Pant Kamal K, Burada Dali R, Bichra Mohamed, Ghosh Amitava, Khan Gufran S, Sinzinger Stefan, Shakher Chandra
Appl Opt. 2018 Feb 10;57(5):1100-1109. doi: 10.1364/AO.57.001100.
In the present work, a spline-based integration technique for the reconstruction of a freeform wavefront from the slope data has been implemented. The slope data of a freeform surface contain noise due to their machining process and that introduces reconstruction error. We have proposed a weighted cubic spline based least square integration method (WCSLI) for the faithful reconstruction of a wavefront from noisy slope data. In the proposed method, the measured slope data are fitted into a piecewise polynomial. The fitted coefficients are determined by using a smoothing cubic spline fitting method. The smoothing parameter locally assigns relative weight to the fitted slope data. The fitted slope data are then integrated using the standard least squares technique to reconstruct the freeform wavefront. Simulation studies show the improved result using the proposed technique as compared to the existing cubic spline-based integration (CSLI) and the Southwell methods. The proposed reconstruction method has been experimentally implemented to a subaperture stitching-based measurement of a freeform wavefront using a scanning Shack-Hartmann sensor. The boundary artifacts are minimal in WCSLI which improves the subaperture stitching accuracy and demonstrates an improved Shack-Hartmann sensor for freeform metrology application.
在当前工作中，实现了一种基于样条的积分技术，用于从斜率数据重建自由曲面波前。自由曲面的斜率数据由于其加工过程而包含噪声，这会引入重建误差。我们提出了一种基于加权三次样条的最小二乘积分方法（WCSLI），用于从有噪声的斜率数据中准确重建波前。在所提出的方法中，将测量得到的斜率数据拟合到分段多项式中。通过使用平滑三次样条拟合方法确定拟合系数。平滑参数在局部为拟合的斜率数据赋予相对权重。然后使用标准最小二乘法对拟合的斜率数据进行积分，以重建自由曲面波前。仿真研究表明，与现有的基于三次样条的积分（CSLI）方法和索思韦尔方法相比，所提出的技术取得了更好的结果。所提出的重建方法已通过实验应用于使用扫描夏克 - 哈特曼传感器对自由曲面波前进行基于子孔径拼接的测量。在WCSLI中边界伪像最少，这提高了子孔径拼接精度，并展示了一种改进的用于自由曲面计量应用的夏克 - 哈特曼传感器。
