Skip to main content

Time-Frequency Analysis in Terahertz-Pulsed Imaging

  • Chapter
Computer Vision Beyond the Visible Spectrum

Part of the book series: Advances in Pattern Recognition ((ACVPR))

Summary

Recent advances in laser and electro-optical technologies have made the previously underutilized terahertz frequency band of the electromagnetic spectrum accessible for practical imaging. Applications are emerging, notably in the biomedical domain. In this chapter the technique of terahertz-pulsed imaging is introduced in some detail. The need for special computer vision methods, which arises from the use of pulses of radiation and the acquisition of a time series at each pixel, is described. The nature of the data is a challenge since we are interested not only in the frequency composition of the pulses, but also how these differ for different parts of the pulse. Conventional and short-time Fourier transforms and wavelets were used in preliminary experiments on the analysis of terahertz-pulsed imaging data. Measurements of refractive index and absorption coefficient were compared, wavelet compression assessed, and image classification by multi dimensional clustering techniques demonstrated. It is shown that the time-frequency methods perform as well as conventional analysis for determining material properties. Wavelet compression gave results that were robust through compressions that used only 20% of the wavelet coefficients. It is concluded that the time-frequency methods hold great promise for optimizing the extraction of the spectroscopic information contained in each terahertz pulse, for the analysis of more complex signals comprising multiple pulses or from recently introduced acquisition techniques.

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

Access this chapter

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 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allen, S.J., Craig, K., Galdrikian, B., Heyman, J.N., Kaminski, J.P., Scott, J.S.: Materials science in the far-IR with electrostatic based FELs. Nuclear Instruments & Methods in Physics Research Section A; Accelerators Spectrometers Detectors and Associated Equipment 35 (1995) 536–539

    Google Scholar 

  2. Jaroszynski, D.A., Ersfeld, B., Giraud, G., Jamison, S., Jones, D.R., Issac, R.C.: The Strathclyde terahertz to optical pulse source (TOPS). Nuclear Instruments & Methods in Physics Research, Section A: Accelerators Spectrometers Detectors and Associated Equipment 445 (2000) 317–31

    Google Scholar 

  3. Grischkowsky, D.R., Mittleman, D.M.: Introduction. In Mittleman, D., ed.: Sensing with Terahertz Radiation. Springer-Verlag, Berlin (2003) 1–38

    Google Scholar 

  4. Auston, D.H., Nuss, M.C.: Electrooptic generation and detection of femtosecond electrical transients. IEEE Journal of Quantum Electronics 24 (1988) 184–197

    Article  Google Scholar 

  5. Kleine-Ostmann, T., Knobloch, P., Koch, M., Hoffmann, S., Breede, M., Hofmann, M.: Continuous-wave THz imaging. Electronics Letters 37 (2001) 1461–146

    Article  Google Scholar 

  6. Siebert, K.J., Quast, H., Leonhardt, R., Loeffler, T., Thomson, M., Bauer, T.: Continuous-wave all-optoelectronic terahertz imaging. Applied Physics Letters 80 (2002) 3003–3005

    Article  Google Scholar 

  7. Gallerano, G.P., Doria, A., Giovenale, E., Renieri, A.: Compact free electron lasers: From Cerenkov to waveguide free electron lasers. Infrared Physics & Technology 40 (1999) 161–174

    Article  Google Scholar 

  8. Grischkowsky, D., Keiding, S., van Exter, M., Fattinger, C.: Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors. Journal of the Optical Society of America, B: Optical Physics 7 (1990) 2006–201

    Google Scholar 

  9. van Exter, M., Grischkowsky, D.R.: Carrier dynamics of electrons and holes in moderately doped silicon. Phys. Rev. B 41 (1990) 12140–12149

    Google Scholar 

  10. Kindt, J.T., Schmuttenmaer, C.A.: Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz-pulse spectroscopy. Journal of Physical Chemistry 100 (1996) 10373–10379

    Article  Google Scholar 

  11. Hu, B.B., Nuss, M.C.: Imaging with terahertz waves. Optics Letters 20 (1995) 1716–171

    Google Scholar 

  12. Wu, Q., Hewitt, T.D., Zhang, X.C.: Two-dimensional electro-optic imaging of THz beams. App. Phy. Lett. 69 (1996) 1026–1028

    Google Scholar 

  13. Herrmann, M., Tani, M., Sakai, K.: Display modes in time-resolved terahertz imaging. Japanese Journal of Applied Physics, Part 1: Regular Papers, Short Notes & Review Papers 39 (2000) 6254–625

    Google Scholar 

  14. Loeffler, T., Bauer, T., Siebert, K.J., Roskos, H.G., Fitzgerald, A., Czasch, S.: Terahertz darkfield imaging of biomedical tissue. Optics Express 9 (2001) 616–62

    Google Scholar 

  15. Ruffin, A.B., Van Rudd, J., Decker, J., Sanchez-Palencia, L., Le Hors, L., Whitaker, J.: Time reversal terahertz imaging. IEEE Journal of Quantum Electronics 38 (2002) 1110–111

    Article  Google Scholar 

  16. Mittleman, D.M., Hunsche, S., Boivin, L., Nuss, M.C.: T-ray tomography. Optics Letters 22 (1997) 904–90

    Google Scholar 

  17. Dorney, T.D., Symes, W.W., Baraniuk, R.G., Mittleman, D.M.: Terahertz multistatic reflection imaging. Journal of the Optical Society of America, A: Optics Image Science and Vision 19 (2002) 1432–144

    Google Scholar 

  18. Ferguson, B., Wang, S.H., Gray, D., Abbot, D., Zhang, X.C.: T-ray computed tomography. Optics Letters 27 (2002) 1312–131

    Google Scholar 

  19. Berry, E., Fitzgerald, A.J., Zinovev, N.N., Walker, G.C., Homer-Vanniasinkam, S., Sudworth, C.D.: Optical properties of tissue measured using terahertz-pulsed imaging. Proceedings of SPIE: Medical Imaging 5030 (2003)

    Google Scholar 

  20. Loeffler, T., Siebert, K.J., Czasch, S., Bauer, T., Roskos, H.G.: Visualization and classification in biomedical terahertz-pulsed imaging. Physics in Medicine and Biology 47 (2002) 3847–3852

    Google Scholar 

  21. Ferguson, B., Wang, S., Gray, D., Abbott, D., Zhang, X.C.: Identification of biological tissue using chirped probe THz imaging. Microelectronics Journal 33 (2002) 1043–105

    Article  Google Scholar 

  22. Mittleman, D.M., Jacobsen, R.H., Nuss, M.C.: T-ray imaging. IEEE Journal of Selected Topics in Quantum Electronics 2 (1996) 679–69

    Article  Google Scholar 

  23. Mickan, S., Abbott, D., Munch, J., Zhang, X., van Doorn, T.: Analysis of system trade-offs for terahertz imaging. Microelectronics Journal 31 (2000) 503–51

    Article  Google Scholar 

  24. Ferguson, B., Abbott, D.: De-noising techniques for terahertz responses of biological samples. Microelectronics Journal 32 (2001) 943–95

    Article  Google Scholar 

  25. Auston, D.H., Cheung, K.P., Valdmanis, J.A., Kleinman, D.A.: Coherent time-domain far-infrared spectroscopy with femtosecond pulses. Journal of the Optical Society of America A: Optics Image Science and Vision 1 (1984) 1278

    Google Scholar 

  26. Zhang, X.C., Jin, Y., Hu, B.B., Li, X., Auston, D.H.: Optoelectronic study of piezoelectric field in strained-layer superlattices. Superlattices and Microstructures 12 (1992) 487–490

    Article  Google Scholar 

  27. Shan, J., Weling, A.S., Knoesel, E., Bartels, L., Bonn, M., Nahata, A.: Single-shot measurement of terahertz electromagnetic pulses by use of electro-optic sampling. Optics Letters 25 (2000) 426–42

    Google Scholar 

  28. Ruffin, A.B., Decker, J., Sanchez-Palencia, L., Le Hors, L., Whitaker, J.F., Norris, T.B.: Time reversal and object reconstruction with single-cycle pulses. Optics Letters 26 (2001) 681–68

    Google Scholar 

  29. Mittleman, D.M., ed.: Sensing with Terahertz Radiation. Springer-Verlag, Berlin (2003)

    Google Scholar 

  30. Zimdars, D.: Commercial T-ray systems accelerate imaging research. Laser Focus World 37 (2001) 91

    Google Scholar 

  31. Arnone, D.D., Ciesla, C.M., Corchia, A., Egusa, S., Pepper, M.: Applications of terahertz (THz) technology to medical imaging. Proceedings of SPIE 3828 (1999) 209–219 Terahertz Spectroscopy and Applications 11; JM Chamberlain (ed.).

    Google Scholar 

  32. Mittleman, D.M., Gupta, M., Neelamani, R., Baraniuk, R.G., Rudd, J.V., Koch, M.: Recent advances in terahertz imaging. Applied Physics B-Lasers and Optics 68 (1999) 1085–109

    Google Scholar 

  33. Smye, S.W., Chamberlain, J.M., Fitzgerald, A.J., Berry, E.: The interaction between terahertz radiation and biological tissue. Physics in Medicine and Biology 46 (2001) R101–R112

    Article  Google Scholar 

  34. Hadjiloucas, S., Karatzas, L.S., Bowen, J.W.: Measurements of leaf water content using terahertz radiation. IEEE Transactions on Microwave Theory and Techniques 47 (1999) 142–149

    Article  Google Scholar 

  35. Boulay, R., Gagnon, R., Rochette, D., Izatt, J.R.: Paper sheet moisture measurements in the far-infrared. International Journal of Infrared and Millimeter Waves 5 (1984) 1221–1234

    Article  Google Scholar 

  36. Cole, B.E., Woodward, R., Crawley, D., Wallace, V.P., Arnone, D.D., Pepper, M.: Terahertz imaging and spectroscopy of human skin, invivo. Commercial and Biomedical Applications of Ultrashort Pulse Lasers; Laser Plasma Generation and Diagnostics 4276 (2001) 1–10

    Google Scholar 

  37. Institute, A.N.S.: American National Standard for Safe Use of Lasers (ANSI Z136.1-2000). Laser Institute of America, Orlando, FL (2000)

    Google Scholar 

  38. Sliney, D.H., Wolbarsht, M.L.: Laser Safety Standards: Evolution and Rationale. Safety with Lasers and Other Optical Sources. Plenum Press, New York (1980)

    Google Scholar 

  39. Clothier, R.H., Bourne, N.: Effect of THz exposure on human primary keratinocyte differentiation and viability. Journal of Biological Physics 29 (2003) 179–185

    Article  Google Scholar 

  40. Scarfi, M.R., Romano, M., Di Pietro, R., Zeni, O., Doria, A., Gallerano, G.P.: THz exposure of whole blood for the study of biological effects on human lymphocytes. Journal of Biological Physics 29 (2003) 171–176

    Google Scholar 

  41. Berry, E., Walker, G.C., Fitzgerald, A.J., Chamberlain, J.M., Smye, S.W., Miles, R.E.: Do in vivo terahertz imaging systems comply with safety guidelines? Journal of Laser Applications 15 (2003) 192–198

    Google Scholar 

  42. Han, P.Y., Tani, M., Usami, M., Kono, S., Kersting, R., Zhang, X.C.: A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy. Journal of Applied Physics 89 (2001) 2357–235

    Google Scholar 

  43. Bolivar, P.H., Brucherseifer, M., Nagel, M., Kurz, H., Bosserhoff, A., Buttner, R.: Label-free probing of genes by time-domain terahertz sensing. Physics in Medicine and Biology 47 (2002) 3815–3821

    Article  Google Scholar 

  44. Bezant, C.D.: Application of THz Pulses in Semiconductor Relaxation and Biomedical Imaging Studies. PhD thesis, Department of Physics (2000)

    Google Scholar 

  45. Han, P.Y., Cho, G.C., Zhang, X.C.: Time-domain transillumination of biological tissues with terahertz pulses. Optics Letters 25 (2000) 242–24

    Google Scholar 

  46. Ciesla, C.M., Arnone, D.D., Corchia, A., Crawley, D., Longbottom, C., Linfield, E.H.: Biomedical applications of terahertz-pulse imaging. Commercial and Biomedical Applications of Ultrafast Lasers II 3934 (2000) 73–8

    Google Scholar 

  47. Knobloch, P., Schildknecht, C., Kleine-Ostmann, T., Koch, M., Hoffmann, S., Hofmann, M.: Medical THz imaging: an investigation of histopathological samples. Physics in Medicine and Biology 47 (2002) 3875–388

    Article  Google Scholar 

  48. Woodward, R.M., Cole, B.E., Wallace, V.P., Pye, R.J., Arnone, D.D., Linfield, E.H.: Terahertz-pulse imaging in reflection geometry of human skin cancer and skin tissue. Physics in Medicine and Biology 47 (2002) 3853–3863

    Article  Google Scholar 

  49. Fitzgerald, A.J., Berry, E., Zinovev, N.N., Walker, G.C., Smith, M.A., Chamberlain, J.M.: An introduction to medical imaging with coherent terahertz frequency radiation. Physics in Medicine and Biology 47 (2002) R67–R8

    Article  Google Scholar 

  50. Hagness, S.C., Taflove, A., Bridges, J.E.: Two-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: Fixed-focus and antenna-array sensors. IEEE Transactions on Biomedical Engineering 45 (1998) 1470–147

    Article  Google Scholar 

  51. Wang, S., Ferguson, B., Mannella, C., Abbott, D., Zhang, X.C.: Powder detection using THz imaging. In: Proceedings of Conference on Lasers and Electro-Optics, Long Beach, CA (2002) 132

    Google Scholar 

  52. McClatchey, K., Reiten, M.T., Cheville, R.A.: Time-resolved synthetic aperture terahertz impulse imaging. Applied Physics Letters 79 (2001) 4485–448

    Article  Google Scholar 

  53. Jacobsen, R.H., Mittleman, D.M., Nuss, M.C.: Chemical recognition of gases and gas mixtures with terahertz waves. Optics Letters 21 (1996) 2011–201

    Google Scholar 

  54. Koch, M.: Biomedical applications of THz imaging. In Mittleman, D., ed.: Sensing with Terahertz Radiation. Springer-Verlag, Berlin (2003) 295–316

    Google Scholar 

  55. Siegel, P.H.: Terahertz technology. IEEE Transactions on Microwave Theory and Techniques 50 (2002) 910–928

    Article  Google Scholar 

  56. Anderton, R.N., Appleby, R., Borrill, J.R., Gleed, D.G., Price, S., Salmon, N.A. In: Prospects of Imaging Applications [Military]. IEE (1997) 4/1–4/10

    Google Scholar 

  57. Papoulis, A.: The Fourier Integral and Its Application. McGraw-Hill, New York (1962)

    Google Scholar 

  58. Akay, M., ed.: Time Frequency and Wavelets in Biomedical Signal Processing. IEEE Press and John Wiley & Sons (1998)

    Google Scholar 

  59. Xu, X.L., Tewfik, A.H., Greenleaf, J.F.: Time-delay estimation using wavelet transform for pulsed-wave ultrasound. Annals of Biomedical Engineering 23 (1995) 612–621

    Google Scholar 

  60. Sonka, M., Hlavac, V., Boyle, R.: Image Processing, Analysis and Machine Vision. second edn. Brooks/Cole Publishing Company, Pacific Grove, CA (1999)

    Google Scholar 

  61. Georgiou, G., Cohen, F.S., Piccoli, C.W., Forsberg, F., Goldberg, B.B.: Tissue characterization using the continuous wavelet transform, part II: Application on breast RF data. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 48 (2001) 364–373

    Google Scholar 

  62. Sun, M., Sclabassi, R.J.: Wavelet feature extraction from neurophysiological signals. In Akay, M., ed.: Time Frequency and Wavelets in Biomedical Signal Processing. IEEE Press and John Wiley & Sons (1998) 305–321

    Google Scholar 

  63. Ching, P.C., So, H.C., Wu, S.Q.: On wavelet denoising and its applications to time delay estimation. IEEE Transactions on Signal Processing 47 (1999) 2879–2882

    Article  Google Scholar 

  64. Coifman, R.R., Wickerhauser, M.V.: Experiments with adapted wavelet de-noising for medical signals and images. In Akay, M., ed.: Time Frequency and Wavelets in Biomedical Signal Processing. IEEE Press and John Wiley & Sons, Piscataway, NJ (1998) 323–346

    Google Scholar 

  65. Sardy, S., Tseng, P., Bruce, A.: Robust wavelet denoising. IEEE Transactions on Signal Processing 49 (2001) 1146–115

    Article  Google Scholar 

  66. Lasch, P., Naumann, D.: FT-IR microspectroscopic imaging of human carcinoma thin sections based on pattern recognition techniques. Cellular and Molecular Biology 44 (1998) 189–20

    Google Scholar 

  67. Carmona, R., Hwang, W.L., Torresani, B.: Practical Time-Frequency Analysis. Academic Press, San Diego (1998)

    Google Scholar 

  68. Gioswami J. C., Chan, A.K.: Fundamentals of Wavelets: Theory, Algorithms, and Applications. John Wiley and Sons, New York (1999)

    Google Scholar 

  69. Weiss, L.G.: Wavelets and wideband correlation processing. IEEE Signal Processing Magazine 11 (1994) 13–32

    Article  Google Scholar 

  70. Young, R.K.: Wavelet Theory and Its Applications. Kluwer, Boston (1993)

    Google Scholar 

  71. MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium 1. (1967) 281–297

    MATH  MathSciNet  Google Scholar 

  72. Kaufmann, L., Rousseeuw, P.J.: Finding groups in data: An introduction to cluster analysis. John Wiley & Sons, New York (1990)

    Google Scholar 

  73. Webb, P.A.: A review of rapid prototyping (RP) techniques in the medical and biomedical sector. Journal of Medical Engineering & Technology 24 (2000) 149–15

    Article  MathSciNet  Google Scholar 

  74. Goulden, C.H.: Methods of Statistical Analysis. second edn. John Wiley and Sons, New York (1956)

    Google Scholar 

  75. Hartigan, J.: Clustering Algorithms. John Wiley and Sons, New York (1975)

    Google Scholar 

  76. Handley, J.W., Fitzgerald, A.J., Berry, E., Boyle, R.D.: Wavelet compression in medical terahertz-pulsed imaging. Physics in Medicine and Biology 47 (2002) 3885–389

    Article  Google Scholar 

  77. Duvillaret, L., Garet, F., Coutaz, J.L.: A reliable method for extraction of material parameters in terahertz time-domain spectroscopy. IEEE Journal of Selected Topics in Quantum Electronics 2 (1996) 739–74

    Article  Google Scholar 

  78. Dorney, T.D., Baraniuk, R.G., Mittleman, D.M.: Material parameter estimation with terahertz time-domain spectroscopy. Journal of the Optical Society of America, A: Optics Image Science and Vision 18 (2001) 1562–157

    Google Scholar 

  79. Highnam, R., Brady, M.: Mammographic Image Analysis. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  80. Cotton, S., Claridge, E., Hall, P.: Noninvasive skin imaging. Information Processing in Medical Imaging 1230 (1997) 501–50

    Google Scholar 

  81. Duvillaret, L., Garet, F., Roux, J.F., Coutaz, J.L.: Analytical modeling and optimization of terahertz time-domain spectroscopy experiments using photoswitches as antennas. IEEE Journal of Selected Topics in Quantum Electronics 7 (2001) 615–62

    Article  Google Scholar 

  82. Lee, Y., Meade, T., Norris, T.B., Galvanauskas, A.: Tunable narrow-band terahertz generation from periodically poled lithium niobate. Applied Physics Letters 78 (2001) 3583–358

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag London Limited

About this chapter

Cite this chapter

Berry, E., Boyle, R.D., Fitzgerald, A.J., Handley, J.W. (2005). Time-Frequency Analysis in Terahertz-Pulsed Imaging. In: Bhanu, B., Pavlidis, I. (eds) Computer Vision Beyond the Visible Spectrum. Advances in Pattern Recognition. Springer, London. https://doi.org/10.1007/1-84628-065-6_9

Download citation

  • DOI: https://doi.org/10.1007/1-84628-065-6_9

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-604-2

  • Online ISBN: 978-1-84628-065-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics