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采用光的波粒二象性观点,用概率波对光栅的塔尔博特(Talbot)效应进行了研究,得到了正、偏自成像和分数成像的相关结果,这些结果与采用光的波动性观点的惠更斯-菲涅耳原理和傅里叶变换等常规方法所得结果相同。引入了调节参量q,并研究了成像过程中,在像的正、偏,像与原物的相位关系和分数成像等相关问题中该参数所起的作用;还利用相关结果讨论了倏逝波问题,得到了与常规方法相同的结果。所采用的光子学方法有助于对光子的波函数及其统计意义的理解。与此同时,提出了塔尔博特效应实际上是光子对周期性空间信息的记忆与再现的过程,从而对光子在光传播过程中携带空间信息产生了一定认识。由于数学处理方法上的简明扼要,所采用的光子学研究方法更易于在基础领域中推广和应用。
Based on the wave-particle duality view of light, the Talbot effect of the grating is studied by probability wave, and the correlation results of positive and partial self-imaging and fractional imaging are obtained. These results are in good agreement with those using the fluctuation of light The views of the Huygens-Fresnel principle and the Fourier transform and other conventional methods have the same result. The parameter q is introduced and the role played by the parameter in the imaging process such as the phase relationship of positive and negative images, the phase relationship with the original image and the fractional imaging are studied. The relative results are also used to discuss the effects of evanescent wave Problem, got the same result as the conventional method. The photon method used helps to understand the wave function of photons and their statistical significance. At the same time, it is proposed that the Talbot effect is actually the process of photon memory and reproduction of periodic spatial information, and thus some understanding of the photon carrying spatial information in the process of light propagation is proposed. Due to the conciseness of mathematical processing methods, the photon research methods used are more easily popularized and applied in the basic fields.