针对已有的相对角差法面形检测的原理验证装置,提出了一种具有更高稳健性的最小二乘积分面形重建算法。利用相对角差改写了经典最小二乘积分技术的代价函数,避免了积分重建中的测量误差累积的问题,空间复杂度和时间复杂度仍分别为O(N²)和O(N³)。仿真结果表明,本文算法的稳健性显著优于Zernike波前重建法与基于样条的最小二乘积分法(SLI);实验结果证明,本文算法可适用于大口径角差法面形检测。

A robust least squares integration surface reconstruction algorithm that exploits the relative angle difference is proposed for a topography measurement device. The cost function of the classical least squares integration technique is rewritten based on relative angle difference to avoid accumulation of measurement errors. The space and time complexities are O(N2) and O(N3), respectively. Simulation results demonstrate that the robustness of the proposed algorithm is significantly better than that of Zernike’s wavefront reconstruction method and spline-based least squares integration method. Experiments show that the algorithm can be applied to topography measurement with large aperture angle difference method.