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The parabolic compound X-ray refractive lenses are a kind of novel optical components, especially suitable for hard X-rays. Due to their parabolic profiles they are free of spherical aberration and are proper devices for sub-micrometer focusing and imaging. The focusing performance of the parabolic compound X-ray refractive lenses is studied theoretically and experimentally in this paper. Firstly, the derivation of the exact focal length formula using matrix optics method and a criterion of the thin lens approximation are described. And the intensity distribution near focus, limiting focal spot size, effective aperture and transmittance are deduced based on the diffraction theory. Several parabolic compound X-ray refractive lenses with PMMA material were fabricated by means of deep X-ray lithography. Then the X-ray microbeam experimental system was built on the 4W1A beamline of Beijing Synchrotron Radiation Facility （BSRF） based on the parabolic compound X-ray refractive lenses we fabricated. The focusing performances of three PMMA parabolic compound X-ray refractive lenses were measured and analyzed under 8 keV monochromatic X-rays. According to the experimental results, it is concluded that the PMMA parabolic compound X-ray refractive lenses promises good hard X-ray focusing performance.
[1] ［1］Hu C, Li H, Zhang L, Wang X, Luo S 2009 Acta Phys. Sin. 58 2424 （in Chinese）［胡春红、 李辉、 张璐、 王雪艳、 罗述谦 2009 物理学报 58 2424］
[2] ［2］Xie H, Hu F, Luo H, Du G, Deng B, Chen R, Xue Y, Shi S, Xiao T 2008 Acta Phys. Sin. 57 7044 （in Chinese）［谢红兰、 胡雯、 罗红心、 杜国浩、 邓彪、 陈荣昌、 薛艳玲、 师绍猛、 肖体乔 2008 物理学报 57 7044］
[3] ［3］Snigirev A, Kohn V, Snigireva I, Lengeler B 1996 Nature 384 49
[4] ［4］Protopopov V, Valiev K 1998 Opt. Commun. 151 297
[5] ［5］Kohn V 2002 JETP Letters 76 600
[6] ［6］Nohammer B, David C, Rothuizen H, Hoszowska J, Simionovici A 2003 Microelectronic Engineering 67 453
[7] ［7］Lengeler B, Schroer C, Richwin M, Tümmler J, Drakopoulos M, Snigirev A, Snigireva I 1999 Appl. Phys. Lett. 74 3924
[8] ［8］Wang C, Pan X, Urisu T 2006 Acta Phys. Sin. 55 6163 （in Chinese）［王长顺、 潘煦、 Urisu T 2006 物理学报 55 6163］
[9] ［9］Arms D, Dufresne E, Clarke R, Dierker S, Pereira N, Foster D 2002 Rev. Sci. Instrum. 73 1492
[10] ］Bohic S, Simionovici A, Snigirev A, Ortega R, Devès G, Heymann D, Schroer C 2001 Appl. Phys. Lett. 78 3544
[11] ］Le Z and Liang J 2003 J. Opt. A: Pure & Appl. Opt. 5 374
[12] ］Le Z, Zhao X, Liang J, Sun Y, Liu K, Zhang M, Guo S, Quan B 2005 Chinese Optics Letters 3 618
[13] ］Le Z, Liang J, Dong W, Zhu P, Peng L, Wang W, Huang W, Yuan Q, Wang J 2007 Chin. Phys. 16 984
[14] ］Zhu Y, Liang J, Liang Z, Huang X, Le Z, Yi F, Hou F, Huang W, Dong W, Wang W, Wang Z, Cui N 2009 Acta Phys. Sin. 58 1526 （in Chinese）［朱燕青、 梁静秋、 梁中翥、 黄鑫华、 乐孜纯、 伊福廷、 侯凤杰、 黄万霞、 董文、 王维彪、 王志立、 崔乃迪 2009 物理学报 58 1526］
[15] ］Gerrard A, Burch J 1975 Introduction to Matrix Methods in Optics （London: Wiley） p28
[16] ］Abramowitz M, Stegun I 1964 Hanndbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables （New York: Dover Publications） p289
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[1] ［1］Hu C, Li H, Zhang L, Wang X, Luo S 2009 Acta Phys. Sin. 58 2424 （in Chinese）［胡春红、 李辉、 张璐、 王雪艳、 罗述谦 2009 物理学报 58 2424］
[2] ［2］Xie H, Hu F, Luo H, Du G, Deng B, Chen R, Xue Y, Shi S, Xiao T 2008 Acta Phys. Sin. 57 7044 （in Chinese）［谢红兰、 胡雯、 罗红心、 杜国浩、 邓彪、 陈荣昌、 薛艳玲、 师绍猛、 肖体乔 2008 物理学报 57 7044］
[3] ［3］Snigirev A, Kohn V, Snigireva I, Lengeler B 1996 Nature 384 49
[4] ［4］Protopopov V, Valiev K 1998 Opt. Commun. 151 297
[5] ［5］Kohn V 2002 JETP Letters 76 600
[6] ［6］Nohammer B, David C, Rothuizen H, Hoszowska J, Simionovici A 2003 Microelectronic Engineering 67 453
[7] ［7］Lengeler B, Schroer C, Richwin M, Tümmler J, Drakopoulos M, Snigirev A, Snigireva I 1999 Appl. Phys. Lett. 74 3924
[8] ［8］Wang C, Pan X, Urisu T 2006 Acta Phys. Sin. 55 6163 （in Chinese）［王长顺、 潘煦、 Urisu T 2006 物理学报 55 6163］
[9] ［9］Arms D, Dufresne E, Clarke R, Dierker S, Pereira N, Foster D 2002 Rev. Sci. Instrum. 73 1492
[10] ］Bohic S, Simionovici A, Snigirev A, Ortega R, Devès G, Heymann D, Schroer C 2001 Appl. Phys. Lett. 78 3544
[11] ］Le Z and Liang J 2003 J. Opt. A: Pure & Appl. Opt. 5 374
[12] ］Le Z, Zhao X, Liang J, Sun Y, Liu K, Zhang M, Guo S, Quan B 2005 Chinese Optics Letters 3 618
[13] ］Le Z, Liang J, Dong W, Zhu P, Peng L, Wang W, Huang W, Yuan Q, Wang J 2007 Chin. Phys. 16 984
[14] ］Zhu Y, Liang J, Liang Z, Huang X, Le Z, Yi F, Hou F, Huang W, Dong W, Wang W, Wang Z, Cui N 2009 Acta Phys. Sin. 58 1526 （in Chinese）［朱燕青、 梁静秋、 梁中翥、 黄鑫华、 乐孜纯、 伊福廷、 侯凤杰、 黄万霞、 董文、 王维彪、 王志立、 崔乃迪 2009 物理学报 58 1526］
[15] ］Gerrard A, Burch J 1975 Introduction to Matrix Methods in Optics （London: Wiley） p28
[16] ］Abramowitz M, Stegun I 1964 Hanndbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables （New York: Dover Publications） p289
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