|
|
|
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; |
|
|
|
|
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
|
|
|
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
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|