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Frontiers of Optoelectronics

ISSN 2095-2759

ISSN 2095-2767(Online)

CN 10-1029/TN

Postal Subscription Code 80-976

Front. Optoelectron.    2010, Vol. 3 Issue (3) : 264-269    https://doi.org/10.1007/s12200-010-0095-8
Research articles
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,
Nano-Photonics and Optoelectronics Research Laboratory, Faculty of Electrical and Computer Engineering, Shahid Rajaee Teacher Training University (SRTTU), Lavizan 16788, Tehran, Iran;
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Abstract Laser heterodyne interferometer is one kind of nano-metrology systems which has been widely used in industry for high-accuracy displacement measurements. The accuracy of the nano-metrology systems based on the laser heterodyne interferometers can be effectively limited by the periodic nonlinearity. In this paper, we present the nonlinearity modeling of the nano-metrology interferometric system using some adaptive filters. The adaptive algorithms consist of the least mean squares (LMS), normalized least mean squares (NLMS), and recursive least squares (RLS). It is shown that the RLS algorithm can obtain optimal modeling parameters of nonlinearity.
Issue Date: 05 September 2010
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Saeed OLYAEE,Mohammad Shams Esfand ABADI,Samaneh HAMEDI, et al. Use of adaptive RLS, LMS, and NLMS algorithms for nonlinearity modeling in a modified laser interferometer[J]. Front. Optoelectron., 2010, 3(3): 264-269.
 URL:  
https://academic.hep.com.cn/foe/EN/10.1007/s12200-010-0095-8
https://academic.hep.com.cn/foe/EN/Y2010/V3/I3/264
Schattenburg M L, Smith H I. The critical role of metrology in nanotechnology. Proceedings of the SPIE, 2002, 4608: 116―124

doi: 10.1117/12.437273
Pieter B. Optical lithography to 2000 and beyond. Solid State Technology, 1999, 42(2): 31―41
Lawall J, Kessler E. Michelsoninterferometry with 10 pm accuracy. Reviewof Scientific Instruments, 2000, 71(7): 2669―2676

doi: 10.1063/1.1150715
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

doi: 10.1088/0957-0233/9/7/003
Rosenbluth A E, Bobroff N. Opticalsources of nonlinearity in heterodyne interferometers. Precision Engineering, 1990, 12(1): 7―11

doi: 10.1016/0141-6359(90)90003-H
Sutton C M. Non-linearity in length measurement using heterodynelaser Michelson interferometry. PhysicsE: Scientific Instruments, 1987, 20(10): 1290―1292

doi: 10.1088/0022-3735/20/10/034
Cosijns S J A G, Haitjema H, Schellekens P H J. Modeling and verifying non-linearitiesin heterodyne displacement interferometry. Precision Engineering, 2002, 26(4): 448―455

doi: 10.1016/S0141-6359(02)00150-2
De Feritas J M. Analysis of laser source birefringence and dichorismon nonlinearity in hetrodyne interferometry. Measurement Science and Technology, 1997, 8(11): 1356―1359

doi: 10.1088/0957-0233/8/11/023
Hou W. Optical parts and the nonlinearity in heterodyne interferometers. Precision Engineering, 2006, 30(3): 337―346

doi: 10.1016/j.precisioneng.2005.11.005
Meyers J F, Lee J W, Schwartz R J. Characterization of measurementerror sources in Doppler global velocimetry. Measurement Science and Technology, 2001, 12(4): 357―368

doi: 10.1088/0957-0233/12/4/301
Schmitz T, Beckwith J F. An investigation of two unexplored periodic error sources in differential-pathinterferometry. Precision Engineering, 2003, 27(3): 311―322

doi: 10.1016/S0141-6359(03)00036-9
Olyaee S, Yoon T H, Hamedi S. Jones matrix analysis of frequency mixingerror in three-longitudinal-mode laser heterodyne interferometer. IET Optoelectronics, 2009, 3(5): 215―224

doi: 10.1049/iet-opt.2009.0015
Olyaee S, Nejad S M. Nonlinearityand frequency-path modelling of three-longitudinal-mode nanometricdisplacement measurement system. IET Optoelectronics, 2007, 1(5): 211―220

doi: 10.1049/iet-opt:20060107
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
Badami V G, Patterson S R. A frequency domain method for the measurement of nonlinearity inheterodyne interferometry. Precision Engineering, 2000, 24(1): 41―49

doi: 10.1016/S0141-6359(99)00026-4
Olyaee S, Nejad S M. Reductionof non-orthogonality effect in nanometrology system by modified opticsand signal conditioner. In: Proceedingsof IEEE 6th Symposium on Communication Systems, Networks and DigitalSignal Processing. 2008, 626―629
Heo G, Lee W, Choi S, Lee J, You K. Adaptive neural network approachfor nonlinearity compensation in laser interferometer. Lecture Notes in Computer Science, 2007, 4694: 251―258

doi: 10.1007/978-3-540-74829-8_31
Lee S C, Heo G H, You K H. Adaptive TLS approach for nonlinearitycompensation in laser interferometer. InternationalJournal of Control and Automation, 2009, 2(1): 31―40
Widrow B, Stearns S D. Adaptive Signal Processing. EnglewoodCliffs: Prentice-Hall, 1985
Widrow B, Hoff M E. Adaptiveswitching circuits. IRE WESCON ConventionRecord, 1960, 4: 96―140
Haykin S. Adaptive Filter Theory. Englewood Cliffs: Prentice-Hall, 2002
Treichler J R, Johnson C R Jr, Larimore M G. Theory and Design of AdaptiveFilters. Englewood Cliffs: Prantice-Hall, 2001
Widrow B, McCool J M, Larimore M G, Johnson C R Jr. Stationary and nonstationary learning characteristicsof the LMS adaptive filter. Proceedingsof the IEEE, 1976, 64: 1151―1162

doi: 10.1109/PROC.1976.10286
Olyaee S, Abadi M S E, Hamedi S, Finizadeh F. AdaptiveRLS algorithm for nonlinearity modeling in the nanometrology system. In: Proceedings of the 18th ICEE Conference, Isfahan,Iran. 2010
Guo J, Zhang Y, Shen S. Compensation of nonlinearity in a newoptical heterodyne interferometer with doubled measurement resolution. Optics Communications, 2000, 184(1―4): 49―55

doi: 10.1016/S0030-4018(00)00934-2
Olyaee S, Ebrahimpour R, Hamedi S. Modeling and compensationof periodic nonlinearity in two-mode interferometer using neural networks. IETE Journal of Research, 2010, 56(2): 102―110

doi: 10.4103/0377-2063.63090
Olyaee S, Hamedi S. Alow-nonlinearity laser heterodyne interferometer with quadrupled resolutionin the displacement measurement. The ArabianJournal for Science and Engineering, 2010 (in press)
Olyaee S, Hamedi S. Correctionof nonlinearity in high-resolution nano-displacement measurements. In: Proceedings of IEEE 5th International Symposiumon High-Capacity Optical Networks and Enabling Technologies HONET. 2008, 116―119
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