Position error correction of position sensitive detector by least squares support vector machine

Abstract

A new method for position error correction of position-sensitive detector (PSD) using least squares support vector machine (LS-SVM) is presented. The LS-SVM is established based on the structural risk minimization principle rather than minimize the empirical error commonly implemented in the neural networks, LS-SVM achieves higher generalization performance than the MLP and RBF neural networks in solving these machine learning problems. Another key property is that unlike MLP’ training that requires non-linear optimization with the danger of getting stuck into local minima, training LS-SVM is equivalent to solving a set of linear equations. Consequently, the solution of LS-SVM is always unique and globally optimal. A difference with the RBF neural networks is that no center parameter vectors of the Gaussians have to be specified and no number of hidden units has to be defined because of Mercer's condition. The position error correction procedure has been illustrated using 2D PSD as example. The results indicate that this approach is effective, and the position detection errors can be reduced from ±300μm to ±10μm.