Modeling and Compensation of Periodic Nonlinearity in Two-mode Interferometer Using Neural Networks

Abstract

The periodic nonlinearity in nano-metrology systems based on heterodyne interferometers is the most important limitation to the accuracy of displacement measurement. It is mainly produced due to the polarization-mixing and frequency-mixing. In this paper, a new approach based on an ensemble of neural networks for modeling and compensation of nonlinearity in a high-resolution laser heterodyne interferometer is presented. We model the periodic nonlinearity arising from elliptical polarization and non-orthogonality of the laser polarized light based on the neural network approaches, including the multi-layer perceptrons and radial basis function as single neural networks and stacked generalization method as ensemble of neural networks. It is also shown that by using the stacked generalization method, the primary periodic nonlinearity of 1.3 nm is significantly compensated by a factor of 168.

Keywords:

• Ensemble of neural networks
• Heterodyne interferometer
• Multi-layer perceptrons
• Nonlinearity reduction
• Stacked generalization

Additional information

Notes on contributors

Saeed Olyaee

Saeed Olyaee received his B.Sc. degree in Electrical Engineering from University of Mazandaran, Babol, Iran, in 1997and the M.Sc. and the Ph.D. degrees in Electrical Engineering specializing in Optoelectronics from Iran University of Science and Technology, Tehran, Iran, in 1999 and 2007, respectively. His doctoral dissertation concerned nanometric displacement measurement based on three-longitudinal-mode laser interferometer. Currently, he is an Assistant Professor in Nano-Photonics and Optoelectronics Research Laboratory (NORLab), Faculty of Electrical and Computer Engineering, Shahid Rajaee University, Tehran, Iran. Dr. Olyaee’s main research interests include nano-displacement measurement, optical instrumentation, and optoelectronic circuits.

E-mail: [email protected]

Reza Ebrahimpour

Reza Ebrahimpour received his B.Sc. degree in Electronics Engineering from Mazandaran University, Mazandaran, Iran and the M.Sc. degree in Biomedical Engineering from Tarbiat Modarres University, Tehran, Iran, in 1999 and 2001, respectively. He received his Ph.D. degree in July 2007 from the School of Cognitive Science, Institute for Studies on Theoretical Physics and Mathematics, where he worked on view-independent face recognition with Mixture of Experts. His research interests include human and machine vision, neural networks, and pattern recognition.

E-mail: [email protected]

Samaneh Hamedi

Samaneh Hamedi received her B.Sc. degree in Electrical Engineering from University of Shiraz, Iran, in 2003 and M.Sc. degree in Electrical Engineering from Shahid Rajaee University, Tehran, Iran in 2009. Her thesis concerned in nanometric displacement measurement systems with nonlinearity reduction. She was the student member of IEEE in 2007–2009. Currently she works as a researcher in Nano-Photonics and Optoelectronics Research Laboratory and Machine Vision Laboratory, Faculty of Electrical Engineering, Shahid Rajaee University. Her research interests include nano-optical instrumentation, optoelectronic circuits, and neural networks.

E-mail: [email protected]