Theoretical Analysis Method of Moiré Display Based on Microlens Array with Regular Hexagonal Aperture and Honeycomb Arrangement

Abstract

The naked-eye 3D printing technology based on microlens array can achieve the naked-eye 3D display effect within 360^o full angle without the help of glasses, helmet and other visual aids or observation skills. It can significantly improve the information display level, interest and anti-counterfeiting performance of the product, increase the visual impact and sensory experience of the product, and greatly enhance the added value of the product, which has significant engineering application values in the fields of printing, publishing, anti-counterfeiting, decoration, display, etc. However, the naked-eye 3D printing technology based on microlens array currently lacks the necessary theoretical analysis method of moiré display, which embody in the following aspect: the existing methods only focus on the array magnification features of moiré pattern, ignoring the spatial direction features and unit magnification features of moiré pattern. In this paper, on the basis of the existing geometric transformation method, a moiré display theoretical analysis method was proposed for microlens array with regular hexagonal aperture and honeycomb arrangement, which gave consideration to the imaging characteristics of moiré pattern, such as periodic amplification, unit amplification and spatial direction. The mathematical relationship between the period, direction angle, period magnification, unit magnification of moiré pattern and the period of microlens array, the period of micrographics array, as well as the superposition angle of them were derived in detail. The two typical cases were selected, and the theoretical and experimental values of the period, the direction angle, the period magnification and the unit magnification of moiré pattern were calculated and tested respectively. The differences between the theoretical and experimental values were then compared. The results show that the deviation rates between the experimental and theoretical values of the period, the direction angle, the period magnification and the unit magnification are all less than 2% in two typical cases, which verified the effectiveness of the proposed moiré display theoretical analysis method.