Abstract

The beam profiles and spatial irradiance distributions of modified fiber tips mainly used in laser angioplasty have been calculated by ray tracing assuming a uniform spatial combined with a weighted angular irradiance distribution. The computations were compared to paraxial theory and to measurements in air and in water. For ball-shaped fibers and hemispherical probes, made of either silica or sapphire, the position of the maximum irradiance in front of the probe in water did not coincide with the calculated paraxial focal point. The maximum irradiance increase was limited by internal backward reflections and by beam divergence. It is expected that beam focusing is minimal when optically modified fiber tips are in contact with tissue. Ray tracing is useful for optimizing the design of optically modified fiber tips when paraxial theory cannot be applied.

© 1991 Optical Society of America

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References

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  1. V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Lens-Ended Fibers for Medical Applications: a New Fabrication Technique,” Appl. Opt. 23, 3277–3283 (1984).
    [Crossref] [PubMed]
  2. C. T. Chang, D. C. Auth, “Radiation Characteristics of a Tapered Cylindrical Optical Fiber,” J. Opt. Soc. Am. 68, 1191–1196 (1978).
    [Crossref]
  3. C. Borst, “Percutaneous Recanalization of Arteries: Status and Prospects of Laser Angioplasty with Modified Fibre Tips,” Lasers Med. Sci. 2, 137–151 (1987).
    [Crossref]
  4. H. J. Geschwind, M. J. Kern, M. G. Vandormael, J. D. Blair, U. Deligonul, H. L. Kennedy, “Efficiency and Safety of Optically Modified Fiber Tips for Laser Angioplasty,” J. Am. Coll. Cardiol. 10, 655–661 (1987).
    [Crossref] [PubMed]
  5. R. M. Verdaasdonk, F. W. Cross, C. Borst, “Physical Properties of Sapphire Fibre Tips for Laser Angioplasty,” Lasers Med. Sci. 2, 183–188 (1987).
    [Crossref]
  6. W. Siegmund, “Fiber Optics,” in Handbook of Optics, W. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978).
  7. H. Ward, “Molding of Laser Energy by Shaped Optic Fiber Tips,” Lasers Surg. Med. 7, 405–413 (1987).
    [Crossref] [PubMed]
  8. D. Royston, R. Waynant, A. Banks, S. R. Ramee, C. J. White, “Optical Properties of Fiber Optic Surgical Tips,” Appl. Opt. 28, 799–803 (1989).
    [Crossref] [PubMed]
  9. E. Hecht, A. Zajak, Optics (Addison-Wesley, Reading, MA, 1979).
  10. V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Characterization of a Microlens-Ended Optical Fiber,” Alta Freq. 52, 194–197 (1983).
  11. J. Lammer, F. Karnel, “Percutaneous Transluminal Laser Angioplasty with Contact Probes,” Radiology 168, 733–737 (1988).
    [PubMed]
  12. S. N. Berengoltz et al., “Percutane transluminale rekanalisatie van afgesloten bovenbeenarterien met laserstraalbehandeling [Percutaneous Transluminal Laser Angioplasty of Occluded Superficial Femoral Arteries],” Ned. Tijdschr. Geneeskd. 31, 1542–1546 (1989).
  13. S. Ashley, S. G. Brooks, A. A. Gehani, R. C. Kester, M. R. Rees, “Thermal Characteristics of Sapphire Contact Probe Delivery Systems for Laser Angioplasty,” Lasers Surg. Med. 10, 234–244 (1990).
    [Crossref] [PubMed]
  14. F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive Index of Some Mammalian Tissues Using a Fiber Optic Cladding Method,” Appl. Opt. 28, 2297–2303 (1989).
    [Crossref] [PubMed]
  15. M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light Distributions in Artery Tissue: Monte Carlo Simulations for Finite-Diameter Laser Beams,” Lasers Surg. Med. 9, 148–154 (1989).
    [Crossref] [PubMed]
  16. R. M. Verdaasdonk, C. Borst, “Ray Tracing of Optically Modified Fiber Tips. 2: Laser Scalpels,” Appl. Opt. 30, 2172–2177 (1May1990).
    [Crossref]
  17. R. M. Cothren, G. B. Hayes, J. R. Kramer, B. Sacks, C. Kittrell, M. S. Feld, “A Multifiber Catheter with an Optical Shield for Laser Angiosurgery,” Lasers Life Sci. 1, 1–12 (1986).
  18. D. Decker-Dunn, D. A. Christensen, G. M. Vincent, “Multifiber Gradient-Index Lens Laser Angioplasty Probe,” Lasers Surg. Med. 10, 85–93 (1990).
    [Crossref] [PubMed]
  19. A. Foschi, G. Myers, W. F. Crick, H. D. Friedberg, D. Snyder, L. A. Nordstrom, “Laser Angioplasty of Totally Occluded Coronary Arteries and Vein Grafts: Preliminary Report on a Current Trial,” Am. J. Cardiol. 63, 9F–13F (1989).
    [PubMed]
  20. V. Russo, S. Sottini, G. Margheri, F. Crea, “A Novel Corolla-Irradiating Fiber Optic Probe for Laser Angioplasty,” Proc. Soc. Photo-Opt. Instrum. Eng. 906, 301–304 (1988).
  21. R. M. Verdaasdonk, E. D. Jansen, F. C. Holstege, C. Borst, “Optically Modified Fiber Tips Penetrate Tissue only when ‘Dirty’,” Proc. Soc. Photo-Opt. Instrum. Eng. 1201, 129–136 (1990).

1990 (4)

S. Ashley, S. G. Brooks, A. A. Gehani, R. C. Kester, M. R. Rees, “Thermal Characteristics of Sapphire Contact Probe Delivery Systems for Laser Angioplasty,” Lasers Surg. Med. 10, 234–244 (1990).
[Crossref] [PubMed]

R. M. Verdaasdonk, C. Borst, “Ray Tracing of Optically Modified Fiber Tips. 2: Laser Scalpels,” Appl. Opt. 30, 2172–2177 (1May1990).
[Crossref]

D. Decker-Dunn, D. A. Christensen, G. M. Vincent, “Multifiber Gradient-Index Lens Laser Angioplasty Probe,” Lasers Surg. Med. 10, 85–93 (1990).
[Crossref] [PubMed]

R. M. Verdaasdonk, E. D. Jansen, F. C. Holstege, C. Borst, “Optically Modified Fiber Tips Penetrate Tissue only when ‘Dirty’,” Proc. Soc. Photo-Opt. Instrum. Eng. 1201, 129–136 (1990).

1989 (5)

A. Foschi, G. Myers, W. F. Crick, H. D. Friedberg, D. Snyder, L. A. Nordstrom, “Laser Angioplasty of Totally Occluded Coronary Arteries and Vein Grafts: Preliminary Report on a Current Trial,” Am. J. Cardiol. 63, 9F–13F (1989).
[PubMed]

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive Index of Some Mammalian Tissues Using a Fiber Optic Cladding Method,” Appl. Opt. 28, 2297–2303 (1989).
[Crossref] [PubMed]

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light Distributions in Artery Tissue: Monte Carlo Simulations for Finite-Diameter Laser Beams,” Lasers Surg. Med. 9, 148–154 (1989).
[Crossref] [PubMed]

S. N. Berengoltz et al., “Percutane transluminale rekanalisatie van afgesloten bovenbeenarterien met laserstraalbehandeling [Percutaneous Transluminal Laser Angioplasty of Occluded Superficial Femoral Arteries],” Ned. Tijdschr. Geneeskd. 31, 1542–1546 (1989).

D. Royston, R. Waynant, A. Banks, S. R. Ramee, C. J. White, “Optical Properties of Fiber Optic Surgical Tips,” Appl. Opt. 28, 799–803 (1989).
[Crossref] [PubMed]

1988 (2)

J. Lammer, F. Karnel, “Percutaneous Transluminal Laser Angioplasty with Contact Probes,” Radiology 168, 733–737 (1988).
[PubMed]

V. Russo, S. Sottini, G. Margheri, F. Crea, “A Novel Corolla-Irradiating Fiber Optic Probe for Laser Angioplasty,” Proc. Soc. Photo-Opt. Instrum. Eng. 906, 301–304 (1988).

1987 (4)

C. Borst, “Percutaneous Recanalization of Arteries: Status and Prospects of Laser Angioplasty with Modified Fibre Tips,” Lasers Med. Sci. 2, 137–151 (1987).
[Crossref]

H. J. Geschwind, M. J. Kern, M. G. Vandormael, J. D. Blair, U. Deligonul, H. L. Kennedy, “Efficiency and Safety of Optically Modified Fiber Tips for Laser Angioplasty,” J. Am. Coll. Cardiol. 10, 655–661 (1987).
[Crossref] [PubMed]

R. M. Verdaasdonk, F. W. Cross, C. Borst, “Physical Properties of Sapphire Fibre Tips for Laser Angioplasty,” Lasers Med. Sci. 2, 183–188 (1987).
[Crossref]

H. Ward, “Molding of Laser Energy by Shaped Optic Fiber Tips,” Lasers Surg. Med. 7, 405–413 (1987).
[Crossref] [PubMed]

1986 (1)

R. M. Cothren, G. B. Hayes, J. R. Kramer, B. Sacks, C. Kittrell, M. S. Feld, “A Multifiber Catheter with an Optical Shield for Laser Angiosurgery,” Lasers Life Sci. 1, 1–12 (1986).

1984 (1)

1983 (1)

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Characterization of a Microlens-Ended Optical Fiber,” Alta Freq. 52, 194–197 (1983).

1978 (1)

Ashley, S.

S. Ashley, S. G. Brooks, A. A. Gehani, R. C. Kester, M. R. Rees, “Thermal Characteristics of Sapphire Contact Probe Delivery Systems for Laser Angioplasty,” Lasers Surg. Med. 10, 234–244 (1990).
[Crossref] [PubMed]

Auth, D. C.

Banks, A.

Berengoltz, S. N.

S. N. Berengoltz et al., “Percutane transluminale rekanalisatie van afgesloten bovenbeenarterien met laserstraalbehandeling [Percutaneous Transluminal Laser Angioplasty of Occluded Superficial Femoral Arteries],” Ned. Tijdschr. Geneeskd. 31, 1542–1546 (1989).

Blair, J. D.

H. J. Geschwind, M. J. Kern, M. G. Vandormael, J. D. Blair, U. Deligonul, H. L. Kennedy, “Efficiency and Safety of Optically Modified Fiber Tips for Laser Angioplasty,” J. Am. Coll. Cardiol. 10, 655–661 (1987).
[Crossref] [PubMed]

Bolin, F. P.

Borst, C.

R. M. Verdaasdonk, C. Borst, “Ray Tracing of Optically Modified Fiber Tips. 2: Laser Scalpels,” Appl. Opt. 30, 2172–2177 (1May1990).
[Crossref]

R. M. Verdaasdonk, E. D. Jansen, F. C. Holstege, C. Borst, “Optically Modified Fiber Tips Penetrate Tissue only when ‘Dirty’,” Proc. Soc. Photo-Opt. Instrum. Eng. 1201, 129–136 (1990).

C. Borst, “Percutaneous Recanalization of Arteries: Status and Prospects of Laser Angioplasty with Modified Fibre Tips,” Lasers Med. Sci. 2, 137–151 (1987).
[Crossref]

R. M. Verdaasdonk, F. W. Cross, C. Borst, “Physical Properties of Sapphire Fibre Tips for Laser Angioplasty,” Lasers Med. Sci. 2, 183–188 (1987).
[Crossref]

Brooks, S. G.

S. Ashley, S. G. Brooks, A. A. Gehani, R. C. Kester, M. R. Rees, “Thermal Characteristics of Sapphire Contact Probe Delivery Systems for Laser Angioplasty,” Lasers Surg. Med. 10, 234–244 (1990).
[Crossref] [PubMed]

Chang, C. T.

Christensen, D. A.

D. Decker-Dunn, D. A. Christensen, G. M. Vincent, “Multifiber Gradient-Index Lens Laser Angioplasty Probe,” Lasers Surg. Med. 10, 85–93 (1990).
[Crossref] [PubMed]

Cothren, R. M.

R. M. Cothren, G. B. Hayes, J. R. Kramer, B. Sacks, C. Kittrell, M. S. Feld, “A Multifiber Catheter with an Optical Shield for Laser Angiosurgery,” Lasers Life Sci. 1, 1–12 (1986).

Crea, F.

V. Russo, S. Sottini, G. Margheri, F. Crea, “A Novel Corolla-Irradiating Fiber Optic Probe for Laser Angioplasty,” Proc. Soc. Photo-Opt. Instrum. Eng. 906, 301–304 (1988).

Crick, W. F.

A. Foschi, G. Myers, W. F. Crick, H. D. Friedberg, D. Snyder, L. A. Nordstrom, “Laser Angioplasty of Totally Occluded Coronary Arteries and Vein Grafts: Preliminary Report on a Current Trial,” Am. J. Cardiol. 63, 9F–13F (1989).
[PubMed]

Cross, F. W.

R. M. Verdaasdonk, F. W. Cross, C. Borst, “Physical Properties of Sapphire Fibre Tips for Laser Angioplasty,” Lasers Med. Sci. 2, 183–188 (1987).
[Crossref]

Decker-Dunn, D.

D. Decker-Dunn, D. A. Christensen, G. M. Vincent, “Multifiber Gradient-Index Lens Laser Angioplasty Probe,” Lasers Surg. Med. 10, 85–93 (1990).
[Crossref] [PubMed]

Deligonul, U.

H. J. Geschwind, M. J. Kern, M. G. Vandormael, J. D. Blair, U. Deligonul, H. L. Kennedy, “Efficiency and Safety of Optically Modified Fiber Tips for Laser Angioplasty,” J. Am. Coll. Cardiol. 10, 655–661 (1987).
[Crossref] [PubMed]

Feld, M. S.

R. M. Cothren, G. B. Hayes, J. R. Kramer, B. Sacks, C. Kittrell, M. S. Feld, “A Multifiber Catheter with an Optical Shield for Laser Angiosurgery,” Lasers Life Sci. 1, 1–12 (1986).

Ference, R. J.

Foschi, A.

A. Foschi, G. Myers, W. F. Crick, H. D. Friedberg, D. Snyder, L. A. Nordstrom, “Laser Angioplasty of Totally Occluded Coronary Arteries and Vein Grafts: Preliminary Report on a Current Trial,” Am. J. Cardiol. 63, 9F–13F (1989).
[PubMed]

Friedberg, H. D.

A. Foschi, G. Myers, W. F. Crick, H. D. Friedberg, D. Snyder, L. A. Nordstrom, “Laser Angioplasty of Totally Occluded Coronary Arteries and Vein Grafts: Preliminary Report on a Current Trial,” Am. J. Cardiol. 63, 9F–13F (1989).
[PubMed]

Gehani, A. A.

S. Ashley, S. G. Brooks, A. A. Gehani, R. C. Kester, M. R. Rees, “Thermal Characteristics of Sapphire Contact Probe Delivery Systems for Laser Angioplasty,” Lasers Surg. Med. 10, 234–244 (1990).
[Crossref] [PubMed]

Geschwind, H. J.

H. J. Geschwind, M. J. Kern, M. G. Vandormael, J. D. Blair, U. Deligonul, H. L. Kennedy, “Efficiency and Safety of Optically Modified Fiber Tips for Laser Angioplasty,” J. Am. Coll. Cardiol. 10, 655–661 (1987).
[Crossref] [PubMed]

Hayes, G. B.

R. M. Cothren, G. B. Hayes, J. R. Kramer, B. Sacks, C. Kittrell, M. S. Feld, “A Multifiber Catheter with an Optical Shield for Laser Angiosurgery,” Lasers Life Sci. 1, 1–12 (1986).

Hecht, E.

E. Hecht, A. Zajak, Optics (Addison-Wesley, Reading, MA, 1979).

Holstege, F. C.

R. M. Verdaasdonk, E. D. Jansen, F. C. Holstege, C. Borst, “Optically Modified Fiber Tips Penetrate Tissue only when ‘Dirty’,” Proc. Soc. Photo-Opt. Instrum. Eng. 1201, 129–136 (1990).

Jacques, S. L.

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light Distributions in Artery Tissue: Monte Carlo Simulations for Finite-Diameter Laser Beams,” Lasers Surg. Med. 9, 148–154 (1989).
[Crossref] [PubMed]

Jansen, E. D.

R. M. Verdaasdonk, E. D. Jansen, F. C. Holstege, C. Borst, “Optically Modified Fiber Tips Penetrate Tissue only when ‘Dirty’,” Proc. Soc. Photo-Opt. Instrum. Eng. 1201, 129–136 (1990).

Karnel, F.

J. Lammer, F. Karnel, “Percutaneous Transluminal Laser Angioplasty with Contact Probes,” Radiology 168, 733–737 (1988).
[PubMed]

Keijzer, M.

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light Distributions in Artery Tissue: Monte Carlo Simulations for Finite-Diameter Laser Beams,” Lasers Surg. Med. 9, 148–154 (1989).
[Crossref] [PubMed]

Kennedy, H. L.

H. J. Geschwind, M. J. Kern, M. G. Vandormael, J. D. Blair, U. Deligonul, H. L. Kennedy, “Efficiency and Safety of Optically Modified Fiber Tips for Laser Angioplasty,” J. Am. Coll. Cardiol. 10, 655–661 (1987).
[Crossref] [PubMed]

Kern, M. J.

H. J. Geschwind, M. J. Kern, M. G. Vandormael, J. D. Blair, U. Deligonul, H. L. Kennedy, “Efficiency and Safety of Optically Modified Fiber Tips for Laser Angioplasty,” J. Am. Coll. Cardiol. 10, 655–661 (1987).
[Crossref] [PubMed]

Kester, R. C.

S. Ashley, S. G. Brooks, A. A. Gehani, R. C. Kester, M. R. Rees, “Thermal Characteristics of Sapphire Contact Probe Delivery Systems for Laser Angioplasty,” Lasers Surg. Med. 10, 234–244 (1990).
[Crossref] [PubMed]

Kittrell, C.

R. M. Cothren, G. B. Hayes, J. R. Kramer, B. Sacks, C. Kittrell, M. S. Feld, “A Multifiber Catheter with an Optical Shield for Laser Angiosurgery,” Lasers Life Sci. 1, 1–12 (1986).

Kramer, J. R.

R. M. Cothren, G. B. Hayes, J. R. Kramer, B. Sacks, C. Kittrell, M. S. Feld, “A Multifiber Catheter with an Optical Shield for Laser Angiosurgery,” Lasers Life Sci. 1, 1–12 (1986).

Lammer, J.

J. Lammer, F. Karnel, “Percutaneous Transluminal Laser Angioplasty with Contact Probes,” Radiology 168, 733–737 (1988).
[PubMed]

Margheri, G.

V. Russo, S. Sottini, G. Margheri, F. Crea, “A Novel Corolla-Irradiating Fiber Optic Probe for Laser Angioplasty,” Proc. Soc. Photo-Opt. Instrum. Eng. 906, 301–304 (1988).

Myers, G.

A. Foschi, G. Myers, W. F. Crick, H. D. Friedberg, D. Snyder, L. A. Nordstrom, “Laser Angioplasty of Totally Occluded Coronary Arteries and Vein Grafts: Preliminary Report on a Current Trial,” Am. J. Cardiol. 63, 9F–13F (1989).
[PubMed]

Nordstrom, L. A.

A. Foschi, G. Myers, W. F. Crick, H. D. Friedberg, D. Snyder, L. A. Nordstrom, “Laser Angioplasty of Totally Occluded Coronary Arteries and Vein Grafts: Preliminary Report on a Current Trial,” Am. J. Cardiol. 63, 9F–13F (1989).
[PubMed]

Prahl, S. A.

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light Distributions in Artery Tissue: Monte Carlo Simulations for Finite-Diameter Laser Beams,” Lasers Surg. Med. 9, 148–154 (1989).
[Crossref] [PubMed]

Preuss, L. E.

Ramee, S. R.

Rees, M. R.

S. Ashley, S. G. Brooks, A. A. Gehani, R. C. Kester, M. R. Rees, “Thermal Characteristics of Sapphire Contact Probe Delivery Systems for Laser Angioplasty,” Lasers Surg. Med. 10, 234–244 (1990).
[Crossref] [PubMed]

Righini, G. C.

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Lens-Ended Fibers for Medical Applications: a New Fabrication Technique,” Appl. Opt. 23, 3277–3283 (1984).
[Crossref] [PubMed]

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Characterization of a Microlens-Ended Optical Fiber,” Alta Freq. 52, 194–197 (1983).

Royston, D.

Russo, V.

V. Russo, S. Sottini, G. Margheri, F. Crea, “A Novel Corolla-Irradiating Fiber Optic Probe for Laser Angioplasty,” Proc. Soc. Photo-Opt. Instrum. Eng. 906, 301–304 (1988).

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Lens-Ended Fibers for Medical Applications: a New Fabrication Technique,” Appl. Opt. 23, 3277–3283 (1984).
[Crossref] [PubMed]

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Characterization of a Microlens-Ended Optical Fiber,” Alta Freq. 52, 194–197 (1983).

Sacks, B.

R. M. Cothren, G. B. Hayes, J. R. Kramer, B. Sacks, C. Kittrell, M. S. Feld, “A Multifiber Catheter with an Optical Shield for Laser Angiosurgery,” Lasers Life Sci. 1, 1–12 (1986).

Siegmund, W.

W. Siegmund, “Fiber Optics,” in Handbook of Optics, W. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978).

Snyder, D.

A. Foschi, G. Myers, W. F. Crick, H. D. Friedberg, D. Snyder, L. A. Nordstrom, “Laser Angioplasty of Totally Occluded Coronary Arteries and Vein Grafts: Preliminary Report on a Current Trial,” Am. J. Cardiol. 63, 9F–13F (1989).
[PubMed]

Sottini, S.

V. Russo, S. Sottini, G. Margheri, F. Crea, “A Novel Corolla-Irradiating Fiber Optic Probe for Laser Angioplasty,” Proc. Soc. Photo-Opt. Instrum. Eng. 906, 301–304 (1988).

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Lens-Ended Fibers for Medical Applications: a New Fabrication Technique,” Appl. Opt. 23, 3277–3283 (1984).
[Crossref] [PubMed]

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Characterization of a Microlens-Ended Optical Fiber,” Alta Freq. 52, 194–197 (1983).

Taylor, R. C.

Trigari, S.

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Lens-Ended Fibers for Medical Applications: a New Fabrication Technique,” Appl. Opt. 23, 3277–3283 (1984).
[Crossref] [PubMed]

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Characterization of a Microlens-Ended Optical Fiber,” Alta Freq. 52, 194–197 (1983).

Vandormael, M. G.

H. J. Geschwind, M. J. Kern, M. G. Vandormael, J. D. Blair, U. Deligonul, H. L. Kennedy, “Efficiency and Safety of Optically Modified Fiber Tips for Laser Angioplasty,” J. Am. Coll. Cardiol. 10, 655–661 (1987).
[Crossref] [PubMed]

Verdaasdonk, R. M.

R. M. Verdaasdonk, C. Borst, “Ray Tracing of Optically Modified Fiber Tips. 2: Laser Scalpels,” Appl. Opt. 30, 2172–2177 (1May1990).
[Crossref]

R. M. Verdaasdonk, E. D. Jansen, F. C. Holstege, C. Borst, “Optically Modified Fiber Tips Penetrate Tissue only when ‘Dirty’,” Proc. Soc. Photo-Opt. Instrum. Eng. 1201, 129–136 (1990).

R. M. Verdaasdonk, F. W. Cross, C. Borst, “Physical Properties of Sapphire Fibre Tips for Laser Angioplasty,” Lasers Med. Sci. 2, 183–188 (1987).
[Crossref]

Vincent, G. M.

D. Decker-Dunn, D. A. Christensen, G. M. Vincent, “Multifiber Gradient-Index Lens Laser Angioplasty Probe,” Lasers Surg. Med. 10, 85–93 (1990).
[Crossref] [PubMed]

Ward, H.

H. Ward, “Molding of Laser Energy by Shaped Optic Fiber Tips,” Lasers Surg. Med. 7, 405–413 (1987).
[Crossref] [PubMed]

Waynant, R.

Welch, A. J.

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light Distributions in Artery Tissue: Monte Carlo Simulations for Finite-Diameter Laser Beams,” Lasers Surg. Med. 9, 148–154 (1989).
[Crossref] [PubMed]

White, C. J.

Zajak, A.

E. Hecht, A. Zajak, Optics (Addison-Wesley, Reading, MA, 1979).

Alta Freq. (1)

V. Russo, G. C. Righini, S. Sottini, S. Trigari, “Characterization of a Microlens-Ended Optical Fiber,” Alta Freq. 52, 194–197 (1983).

Am. J. Cardiol. (1)

A. Foschi, G. Myers, W. F. Crick, H. D. Friedberg, D. Snyder, L. A. Nordstrom, “Laser Angioplasty of Totally Occluded Coronary Arteries and Vein Grafts: Preliminary Report on a Current Trial,” Am. J. Cardiol. 63, 9F–13F (1989).
[PubMed]

Appl. Opt. (4)

J. Am. Coll. Cardiol. (1)

H. J. Geschwind, M. J. Kern, M. G. Vandormael, J. D. Blair, U. Deligonul, H. L. Kennedy, “Efficiency and Safety of Optically Modified Fiber Tips for Laser Angioplasty,” J. Am. Coll. Cardiol. 10, 655–661 (1987).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

Lasers Life Sci. (1)

R. M. Cothren, G. B. Hayes, J. R. Kramer, B. Sacks, C. Kittrell, M. S. Feld, “A Multifiber Catheter with an Optical Shield for Laser Angiosurgery,” Lasers Life Sci. 1, 1–12 (1986).

Lasers Med. Sci. (2)

C. Borst, “Percutaneous Recanalization of Arteries: Status and Prospects of Laser Angioplasty with Modified Fibre Tips,” Lasers Med. Sci. 2, 137–151 (1987).
[Crossref]

R. M. Verdaasdonk, F. W. Cross, C. Borst, “Physical Properties of Sapphire Fibre Tips for Laser Angioplasty,” Lasers Med. Sci. 2, 183–188 (1987).
[Crossref]

Lasers Surg. Med. (4)

D. Decker-Dunn, D. A. Christensen, G. M. Vincent, “Multifiber Gradient-Index Lens Laser Angioplasty Probe,” Lasers Surg. Med. 10, 85–93 (1990).
[Crossref] [PubMed]

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light Distributions in Artery Tissue: Monte Carlo Simulations for Finite-Diameter Laser Beams,” Lasers Surg. Med. 9, 148–154 (1989).
[Crossref] [PubMed]

H. Ward, “Molding of Laser Energy by Shaped Optic Fiber Tips,” Lasers Surg. Med. 7, 405–413 (1987).
[Crossref] [PubMed]

S. Ashley, S. G. Brooks, A. A. Gehani, R. C. Kester, M. R. Rees, “Thermal Characteristics of Sapphire Contact Probe Delivery Systems for Laser Angioplasty,” Lasers Surg. Med. 10, 234–244 (1990).
[Crossref] [PubMed]

Ned. Tijdschr. Geneeskd. (1)

S. N. Berengoltz et al., “Percutane transluminale rekanalisatie van afgesloten bovenbeenarterien met laserstraalbehandeling [Percutaneous Transluminal Laser Angioplasty of Occluded Superficial Femoral Arteries],” Ned. Tijdschr. Geneeskd. 31, 1542–1546 (1989).

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

V. Russo, S. Sottini, G. Margheri, F. Crea, “A Novel Corolla-Irradiating Fiber Optic Probe for Laser Angioplasty,” Proc. Soc. Photo-Opt. Instrum. Eng. 906, 301–304 (1988).

R. M. Verdaasdonk, E. D. Jansen, F. C. Holstege, C. Borst, “Optically Modified Fiber Tips Penetrate Tissue only when ‘Dirty’,” Proc. Soc. Photo-Opt. Instrum. Eng. 1201, 129–136 (1990).

Radiology (1)

J. Lammer, F. Karnel, “Percutaneous Transluminal Laser Angioplasty with Contact Probes,” Radiology 168, 733–737 (1988).
[PubMed]

Other (2)

E. Hecht, A. Zajak, Optics (Addison-Wesley, Reading, MA, 1979).

W. Siegmund, “Fiber Optics,” in Handbook of Optics, W. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978).

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Figures (14)

Fig. 1
Fig. 1

(A) In the ray tracing program the rays start at fifty equally spaced steps dX positioned along the fiber surface. At each step seventeen rays are emitted equally distributed over an angle of 10°. A relative irradiance factor is ascribed to a ray depending on the starting angle with the optical axis to obtain a Gaussian irradiance distribution in the far field. (B) Calculated beam shape from the bare fiber with the irradiance distributions at Rf, 8*Rf, and 16*Rf. The bars denote the radius of the fiber Rf.

Fig. 2
Fig. 2

Top: the geometry of the spherical fiber tips is determined by the radius Rs of the sphere and radius Rf of the fiber. The fiber tip was assumed to end at R s + R s ( R s is the radius of the sphere minus the part that is embedded in the fiber) proximal to the front surface of the sphere with refractive index n2 (environment n1). Considering paraxial optics a proximal and distal focal point F1 and F2 can be situated. Bottom: the geometry of hemispherical fiber tips can be converted to the geometry of spherical fiber tips by translating the fiber tip to a distance of R s + R s proximal to the hemispherical surface and taking Rf as the actual fiber radius.

Fig. 3
Fig. 3

Top: example of beam profile produced with ray tracing program. Bottom: corresponding isoirradiance graph calculated using twenty equally spaced irradiance planes in front of the probe.

Fig. 4
Fig. 4

(A) From left to right: 600-μm bare fiber, homemade ball-shaped fibers 0.95, 1.05, 1.4, and 1.7 mm in diameter and a 1.5-mm ball-shaped fiber (Advanced Cardiovascular Systems). (B) Hemispherical contact probes: 3.0, 2.2, and 1.8 mm in diameter (Surgical Laser Technologies).

Fig. 5
Fig. 5

Calculated (solid line) and measured (broken line) irradiance distributions of a 0.6-mm bare fiber: Top: Uniform distribution at distance Z = Rf in front of the fiber tip (near field). Middle: top hat distribution at Z = 8*Rf distal from the tip. Bottom: Gaussian distribution at Z = 16*Rf distal from the tip (far field). The horizontal axis is in millimeters; the vertical axis shows the irradiance in arbitrary units.

Fig. 6
Fig. 6

Beam profiles of ball-shaped fiber tips photographed in air and water and their corresponding profiles calculated by ray tracing. From left to right: probe shape, calculated beam in air, observed beam in air, calculated beam in water, observed beam in water. From top to bottom: 600-μm fiber, 0.95-mm ball tip, 1.5-mm ACS ball. In air the spherical probes have focusing properties which are almost absent in water. The bars denote 1 mm.

Fig. 7
Fig. 7

Beam profiles of hemispherical probes. For legend, see Fig. 6. From top to bottom: 2.2-mm silica Surgical Laser Technologies, 2.2-mm sapphire LaserSonics, 1.5-mm sapphire Pilking-ton. The focusing properties of the hemispherical sapphire probes in air are still present in water. The bars denote 1 mm.

Fig. 8
Fig. 8

Calculated percentage transmission through silica (solid lines) and sapphire (broken lines) spherical probes in relation to the sphere/fiber radius ratio in air and in water. Measurements are indicated with dots. [○,● = water; △,▲ = air; ●,▲ = ball-shaped fibers; ○,△ = hemispherical probes.] The figures are presented compared to the transmission of a bare fiber. Note that at small ratios the transmission drops due to internal reflections.

Fig. 9
Fig. 9

Isoirradiance graphs of various tips in air. The upper section of each panel shows the measured irradiance distribution. The lower section shows the calculated irradiance distribution. Upper left panel: 600-μm bare fiber; upper right panel: 1.0-mm ball-shaped fiber; lower left panel: 1.5-mm ball-shaped fiber ACS; lower right panel: 2.2-mm hemispherical contact probe. Abscissa: distance along the optical axis starting at the surface of the probe (millimeters). Ordinate: distance from the optical axis (millimeters). Note the different scaling of the abscissa.

Fig. 10
Fig. 10

Position of the highest irradiance in relation to the sphere/fiber radius ratio determined from isoirradiance graphs for silica (top) and sapphire (bottom) spherical tips in air and water (broken lines) compared with the position of the focal point calculated with paraxial theory (solid lines). The distance from the tip along the optical axis Z was normalized to the radius of the fiber Rf.

Fig. 11
Fig. 11

(A) Maximum increase in irradiance normalized to the irradiance at the bare fiber tip calculated for 2-D cross sections at the level of the highest power density. The broken lines indicate the results if there were no losses due to internal reflections. The solid curves show that there is an optimum ratio of sphere/fiber radius for a maximum irradiance increase. (B) Maximum power density increase normalized to the power density at the bare fiber tip for a 3-D situation using the cross-sectional area of the calculated waist of the beam (e−2 level) and taking internal reflections into account. Small waist diameters resulted in increased scatter of the data points due to the limited spatial resolution of the ray tracing program.

Fig. 12
Fig. 12

The 2.2-mm hemispherical probes. Left: coated silica probe (Surgical Laser Technologies). Right: gleaming polished sapphire probe (LaserSonics).

Fig. 13
Fig. 13

Discrepancy between paraxial theory and ray tracing in predicting the behavior of beams propagating from fibers. In air, both the paraxial beam (A) and the fiber beam (B) are focused at Fa. In water, on the other hand, the paraxial beam is still focused at Fw (C), but the fiber beam diverges (D). Consequently, the position of the highest local irradiance Imax does not coincide with the focal point F w .

Fig. 14
Fig. 14

Condition for a parallel beam profile. Rays starting at the rim of the fiber with radius Rf at the largest divergence angle (0.5α) refract at the probe surface parallel to the optical axis. The distance between the fictional focal point F2 and the front surface of the probe is equal to twice the radius of the sphere Rs minus the part of the sphere that is embodied in the fiber end ( R s + R s ) plus the distance Df the focal point lays in the fiber.

Tables (2)

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Table I Calculated and Measured Characteristics of Probes In Relation to Rf

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Table II Characteristics of Spherical Fiber Tips Calculated with Fresnel Reflection Theory and Paraxial Optical Theory9

Equations (9)

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F 1 = R s n 1 / ( n 2 - n 1 ) ,
F 2 = R s n 2 / ( n 2 - n 1 ) ,
R s / R f = [ T ( N - 1 ) + sqrt [ T 2 - N ( N - 2 ) ] ] / [ N ( N - 2 ) ] ,
E ( r ) = E 0 · exp ( - 2 r 2 / w 2 ) ,
WF ( β ) = exp ( - 2 β 2 / A 2 ) ,
F 2 = R s + R s + D f ,
F 2 = R s + ( R s 2 - R f 2 ) 0.5 + R f / tan ( 0.5 α ) .
R s + ( R s 2 - R f 2 ) 0.5 + R f / tan ( 0.5 α ) = R s n 2 / ( n 2 - n 1 ) .
R s / R f = [ T ( N - 1 ) + sqrt [ T 2 - N ( N - 2 ) ] ] / [ N ( N - 2 ) ] ,

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