Abstract We elaborate an elliptic averaging procedure to estimate astigmatism and defocus of optical transfer functions that allows to reduce the problem to a simpler one of estimating defocus only. Based on approximate closed-form formulas for the zeros of defocus optical transfer functions, we reparametrise the frequency domain and derive a class of nonlinear transformations that turn elliptic null-curves of astigmatic optical transfer functions into circles. Our results make astigmatic images amenable to restoration.

中文翻译：

---

用于估计散光和散焦的光学传递函数的椭圆平均

摘要 我们详细阐述了一种椭圆平均程序来估计光学传递函数的像散和散焦，从而可以将问题简化为仅估计散焦的简单问题。基于散焦光学传递函数零点的近似闭式公式，我们重新参数化频域并推导出一类非线性变换，将像散光学传递函数的椭圆零曲线变成圆。我们的结果使散光图像易于恢复。