离轴非球面元件的应用可以使光学系统在成像质量和轻量化程度上得到最大限度的提高。但最接近球面以及研磨去除量的求解仍然是加工环节中极为重要的问题,为此, 提出了一种同时考虑研磨去除量最小准则和研磨变化量要求的最接近球面及研磨去除量的求解方法, 可适用于二次及高次离轴非球面最接近球面及研磨去除量的精确求解, 具有普遍意义。通过编程实例计算了最接近球面的半径、最大研磨去除量和研磨去除总量, 与经验公式计算结果的比较表明了该方法求解结果的优势, 同时离轴非球面加工中的实际应用也证明了该方法的正确性。该方法的提出对离轴非球面加工具有一定的理论和实际指导意义。

The application of off-axis aspheres can improve the imaging quality and the compactness of the optical system furthest. The resolving of the best-fit sphere and the material removal, however, is a very important problem during the fabrications. In this paper, an algorithm available for the precise calculation of the conic and high order off-axis asphere is proposed, considering the requirement of minimum material removal and the slope of material removal. The radius of the best-fit sphere, the maximum material removal and the total volume of material removal are calculated by programming. The advantage of the algorithm is shown by the comparison of results derived from new algorithm and empirical equation. At the same time, the application in the off-axis asphere fabrication also proves the correctness of the algorithm. This algorithm is very helpful for the theory and practice of the fabrications of off-axis asphere.