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The nano-metrology systems implemented based on the heterodyne interferometers are widely used today. The nonlinearity in these systems is the most important factor to limit the accuracy. An effective approach for nonlinearity modeling in these systems is based on the neural network approaches. In this paper, a neural network for nonlinearity modeling in the modified nano-metrology system using a three-mode heterodyne interferometer setup is presented. A hybrid algorithm in order to modeling of periodic nonlinearity error resulting from elliptical polarization and non-orthogonality of polarizing laser beams is implemented by applying a multi-layer perceptron (MLP). It is also shown that by using our hybrid analytical approach, mean square error (MSE) reaches an optimum point about 10-10.