Theoretical And Experimental Study On The Talbot Effect Of Two-dimensional Gratings

The research scale of micro-optics is in the micron and sub-micron scales.Microoptical devices can be classified into diffractive micro-optical elements and refractive micro-optical elements according to the mode of light propagation.Binary optics are diffractive microstructures,while microlens arrays are refractive microstructures.With the continuous development of micro-optics,the application field of micro-optics continues to expand.Micro-optical devices have been widely used in optical communication,optical computing,optical interconnection,beam shaping,imaging,and so on.Gratings are important optical device,and any diffraction structure with spatial periodicity can be called a diffraction grating.Scribing gratings and holographic gratings have had a major impact on the development of disciplines such as physics,astronomy,chemistry and biology.Fiber Bragg Gratings and arrayed waveguide gratings greatly drive the development of Fiber optic communications.Pulse compression grating is an indispensable part of laser nuclear fusion device.As a beam splitter,Dammann grating plays an extremely important role in photoelectronic lighting technology.Various new types of gratings have emerged that have played an important role in the fields of lasers,optical communication,optical interconnection,optical information processing,and optical precision measurement.This paper mainly studies the two-dimensional transmission grid composed of grid arrays formed by crisscrossing grid lines,and analyzes the theory and experiment of Talbot effect and Moiré fringe generated by twodimensional grid,including the following work:(1)Light has wave-particle duality.First,the wave function of the free particle in quantum mechanics is used to explain Fraunhofer diffraction of the light at a rectangular aperture,and the result is consistent with the Huygens-Fresnel principle in wave optics.Then probabilistic wave method is used to analyze the Talbot effect of a two-dimensional grating.The results show that the photons at the Talbot distance and incident photons are described by the same probability wave.This explains why the Talbot image came into being.Finally,Talbot distance formula is used to measure the period of the twodimensional grating.The measured and calculated values of the period are identical.(2)Moiré fringes can be produced when two gratings with periodicity are overlapped at an angle,and the moiré fringes can be observed on the surface of the grating.This paper mainly studies the moiré fringes produced by the Talbot effect of two-dimensional grid.Parallel light passes through the first two-dimensional grid and generates a series of Talbot images.Placing a periodic micro-pattern array grid behind the Talbot image somewhere,the overlapping of the Talbot image and the micro-pattern will produce the Moiré fringes.The pitch of the moiré fringes can be measured from the resulting moiré fringes.The measured value of the pitch is consistent with the calculated value.