Talbot effect in linear canonical transformation

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 Faourier 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.