线性正则变换中的泰伯效应  

Talbot Effect in Linear Canonical Transformation

作　　者：孙琼阁[1] 马金鹏[2] 杨瑀[1] 李辰[1] 刘正君[3] 刘树田[4] 

机构地区：[1]北京空间机电研究所,北京100091 [2]天津津航技术物理研究所,天津300000 [3]哈尔滨工业大学自动化测试与控制系,黑龙江哈尔滨150001 [4]哈尔滨工业大学物理系,黑龙江哈尔滨150001

出　　处：《光学学报》2014年第7期93-97,共5页Acta Optica Sinica

摘　　要：提出了在一定的条件下,周期函数经过线性正则变换,结果仍然是周期函数,即利用线性正则变换可以产生泰伯效应,并从理论上给出了证明,得出了产生泰伯效应的条件。推导了特殊形式的线性正则变换(菲涅耳衍射、分数傅里叶变换和Gyrator变换)产生泰伯效应的条件,通过数值模拟验证了Gyrator变换的自成像条件,证明了该理论的正确性,从而将泰伯效应推广到了线性正则变换域。It demonstrates that the periodic function after the linear canonical transform （LCT） still results in a periodic function. When certain conditions are satisfied, the periodic functions are still periodic functions, which is Talbot effect in LCT. The Talbot effect in LCT is theoretically proved, and their self-image conditions are obtained. The conditions of Talbot effect in the special forms of the LCT （such as Fresnel diffraction, fractional Fourier transform and Gyrator transform） are also presented. The self-image condition of Gyrator transform is obtained and proved by numerical simulation, which suggests the Talbot effect is extended to the domain of LCT.

关 键 词：信号处理 线性正则变换 泰伯效应 自成像条件 

分 类 号：O436[机械工程—光学工程]