光谱法分析场频对重建精度的影响

数值模拟重建场,采用光谱法讨论了场的属性,尤其频率对重建精度的影响.用Gauss函数建立了双峰模型场,并对其进行了Fourier频谱分析.使用代数迭代法对模型场进行了重建,并对重建场进行了误差分析,结果发现重建场的峰分布、方向和形状都与原场相似,但峰高有所下降,边界出现波动.文章认为出现这种现象的主要原因是滤波造成的,并通过改变Gauss函数的收敛因子来改变场频,采用数值分析方法对这一观点进行论证,结果证明该观点是正确的.同时发现,边界对重建精度影响较大,边界为零的近似误差增大时,重建精度下降,甚至导致迭代不收敛.所以应用代数迭代重建场时,必须注意边界为零的条件.

Analyzing the Effect of Field Frequencies on Reconstructive Accuracy of Rebuilt Field with Spectroscopy

The field to be reconstructed was simulated with numerical simulation technique. The effect of a three-dimensional field's characteristics,especially,its frequency components,on the reconstructive accuracy was discussed with spectroscopy.A double-peaked field model was built with Gaussian function,and its frequency components were analyzed by Fourier transform.With algebraic reconstruction technique,the model field was reconstructed.The reconstructed field was analyzed with many error indexes.As a result,the reconstructed field was similar to the model one in respect of the position,pointing and shape of the peaks,but the heights of the peaks were shorter than those of corresponding ones in the model.The border of the reconstructive field showed obvious fluctuation.It was considered that the main causation of the reconstructive result was the filtering inserted in iterating process.To confirm this idea,the convergence factor,represented with A,of Gaussian function was changed from six to thirty in order to change the frequency components of the model field,and the same numerical simulation as the one for the first model field with A=18 was carried out for these new model ones consisting of different frequency.As a result,the idea proved to be right.At the same time,it was found that the characteristics of the field at the edge of the reconstructed zone had a deeper effect on the reconstructive accuracy.When the precondition that the field edge approximated to zero could no longer existed,the reconstructive accuracy declined,and furthermore,it would make iterating process divergent.From all the above,the characteristics of the field at the edge should draw much attention when we reconstruct a field with Algebraic reconstruction technique.