K空间抽样格林函数在正向重构时的误差分析

Error Analysis of Green′s Function Sampled in K-space for Forward Reconstruction

在近场声全息重构过程中,当采用K空间抽样格林函数进行大距离正向重构时,会产生极大的误差,而传统的加窗处理不能有效抑制这种误差的产生。文中在分析了误差是K空间抽样格林函数幅值突变而产生的频谱泄露和边缘吉布斯效应的基础上,提出了有针对性的改变窗函数的截止波数,使格林函数幅值突变部位得到有效平滑,进而抑制这种误差产生的方法。仿真结果表明,经改进的窗函数能够对K空间抽样格林函数大距离正向重构时的误差起到明显的抑制作用,使此条件下的全息重构具有更加良好的效果。

During the near-field acoustic holographic reconstruction,tremendous errors will appear when using Green′s function sampled in K-space for long distance forward reconstruction,and conventional window function cannot restrain the error efficiently.In this paper,the error is analyzed to be generated by spectrum leakage and edge Gibbs phenomenon derived from amplitude discontinuity of Green′s function sampled in K-space,hence a corresponding method for changing the cut-off wave number of window function is represented to smooth the amplitude discontinuity and further to restrain the error.Simulation result shows that the improved window function can obviously reduce the error in the holographic aperture,and the present method is efficient in restraining the error generated by spectrum leakage and Gibbs phenomenon derived from amplitude discontinuity of Green′s function sampled in K-space.