Influence of machining errors on form errors of microlens arrays in ultra-precision turning

• We established a machining error model of microlens array.
• The integral distribution of the form errors is axisymmetric.
•
• The optical performance has the same correlation as the form errors.
• A machining method is proposed to achieve the high form accuracy and the high uniform.

Ultra-precision turning is widely used in machining microlens arrays. Machining errors have an effect on the form accuracy of the whole microlens array, but they have not been fully studied, especially the effect on the optical performance. A machining error model of microlens arrays is built to analyse the coordinate distortions and form errors easily based on multi-body system theory and a homogeneous transformation matrix. The simulative and experimental results verified the influence of three major machining errors (tool alignment errors (∆x, ∆y), tool nose radius error (∆R) and squareness error (∆θ) from the proposed approach. Through the simulation and experimental approach, this study describes the distribution of the form errors as axisymmetric; the form error of the centre part of the row and column cells is minimal, whereas that of the diagonal cells is the maximum. The optical performance of the cells has the same correlation as the form errors. Based on the above study, a horizontal off-centring machining method is proposed to achieve high form accuracy and uniform optical performance.