平面微透镜阵列与匹配的微图案阵列叠合时,会产生叠栅效应,在微透镜阵列立体防伪技术和高精度测量方面具有潜在的应用价值。基于游标叠栅效应原理建立了叠栅图案的放大倍数和方向与微图案阵列层、平面微透镜阵列层矢量之间的关系式,即叠栅图案相对于微图案的放大倍数约等于微透镜阵列周期矢量与平面微透镜阵列、微图案阵列周期矢量差的比值,该公式能够预测微图案映射的位置和大小。采用孔径边长为0.3 mm、周期为0.315 mm的方形孔径平面微透镜阵列与不同周期、角度的微图案贴合进行验证,叠栅图案的位置、大小的实验结果与理论预测一致。

The moiré effect, which can expand attractive application in the stereoscopic anti-counterfeiting technology and high-precision measurement of the micro-lens array, will occur when the planar micro-lens array is overlapped with the matching micro-pattern array. The relationship between the magnification factor and the direction of the moiré pattern and the vectors of the micro-pattern array layer and the planar micro-lens array layer is obtained based on the principle of the vernier moiré effect. Consequently, the magnification of the moiré pattern relative to the micro-pattern array is found to be approximately equal to the ratio of the periodic vector of the micro-lens array to the difference of periodic vectors of the planar micro-lens array and the micro-pattern array. The formula can predict the position and size of the micro-pattern mapping. For verification, the square aperture planar micro-lens array with an aperture side length of 0.3 mm and a period of 0.315 mm is applied to the micro patterns with different periods and angles. The experimental results of the location and size of the moiré patterns are consistent with the theoretical predictions.