【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。更多还原

【Abstract】 The self-imaging phenomenon of two-dimensional periodic object is studied based on the scalar diffraction theory,and the self-imaging 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 self-imaging. 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 self-imaging. Furthermore,the numerical relation between equivalent combinations of period lengths and angles,which describe the same two-dimensional 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.更多还原