Fourier and Wavelet Analysis for Optical Fibre Sensor Networks: A Review

A review of the current state of research of Fourier analysis as applied to the field of optical fibre sensing is presented. The implications that using Fourier based multiplexing schemes have on the requirements for sensor design and network configuration is discussed. The flexibility of Fourier techniques is also demonstrated, with the ability to profile the fringe visibility or chirp of an interference spectrum. Generalisations of Fourier analysis to wavelet and chirplet analyses and their relevance to optical fibre sensor networks are also discussed.

[1]  Ian Bennion,et al.  Chirped fibre Bragg grating optical wear sensor , 2004 .

[2]  L. Poladian,et al.  Group-delay reconstruction for fiber Bragg gratings in ref lection and transmission. , 1997, Optics letters.

[3]  Anbo Wang,et al.  Multiplexed Fiber Fabry–Pérot Interferometer Sensors Based on Ultrashort Bragg Gratings , 2007, IEEE Photonics Technology Letters.

[4]  Jeanette G. Grasselli,et al.  “On the Relative Motion of the Earth and the Luminiferous Ether” , 1987 .

[5]  Gang-Ding Peng,et al.  Simultaneous demodulation technique for a multiplexed fiber Fizeau interferometer and fiber Bragg grating sensor system. , 2006, Optics letters.

[6]  D. Esteban,et al.  Application of quadrature mirror filters to split band voice coding schemes , 1977 .

[7]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[8]  J. E. Bridges,et al.  Orthogonal detection to reduce common channel interference , 1964 .

[9]  Marshall C. Pease,et al.  An Adaptation of the Fast Fourier Transform for Parallel Processing , 1968, JACM.

[10]  S.W. James,et al.  Multiplexing of Fiber-Optic Long-Period Grating-Based Interferometric Sensors , 2007, Journal of Lightwave Technology.

[11]  Sailing He,et al.  Multiplexing Scheme for Self-Interfering Long-Period Fiber Gratings Using a Low-Coherence Reflectometry , 2007, IEEE Sensors Journal.

[12]  Shah M. Musa,et al.  Real-Time Signal Processing and Hardware Development for a Wavelength Modulated Optical Fiber Sensor System , 1997 .

[13]  R. A. Sammut,et al.  Optimised time-frequency domain layer-peeling algorithm to reconstruct fibre Bragg gratings , 2004 .

[14]  Amir Rosenthal,et al.  Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings , 2003 .

[15]  Gang Ding Peng,et al.  Strain-sensing system based on carrier-modulated gratings for the monitoring of a large number of channels , 2006, Journal of Lightwave Technology.

[16]  Evgueni M. Dianov,et al.  In-fiber Mach-Zehnder interferometer based on a pair of long-period gratings , 1996, Proceedings of European Conference on Optical Communication.

[17]  Y. Rao,et al.  Fiber-optic Fabry-Perot sensors based on a combination of spatial-frequency division multiplexing and wavelength division multiplexing formed by chirped fiber Bragg grating pairs. , 2006, Applied optics.

[18]  A. Kersey,et al.  Multiplexed fiber Bragg grating strain-sensor system with a fiber Fabry - Perot wavelength filter. , 1993, Optics letters.

[19]  Gang-Ding Peng,et al.  Spectrally-overlapped chirped fibre Bragg grating sensor system for simultaneous two-parameter sensing , 2007 .

[20]  Amir Rosenthal,et al.  Reconstruction of long-period fiber gratings from their core-to-core transmission function. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[21]  Nobuo Takeda,et al.  Application of chirped fiber Bragg grating sensors for identification of crack locations in composites , 2004 .

[22]  Gang-Ding Peng,et al.  Multiplexing technique using amplitude-modulated chirped fiber Bragg gratings. , 2007, Optics letters.

[23]  G. Cranch,et al.  Rapid characterization of the ultraviolet induced fiber Bragg grating complex coupling coefficient as a function of irradiance and exposure time. , 2007, Applied optics.

[24]  E. Podivilov,et al.  Efficient numerical method of the fiber Bragg grating synthesis , 2006, physics/0611039.

[25]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[26]  Pierre L. Goupillaud,et al.  AN APPROACH TO INVERSE FILTERING OF NEAR-SURFACE LAYER EFFECTS FROM SEISMIC RECORDS* , 1961 .

[27]  Junji Nishii,et al.  Self-interference of long-period fibre grating and its application as temperature sensor , 1998 .

[28]  Min Zhang,et al.  Relative Humidity Sensor Based on Cascaded Long-Period Gratings With Hydrogel Coatings and Fourier Demodulation , 2009, IEEE Photonics Technology Letters.

[29]  Gang-Ding Peng,et al.  Spectrally-coded multiplexing in a strain sensor system based on carrier-modulated fiber Bragg gratings , 2005, SPIE/COS Photonics Asia.

[30]  J. Skaar,et al.  On the synthesis of fiber Bragg gratings by layer peeling , 2001 .

[31]  Gang-Ding Peng,et al.  Multiplexed fibre Fizeau interferometer and fibre Bragg grating sensor system for simultaneous measurement of quasi-static strain and temperature using discrete wavelet transform , 2006 .

[32]  Simon Haykin,et al.  Adaptive chirplet: an adaptive generalized wavelet-like transform , 1991, Optics & Photonics.

[33]  Serguei V. Miridonov,et al.  Twin-grating fiber optic sensor demodulation , 2001 .

[34]  Gang-Ding Peng,et al.  An in-line in-fibre ring cavity sensor for localized multi-parameter sensing , 2008 .

[35]  P. Childs,et al.  An FBG sensing system utilizing both WDM and a novel harmonic division scheme , 2005, Journal of Lightwave Technology.

[36]  Lipo Wang,et al.  Layer peeling algorithm for reconstruction of long-period fibre gratings , 2001 .

[37]  S Huang,et al.  Bragg intragrating structural sensing. , 1995, Applied optics.

[38]  Thompson Fourier Transforms in VLSI , 1983, IEEE Transactions on Computers.

[39]  Michalis N. Zervas,et al.  An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings , 1999 .

[40]  B. Lee,et al.  Dependence of fringe spacing on the grating separation in a long-period fiber grating pair. , 1999, Applied optics.

[41]  Yicheng Lai,et al.  Distributed temperature sensing using a chirped fibre Bragg grating , 2004 .

[42]  Alfred M. Bruckstein,et al.  Inverse scattering with noisy data , 1986 .

[43]  Albert A. Michelson,et al.  LVIII. On the relative motion of the earth and the luminiferous Æther , 1887 .

[44]  T. Barnwell,et al.  A procedure for designing exact reconstruction filter banks for tree-structured subband coders , 1984, ICASSP.

[45]  Johannes Skaar,et al.  Reconstruction of gratings from noisy reflection data. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[46]  Gang-Ding Peng,et al.  Measurement of crack formation in concrete using embedded optical fibre sensors and differential strain analysis , 2008 .

[47]  Christopher Heil,et al.  Continuous representation theory using the affine group , 2009 .

[48]  Steven G. Johnson,et al.  The Design and Implementation of FFTW3 , 2005, Proceedings of the IEEE.

[49]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[50]  L. Reekie,et al.  Grating writing model for materials with nonlinear photosensitive response , 2003 .

[51]  David A. Shapiro,et al.  Finite Bragg grating synthesis by numerical solution of Hermitian Gel'fand-Levitan-Marchenko equations , 2006 .

[52]  J. Bland-Hawthorn,et al.  Comparison of inverse scattering algorithms for designing ultrabroadband fibre Bragg gratings. , 2009, Optics express.

[53]  H Y Fu,et al.  Multiplexing of polarization-maintaining photonic crystal fiber based Sagnac interferometric sensors. , 2009, Optics express.

[54]  Serguei V. Miridonov,et al.  Multiplexing of grating-based fiber sensors using broadband spectral coding , 1999, Other Conferences.