A NEW REGULARIZATION METHOD TO DETERMINE STRAIN/STRESS DEPTH PROFILES FROM DIFFRACTION EXPERIMENTS

摘要

Inverse problems which are involved in x-ray or neutron diffraction analysis are known to bernextremely ill-conditioned. The reason is that that the linear system of equations which has tornbe solved for the τ- or true depth gradients from the measured τ-profiles becomes singular.rnFrom the mathematical point of view, regularization methods are recommended to overcomernthe non-uniqueness of the obtained solution. However, all regularization methods reported inrnthe literature are not suitable to the above problem due to several reasons. Therefore, a newrnmethod has been developed. In principle it follows the ideas of the Tikhonov regularizationrnbut uses a complete different functional to be minimized. Using a matrix decompositionrntechnique, it is shown that the six independent τ-gradients can be separated from a usualrnmeasurement series. The true depth profiles are then calculated using orthonormal waveletrnbasis functions.