基于偏折光谱的非线性迭代层析数值模拟

Numerical Simulation of a New Nonlinear Iteration Tomography Based on Deflection Spectra

模拟流场,校验自研发的偏折层析系统。根据光线偏折的光学原理,以及层析的数学、物理意义,研究开发了偏折层析程序。结合自研发的简单自相关代数迭代重建技术（simple self-correlative algebraic reconstruction technique：SSART）,开发了一种新的层析系统,文章称“基于偏折光谱的非线性迭代层析系统”。用Gauss函数模拟复杂流场的一个切片,根据偏折层析算法计算该切片的偏折光谱,从偏折光谱中提取投影。采用SSART迭代重建算法重建截面。比较模拟重建结果与原场的差别,采用均方差（mean-squareerror：MSE）和峰差（peak error：PE）指数标定重建效果,以检验算法的有效性。结果发现,应用开发的偏折层析程序,采用SSART迭代算法,能够精确重建模拟场,MSE稳定在0.000 09-0.000 11范围,PE稳定在0.007-0.013之间。因此,基于偏折光谱的非线性迭代层析系统能够根据偏折信息精确重建复杂流场。

A new deflection tomography was suggested and verified with a simulated flow field. The deflection programs for projection and inverse-projection were produced based on optical principle of refraction and mathematical, physical significance of tomography. With the authors＇ home-made simple self-correlative algebraic reconstruction technique （SSART）, the program system for the new deflection tomography was worked out and named Nonlinear Iteration Tornography Based on Deflection Spectra. A section of a complex flow field was simulated with Gauss function. The deflection spectra of a beam of parallel rays, as they passed through the field, were figured out according to the deflection program for projection, and the relative projections were acquired from the spectra. The section was reconstructed with the projections by SSART. The reconstructed result was compared with the model in order to test the deflection programs for validity. The reconstruction effect was scaled with mean- square error （MSE） and peak error （PE）. As a result, with SSART, the deflection programs could be used to reconstruct the simulated field accurately. The MSE of reconstruction in this case was about 0. 000 09 to 0. 000 11 after 503 iterations, and PE was about 0. 007 to 0. 013. So, the program system, Nonlinear Iteration Tomography Based on Deflection Spectra, can accurately reconstruct complex flow fields based on deflection information.