An Investigation Of Theory And Application Of New Methods On Depth Profile Recognition Based On Photoacoustic And Photothermal Detect Technology

In this thesis, based on photoacoustic and photothermal nondestructive detection technology, theorems of applied mathematics and modern computation methods we research theoretical and applied problems on depth profile recognition with photothermal signal induced by laser.We first research the thermal conduction model of sample impulsed by laser and obtain the analytic form of Green function by using a novel approach. Then we construct a algorithm solving the direct problem of the model, which is more stable and accurate than the traditional layered or Laplacian algorithm. Furthermore the result obtained in this part is the foundation for reaching related inverse problems.After the studying of direct problem, we investigate depth profiling reconstruction method on optical parameters of inhomogeneous materials. We rebuild the objective function by using singular value decomposition (SVD) and spectrum decomposition, with employing the regularization method or truncated SVD (TSVD) method. Because the Green function is the key function which plays an important role through this thesis, we make eigen analysis of Green function (matrix) and further analyze the sensitivity of physical responding to parameters. These are important to noise analysis and establish a new method of solving inverse problem.As it well known, the noise disturbance, which may induce the solution unstable or diverging, is a fatal factor which restricts practical application for inverse methods. So we also explore the impact of noise in detail based on eigen analysis, and make it clear of noise effect on solution diverging. Base on these works, we suggest a new way to rebuild depth profile of object parameters. The idea is that make a truncation by TSVD at a low order term of the objective function (series), and optimize the higher order terms by Monte Carlo method. The calculation results indicate that its ability of resisting noise is obviously improved versus the regularization method and neural network method.