光偏折层析的Tikhonov正则化重建技术

从不适定问题的求解思想出发,建立了使用Tikhonov正则化方法计算流场参量分布的光偏折层析重建技术。理论上详细讨论了偏折信息的转化、投影方程组的正则化、以及由共轭梯度法实现求解等三个主要步骤。用数值模拟考察该方法对非对称温度分布的重建效果,分别计算了对应不同采样数的欠定与超定投影方程组。结果表明,10次迭代后重建分布的平均误差和峰值误差分别为2.1%和5.2%。使用正则化方法对采集的多方向叠栅偏折投影进行计算,重建出双峰温度场。结果表明,使用正则化方法的双峰值相对误差略高,迭代次数减少,可提高重建效率。

Tikhonov Regularization Method for Deflectometric Tomographic Reconstruction

The problems arising in the computed tomography area are well known for their high dimensions and ill-posed. Tikhonov regularization method is developed to reconstruct temperature distribution from deflectometric projection data. Beam deflection angles obtained from moiré deflectograms are integrated to optical path length differences, and a modified regularization method is applied to the linear projection equations. The conjugate gradient method is used to compute the regularized solution for the least-square equations. In numerical simulation, the approach produced reliable reconstructions by computing underdetermined equations and overdetermined equations respectively for asymmetrical distribution. The average errors were 2.1% and the maximum value errors were 5.2% after 10 iterations, which provided a good indication of the precision and convergence of the method. The experimental results of reconstruction from real projection data were satisfactory when compared with the reconstruction results by deflection angle revision reconstruction technique (DARRT) and the direct thermocouple measurements.