Ma Shuiliang, Gao Hongming, Wu Lin
State Key Laboratory of Advanced Welding Production Technology, Harbin Institute of Technology, Harbin 150001, China.
Appl Opt. 2008 Mar 20;47(9):1350-7. doi: 10.1364/ao.47.001350.
Errors in discrete Abel inversion methods using Fourier transform techniques have been analyzed. The Fourier expansion method is very accurate but sensitive to noise. The Fourier-Hankel method has a significant systematic negative deviation, which increases with the radius; inversion error of the method can be reduced by adjusting the value of a factor. With a decrease of the factor both methods show a noise filtering property. Based on the analysis, a modified Fourier-Hankel method that is accurate, computationally efficient, and has the ability to filter noise in the inversion process is proposed for applying to experimental data.
对使用傅里叶变换技术的离散阿贝尔反演方法中的误差进行了分析。傅里叶展开方法非常精确，但对噪声敏感。傅里叶 - 汉克尔方法存在显著的系统性负偏差，该偏差随半径增加；通过调整一个因子的值可以减小该方法的反演误差。随着该因子的减小，两种方法都表现出噪声滤波特性。基于上述分析，提出了一种改进的傅里叶 - 汉克尔方法，该方法精确、计算效率高，并且在反演过程中具有滤除噪声的能力，适用于实验数据。
