基于方形孔径微透镜阵列二维叠栅条纹的微小角度测量

Micro-Angle Measurement Based on Two-Dimensional Moire Fringes Generated by Square Aperture Micro-Lens Array

提出了一种利用方形孔径微透镜阵列和微图形阵列产生的二维叠栅条纹测量微小角度的方法。分析了不同尺寸阵列产生的二维叠栅条纹的节距变化规律,推导了微小旋转角度的表达式,对叠栅条纹的节距与阵列夹角之间的关系进行了理论分析与实验测量。研究结果表明,当微图形阵列的窗口边长小于微透镜阵列的透镜元宽度时,叠栅条纹的节距变化较平缓,且对微图形与微透镜阵列间的夹角θ的变化较敏感,这有利于提高测量结果的准确性;当微图形阵列的窗口边长为0.3mm,微透镜阵列的透镜元宽度为0.4mm时,节距与夹角θ间关系的实验结果与理论结果总体一致。

A micro-angle measurement method based on the two-dimensional moire fringes generated by square aperture micro-lens array and micro-graphic array is proposed.The variation principle of the moire fringe pitch formed by these arrays with different sizes is analyzed.The expression of small rotation angle is deduced.The theoretical analysis and experimental measurement are carried out on the relationship between the moire fringe pitch and the included angle of arrays.The research results show that,when the graphic element size of the micro-graphic array is shorter than the lens element size of the micro-lens array,the moire fringe pitch changes gently and is sensitive to the variation of the included angleθbetween micrographics and microlens array,which is helpful for the improvement of the measurement accuracy.When the graphic element size is 0.3 mm and the lens element size is0.4 mm,the experimental result on the relationship between the pitch and the included angleθis basically consistent with the theoretical one.