The study of wave motion in the Talbot interferometer with a lens

•We present the study of the wave motion in the Talbot interferometer with an additional element such as a lens.•Our alternative method is based on the wave propagation through the transmission functions of the grating and the lens.•Our method is simple and in the analytic form.•Our approach method is capable for using in many applications such as in optical or measurement systems.

We present the study of the wave motion in the Talbot interferometer with an additional element such as a lens for all related audiences. Our solutions are in the analytic form. A general principle of the Talbot effect, which is the optical near-field effect, is the Fresnel diffraction. The Fresnel integral is rather complicated. We therefore introduce an alternative method which is based on the wave propagation through the transmission functions of the grating and the lens. Our method has been proved by a simple experimental setup.