Study On The Moiré Imaging Effect Based On The Fixed Point

People can often find moiré fringes in the superposition of one-dimensional grating lines or two-dimensional mesh grids.The moiré phenomenon occurs when two or more layers of related structures superimposed in certain way.Since1990s,the micro-lens array(MLA)have been introduced into the moiré devices as a revealing layer,together with the micro-pattern array(MPA)as base layer.A moiré pattern with a magnification factor of several hundred,so-called the moiré imaging effect,will appear.The physical mechanism of the moiré imaging effect can be explained as an amplified pattern formed by sampling of the MPA with the MLA.The moiré imaging effect the general law of the moiré phenomenon,and can create strikingly visual effects.In this paper,the fixed point in the moiré imaging effect is studied.We conduct theoretical and experimental research on the dynamic effect of the moiré image at different viewing angle by using of the fixed point theorem.The algorithm for calculating the magnitude and direction of the moiré vector under different transformation function is proposed.What's more,the influence of the alignment error between the MLA and MPA on the moiré image is discussed.The main content of the paper can be summarized as follows:(1)Based on the fixed point theorem,the dynamics of the fixed point in the moiré imaging effect is studied.It is found that the location of the fixed point is closely related to the appearance of the moiré imaging.A method for analyzing the dynamic effect in the moiré imaging film was obtained.(2)The kinetics of the moiré image under both linear and nonlinear transformation is studied by numerical simulation.In the linear transformation case,the parallactic movement in scaling transformation and the orthoparallactic movement in rotation transformation is discussed.In the nonlinear transformation case,the radial and rotating movement in ring transformation is analyzed.(3)By combination of laser direct writing and nanoimprint technology,the moiré imaging film is fabricated.The feature linewidth is more than 10000 dpi and the diameter of the aperture is 42 microns.The film thickness is 70 microns.The motion effect of the moiré image is in good agreement with the simulation result.A proposal on the analysis of the dynamics of the moiré pattern is studied,which can be applied to other MLA-MPA pattern.By delicately choosing the arrangement,a variety of dynamic effect can be obtained,which has potential application in the field of visual anti-counterfeiting,packaging,and precision inspection etc.