光学学报, 2010, 30 (9): 2562, 网络出版: 2014-05-15   

二维周期物体自成像条件的扩展

Extended SelfImaging Conditions for TwoDimensional Periodic Object
作者单位
浙江大学光电系现代光学仪器国家重点实验室, 浙江 杭州 310027
摘要
基于标量衍射理论研究了二维周期物体自成像现象,进一步地扩展了二维周期物体的自成像条件。研究表明,只要两个方向周期长度的平方满足整数比,就存在相应的周期夹角满足自成像要求;另一方面,只要两个方向周期夹角的余弦值的平方是有理数,理论上也就能找到比例合适的周期长度实现自成像。分析了同一个二维周期物体用不同的周期长度及夹角组合来表示时,这些组合之间的数值关系。根据这些关系,给出了判断两个不同的周期长度及夹角的组合是否等价的方法。最后用数值模拟验证了相关的理论分析。
Abstract
The selfimaging phenomenon of twodimensional periodic object is studied based on the scalar diffraction theory, and the selfimaging conditions are extended. It is pointed out that if the square ratio of the two period lengths can be expressed as a quotient of two integers, there exist period angles between the two period directions that can achieve selfimaging. On the other hand, if the square of cosine of the period angle between the two period directions is a rational number, it is possible to find a proper proportion of the two period lengths to satisfy selfimaging. Furthermore, the numerical relation between equivalent combinations of period lengths and angles, which describe the same twodimensional periodic object, is analyzed. The analysis can be utilized to determine whether two combinations of period lengths and angles are equivalent. The simulation result agrees well with the discussion.
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严欣欣, 张磊, 张文字, 刘钦晓, 余飞鸿. 二维周期物体自成像条件的扩展[J]. 光学学报, 2010, 30(9): 2562. Yan Xinxin, Zhang Lei, Zhang Wenzi, Liu Qinxiao, Yu Feihong. Extended SelfImaging Conditions for TwoDimensional Periodic Object[J]. Acta Optica Sinica, 2010, 30(9): 2562.

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