Efficient performance of neural networks for nonlinearity error modeling of three-longitudinal-mode interferometer in nano-metrology system

Nano-metrology has a crucial role in order to produce nano-materials and devices with a high degree of accuracy and reliability. Laser heterodyne interferometers are non-contact, high-resolution measurement systems which are commonly used in the displacement measurement systems. In this paper, an approach based on neural networks (NNs) for nonlinearity modeling in a three-longitudinal-mode laser heterodyne interferometer (TLMI) for length and displacement measurements is presented considering the experimental deviation parameters. We model nonlinearity errors that arise from elliptically and non-orthogonally polarized laser beams, rotational error in the alignment of the laser head with respect to the polarizing beam splitter axis, rotational error in the alignment of the mixing polarizer, and unequal transmission coefficients of the polarizing beam splitter. Here, we use the neural network algorithms including radial basis function (RBF) and multi-layer perceptron (MLP) networks and stacked generalization method. The simulation results show that multi-layer feed forward perceptron network and stacked generalization method is successfully applicable to real noisy interferometer signals. The one-hidden layer network with 5 neurons gives a good quality of fit for the training and test sets for the measurement system with RBF and MLP networks and three MLP networks with one-hidden layer for stacked generalization method. The numbers of neurons and hidden layers are selected for the best mean square error (MSE) and minimum time consuming.