Theoretical And Experimental Research On The Talbot Effect Of The 2D Amplitude Grating Illuminated By The Spherical Wave

The main research content in the field of micro optics includes optical effects from nanometers to millimeters and optical components developed by optical micromachining technology.The grating plays an important role in the diffraction compound imaging effect.The 2D amplitude grating is the object of this article.It focuses on the study of the Talbot effect of the spherical wave,reveals its imaging laws and imaging characteristics,and discusses the difference and connection between the spherical wave and the plane wave of the Talbot effect of the grating.The Talbot effect of the grating refers to the phenomenon of diffraction self-imaging.The self-imaging phenomenon of periodic objects is observed without the lens only by light diffraction.The Talbot effect imaging system can be roughly divided into the light source incident part,the periodic object transfer part,and the imaging part.Among them,there are many related researches on the transmission of periodic objects,such as amplitude grating,phase grating,curved grating and fractal grating,etc.The essence is to discuss the influence of different transmittance functions on imaging.There is also a lot of research on the imaging part,such as the Talbot conjugation phenomenon and the symmetry principle.However,there are few studies on the incident light source being a spherical wave.Most light sources in nature are spherical waves.Therefore,the study of the Talbot effect of the spherical wave will improve the basic theory of the Talbot effect and expand the application of the Talbot effect.We use the Fresnel-Kirchhoff diffraction theory to analyze the light field distribution of the spherical wave incident 2D amplitude grating in the Fresnel diffraction field.Discuss the imaging laws of the Talbot image,the phase-inverted Talbot image and the fractional Talbot image produced by the spherical wave illumination grating.The theory found that: When spherical wave illumination,the imaging law of the Talbot effect is significantly different from that of plane wave illumination.The imaging distance is positively correlated with the vertical distance from the light source to the object plane,which satisfies the relationship of the inverse proportional function.Compared with the Talbot image observed by the plane wave illumination,the spherical wave illumination can observe the enlarged Talbot image.In addition,when the spherical wave is illuminated,the Talbot distance is equal to the product of its periodic magnification and the Talbot distance when the plane wave is illuminated.In the experiment,the Talbot image,the image around Talbot distance,the phase-inverted Talbot image,and the Talbot sub-image are given in the first part of the experiment.It is found that only the clear diffraction self-imaging pattern can be observed at the distance deduced by the theory of this paper,the self-images around the Talbot distance are all blurry,which proves the correctness of the theoretical analysis of the Talbot effect when the spherical wave is irradiated in this chapter.The distance from the light source to the grating plane was changed,and Talbot images of different sizes and different periods were observed.The change trend of the imaging distance,imaging size and period is relatively fast when the light source is close to the grating plane,and when the light source is far away from the grating plane,the change trend is slower.If the distance between the light source and the grating plane is far enough,the imaging law of the Talbot effect will be the same when the plane wave illuminates the grating.The fractional Talbot image is given.According to the degree of overlap of pixels,the fractional Talbot image can be divided into two cases: point-like discrete distribution and regular grid distribution.Among them,the pixels in the Talbot sub-image are completely overlapped,the illumination intensity is uniform,and it is distributed in a regular,full-bright grid.Except for the Talbot sub-image,the fractional Taber image pixels are not completely overlapped,and are discretely distributed in dots.Finally,the application prospect of the Talbot effect of spherical wave in long-distance measurement is discussed.According to the discussion in the second part of the experiment,it is found that the plane wave Talbot effect ranging method is better for short-distance measurement;while for the long distance measurement,the plane wave Talbot effect ranging method will face inconvenience and unclear self-imaging.The problem,at this time,it is more appropriate to choose the spherical wave Talbot effect ranging method.The research in this article will expand the application of spherical Talbot effect in long-distance measurement.