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

Abstract The reconstruction algorithm used for a new spatially resolved plasma optical emission spectroscopy sensor is described. The sensor has a wedge shaped field of view which is rotated horizontally across the plasma. The resulting signal as a function of angle defines an ill-posed linear problem that must be solved to determine the emissivity as a function of radius in the plasma. This problem is solved by modified Tikhonov regularization using a finite difference regularizer which discourages rapid variation in the reconstructed emission. The optimal regularization parameter is determined by minimizing the product of the norm of the residual and the norm of this regularizer. The robustness of the algorithm against noise introduced into idealized data is demonstrated, both for a standard Abel inversion problem and for 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 9400 plasma processing tool; these reconstructions show qualitatively correct behaviors.