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本文在平行相干光照明条件下，推导出了二维光栅剪切成像系统的角度信号响应函数，并描绘出了角度响应函数二维曲面. 虽然光栅剪切成像系统常用的分束光栅有四种，分析光栅有三种，分析光栅和分束光栅之间还存在多种不同组合，但是产生的角度信号响应函数曲面却只有三种，即峰型位移曲面、谷型位移曲面和峰谷对称型位移曲面. 其中峰型位移曲面和谷型位移曲面之间具有数值互补关系，由此还可以把峰型位移曲面和谷型位移曲面归纳为一种，最终只需要考虑两种位移曲面. 这个理论结果无疑显著简化了人们对二维光栅剪切成像的认识，将对今后讨论定量提取二维角度信号的工作奠定基础.In this paper, we derive the response function of angle signal in a two-dimensional X-ray grating interferometry system under the condition of parallel coherent light, and depict the surface of the function with Matlab.Although there are four kinds of commonly used beam splitter gratings and three kinds of analyzer gratings, and there are still different compound modes between them, we may find that the ultimate surface of the response function of angle signal can only be of three kinds: the peak type, the valley type, and the peak-valley symmetry type of shifting surfaces. As there is a numerical complementary ralationship between the peak type and the valley type of shifting surfaces, we can take the two kinds as one; and finally we only need to consider two kinds of shifting surface.This conclusion simplies the common understanding of the two-dimensional X-ray grating interferometry method, and lays the foundation for the research of quantitatively extracting the two-demensional signal in the future.
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Keywords:
- two-dimensional X-ray grating interferometry /
- phase contrast imaging /
- shifting surface /
- shifting curve
[1] Fitzgerald R 2000 Phys. Today 53 23
[2] Huang W X, Yuan Q X, Tian Y L, Zhu P P, Jiang X M, Wang J Y 2005 Acta Phys. Sin. 54 6 (in Chinese) [黄万霞, 袁清习, 田玉莲, 朱佩平, 姜晓明, 王寯越2005 54 6]
[3] Pfeiffer F, Bech M, Bunk O, Kraft P, Eikenberry E F, Bronnimann C, Grunzweig C, David C 2008 Nature Materials 7 134
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[9] Pfeiffer F, Weitkamp T, Bunk O, David C 2006 Nature Physics 2 258
[10] Weitkamp T, Diaz A, David C, Pfeiffer F, Stampanoni M, Cloetens P, Ziegler E 2005 Optics Express 13 6296
[11] Yang Q, Liu X, Guo J C, Lei Y H, Huang J H, Niu H B 2012 Acta Phys. Sin. 61 160702 (in Chinese)[杨强, 刘鑫, 郭金川, 雷耀虎, 黄建衡, 牛憨笨2012 61 160702]
[12] Zhu P P, Wu Z Y 2007 Physics 36 443 (in Chinese) [朱佩平, 吴自玉2007 物理36 443]
[13] Momose A, Kawamoto S, Koyama I, Hamaishi Y, Takai K, Suzuki Y 2003 Jpn. J. Appl. Phys. 42 866
[14] Chen B, Zhu P P, Liu Y J, Wang Y, Yuan Q X, Huang W X, Ming H, Wu Z Y 2008 Acta Phys. Sin. 57 1576 (in Chinese)[陈博, 朱佩平, 刘宜晋, 王越, 袁清习, 黄万霞, 明海, 吴自玉2008 57 1576]
[15] Zhu P, Zhang K, Wang Z, Liu Y, Liu X, Wu Z, McDonald S, Marone F, Stampanoni M 2010 Proc. Natl. Acad. Sci. 107 13576
[16] Liu X S, Li N R, Zhu P P, Liu Y J, Zhang K, Wang Z L, Hong Y L, Zhang H T, Yuan Q X, Huang W X, Wu Z Y 2010 Chin. Phys. B 19 040701
[17] Zanette I, Weitkamp T, Donath T, Rutishauser S, David C 2010 Physical Review Letters 105 248102
[18] L N G 2006 Fourier optics (Beijing: China Machine Press) p90 (in Chinese) [吕乃光2006 傅里叶光学(北京: 机械工业出版社) 第90 页]
[19] David C, Weitkamp T, Pfeiffer F, Diaz A, Bruder J, Rohbeck T, Groso A, Bunk O, Stampanoni M, Cloetens P 2007 Spectrochimica Acta B 62 626
[20] Zanette I, David C, Rutishauser S, Weitkamp T 2010 XRay Optics and Microanalysis: Proceedings of the 20th International Congress Karlsruhe, Germany, September 15-18, 2009 p73
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[1] Fitzgerald R 2000 Phys. Today 53 23
[2] Huang W X, Yuan Q X, Tian Y L, Zhu P P, Jiang X M, Wang J Y 2005 Acta Phys. Sin. 54 6 (in Chinese) [黄万霞, 袁清习, 田玉莲, 朱佩平, 姜晓明, 王寯越2005 54 6]
[3] Pfeiffer F, Bech M, Bunk O, Kraft P, Eikenberry E F, Bronnimann C, Grunzweig C, David C 2008 Nature Materials 7 134
[4] Bonse U, Hart M 1965 Appl. Phys. Lett. 6 155156
[5] Momose A 1995 Nucl. Instrum. Meth. A 352 622628
[6] Chapman D, Thomlinson W, Johnston R, Washburn D, Pisano E, Gmur N, Zhong Z, Menk R, Arfelli F, Sayers D 1997 Phys. Med. Biol. 42 2015
[7] Zhu P P, Yuan Q X, Huang W X, Wang J Y, Shu H, Wu Z Y, Xian D C 2006 Acta Phys. Sin. 55 1089 (in Chinese)[朱佩平, 袁清习, 黄万霞, 王寯越, 舒航, 吴自玉, 冼鼎昌2006 55 1089]
[8] Snigirev A, Snigireva I, Kohn V, Kuznetsov S, Schelokov I 1995 Rev. Sci. Instrum. 66 5486
[9] Pfeiffer F, Weitkamp T, Bunk O, David C 2006 Nature Physics 2 258
[10] Weitkamp T, Diaz A, David C, Pfeiffer F, Stampanoni M, Cloetens P, Ziegler E 2005 Optics Express 13 6296
[11] Yang Q, Liu X, Guo J C, Lei Y H, Huang J H, Niu H B 2012 Acta Phys. Sin. 61 160702 (in Chinese)[杨强, 刘鑫, 郭金川, 雷耀虎, 黄建衡, 牛憨笨2012 61 160702]
[12] Zhu P P, Wu Z Y 2007 Physics 36 443 (in Chinese) [朱佩平, 吴自玉2007 物理36 443]
[13] Momose A, Kawamoto S, Koyama I, Hamaishi Y, Takai K, Suzuki Y 2003 Jpn. J. Appl. Phys. 42 866
[14] Chen B, Zhu P P, Liu Y J, Wang Y, Yuan Q X, Huang W X, Ming H, Wu Z Y 2008 Acta Phys. Sin. 57 1576 (in Chinese)[陈博, 朱佩平, 刘宜晋, 王越, 袁清习, 黄万霞, 明海, 吴自玉2008 57 1576]
[15] Zhu P, Zhang K, Wang Z, Liu Y, Liu X, Wu Z, McDonald S, Marone F, Stampanoni M 2010 Proc. Natl. Acad. Sci. 107 13576
[16] Liu X S, Li N R, Zhu P P, Liu Y J, Zhang K, Wang Z L, Hong Y L, Zhang H T, Yuan Q X, Huang W X, Wu Z Y 2010 Chin. Phys. B 19 040701
[17] Zanette I, Weitkamp T, Donath T, Rutishauser S, David C 2010 Physical Review Letters 105 248102
[18] L N G 2006 Fourier optics (Beijing: China Machine Press) p90 (in Chinese) [吕乃光2006 傅里叶光学(北京: 机械工业出版社) 第90 页]
[19] David C, Weitkamp T, Pfeiffer F, Diaz A, Bruder J, Rohbeck T, Groso A, Bunk O, Stampanoni M, Cloetens P 2007 Spectrochimica Acta B 62 626
[20] Zanette I, David C, Rutishauser S, Weitkamp T 2010 XRay Optics and Microanalysis: Proceedings of the 20th International Congress Karlsruhe, Germany, September 15-18, 2009 p73
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