Use of adaptive RLS, LMS, and NLMS algorithms for nonlinearity modeling in a modified laser interferometer

Saeed OLYAEE; Mohammad Shams Esfand ABADI; Samaneh HAMEDI; Fatemeh FINIZADEH

doi:10.1007/s12200-010-0095-8

[1] Schattenburg M L, Smith H I. The critical role of metrology in nanotechnology. Proceedings of the SPIE, 2002, 4608: 116-124

[2] Pieter B. Optical lithography to 2000 and beyond. Solid State Technology, 1999, 42(2): 31-41

[3] Lawall J, Kessler E. Michelson interferometry with 10 pm accuracy. Review of Scientific Instruments, 2000, 71(7): 2669-2676

[4] Demarest F C. High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics. Measurement Science and Technology, 1998, 9(7): 1024-1030

[5] Rosenbluth A E, Bobroff N. Optical sources of nonlinearity in heterodyne interferometers. Precision Engineering, 1990, 12(1): 7-11

[6] Sutton C M. Non-linearity in length measurement using heterodyne laser Michelson interferometry. Physics E: Scientific Instruments, 1987, 20(10): 1290-1292

[7] Cosijns S J A G, Haitjema H, Schellekens P H J. Modeling and verifying non-linearities in heterodyne displacement interferometry. Precision Engineering, 2002, 26(4): 448-455

[8] De Feritas JM. Analysis of laser source birefringence and dichorism on nonlinearity in hetrodyne interferometry. Measurement Science and Technology, 1997, 8(11): 1356-1359

[9] Hou W. Optical parts and the nonlinearity in heterodyne interferometers. Precision Engineering, 2006, 30(3): 337-346

[10] Meyers J F, Lee J W, Schwartz R J. Characterization of measurement error sources in Doppler global velocimetry. Measurement Science and Technology, 2001, 12(4): 357-368

[11] Schmitz T, Beckwith J F. An investigation of two unexplored periodic error sources in differential-path interferometry. Precision Engineering, 2003, 27(3): 311-322

[12] Olyaee S, Yoon T H, Hamedi S. Jones matrix analysis of frequency mixing error in three-longitudinal-mode laser heterodyne interferometer. IET Optoelectronics, 2009, 3(5): 215-224

[13] Olyaee S, Nejad SM. Nonlinearity and frequency-path modelling of three-longitudinal-mode nanometric displacement measurement system. IET Optoelectronics, 2007, 1(5): 211-220

[14] Olyaee S, Nejad S M. Error analysis, design and modeling of an improved heterodyne nano-displacement interferometer. Iranian Journal of Electrical and Electronic Engineering, 2007, 3(3-4): 53-63

[15] Badami V G, Patterson S R. A frequency domain method for the measurement of nonlinearity in heterodyne interferometry. Precision Engineering, 2000, 24(1): 41-49

[16] Olyaee S, Nejad S M. Reduction of non-orthogonality effect in nanometrology system by modified optics and signal conditioner. In: Proceedings of IEEE 6th Symposium on Communication Systems, Networks and Digital Signal Processing. 2008, 626-629

[17] Heo G, Lee W, Choi S, Lee J, You K. Adaptive neural network approach for nonlinearity compensation in laser interferometer. Lecture Notes in Computer Science, 2007, 4694: 251-258

[18] Lee S C, Heo G H, You K H. Adaptive TLS approach for nonlinearity compensation in laser interferometer. International Journal of Control and Automation, 2009, 2(1): 31-40

[19] Widrow B, Stearns S D. Adaptive Signal Processing. Englewood Cliffs: Prentice-Hall, 1985

[20] Widrow B, Hoff M E. Adaptive switching circuits. IRE WESCON Convention Record, 1960, 4: 96-140

[21] Haykin S. Adaptive Filter Theory. Englewood Cliffs: Prentice-Hall, 2002

[22] Treichler J R, Johnson C R Jr, Larimore M G. Theory and Design of Adaptive Filters. Englewood Cliffs: Prantice-Hall, 2001

[23] Widrow B, McCool J M, Larimore M G, Johnson C R Jr. Stationary and nonstationary learning characteristics of the LMS adaptive filter. Proceedings of the IEEE, 1976, 64: 1151-1162

[24] Olyaee S, Abadi M S E, Hamedi S, Finizadeh F. Adaptive RLS algorithm for nonlinearity modeling in the nanometrology system. In: Proceedings of the 18th ICEE Conference, Isfahan, Iran. 2010

[25] Guo J, Zhang Y, Shen S. Compensation of nonlinearity in a new optical heterodyne interferometer with doubled measurement resolution. Optics Communications, 2000, 184(1-4): 49-55

[26] Olyaee S, Ebrahimpour R, Hamedi S. Modeling and compensation of periodic nonlinearity in two-mode interferometer using neural networks. IETE Journal of Research, 2010, 56(2): 102-110

[27] Olyaee S, Hamedi S. A low-nonlinearity laser heterodyne interferometer with quadrupled resolution in the displacement measurement. The Arabian Journal for Science and Engineering, 2010 (in press)

[28] Olyaee S, Hamedi S. Correction of nonlinearity in high-resolution nano-displacement measurements. In: Proceedings of IEEE 5th International Symposium on High-Capacity Optical Networks and Enabling Technologies HONET. 2008, 116-119