Abstract

This paper describes a novel optical system for clinical diagnosis of dental enamel based on its elasticity. Current examination techniques are typically destructive, and frequently impractical for in-vivo inspection. This paper describes the first application of a laser ultrasonic non-destructive evaluation (NDE) method for clinical dental diagnosis. It performs remote elasticity evaluation on small dimension samples. A focused laser line-source generates broadband surface acoustic wave (SAW) impulses which are detected with a simplified optical fibre interferometer. The measured SAW velocity dispersion spectrum was in turn used to characterise the elasticity of the specimen. Different metal structures were measured to verify the system performance. The results agree well with theoretical values and confirm the reliability and accuracy of the laser NDE system. This technique was then applied to evaluate the surface of sound natural human dental enamel. The measured dispersion spectra match theoretical expectations and the influences of both the enamel and the underlying dentin on the surface wave propagation were observed. This is the first time, to the best of our knowledge, that a laser based SAW velocity dispersion technique has been successfully applied on human dental enamel. As a remote, non-destructive technique it is applicable in-vivo and opens the way for early diagnosis of dental caries.

© 2009 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. D. Miller, “Agency of micro-organisms in decay of the teeth”, Dental Cosmos, 1883.
  2. B. Krasse, “Biological factors as indicators of future caries,” Int. Dent. J. 38(4), 219–225 (1988).
    [PubMed]
  3. F. Feagin, T. Koulourides, and W. Pigman, “The characterization of enamel surface demineralization, remineralization, and associated hardness changes in human and bovine material,” Arch. Oral Biol. 14(12), 1407–1417 (1969).
    [CrossRef] [PubMed]
  4. S. Habelitz, S. J. Marshall, G. W. Marshall, and M. Balooch, “Mechanical properties of human dental enamel on the nanometre scale,” Arch. Oral Biol. 46(2), 173–183 (2001).
    [CrossRef] [PubMed]
  5. J. L. Cuy, A. B. Mann, K. J. Livi, M. F. Teaford, and T. P. Weihs, “Nanoindentation mapping of the mechanical properties of human molar tooth enamel,” Arch. Oral Biol. 47(4), 281–291 (2002).
    [CrossRef] [PubMed]
  6. A. I. Ismail, “Visual and visuo-tactile detection of dental caries,” J. Dent. Res. 83 (1), C56–C66 (2004).
    [CrossRef] [PubMed]
  7. F. Lippert, D. M. Parker, and K. D. Jandt, “In vitro demineralization/remineralization cycles at human tooth enamel surfaces investigated by AFM and nanoindentation,” J. Colloid Interface Sci. 280(2), 442–448 (2004).
    [CrossRef] [PubMed]
  8. T. Kundu, ed., Ultrasonic nondestructive evaluation: engineering and biological material characterization. 2004, CRC Press.
  9. D. Schneider, B. Schultrich, H. J. Scheibe, H. Ziegele, and M. Griepentrog, “A laser-acoustic method for testing and classifying hard surface layers,” Thin Solid Films 332(1–2), 157–163 (1998).
    [CrossRef]
  10. C. Glorieux, W. Gao, S. E. Kruger, K. Van de Rostyne, W. Lauriks, and J. Thoen, “Surface acoustic wave depth profiling of elastically inhomogeneous materials,” J. Appl. Phys. 88(7), 4394–4400 (2000).
    [CrossRef]
  11. J. A. Rogers, A. A. Maznev, M. J. Banet, and K. A. Nelson, “Optical Generation and Characterization of Acoustic Waves in Thin Films: Fundamentals and Applications,” Annu. Rev. Mater. Sci. 30(1), 117–157 (2000).
    [CrossRef]
  12. Y. C. Lee, J. O. Kim, and J. D. Achenbach, “Measurement of elastic constants and mass density by acoustic microscopy”, IEEE Ultrasonics Symposium, vol.1, pp.607–612, October 1993.
  13. C. S. Scruby, and L. E. Drain, Laser Ultrasonics: Techniques and Applications. 1990: Adam Hilger Ltd.
  14. A. Neubrand and P. Hess, “Laser generation and detection of surface acoustic waves: Elastic properties of surface layers,” J. Appl. Phys. 71(1), 227–238 (1991).
    [CrossRef]
  15. J. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33(5), 485–499 (1986).
    [CrossRef]
  16. R. J. Dewhurst and Q. Shan, “Optical remote measurement of ultrasound,” Meas. Sci. Technol. 10(11), R139–R168 (1999).
    [CrossRef]
  17. B. Mitra, A. Shelamoff, and D. J. Booth, “An optical fibre interferometer for remote detection of laser generated ultrasonics,” Meas. Sci. Technol. 9(9), 1432–1436 (1998).
    [CrossRef]
  18. A. J. A. Bruinsma and J. A. Vogel, “Ultrasonic noncontact inspection system with optical fiber methods,” Appl. Opt. 27(22), 4690–4695 (1988).
    [CrossRef] [PubMed]
  19. T. D. Dudderar, C. P. Burger, J. A. Gilbert, J. A. Smith, and B. R. Peters, “Fiber optic sensing for ultrasonic NDE,” J. Nondestructive Evaluation 6(3), 135–146 (1987).
    [CrossRef]
  20. H. S. Park, G. Thursby, and B. Culshaw, “Detection of laser-generated ultrasound based on phase demodulation technique using a fibre Fabry-Perot interferometer,” Meas. Sci. Technol. 16(6), 1261–1266 (2005).
    [CrossRef]
  21. 21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
    [CrossRef]
  22. E. Soczkiewicz, “The Penetration Depth of the Rayleigh Surface Waves,” Nondestructive Testing and Evaluation 13(2), 113–119 (1997).
    [CrossRef]
  23. J. D. Achenbach, Wave Propagation in Elastic Solids. 1984: Elsevier Science Ltd.
  24. J. L. Rose, Ultrasonic Waves in Solid Media. 1999: Cambridge University Press.
  25. I. Arias and J. D. Achenbach, “Thermoelastic generation of ultrasound by line-focused laser irradiation,” Int. J. Solids Struct. 40(25), 6917–6935 (2003).
    [CrossRef]
  26. H. C. Wang, S. Fleming, and Y. C. Lee, “Simple, all-optical, noncontact, depth-selective, narrowband surface acoustic wave measurement system for evaluating the Rayleigh velocity of small samples or areas,” Appl. Opt. 48(8), 1444–1451 (2009).
    [CrossRef] [PubMed]
  27. D. Schneider and T. Schwarz, “A photoacoustic method for characterising thin films,” Surf. Coat. Tech. 91(1–2), 136–146 (1997).
    [CrossRef]
  28. D. Schneider, T. Witke, T. Schwarz, B. Schoneich, and B. Schultrich, “Testing ultra-thin films by laser-acoustics,” Surf. Coat. Tech. 126(2–3), 136–141 (2000).
    [CrossRef]
  29. T. T. Wu and Y. C. Chen, “Dispersion of laser generated surface waves in an epoxy-bonded layered medium,” Ultrasonics 34(8), 793–799 (1996).
    [CrossRef]
  30. A. Briggs, Acoustic Microscopy. 1992: Clarendon Press. Oxford.
  31. H. C. Wang, S. Fleming, and Y. C. Lee, “A remote, non-destructive laser ultrasonic material evaluation system with simplified optical fibre interferometer detection,” J. Nondestructive Evaluation 28(2), 75–83 (2009).
    [CrossRef]
  32. J. Kushibiki, K. L. Ha, H. Kato, N. Chubachi, and F. Dunn, “Application of Acoustic Microscopy to Dental Material Characterization”, IEEE 1987 Ultrasonics Symposium, pp.837–842, 1987.
  33. S. D. Peck, J. M. Rowe, and G. A. Briggs, “Studies on sound and carious enamel with the quantitative acoustic microscope,” J. Dent. Res. 68(2), 107–112 (1989).
    [CrossRef] [PubMed]
  34. H. C. Wang, S. Fleming, S. Law, and T. Huang, Selection of an appropriate laser wavelength for launching surface acoustic waves on tooth enamel. in Proceedings of IEEE Australian Conference on Optical Fibre Technology/Australian Optical Society (ACOFT/AOS). 2006. Melbourne, Australia.
  35. R. G. Maev, L. A. Denisova, E. Y. Maeva, and A. A. Denissov, “New data on histology and physico-mechanical properties of human tooth tissue obtained with acoustic microscopy,” Ultrasound Med. Biol. 28(1), 131–136 (2002).
    [CrossRef] [PubMed]
  36. D. W. Blodgett, “Applications of laser-based ultrasonics to the characterization of the internal structure of teeth,” J. Acoust. Soc. Am. 114(1), 542–549 (2003).
    [CrossRef] [PubMed]
  37. N. Carlson and J. Johnson, “Pulsed laser energy through fiberoptics for generation of ultrasound,” J. Nondestructive Evaluation 12(3), 187–192 (1993).
    [CrossRef]

2009 (2)

H. C. Wang, S. Fleming, and Y. C. Lee, “Simple, all-optical, noncontact, depth-selective, narrowband surface acoustic wave measurement system for evaluating the Rayleigh velocity of small samples or areas,” Appl. Opt. 48(8), 1444–1451 (2009).
[CrossRef] [PubMed]

H. C. Wang, S. Fleming, and Y. C. Lee, “A remote, non-destructive laser ultrasonic material evaluation system with simplified optical fibre interferometer detection,” J. Nondestructive Evaluation 28(2), 75–83 (2009).
[CrossRef]

2005 (1)

H. S. Park, G. Thursby, and B. Culshaw, “Detection of laser-generated ultrasound based on phase demodulation technique using a fibre Fabry-Perot interferometer,” Meas. Sci. Technol. 16(6), 1261–1266 (2005).
[CrossRef]

2004 (2)

A. I. Ismail, “Visual and visuo-tactile detection of dental caries,” J. Dent. Res. 83 (1), C56–C66 (2004).
[CrossRef] [PubMed]

F. Lippert, D. M. Parker, and K. D. Jandt, “In vitro demineralization/remineralization cycles at human tooth enamel surfaces investigated by AFM and nanoindentation,” J. Colloid Interface Sci. 280(2), 442–448 (2004).
[CrossRef] [PubMed]

2003 (2)

I. Arias and J. D. Achenbach, “Thermoelastic generation of ultrasound by line-focused laser irradiation,” Int. J. Solids Struct. 40(25), 6917–6935 (2003).
[CrossRef]

D. W. Blodgett, “Applications of laser-based ultrasonics to the characterization of the internal structure of teeth,” J. Acoust. Soc. Am. 114(1), 542–549 (2003).
[CrossRef] [PubMed]

2002 (3)

R. G. Maev, L. A. Denisova, E. Y. Maeva, and A. A. Denissov, “New data on histology and physico-mechanical properties of human tooth tissue obtained with acoustic microscopy,” Ultrasound Med. Biol. 28(1), 131–136 (2002).
[CrossRef] [PubMed]

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

J. L. Cuy, A. B. Mann, K. J. Livi, M. F. Teaford, and T. P. Weihs, “Nanoindentation mapping of the mechanical properties of human molar tooth enamel,” Arch. Oral Biol. 47(4), 281–291 (2002).
[CrossRef] [PubMed]

2001 (1)

S. Habelitz, S. J. Marshall, G. W. Marshall, and M. Balooch, “Mechanical properties of human dental enamel on the nanometre scale,” Arch. Oral Biol. 46(2), 173–183 (2001).
[CrossRef] [PubMed]

2000 (3)

C. Glorieux, W. Gao, S. E. Kruger, K. Van de Rostyne, W. Lauriks, and J. Thoen, “Surface acoustic wave depth profiling of elastically inhomogeneous materials,” J. Appl. Phys. 88(7), 4394–4400 (2000).
[CrossRef]

J. A. Rogers, A. A. Maznev, M. J. Banet, and K. A. Nelson, “Optical Generation and Characterization of Acoustic Waves in Thin Films: Fundamentals and Applications,” Annu. Rev. Mater. Sci. 30(1), 117–157 (2000).
[CrossRef]

D. Schneider, T. Witke, T. Schwarz, B. Schoneich, and B. Schultrich, “Testing ultra-thin films by laser-acoustics,” Surf. Coat. Tech. 126(2–3), 136–141 (2000).
[CrossRef]

1999 (1)

R. J. Dewhurst and Q. Shan, “Optical remote measurement of ultrasound,” Meas. Sci. Technol. 10(11), R139–R168 (1999).
[CrossRef]

1998 (2)

B. Mitra, A. Shelamoff, and D. J. Booth, “An optical fibre interferometer for remote detection of laser generated ultrasonics,” Meas. Sci. Technol. 9(9), 1432–1436 (1998).
[CrossRef]

D. Schneider, B. Schultrich, H. J. Scheibe, H. Ziegele, and M. Griepentrog, “A laser-acoustic method for testing and classifying hard surface layers,” Thin Solid Films 332(1–2), 157–163 (1998).
[CrossRef]

1997 (2)

E. Soczkiewicz, “The Penetration Depth of the Rayleigh Surface Waves,” Nondestructive Testing and Evaluation 13(2), 113–119 (1997).
[CrossRef]

D. Schneider and T. Schwarz, “A photoacoustic method for characterising thin films,” Surf. Coat. Tech. 91(1–2), 136–146 (1997).
[CrossRef]

1996 (1)

T. T. Wu and Y. C. Chen, “Dispersion of laser generated surface waves in an epoxy-bonded layered medium,” Ultrasonics 34(8), 793–799 (1996).
[CrossRef]

1993 (1)

N. Carlson and J. Johnson, “Pulsed laser energy through fiberoptics for generation of ultrasound,” J. Nondestructive Evaluation 12(3), 187–192 (1993).
[CrossRef]

1991 (1)

A. Neubrand and P. Hess, “Laser generation and detection of surface acoustic waves: Elastic properties of surface layers,” J. Appl. Phys. 71(1), 227–238 (1991).
[CrossRef]

1989 (1)

S. D. Peck, J. M. Rowe, and G. A. Briggs, “Studies on sound and carious enamel with the quantitative acoustic microscope,” J. Dent. Res. 68(2), 107–112 (1989).
[CrossRef] [PubMed]

1988 (2)

1987 (1)

T. D. Dudderar, C. P. Burger, J. A. Gilbert, J. A. Smith, and B. R. Peters, “Fiber optic sensing for ultrasonic NDE,” J. Nondestructive Evaluation 6(3), 135–146 (1987).
[CrossRef]

1986 (1)

J. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33(5), 485–499 (1986).
[CrossRef]

1969 (1)

F. Feagin, T. Koulourides, and W. Pigman, “The characterization of enamel surface demineralization, remineralization, and associated hardness changes in human and bovine material,” Arch. Oral Biol. 14(12), 1407–1417 (1969).
[CrossRef] [PubMed]

Achenbach, J. D.

I. Arias and J. D. Achenbach, “Thermoelastic generation of ultrasound by line-focused laser irradiation,” Int. J. Solids Struct. 40(25), 6917–6935 (2003).
[CrossRef]

Arias, I.

I. Arias and J. D. Achenbach, “Thermoelastic generation of ultrasound by line-focused laser irradiation,” Int. J. Solids Struct. 40(25), 6917–6935 (2003).
[CrossRef]

Balooch, M.

S. Habelitz, S. J. Marshall, G. W. Marshall, and M. Balooch, “Mechanical properties of human dental enamel on the nanometre scale,” Arch. Oral Biol. 46(2), 173–183 (2001).
[CrossRef] [PubMed]

Banet, M. J.

J. A. Rogers, A. A. Maznev, M. J. Banet, and K. A. Nelson, “Optical Generation and Characterization of Acoustic Waves in Thin Films: Fundamentals and Applications,” Annu. Rev. Mater. Sci. 30(1), 117–157 (2000).
[CrossRef]

Blodgett, D. W.

D. W. Blodgett, “Applications of laser-based ultrasonics to the characterization of the internal structure of teeth,” J. Acoust. Soc. Am. 114(1), 542–549 (2003).
[CrossRef] [PubMed]

Booth, D. J.

B. Mitra, A. Shelamoff, and D. J. Booth, “An optical fibre interferometer for remote detection of laser generated ultrasonics,” Meas. Sci. Technol. 9(9), 1432–1436 (1998).
[CrossRef]

Briggs, G. A.

S. D. Peck, J. M. Rowe, and G. A. Briggs, “Studies on sound and carious enamel with the quantitative acoustic microscope,” J. Dent. Res. 68(2), 107–112 (1989).
[CrossRef] [PubMed]

Bruinsma, A. J. A.

Burger, C. P.

T. D. Dudderar, C. P. Burger, J. A. Gilbert, J. A. Smith, and B. R. Peters, “Fiber optic sensing for ultrasonic NDE,” J. Nondestructive Evaluation 6(3), 135–146 (1987).
[CrossRef]

Carlson, N.

N. Carlson and J. Johnson, “Pulsed laser energy through fiberoptics for generation of ultrasound,” J. Nondestructive Evaluation 12(3), 187–192 (1993).
[CrossRef]

Chen, Y. C.

T. T. Wu and Y. C. Chen, “Dispersion of laser generated surface waves in an epoxy-bonded layered medium,” Ultrasonics 34(8), 793–799 (1996).
[CrossRef]

Culshaw, B.

H. S. Park, G. Thursby, and B. Culshaw, “Detection of laser-generated ultrasound based on phase demodulation technique using a fibre Fabry-Perot interferometer,” Meas. Sci. Technol. 16(6), 1261–1266 (2005).
[CrossRef]

Cuy, J. L.

J. L. Cuy, A. B. Mann, K. J. Livi, M. F. Teaford, and T. P. Weihs, “Nanoindentation mapping of the mechanical properties of human molar tooth enamel,” Arch. Oral Biol. 47(4), 281–291 (2002).
[CrossRef] [PubMed]

Denisova, L. A.

R. G. Maev, L. A. Denisova, E. Y. Maeva, and A. A. Denissov, “New data on histology and physico-mechanical properties of human tooth tissue obtained with acoustic microscopy,” Ultrasound Med. Biol. 28(1), 131–136 (2002).
[CrossRef] [PubMed]

Denissov, A. A.

R. G. Maev, L. A. Denisova, E. Y. Maeva, and A. A. Denissov, “New data on histology and physico-mechanical properties of human tooth tissue obtained with acoustic microscopy,” Ultrasound Med. Biol. 28(1), 131–136 (2002).
[CrossRef] [PubMed]

Dewhurst, R. J.

R. J. Dewhurst and Q. Shan, “Optical remote measurement of ultrasound,” Meas. Sci. Technol. 10(11), R139–R168 (1999).
[CrossRef]

Dudderar, T. D.

T. D. Dudderar, C. P. Burger, J. A. Gilbert, J. A. Smith, and B. R. Peters, “Fiber optic sensing for ultrasonic NDE,” J. Nondestructive Evaluation 6(3), 135–146 (1987).
[CrossRef]

Feagin, F.

F. Feagin, T. Koulourides, and W. Pigman, “The characterization of enamel surface demineralization, remineralization, and associated hardness changes in human and bovine material,” Arch. Oral Biol. 14(12), 1407–1417 (1969).
[CrossRef] [PubMed]

Fleming, S.

H. C. Wang, S. Fleming, and Y. C. Lee, “A remote, non-destructive laser ultrasonic material evaluation system with simplified optical fibre interferometer detection,” J. Nondestructive Evaluation 28(2), 75–83 (2009).
[CrossRef]

H. C. Wang, S. Fleming, and Y. C. Lee, “Simple, all-optical, noncontact, depth-selective, narrowband surface acoustic wave measurement system for evaluating the Rayleigh velocity of small samples or areas,” Appl. Opt. 48(8), 1444–1451 (2009).
[CrossRef] [PubMed]

Gao, W.

C. Glorieux, W. Gao, S. E. Kruger, K. Van de Rostyne, W. Lauriks, and J. Thoen, “Surface acoustic wave depth profiling of elastically inhomogeneous materials,” J. Appl. Phys. 88(7), 4394–4400 (2000).
[CrossRef]

Gilbert, J. A.

T. D. Dudderar, C. P. Burger, J. A. Gilbert, J. A. Smith, and B. R. Peters, “Fiber optic sensing for ultrasonic NDE,” J. Nondestructive Evaluation 6(3), 135–146 (1987).
[CrossRef]

Glorieux, C.

C. Glorieux, W. Gao, S. E. Kruger, K. Van de Rostyne, W. Lauriks, and J. Thoen, “Surface acoustic wave depth profiling of elastically inhomogeneous materials,” J. Appl. Phys. 88(7), 4394–4400 (2000).
[CrossRef]

Griepentrog, M.

D. Schneider, B. Schultrich, H. J. Scheibe, H. Ziegele, and M. Griepentrog, “A laser-acoustic method for testing and classifying hard surface layers,” Thin Solid Films 332(1–2), 157–163 (1998).
[CrossRef]

Habelitz, S.

S. Habelitz, S. J. Marshall, G. W. Marshall, and M. Balooch, “Mechanical properties of human dental enamel on the nanometre scale,” Arch. Oral Biol. 46(2), 173–183 (2001).
[CrossRef] [PubMed]

Hess, P.

A. Neubrand and P. Hess, “Laser generation and detection of surface acoustic waves: Elastic properties of surface layers,” J. Appl. Phys. 71(1), 227–238 (1991).
[CrossRef]

Ismail, A. I.

A. I. Ismail, “Visual and visuo-tactile detection of dental caries,” J. Dent. Res. 83 (1), C56–C66 (2004).
[CrossRef] [PubMed]

Jandt, K. D.

F. Lippert, D. M. Parker, and K. D. Jandt, “In vitro demineralization/remineralization cycles at human tooth enamel surfaces investigated by AFM and nanoindentation,” J. Colloid Interface Sci. 280(2), 442–448 (2004).
[CrossRef] [PubMed]

Jang, T. S.

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

Johnson, J.

N. Carlson and J. Johnson, “Pulsed laser energy through fiberoptics for generation of ultrasound,” J. Nondestructive Evaluation 12(3), 187–192 (1993).
[CrossRef]

Koulourides, T.

F. Feagin, T. Koulourides, and W. Pigman, “The characterization of enamel surface demineralization, remineralization, and associated hardness changes in human and bovine material,” Arch. Oral Biol. 14(12), 1407–1417 (1969).
[CrossRef] [PubMed]

Krasse, B.

B. Krasse, “Biological factors as indicators of future caries,” Int. Dent. J. 38(4), 219–225 (1988).
[PubMed]

Kruger, S. E.

C. Glorieux, W. Gao, S. E. Kruger, K. Van de Rostyne, W. Lauriks, and J. Thoen, “Surface acoustic wave depth profiling of elastically inhomogeneous materials,” J. Appl. Phys. 88(7), 4394–4400 (2000).
[CrossRef]

Kwon, I. B.

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

Lauriks, W.

C. Glorieux, W. Gao, S. E. Kruger, K. Van de Rostyne, W. Lauriks, and J. Thoen, “Surface acoustic wave depth profiling of elastically inhomogeneous materials,” J. Appl. Phys. 88(7), 4394–4400 (2000).
[CrossRef]

Lee, J. J.

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

Lee, S. S.

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

Lee, W. J

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

Lee, W. J.

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

Lee, Y. C.

H. C. Wang, S. Fleming, and Y. C. Lee, “A remote, non-destructive laser ultrasonic material evaluation system with simplified optical fibre interferometer detection,” J. Nondestructive Evaluation 28(2), 75–83 (2009).
[CrossRef]

H. C. Wang, S. Fleming, and Y. C. Lee, “Simple, all-optical, noncontact, depth-selective, narrowband surface acoustic wave measurement system for evaluating the Rayleigh velocity of small samples or areas,” Appl. Opt. 48(8), 1444–1451 (2009).
[CrossRef] [PubMed]

Lee,, J. J.

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

Lippert, F.

F. Lippert, D. M. Parker, and K. D. Jandt, “In vitro demineralization/remineralization cycles at human tooth enamel surfaces investigated by AFM and nanoindentation,” J. Colloid Interface Sci. 280(2), 442–448 (2004).
[CrossRef] [PubMed]

Livi, K. J.

J. L. Cuy, A. B. Mann, K. J. Livi, M. F. Teaford, and T. P. Weihs, “Nanoindentation mapping of the mechanical properties of human molar tooth enamel,” Arch. Oral Biol. 47(4), 281–291 (2002).
[CrossRef] [PubMed]

Maev, R. G.

R. G. Maev, L. A. Denisova, E. Y. Maeva, and A. A. Denissov, “New data on histology and physico-mechanical properties of human tooth tissue obtained with acoustic microscopy,” Ultrasound Med. Biol. 28(1), 131–136 (2002).
[CrossRef] [PubMed]

Maeva, E. Y.

R. G. Maev, L. A. Denisova, E. Y. Maeva, and A. A. Denissov, “New data on histology and physico-mechanical properties of human tooth tissue obtained with acoustic microscopy,” Ultrasound Med. Biol. 28(1), 131–136 (2002).
[CrossRef] [PubMed]

Mann, A. B.

J. L. Cuy, A. B. Mann, K. J. Livi, M. F. Teaford, and T. P. Weihs, “Nanoindentation mapping of the mechanical properties of human molar tooth enamel,” Arch. Oral Biol. 47(4), 281–291 (2002).
[CrossRef] [PubMed]

Marshall, G. W.

S. Habelitz, S. J. Marshall, G. W. Marshall, and M. Balooch, “Mechanical properties of human dental enamel on the nanometre scale,” Arch. Oral Biol. 46(2), 173–183 (2001).
[CrossRef] [PubMed]

Marshall, S. J.

S. Habelitz, S. J. Marshall, G. W. Marshall, and M. Balooch, “Mechanical properties of human dental enamel on the nanometre scale,” Arch. Oral Biol. 46(2), 173–183 (2001).
[CrossRef] [PubMed]

Maznev, A. A.

J. A. Rogers, A. A. Maznev, M. J. Banet, and K. A. Nelson, “Optical Generation and Characterization of Acoustic Waves in Thin Films: Fundamentals and Applications,” Annu. Rev. Mater. Sci. 30(1), 117–157 (2000).
[CrossRef]

Mitra, B.

B. Mitra, A. Shelamoff, and D. J. Booth, “An optical fibre interferometer for remote detection of laser generated ultrasonics,” Meas. Sci. Technol. 9(9), 1432–1436 (1998).
[CrossRef]

Monchalin, J.

J. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33(5), 485–499 (1986).
[CrossRef]

Nelson, K. A.

J. A. Rogers, A. A. Maznev, M. J. Banet, and K. A. Nelson, “Optical Generation and Characterization of Acoustic Waves in Thin Films: Fundamentals and Applications,” Annu. Rev. Mater. Sci. 30(1), 117–157 (2000).
[CrossRef]

Neubrand, A.

A. Neubrand and P. Hess, “Laser generation and detection of surface acoustic waves: Elastic properties of surface layers,” J. Appl. Phys. 71(1), 227–238 (1991).
[CrossRef]

Park, H. S.

H. S. Park, G. Thursby, and B. Culshaw, “Detection of laser-generated ultrasound based on phase demodulation technique using a fibre Fabry-Perot interferometer,” Meas. Sci. Technol. 16(6), 1261–1266 (2005).
[CrossRef]

Parker, D. M.

F. Lippert, D. M. Parker, and K. D. Jandt, “In vitro demineralization/remineralization cycles at human tooth enamel surfaces investigated by AFM and nanoindentation,” J. Colloid Interface Sci. 280(2), 442–448 (2004).
[CrossRef] [PubMed]

Peck, S. D.

S. D. Peck, J. M. Rowe, and G. A. Briggs, “Studies on sound and carious enamel with the quantitative acoustic microscope,” J. Dent. Res. 68(2), 107–112 (1989).
[CrossRef] [PubMed]

Peters, B. R.

T. D. Dudderar, C. P. Burger, J. A. Gilbert, J. A. Smith, and B. R. Peters, “Fiber optic sensing for ultrasonic NDE,” J. Nondestructive Evaluation 6(3), 135–146 (1987).
[CrossRef]

Pigman, W.

F. Feagin, T. Koulourides, and W. Pigman, “The characterization of enamel surface demineralization, remineralization, and associated hardness changes in human and bovine material,” Arch. Oral Biol. 14(12), 1407–1417 (1969).
[CrossRef] [PubMed]

Rogers, J. A.

J. A. Rogers, A. A. Maznev, M. J. Banet, and K. A. Nelson, “Optical Generation and Characterization of Acoustic Waves in Thin Films: Fundamentals and Applications,” Annu. Rev. Mater. Sci. 30(1), 117–157 (2000).
[CrossRef]

Rowe, J. M.

S. D. Peck, J. M. Rowe, and G. A. Briggs, “Studies on sound and carious enamel with the quantitative acoustic microscope,” J. Dent. Res. 68(2), 107–112 (1989).
[CrossRef] [PubMed]

Scheibe, H. J.

D. Schneider, B. Schultrich, H. J. Scheibe, H. Ziegele, and M. Griepentrog, “A laser-acoustic method for testing and classifying hard surface layers,” Thin Solid Films 332(1–2), 157–163 (1998).
[CrossRef]

Schneider, D.

D. Schneider, T. Witke, T. Schwarz, B. Schoneich, and B. Schultrich, “Testing ultra-thin films by laser-acoustics,” Surf. Coat. Tech. 126(2–3), 136–141 (2000).
[CrossRef]

D. Schneider, B. Schultrich, H. J. Scheibe, H. Ziegele, and M. Griepentrog, “A laser-acoustic method for testing and classifying hard surface layers,” Thin Solid Films 332(1–2), 157–163 (1998).
[CrossRef]

D. Schneider and T. Schwarz, “A photoacoustic method for characterising thin films,” Surf. Coat. Tech. 91(1–2), 136–146 (1997).
[CrossRef]

Schoneich, B.

D. Schneider, T. Witke, T. Schwarz, B. Schoneich, and B. Schultrich, “Testing ultra-thin films by laser-acoustics,” Surf. Coat. Tech. 126(2–3), 136–141 (2000).
[CrossRef]

Schultrich, B.

D. Schneider, T. Witke, T. Schwarz, B. Schoneich, and B. Schultrich, “Testing ultra-thin films by laser-acoustics,” Surf. Coat. Tech. 126(2–3), 136–141 (2000).
[CrossRef]

D. Schneider, B. Schultrich, H. J. Scheibe, H. Ziegele, and M. Griepentrog, “A laser-acoustic method for testing and classifying hard surface layers,” Thin Solid Films 332(1–2), 157–163 (1998).
[CrossRef]

Schwarz, T.

D. Schneider, T. Witke, T. Schwarz, B. Schoneich, and B. Schultrich, “Testing ultra-thin films by laser-acoustics,” Surf. Coat. Tech. 126(2–3), 136–141 (2000).
[CrossRef]

D. Schneider and T. Schwarz, “A photoacoustic method for characterising thin films,” Surf. Coat. Tech. 91(1–2), 136–146 (1997).
[CrossRef]

Shan, Q.

R. J. Dewhurst and Q. Shan, “Optical remote measurement of ultrasound,” Meas. Sci. Technol. 10(11), R139–R168 (1999).
[CrossRef]

Shelamoff, A.

B. Mitra, A. Shelamoff, and D. J. Booth, “An optical fibre interferometer for remote detection of laser generated ultrasonics,” Meas. Sci. Technol. 9(9), 1432–1436 (1998).
[CrossRef]

Smith, J. A.

T. D. Dudderar, C. P. Burger, J. A. Gilbert, J. A. Smith, and B. R. Peters, “Fiber optic sensing for ultrasonic NDE,” J. Nondestructive Evaluation 6(3), 135–146 (1987).
[CrossRef]

Soczkiewicz, E.

E. Soczkiewicz, “The Penetration Depth of the Rayleigh Surface Waves,” Nondestructive Testing and Evaluation 13(2), 113–119 (1997).
[CrossRef]

Teaford, M. F.

J. L. Cuy, A. B. Mann, K. J. Livi, M. F. Teaford, and T. P. Weihs, “Nanoindentation mapping of the mechanical properties of human molar tooth enamel,” Arch. Oral Biol. 47(4), 281–291 (2002).
[CrossRef] [PubMed]

Thoen, J.

C. Glorieux, W. Gao, S. E. Kruger, K. Van de Rostyne, W. Lauriks, and J. Thoen, “Surface acoustic wave depth profiling of elastically inhomogeneous materials,” J. Appl. Phys. 88(7), 4394–4400 (2000).
[CrossRef]

Thursby, G.

H. S. Park, G. Thursby, and B. Culshaw, “Detection of laser-generated ultrasound based on phase demodulation technique using a fibre Fabry-Perot interferometer,” Meas. Sci. Technol. 16(6), 1261–1266 (2005).
[CrossRef]

Van de Rostyne, K.

C. Glorieux, W. Gao, S. E. Kruger, K. Van de Rostyne, W. Lauriks, and J. Thoen, “Surface acoustic wave depth profiling of elastically inhomogeneous materials,” J. Appl. Phys. 88(7), 4394–4400 (2000).
[CrossRef]

Vogel, J. A.

Wang, H. C.

H. C. Wang, S. Fleming, and Y. C. Lee, “Simple, all-optical, noncontact, depth-selective, narrowband surface acoustic wave measurement system for evaluating the Rayleigh velocity of small samples or areas,” Appl. Opt. 48(8), 1444–1451 (2009).
[CrossRef] [PubMed]

H. C. Wang, S. Fleming, and Y. C. Lee, “A remote, non-destructive laser ultrasonic material evaluation system with simplified optical fibre interferometer detection,” J. Nondestructive Evaluation 28(2), 75–83 (2009).
[CrossRef]

Weihs, T. P.

J. L. Cuy, A. B. Mann, K. J. Livi, M. F. Teaford, and T. P. Weihs, “Nanoindentation mapping of the mechanical properties of human molar tooth enamel,” Arch. Oral Biol. 47(4), 281–291 (2002).
[CrossRef] [PubMed]

Witke, T.

D. Schneider, T. Witke, T. Schwarz, B. Schoneich, and B. Schultrich, “Testing ultra-thin films by laser-acoustics,” Surf. Coat. Tech. 126(2–3), 136–141 (2000).
[CrossRef]

Wu, T. T.

T. T. Wu and Y. C. Chen, “Dispersion of laser generated surface waves in an epoxy-bonded layered medium,” Ultrasonics 34(8), 793–799 (1996).
[CrossRef]

Ziegele, H.

D. Schneider, B. Schultrich, H. J. Scheibe, H. Ziegele, and M. Griepentrog, “A laser-acoustic method for testing and classifying hard surface layers,” Thin Solid Films 332(1–2), 157–163 (1998).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

J. A. Rogers, A. A. Maznev, M. J. Banet, and K. A. Nelson, “Optical Generation and Characterization of Acoustic Waves in Thin Films: Fundamentals and Applications,” Annu. Rev. Mater. Sci. 30(1), 117–157 (2000).
[CrossRef]

Appl. Opt. (2)

Arch. Oral Biol. (3)

F. Feagin, T. Koulourides, and W. Pigman, “The characterization of enamel surface demineralization, remineralization, and associated hardness changes in human and bovine material,” Arch. Oral Biol. 14(12), 1407–1417 (1969).
[CrossRef] [PubMed]

S. Habelitz, S. J. Marshall, G. W. Marshall, and M. Balooch, “Mechanical properties of human dental enamel on the nanometre scale,” Arch. Oral Biol. 46(2), 173–183 (2001).
[CrossRef] [PubMed]

J. L. Cuy, A. B. Mann, K. J. Livi, M. F. Teaford, and T. P. Weihs, “Nanoindentation mapping of the mechanical properties of human molar tooth enamel,” Arch. Oral Biol. 47(4), 281–291 (2002).
[CrossRef] [PubMed]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

J. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33(5), 485–499 (1986).
[CrossRef]

21T. S. Jang, S. S. Lee, I. B. Kwon, W. J. Lee, J. J. Lee, T. S. Jang, S. S. Lee, I. B. Kwon, W. J Lee, and J. J. Lee, “Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 767–775 (2002).
[CrossRef]

Int. Dent. J. (1)

B. Krasse, “Biological factors as indicators of future caries,” Int. Dent. J. 38(4), 219–225 (1988).
[PubMed]

Int. J. Solids Struct. (1)

I. Arias and J. D. Achenbach, “Thermoelastic generation of ultrasound by line-focused laser irradiation,” Int. J. Solids Struct. 40(25), 6917–6935 (2003).
[CrossRef]

J. Acoust. Soc. Am. (1)

D. W. Blodgett, “Applications of laser-based ultrasonics to the characterization of the internal structure of teeth,” J. Acoust. Soc. Am. 114(1), 542–549 (2003).
[CrossRef] [PubMed]

J. Appl. Phys. (2)

A. Neubrand and P. Hess, “Laser generation and detection of surface acoustic waves: Elastic properties of surface layers,” J. Appl. Phys. 71(1), 227–238 (1991).
[CrossRef]

C. Glorieux, W. Gao, S. E. Kruger, K. Van de Rostyne, W. Lauriks, and J. Thoen, “Surface acoustic wave depth profiling of elastically inhomogeneous materials,” J. Appl. Phys. 88(7), 4394–4400 (2000).
[CrossRef]

J. Colloid Interface Sci. (1)

F. Lippert, D. M. Parker, and K. D. Jandt, “In vitro demineralization/remineralization cycles at human tooth enamel surfaces investigated by AFM and nanoindentation,” J. Colloid Interface Sci. 280(2), 442–448 (2004).
[CrossRef] [PubMed]

J. Dent. Res. (2)

A. I. Ismail, “Visual and visuo-tactile detection of dental caries,” J. Dent. Res. 83 (1), C56–C66 (2004).
[CrossRef] [PubMed]

S. D. Peck, J. M. Rowe, and G. A. Briggs, “Studies on sound and carious enamel with the quantitative acoustic microscope,” J. Dent. Res. 68(2), 107–112 (1989).
[CrossRef] [PubMed]

J. Nondestructive Evaluation (3)

N. Carlson and J. Johnson, “Pulsed laser energy through fiberoptics for generation of ultrasound,” J. Nondestructive Evaluation 12(3), 187–192 (1993).
[CrossRef]

H. C. Wang, S. Fleming, and Y. C. Lee, “A remote, non-destructive laser ultrasonic material evaluation system with simplified optical fibre interferometer detection,” J. Nondestructive Evaluation 28(2), 75–83 (2009).
[CrossRef]

T. D. Dudderar, C. P. Burger, J. A. Gilbert, J. A. Smith, and B. R. Peters, “Fiber optic sensing for ultrasonic NDE,” J. Nondestructive Evaluation 6(3), 135–146 (1987).
[CrossRef]

Meas. Sci. Technol. (3)

H. S. Park, G. Thursby, and B. Culshaw, “Detection of laser-generated ultrasound based on phase demodulation technique using a fibre Fabry-Perot interferometer,” Meas. Sci. Technol. 16(6), 1261–1266 (2005).
[CrossRef]

R. J. Dewhurst and Q. Shan, “Optical remote measurement of ultrasound,” Meas. Sci. Technol. 10(11), R139–R168 (1999).
[CrossRef]

B. Mitra, A. Shelamoff, and D. J. Booth, “An optical fibre interferometer for remote detection of laser generated ultrasonics,” Meas. Sci. Technol. 9(9), 1432–1436 (1998).
[CrossRef]

Nondestructive Testing and Evaluation (1)

E. Soczkiewicz, “The Penetration Depth of the Rayleigh Surface Waves,” Nondestructive Testing and Evaluation 13(2), 113–119 (1997).
[CrossRef]

Surf. Coat. Tech. (2)

D. Schneider and T. Schwarz, “A photoacoustic method for characterising thin films,” Surf. Coat. Tech. 91(1–2), 136–146 (1997).
[CrossRef]

D. Schneider, T. Witke, T. Schwarz, B. Schoneich, and B. Schultrich, “Testing ultra-thin films by laser-acoustics,” Surf. Coat. Tech. 126(2–3), 136–141 (2000).
[CrossRef]

Thin Solid Films (1)

D. Schneider, B. Schultrich, H. J. Scheibe, H. Ziegele, and M. Griepentrog, “A laser-acoustic method for testing and classifying hard surface layers,” Thin Solid Films 332(1–2), 157–163 (1998).
[CrossRef]

Ultrasonics (1)

T. T. Wu and Y. C. Chen, “Dispersion of laser generated surface waves in an epoxy-bonded layered medium,” Ultrasonics 34(8), 793–799 (1996).
[CrossRef]

Ultrasound Med. Biol. (1)

R. G. Maev, L. A. Denisova, E. Y. Maeva, and A. A. Denissov, “New data on histology and physico-mechanical properties of human tooth tissue obtained with acoustic microscopy,” Ultrasound Med. Biol. 28(1), 131–136 (2002).
[CrossRef] [PubMed]

Other (9)

A. Briggs, Acoustic Microscopy. 1992: Clarendon Press. Oxford.

J. D. Achenbach, Wave Propagation in Elastic Solids. 1984: Elsevier Science Ltd.

J. L. Rose, Ultrasonic Waves in Solid Media. 1999: Cambridge University Press.

J. Kushibiki, K. L. Ha, H. Kato, N. Chubachi, and F. Dunn, “Application of Acoustic Microscopy to Dental Material Characterization”, IEEE 1987 Ultrasonics Symposium, pp.837–842, 1987.

H. C. Wang, S. Fleming, S. Law, and T. Huang, Selection of an appropriate laser wavelength for launching surface acoustic waves on tooth enamel. in Proceedings of IEEE Australian Conference on Optical Fibre Technology/Australian Optical Society (ACOFT/AOS). 2006. Melbourne, Australia.

Y. C. Lee, J. O. Kim, and J. D. Achenbach, “Measurement of elastic constants and mass density by acoustic microscopy”, IEEE Ultrasonics Symposium, vol.1, pp.607–612, October 1993.

C. S. Scruby, and L. E. Drain, Laser Ultrasonics: Techniques and Applications. 1990: Adam Hilger Ltd.

T. Kundu, ed., Ultrasonic nondestructive evaluation: engineering and biological material characterization. 2004, CRC Press.

W. D. Miller, “Agency of micro-organisms in decay of the teeth”, Dental Cosmos, 1883.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Surface wave dispersion in a two-layer system.

Fig. 2
Fig. 2

Arrangement of the laser NDE system and the SAW dispersion measurement.

Fig. 3
Fig. 3

Comparison between large and small probe-to-sample separation.

Fig. 4
Fig. 4

Rayleigh waves on the aluminium sample measured at different locations away from the source. [N.B.: the traces are identically scaled arbitrary units, see text for details.]

Fig. 5
Fig. 5

Experimental Rayleigh phase velocities for aluminium and brass sample.

Fig. 6
Fig. 6

Surface waves on a two-layer system of Ni film on glass substrate measured at locations 1 mm to 6 mm away from the source. [N.B.: Y-axis as per Fig. 4.]

Fig. 7
Fig. 7

Cross-power spectrum between signals measured at 1 mm and 6 mm from the source. The usable bandwidth spanned ~20 MHz.

Fig. 8
Fig. 8

Experimental and theoretical dispersion curves for nickel film on glass substrate.

Fig. 9
Fig. 9

The front surface of incisor A was irradiated with the line-source and the OFI detection tip was placed a few mm away.

Fig. 10
Fig. 10

Rayleigh waves recorded at different locations from the line-source on the front surface of (a) sample A and (b) sample B. [N.B. Y-axis as per Fig. 4.]

Fig. 11
Fig. 11

Cross power spectra from one of the sample A measurements.

Fig. 12
Fig. 12

Dispersion curves of the final averaged results from sample A and B.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

zλ=cR/f,
cR0 .87+1 .12v1+vE2ρ(1+v),
c(f)=2πfx2x1φ(f).

Metrics