A reconstruction algorithm for a spatially resolved plasma optical emission spectroscopy sensor

The reconstruction algorithm used for a new spatially resolved plasma optic al emission spectroscopy sensor is described. The sensor has a wedge shaped field of view which is rotated horizontally across the plasma. The resulti ng signal as a function of angle defines an ill-posed linear problem that m ust be solved to determine the emissivity as a function of radius in the pl asma. This problem is solved by modified Tikhonov regularization using a fi nite difference regularizer which discourages rapid variation in the recons tructed emission, The optimal regularization parameter is determined by min imizing the product of the norm of the residual and the norm of this regula rizer. The robustness of the algorithm against noise introduced into ideali zed data is demonstrated, both for a standard Abel inversion problem and fo r test data based on the sensor model. The algorithm is used to reconstruct emitted power density profiles and to perform actinometry in a Lam TCP 940 0 plasma processing tool; these reconstructions show qualitatively correct behaviors. (C) 2000 Elsevier Science Ltd. All rights reserved.