Skip to main content

Mathematical techniques in fiber optic sensor applications

  • Chapter
  • 1180 Accesses

Part of the book series: Optoelectronics, Imaging and Sensing Series ((OISS,volume 3))

Abstract

There is a continuing need for high quality and repeatable measurement techniques for application in a wide variety of industries, and with that the requirement for reliable and trustworthy instrumentation. Fiber optics have a significant part to play in achieving this goal and could result in an opportunity for cost savings, which increases the competitive potential, with benefits being passed on to the customer. Further, the meeting of increased legislative requirements world-wide are often seen to be driving the field, especially in safety and environmental matters. The technology has developed rapidly in recent years, and is now being used by physicists, chemists, engineers and biologists, as well as those comparatively untrained in the fundamentals of the subject. With the wide variety of techniques (which include optical fiber systems) available to these investigators, it is essential that there is a clear understanding of the appropriate guidelines for the selection and use of any particular method of instrumentation, and its limitations as well as its desirable features. Also, the degree to which it is ‘user friendly’ can considerably influence its acceptability for any specific application.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Finkelstein, L. and Grattan, K. T. V. Concise Encyclopedia of Measurement and Instrumentation, Pergamon Press, Oxford, 1994.

    Google Scholar 

  2. James, J. R. and Gallett, I. N. L. Point-matched solutions for propagating modes on arbitrarily shaped dielectric rods, Radio Electron. Eng., 42, 103, 1972.

    Article  Google Scholar 

  3. Chiang, K. S. Analysis of optical fibers by effective-index method, Appl. Opt., 25, 348354, 1986.

    Google Scholar 

  4. Su, C. C. and Chen, C. H. Calculation of propagation constants and cutoff frequencies of radially inhomogeneous optical fibers, IEEE Trans. Microwave Theory Technol., MTT-34, 328–332, 1986.

    Google Scholar 

  5. Rahman, B. M. A. and Davies, J. B. Finite-element solution of integrated optical waveguides, J. Lightwave Technol., LT-2, 682–688, 1984.

    Google Scholar 

  6. Wang, D. N., Ning, Y. N., Grattan, K. T. V., Palmer, A. W. and Weir, K. Optimized multiwavelength combination sources for interferometric use, Appl. Opt., 33, 73267333, 1994.

    Google Scholar 

  7. Wang, D. N., Grattan, K. T. V. and Palmer, A. W. Dispersion effect analysis with multiwavelength combination sources in optical sensor applications, Opt. Commun., 127, 19–24, 1996.

    Article  Google Scholar 

  8. Grattan, K. T. V., Selli, R. K. and Palmer, A. W. Ruby decay-time fluorescence thermometer in a fibre optic configuration, Rev. Sci. Instrum., 59, 1328–1335, 1988.

    Article  Google Scholar 

  9. Zhang, Z., Grattan, K. T. V. and Palmer, A. W. A fibre optic high temperature sensor based on the fluorescence of alexandrite, Rev. Sci. Instrum., 63, 3869–3873, 1992.

    Article  Google Scholar 

  10. Zhang, Z., Grattan, K. T. V. and Palmer, A. W. Temperature dependencies of fluorescence lifetimes in Cr+3-doped insulating crystals, Phys. Rev. B., 48, 7772–7778, 1993.

    Article  Google Scholar 

  11. Goell, J. E. A circular harmonic computer analysis of rectangular dielectric wave-guides, Bell Syst. Tech. J., 48, 2133–2160, 1969.

    Article  Google Scholar 

  12. Marcatili, E. A. J. Dielectric rectangular waveguide and directional coupler for integrated optics, Bell Syst. Tech. J., 48, 2071–2102, 1969.

    Article  Google Scholar 

  13. Knox, R. M. and Toulios, P. P. Integrated circuits for the millimetre through optical frequency range, Proc. MRI Symp. Submilimeter Waves, Brooklyn Poly Inst., Brooklyn, pp. 497–516, 1970.

    Google Scholar 

  14. Sharma, E. K., Ghatak, A. K. and Goyal, I. C. Matrix method for determining propagation characteristics of optical waveguides IEEE J. Quantum Electron, QE-19, 1231–1233, 1983.

    Google Scholar 

  15. Stern, M. S., Kendall, P. C. and Mcllroy, P. W. A. Analysis of the spectral index method for vector mode of rib waveguides, Proc. IEE, J. Optoelectron., 137, 21–26, 1990.

    Google Scholar 

  16. Rogge, U. and Pregla, R. Method of lines for the analysis of strip-loaded optical waveguides, J. Opt. Soc. Am. B, 8, 459–463, 1991.

    Article  Google Scholar 

  17. Bierwirth, K. N., Schulz, M. and Arndt, F. Finite difference analysis of rectangular dielectric waveguide structures, IEEE Microwave Theory Technol., MTT-34, 11041114, 1986.

    Google Scholar 

  18. Dagli, N. and Fonstad, C. G. Analysis of rib dielectric waveguides, IEEE J. Quantum Electron., QE-21, 315–321, 1985.

    Google Scholar 

  19. Huang, W. P. Methods for Modelling and Simulations of Guided-Wave Optoelectronic Devices. Part I. Modes and Couplings. Part II. Waves and Interactions. EMW Publishing, Cambridge, MA, 1995.

    Google Scholar 

  20. Rahman, B. M. A., Fernandes, F. A. and Davies, J. B. Review of finite element methods for microwave and optical waveguides, Proc. IEEE, 79, 1442–1448, 1991.

    Article  Google Scholar 

  21. Silvester, P. P. and Ferrari, R. L. Finite Elements for Electrical Engineers, 2nd edn, Cambridge University Press, Cambridge, 1990.

    Google Scholar 

  22. Yeh, C., Ha, K., Dong, S. B. and Brown, W. P. Single-mode optical waveguides, Appl. Opt., 18, 1490–1504, 1979.

    Article  Google Scholar 

  23. Mabaya, M., Lagasse, P. E. and Vandenbulcke, P. Finite element analysis of optical waveguides, IEEE, MTT-29, 600–605, 1981.

    Google Scholar 

  24. Rahman, B. M. A. and Davies, J. B. Finite-element analysis of optical and microwave waveguide problems, IEEE Trans. Microwave Theory Technol., MTT-32, 20–28, 1984.

    Google Scholar 

  25. Koshiba, M., Hayata, K. and Suzuki, M. Improved finite-element formulation in terms of magnetic field vector for dielectric waveguides, IEEE Trans. Microwave Theory Technol., MTT-33, 227–233, 1985.

    Google Scholar 

  26. Koshiba, M., Hayata, K. and Suzuki, M. Approximate scalar finite-element analysis of anisotropie optical waveguides with off-diagonal elements in a permittivity tensor, IEEE Trans. Microwave Theory Technol., MTT-32, 587–593, 1984.

    Google Scholar 

  27. Davies, J. B., Fernandez, F. A. and Philippou, G. Y. Finite element analysis of all modes in cavities with circular symmetry, IEEE Trans. Microwave Theory Technol., MTT-30, 1975–1980, 1982.

    Google Scholar 

  28. Rahman, B. M. A. and Davies, J. B. Vector-H finite element solution of GaAs/GaA1As rib waveguides, Proc. IEE, J. Optoelectron., 132, 349–353, 1988.

    Google Scholar 

  29. Katrisku, F., Rahman, B. M. A. and Grattan, K. T. V. Finite element analysis of diffused anisotropic channel waveguides, J. Lightwave Technol., 14, 780–786, 1996.

    Article  Google Scholar 

  30. Austin, M. W. Theoretical and experimental investigation of GaAs/GaAlAs and n/n+ GaAs rib waveguides, J. Lightwave Technol., LT-2, 688–694, 1984.

    Google Scholar 

  31. Liu, Y., Rahman, B. M. A. and Grattan, K. T. V. Thermal stress induced birefringence in bow-tie fibers using finite element method, Appl. Opt., 33, 5611–5616, 1994.

    Article  Google Scholar 

  32. Liu, Y., Rahman, B. M. A. and Grattan, K. T. V. Analysis of birefringence properties of optical fibers made by a preform deformation technique, J. Lightwave Technol., LT-13, 142–147, 1995.

    Google Scholar 

  33. Rahman, B. M. A., Souza, J. R. and Davies, J. B. Numerical analysis of nonlinear bistable-optical waveguides, IEEE Photonics Technol. Lett., 2, 265–267, 1990.

    Article  Google Scholar 

  34. Ettinger, R. D., Fernandez, F. A., Davies, J. B. and Rahman, B. M. A. Finite element analysis of slab-loaded nonlinear waveguide with saturable media, IEEE Photonics Technol. Lett., 3, 147–149, 1991.

    Google Scholar 

  35. Rahman, B. M. A., Liu, Y. and Grattan, K. T. V. Finite element modelling of one-and two-dimensional MQW semiconductor optical waveguides, IEEE Photonics Technol. Lett., 5, 928–931, 1993.

    Article  Google Scholar 

  36. Fernandez, F. A. and Lu, Y. Variational finite element analysis of dielectric wave-guides with no spurious modes, Electron. Lett., 26, 2125–2126, 1990.

    Article  Google Scholar 

  37. Themistos, C., Rahman, B. M. A., Hadjicharalambous, A. and Grattan, K. T. V. Loss/ gain analysis of optical waveguides, IEEE J. Lightwave Technol., 13, 1760–1765, 1995.

    Article  Google Scholar 

  38. Feit, M. D. and Fleck, Jr. J. A. Light propagation in graded-index optical fibres, Appl. Opt., 17, 3990–3998, 1978.

    Article  Google Scholar 

  39. Yevick, D. and Hermansson, B. Efficient beam propagation techniques, QE-26, 109112, 1990.

    Google Scholar 

  40. Huang, W. P., Xu, C. L., Chu, S. T. and Chaudhuri, S. K. A finite difference vector beam propagation method: analysis and assessment, JLT-10, 295–305, 1992.

    Google Scholar 

  41. Buah, P. A., Rahman, B. M. A. and Grattan, K. T. V. Numerical simulation of pulse propagation in nonlinear tapered waveguide, Proc. SPIE, 2212, 66–72, April 1994.

    Article  Google Scholar 

  42. Hernadez-Figueroa, H. E. Nonlinear nonparaxial beam-propagation method, Electronic Lett., 30, 352–353, 1994.

    Article  Google Scholar 

  43. Buah, P. A., Rahman, B. M. A. and Grattan, K. T. V. A split-step finite element scheme for spatio-temporal analysis of pulse propagation in nonlinear waveguides, OSA Nonlinear Guided-Wave Phenomena, Vol. 15, pp. 208–211, Cambridge, MA, 1993.

    Google Scholar 

  44. Rahman, B. M. A. and Davies, J. B. Analysis of optical waveguide discontinuities, J. Lightwave Technol., LT-6, 52–57, 1988.

    Google Scholar 

  45. Rahman, B. M. A., Wongcharoen, T. and Grattan, K. T. V. Finite element analysis of nonsynchronous directional couplers, Fiber Integrated Opt., 13, 331, 1994.

    Article  Google Scholar 

  46. Wongcharoen, T., Rahman, B. M. A. and Grattan, K. T. V. Power coupling for electrooptic directional coupler switch, in Guided-Wave Optoelectronics (Ed. T. Tamir ), pp. 213–219, Plenum Press, New York, 1995.

    Chapter  Google Scholar 

  47. Wongcharoen, T., Rahman, B. M. A. and Grattan, K. T. V. Accurate characterization of optical filters with two-dimensional confinement, J. Lightwave Technol, November 1996.

    Google Scholar 

  48. Mustacich, R. V. Scalar finite element analysis of electro-optic modulation in diffused channel waveguides and poled waveguides in polymer thin films, Appl. Opt., 27, 3732, 1988.

    Article  Google Scholar 

  49. Young, T. P., Armstrong, G. A. and Smith, W. P. SPIE, 1141, 103, 1989.

    Article  Google Scholar 

  50. Rajarajan, M., Rahman, B. M. A. and Grattan, K. T. V. Accurate characterization of MMI devices with two-dimensional confinement, J. Lightwave Technol., September 1996.

    Google Scholar 

  51. Hayata, K. and Koshiba, M. Numerical study of guided-wave sum-frequency generation through second-order nonlinear parametric process, J. Opt. Soc. Am. B, 8, 449–458, 1991.

    Article  Google Scholar 

  52. Bava, G. P., Montrosset, I., Sohler, W. and Suche, H. Numerical modelling of Ti:LiNbO3 integrated optical parametric oscillators. QE-23, 42–51, 1987.

    Google Scholar 

  53. Wilt, D. P. and Yariv, A. A self-consistent static model of the double-heterostructure laser, IEEE J. Quantum Electron., QE-17, 1941, 1981.

    Google Scholar 

  54. Tan, G., Bewtra, N., Lee, K. and Xu, J. M. A two-dimensional nonisothermal finite clement simulation of laser diodes, IEEE J. Quantum Electron., QE-29, 822–835, 1993.

    Google Scholar 

  55. Rahman, B. M. A., Lepkowski, P. and Grattan, K. T. V. Thermal modelling of vertical cavity surface emitting lasers, Proc. IEE J. Optoelectron., 82–86, 1995.

    Google Scholar 

  56. Johnson, M. Neural network techniques in instrumentation, Meas. Control, 6, 248–253, 1996.

    Google Scholar 

  57. Benjathapanum, N., Boyle, W. J. O. and Grattan, K. T. V. Binary encoded 2nd differential spectrometry using UV-vis spectral data and neural networks in the estimation of species type and concentration, IEE Proc. Sci. Meas. Technol., 144, 73–80, 1997.

    Article  Google Scholar 

  58. Bhandare, P., Mendelson, Y., Peura, R. A., Janatsch, G., Kruse-Jares, J. D., Marbach, R. and Heise, H. M. Multivariate determination of glucose in whole blood using partial least squares and artificial neural networks using mid-infrared spectroscopy, Appl. Spectrosc., 47, 1214–1222, 1993.

    Article  Google Scholar 

  59. Ham, F. M., Cohen, G. M. and Cho, B. Neural network based real-time detection of glucose using a non-chemical optical sensor approach. Proc. 12th Annual Conf., IEEE Engineering in Medicine and Biology Society, Vol. 2, LRW Associates, Arnold, MD, Philadelphia, PA, pp. 480–482, 1990.

    Google Scholar 

  60. Liu, Y., Upadhyaya, B. R. and Naghedolfeizi, M. Chemometric data analysis using artificial neural networks, Appl. Spectrosc., 47, 12–23, 1993.

    Article  Google Scholar 

  61. Boger, Z. Application of neural networks to water and wastewater treatment plant operation, Instrum. Soc. Am., 31, 25–33, 1992.

    Google Scholar 

  62. Remelhart, D. E. and McClelland, J. L. in Forming internal representation by error propagation, Parallel Distributed Processing, Vol. I. Foundation, Chap. 8, MIT Press, Boston, MA, 1992.

    Google Scholar 

  63. Sommer, L. Analytical Absorption Spectrophotometry in the Visible and Ultraviolet: The Principles, Elsevier, Amsterdam, 1996.

    Google Scholar 

  64. Ares, R. E., Lidiard, D. P. and Spragg, R. A. Principle component analysis, Chem. Br., 821–824, 1991.

    Google Scholar 

  65. Patrick, H., Williams, G. M., Kersey, A. D., Pedrazzani, J. R. and Vengsarkar, A. M. Strain/temperature discrimination using combined fiber Bragg and long-period grating sensors, OFS 11th Int. Conf. Optical Sensors. Advanced Sensing Photonics, pp. 96–99, May 1996.

    Google Scholar 

  66. Brignell, J. E. Measurement and control feature on intelligent instruments, Meas. Control, 29, 164, 1996.

    Google Scholar 

  67. Tanner, A. H. and White, N. M. Virtual instrumentation: a solution to the problem of design complexity in intelligent instruments, Meas. Control, 29, 165–171, 1996.

    Google Scholar 

  68. Grattan, K. T. V., Saini, D. P. S. and Palmer, A. W. Optical vibrating quartz crystal pressure sensor using frustrated-total-internal-reflection readout techniques, J. Light-wave Technol., LT5, 972–979, 1987.

    Google Scholar 

  69. Pinnock, R. A. Micromachined silicon resonant sensors with robust optical interrogation, Paper presented at Sensors and their Applications VI, Manchester, 1993. Published in Sensors VI: Technology Systems and Applications, Institute of Physics Publishing, Bristol (Eds K. T. V. Grattan and A. T. Augousti), pp. 141146, 1993.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Grattan, K.T.V., Rahman, B.M.A. (1999). Mathematical techniques in fiber optic sensor applications. In: Grattan, K.T.V., Meggitt, B.T. (eds) Optical Fiber Sensor Technology. Optoelectronics, Imaging and Sensing Series, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6077-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-6077-4_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4736-9

  • Online ISBN: 978-1-4757-6077-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics