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.