A Lens-Array-Based Measurement Technique for Spatial Angle

Accurate measurement of the spatial angle is key for plane flatness and guide rail straightness detection. This paper presents a lens-array-based optical system and an analytical model for micro-spatial angle measurements. In this system, a collimated light beam passes through four-array lenses arranged in a pyramid shape and forms regular array spots on a charge-coupled device sensor. The angles with respect to the X and Y axes are calculated by analyzing the distance of these spots on the CCD, the distance between adjacent apertures on the lens array, and the inclination angle between the lens array and the CCD. Using the coordinate value of the array spots on the CCD, the angle around the Z-axis can also be calculated simultaneously. Finally, the accuracy of the proposed method was verified by comparing the measured results with those of the autocollimator, and it was shown that the proposed approach enabled the achievement of RMS <= 0.1 ''. Additionally, this measurement system which is consists of a laser source, lens arrays and CCD, compared with other methods, is smaller in volume and more convenient to carry.