基于自准直仪的偏折轮廓术重建二次曲面
Reconstruction of a conic-section surface from autocollimator-based deflectometric profilometry
摘要：
我们提出了一种描述我们的方法来处理一组基于自准直仪的偏转仪1维线扫描采取了一个大的光学表面，并将它们重建到一个最适合的圆锥截面表面。我们的任务的挑战是，每个线扫描是在一个不同的（未知的）坐标参考系相对于其他线扫描的集合。这个问题的出现是由于偏转仪中使用的自准直仪的有限角度测量范围以及需要在更大范围内进行测量;这导致在每次扫描之间被测量的光学器件被旋转（俯仰和滚动）以使自准直仪回到测量范围内，因此每次扫描都在不同的坐标系中进行。我们描述了一种方法，使用6 N +2维优化（其中N是跨镜扫描线的数量），该方法使用基于梯度的非线性最小二乘拟合与多起点全局搜索策略相结合，以找到最佳拟合表面。仔细制定的问题，需要减少数值噪声，并允许例程收敛到所需的精度的解决方案。
英文摘要：
We present a description of our method to process a set of autocollimator-based deflectometer 1-dimensional line-scans taken over a large optical surface and reconstruct them to a best-fit conic-section surface. The challenge with our task is that each line-scan is in a different (unknown) coordinate reference frame with respect to the other line-scans in the set. This problem arises due to the limited angular measurement range of the autocollimator used in the deflectometer and the need to measure over a greater range; this results in the optic under measurement being rotated (in pitch and roll) between each scan to bring the autocollimator back into measurement range and therefore each scan is taken in a different coordinate frame. We describe an approach using a 6N+2 dimension optimisation (where N is the number of scan lines taken across the mirror) that uses a gradient-based non-linear least squares fitting combined with a multi-start global search strategy to find the best-fit surface. Careful formulation of the problem is required to reduce numerical noise and allow the routine to converge on a solution of the required accuracy.
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