M, Chen W, Huang W, Zhu Z 1998 Opt. Lett. 23 409
[17] Guizar-Sicairos M, Gutiérrez-Vega J C 2004 J. Opt. Soc. Am. A 21 53
[18] You K M, Wen S C, Chen L Z, Wang Y W, Hu Y H 2009 Chin. Phys. B 18 3893
[19] Wang Z, Gao C Q, Xin J T 2012 Acta Phys. Sin. 61 124209 (in Chinese) [王铮, 高春清, 辛璟焘 2012 61 124209]
[20] Gutie'rrez-Vega J C, Rodríguez-Masegosa R, Cha'vez-Cerda S 2003 Pure Appl. Opt. 5 276
[21] Zhang Q A, Wu F T, Zheng W T, Pu J X 2011 Sci. Sin. Phys. Mech. Astron. 41 1131 (in Chinese) [张前安, 吴逢铁, 郑维涛, 蒲继雄 2011中国科学: 物理学·力学·天文学 41 1131]
[22] Arfken G B, Weber H J 2001 Mathematical Methods for Physicists (California: Harcourt-Academic)
[23] Wolfram S 1991 Mathematica: A System for Doing Mathematics by Computer (Massachusetts: Addison-Wesley)
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[1] Du G H 1988 Acta Phys. Sin. 37 769 (in Chinese) [杜功焕 1988 37 769]
[2] Yan C C, Xue G G, Liu C, Gao S M 2005 Acta Phys. Sin. 54 3058 (in Chinese) [闰长春, 薛国刚, 刘诚, 高淑梅 2005 54 3058]
[3] Yang X J, Zang W P, Tian J G, Liu Z B, Zhou W Y, Zhang C P, Zhang G Y 2005 Acta Phys. Sin. 54 2735 (in Chinese) [杨新江, 臧维平, 田建国, 刘智波, 周文远, 张春平, 张光寅 2005 54 2735]
[4] Chen G B, Wang H N, Yao J J, Han Z Y, Yang S W 2009 Acta Phys. Sin. 58 1608 (in Chinese) [陈桂波, 汪宏年, 姚敬金, 韩子夜, 杨守文 2009 58 1608]
[5] Siegman E 1977 Opt. Lett. 1 13
[6] Agrawal G P 1981 Opt. Lett. 6 171
[7] Magni V, Cerulle G, De Silvestri S 1992 J. Opt. Soc. Am. A 9 2031
[8] Agnesi A, Reali G C, Patrini G, Tomaselli A 1993 J. Opt. Soc. Am. A 10 1872
[9] Ferrari J A 1995 J. Opt. Soc. Am. A 12 1812
[10] Ferrari J A, Perciante D, Dubra A 1999 J. Opt. Soc. Am. A 16 2581
[11] Perciante C D 2004 J. Opt. Soc. Am. A 2 1911
[12] Markham J, Conchello A J 2003 J. Opt. Soc. Am. A 20 621
[13] Knockaert L 2000 IEEE Trans. Signal Process. 48 1695
[14] Liu Q H, Zhang Z Q 1999 Appl. Opt. 38 6705
[15] Cerjan C 2007 J. Opt. Soc. Am. A 24 1609
[16] Yu L, Huang M, Chen M, Chen W, Huang W, Zhu Z 1998 Opt. Lett. 23 409
[17] Guizar-Sicairos M, Gutiérrez-Vega J C 2004 J. Opt. Soc. Am. A 21 53
[18] You K M, Wen S C, Chen L Z, Wang Y W, Hu Y H 2009 Chin. Phys. B 18 3893
[19] Wang Z, Gao C Q, Xin J T 2012 Acta Phys. Sin. 61 124209 (in Chinese) [王铮, 高春清, 辛璟焘 2012 61 124209]
[20] Gutie'rrez-Vega J C, Rodríguez-Masegosa R, Cha'vez-Cerda S 2003 Pure Appl. Opt. 5 276
[21] Zhang Q A, Wu F T, Zheng W T, Pu J X 2011 Sci. Sin. Phys. Mech. Astron. 41 1131 (in Chinese) [张前安, 吴逢铁, 郑维涛, 蒲继雄 2011中国科学: 物理学·力学·天文学 41 1131]
[22] Arfken G B, Weber H J 2001 Mathematical Methods for Physicists (California: Harcourt-Academic)
[23] Wolfram S 1991 Mathematica: A System for Doing Mathematics by Computer (Massachusetts: Addison-Wesley)
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