Abstract

An ABCD beam-propagation method was used to build a first-order mathematical model of a thermal lens effect from a near-infrared laser beam in water and ocular media. The model was found to fit experimental z-scan data best when the thermo-optic coefficient dndT of liquid water at 292K was 4.46×105K1. The physiological parameters of the human eye were simulated in a simple eye model using this fitted dndT value. Conservative model simulations for 1150 and 1318nm laser radiation include parameter sets used in experimental ocular exposures performed by Zuclich et al. [Health Phys. 92, 15 (2007)] to illustrate the transient response of the thermal lens approaching the limits of the retinal damage thresholds for equivalent laser radiation sources.

© 2009 Optical Society of America

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Errata

Rebecca L. Vincelette, Robert J. Thomas, Benjamin A. Rockwell, Clifton D. Clark, III, and Ashley J. Welch, "First-order model of thermal lensing in a virtual eye: errata," J. Opt. Soc. Am. A 27, 1202-1202 (2010)
https://www.osapublishing.org/josaa/abstract.cfm?uri=josaa-27-5-1202

References

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    [CrossRef] [PubMed]
  2. C. D. Clark, L. J. Irvin, P. D. S. Maseberg, G. D. Buffington, R. J. Thomas, M. L. Edwards, and J. Stolarski, “BTEC Thermal Model,” Report AFRL-RH-BR-TR-2008-0006 (Air Force Research Laboratory, San Antonio, 2008).
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    [CrossRef]
  4. D. J. Lund, P. Edsall, and B. E. Stuck, “Spectral dependence of retinal thermal injury,” Proc. SPIE 3902, 22-34 (2000).
    [CrossRef]
  5. D. J. Lund and P. Edsall, “Action spectrum for retinal thermal injury,” Proc. SPIE 3591, 324-334 (1999).
    [CrossRef]
  6. J. P. Gordon, R. C. Leite, R. S. Moore, S. P. Porto, and J. R. Whinnery, “Long transient effects of lasers with inserted liquid samples,” J. Appl. Phys. 36, 3-8 (1965).
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    [CrossRef]
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  21. R. J. Thomas, R. L. Vincelette, C. D. Clark, III, J. Stolarski, L. J. Irvin, and G. D. Buffington, “Propagation effects in the assessment of laser damage thresholds to the eye and skin,” Proc. SPIE 6435, A1-12 (2007).
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  27. R. L. Swofford and J. Morrell, “Analysis of the repetitively pulsed dual-beam thermo-optical absorption spectrometer,” J. Appl. Phys. 49, 3667-3674 (1978).
    [CrossRef]
  28. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
    [CrossRef]
  29. D. A. Atchison and G. Smith, Optics of the Human Eye (Elsevier, 2002).
  30. G. Li, H. Zwick, B. Stuck, and D. J. Lund, “On the use of schematic eye models to estimate retinal image quality,” J. Biomed. Opt. 5, 307-314 (2000).
    [CrossRef] [PubMed]
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  32. E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, and P. Artal, “Ocular aberrations as a function of wavelength in the near infrared measured with a femtosecond laser,” Opt. Express 13, 400-409 (2005).
    [CrossRef] [PubMed]
  33. T. Okuno, M. Kojima, I. Hata, and D. H. Sliney, “Temperature rises in the crystalline lens from focal irradiation,” Health Phys. 88, 214-222 (2005).
    [CrossRef] [PubMed]
  34. J. A. Zuclich, D. J. Lund, B. E. Stuck, and P. R. Edsall, “Ocular effects and safety standard implications for high-power lasers in the 1.3-1.4 μm wavelength range,” (Air Force Research Laboratory, Laser Radiation Branch, San Antonio, Texas, 2004).
  35. M. Motamedi, A. J. Welch, W. F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biological medium,” IEEE J. Quantum Electron. 24, 693-696 (1988).
    [CrossRef]
  36. C. E. Buffett and M. D. Morris, “Convective effects in thermal lens spectroscopy,” Appl. Spectrosc. 37, 455-458 (1983).
    [CrossRef]
  37. E. F. S. Alfonso, M. A. R. Revert, M. C. G. Alvarez-Coque, and G. R. Ramos, “Reduction of convective low-frequency noise in thermal lens spectrometry,” Appl. Spectrosc. 44, 1501-1507 (1990).
    [CrossRef]
  38. P. Artal, A. Benito, and J. Tabernero, “The human eye is an example of robust optical design,” J. Vision 6, 1-7 (2006).
    [CrossRef]
  39. J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLS to correct spherical aberration,” Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
    [CrossRef]
  40. E. J. Fernandez, A. Unterhuber, B. Povazay, B. Hermann, P. Artal, and W. Drexler, “Chromatic aberration correction of the human eye for retinal imaging in the near infrared,” Opt. Express 14, 6213-6225 (2006).
    [CrossRef] [PubMed]

2008

R. L. Vincelette, B. A. Rockwell, R. J. Thomas, D. J. Lund, and A. J. Welch, “Thermal lensing in ocular media exposed to continuous-wave near-infrared radiation: 1150-1350 nm region,” J. Biomed. Opt. 13, 054005 (2008).
[CrossRef] [PubMed]

2007

J. A. Zuclich, D. J. Lund, and B. E. Stuck, “Wavelength dependence of ocular damage thresholds in the near-IR to far-IR transition region: Proposed revisions to MPEs,” Health Phys. 92, 15-23 (2007).
[CrossRef]

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “Thermal lensing in the ocular media,” Proc. SPIE 6435, 0C1-7 (2007).

R. J. Thomas, R. L. Vincelette, C. D. Clark, III, J. Stolarski, L. J. Irvin, and G. D. Buffington, “Propagation effects in the assessment of laser damage thresholds to the eye and skin,” Proc. SPIE 6435, A1-12 (2007).

2006

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “A comparison of a first-order thermal lensing model to a closed aperture Z-scan for the propagation of light in ocular media,” Proc. SPIE 6084, 0G1-0G9 (2006).

P. Artal, A. Benito, and J. Tabernero, “The human eye is an example of robust optical design,” J. Vision 6, 1-7 (2006).
[CrossRef]

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLS to correct spherical aberration,” Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

E. J. Fernandez, A. Unterhuber, B. Povazay, B. Hermann, P. Artal, and W. Drexler, “Chromatic aberration correction of the human eye for retinal imaging in the near infrared,” Opt. Express 14, 6213-6225 (2006).
[CrossRef] [PubMed]

2005

2000

G. Li, H. Zwick, B. Stuck, and D. J. Lund, “On the use of schematic eye models to estimate retinal image quality,” J. Biomed. Opt. 5, 307-314 (2000).
[CrossRef] [PubMed]

D. J. Lund, P. Edsall, and B. E. Stuck, “Spectral dependence of retinal thermal injury,” Proc. SPIE 3902, 22-34 (2000).
[CrossRef]

1999

1998

A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761-774 (1998).
[CrossRef]

1996

M. Franko and C. D. Tran, “Analytical thermal lens instrumentation,” Rev. Sci. Instrum. 67, 1-18 (1996).
[CrossRef]

1993

1992

1991

1990

E. F. S. Alfonso, M. A. R. Revert, M. C. G. Alvarez-Coque, and G. R. Ramos, “Reduction of convective low-frequency noise in thermal lens spectrometry,” Appl. Spectrosc. 44, 1501-1507 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

1988

M. Motamedi, A. J. Welch, W. F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biological medium,” IEEE J. Quantum Electron. 24, 693-696 (1988).
[CrossRef]

1983

1979

H. L. Fang and R. Swofford, “Analysis of the thermal lensing effect for an optically thick sample-A revised model,” J. Appl. Phys. 50, 6609-6615 (1979).
[CrossRef]

1978

R. L. Swofford and J. Morrell, “Analysis of the repetitively pulsed dual-beam thermo-optical absorption spectrometer,” J. Appl. Phys. 49, 3667-3674 (1978).
[CrossRef]

1973

1965

J. P. Gordon, R. C. Leite, R. S. Moore, S. P. Porto, and J. R. Whinnery, “Long transient effects of lasers with inserted liquid samples,” J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

Alda, J.

Alfonso, E. F. S.

Alvarez-Coque, M. C. G.

Artal, P.

E. J. Fernandez, A. Unterhuber, B. Povazay, B. Hermann, P. Artal, and W. Drexler, “Chromatic aberration correction of the human eye for retinal imaging in the near infrared,” Opt. Express 14, 6213-6225 (2006).
[CrossRef] [PubMed]

P. Artal, A. Benito, and J. Tabernero, “The human eye is an example of robust optical design,” J. Vision 6, 1-7 (2006).
[CrossRef]

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLS to correct spherical aberration,” Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, and P. Artal, “Ocular aberrations as a function of wavelength in the near infrared measured with a femtosecond laser,” Opt. Express 13, 400-409 (2005).
[CrossRef] [PubMed]

Atchison, D. A.

D. A. Atchison and G. Smith, Optics of the Human Eye (Elsevier, 2002).

Beck, J. V.

J. V. Beck, K. D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat Conduction Using Green's Functions (Hemisphere Publishing Corp., 1992), pp. 201-216.

Belanger, P. A.

Benito, A.

P. Artal, A. Benito, and J. Tabernero, “The human eye is an example of robust optical design,” J. Vision 6, 1-7 (2006).
[CrossRef]

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLS to correct spherical aberration,” Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

Bernabeu, E.

Blackburn, D. H.

Buffett, C. E.

Buffington, G. D.

R. J. Thomas, R. L. Vincelette, C. D. Clark, III, J. Stolarski, L. J. Irvin, and G. D. Buffington, “Propagation effects in the assessment of laser damage thresholds to the eye and skin,” Proc. SPIE 6435, A1-12 (2007).

R. J. Thomas, R. L. Vincelette, G. D. Buffington, A. D. Strunk, M. A. Edwards, B. A. Rockwell, and A. J. Welch, “A first order model of thermal lensing of laser propagation in the eye and implications for laser safety,” in International Laser Safety Conference (Laser Institute of America, 2005), 147-154.

C. D. Clark, L. J. Irvin, P. D. S. Maseberg, G. D. Buffington, R. J. Thomas, M. L. Edwards, and J. Stolarski, “BTEC Thermal Model,” Report AFRL-RH-BR-TR-2008-0006 (Air Force Research Laboratory, San Antonio, 2008).

Cheong, W. F.

M. Motamedi, A. J. Welch, W. F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biological medium,” IEEE J. Quantum Electron. 24, 693-696 (1988).
[CrossRef]

Clark, C. D.

R. J. Thomas, R. L. Vincelette, C. D. Clark, III, J. Stolarski, L. J. Irvin, and G. D. Buffington, “Propagation effects in the assessment of laser damage thresholds to the eye and skin,” Proc. SPIE 6435, A1-12 (2007).

C. D. Clark, L. J. Irvin, P. D. S. Maseberg, G. D. Buffington, R. J. Thomas, M. L. Edwards, and J. Stolarski, “BTEC Thermal Model,” Report AFRL-RH-BR-TR-2008-0006 (Air Force Research Laboratory, San Antonio, 2008).

Cole, K. D.

J. V. Beck, K. D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat Conduction Using Green's Functions (Hemisphere Publishing Corp., 1992), pp. 201-216.

Cranmer, D. C.

Drexler, W.

Edsall, P.

D. J. Lund, P. Edsall, and B. E. Stuck, “Spectral dependence of retinal thermal injury,” Proc. SPIE 3902, 22-34 (2000).
[CrossRef]

D. J. Lund and P. Edsall, “Action spectrum for retinal thermal injury,” Proc. SPIE 3591, 324-334 (1999).
[CrossRef]

Edsall, P. R.

J. A. Zuclich, D. J. Lund, B. E. Stuck, and P. R. Edsall, “Ocular effects and safety standard implications for high-power lasers in the 1.3-1.4 μm wavelength range,” (Air Force Research Laboratory, Laser Radiation Branch, San Antonio, Texas, 2004).

Edwards, M. A.

R. J. Thomas, R. L. Vincelette, G. D. Buffington, A. D. Strunk, M. A. Edwards, B. A. Rockwell, and A. J. Welch, “A first order model of thermal lensing of laser propagation in the eye and implications for laser safety,” in International Laser Safety Conference (Laser Institute of America, 2005), 147-154.

Edwards, M. L.

C. D. Clark, L. J. Irvin, P. D. S. Maseberg, G. D. Buffington, R. J. Thomas, M. L. Edwards, and J. Stolarski, “BTEC Thermal Model,” Report AFRL-RH-BR-TR-2008-0006 (Air Force Research Laboratory, San Antonio, 2008).

Fang, H. L.

H. L. Fang and R. Swofford, “Analysis of the thermal lensing effect for an optically thick sample-A revised model,” J. Appl. Phys. 50, 6609-6615 (1979).
[CrossRef]

Fernandez, E. J.

Fernández, E. J.

Franko, M.

M. Franko and C. D. Tran, “Analytical thermal lens instrumentation,” Rev. Sci. Instrum. 67, 1-18 (1996).
[CrossRef]

Gallagher, J. S.

A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761-774 (1998).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

Ghaffari, S. A.

M. Motamedi, A. J. Welch, W. F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biological medium,” IEEE J. Quantum Electron. 24, 693-696 (1988).
[CrossRef]

Gordon, J. P.

J. P. Gordon, R. C. Leite, R. S. Moore, S. P. Porto, and J. R. Whinnery, “Long transient effects of lasers with inserted liquid samples,” J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

Hagan, D. J.

Haji-Sheikh, A.

J. V. Beck, K. D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat Conduction Using Green's Functions (Hemisphere Publishing Corp., 1992), pp. 201-216.

Hale, G. M.

Harvey, A. H.

A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761-774 (1998).
[CrossRef]

Hata, I.

T. Okuno, M. Kojima, I. Hata, and D. H. Sliney, “Temperature rises in the crystalline lens from focal irradiation,” Health Phys. 88, 214-222 (2005).
[CrossRef] [PubMed]

Hermann, B.

Irvin, L. J.

R. J. Thomas, R. L. Vincelette, C. D. Clark, III, J. Stolarski, L. J. Irvin, and G. D. Buffington, “Propagation effects in the assessment of laser damage thresholds to the eye and skin,” Proc. SPIE 6435, A1-12 (2007).

C. D. Clark, L. J. Irvin, P. D. S. Maseberg, G. D. Buffington, R. J. Thomas, M. L. Edwards, and J. Stolarski, “BTEC Thermal Model,” Report AFRL-RH-BR-TR-2008-0006 (Air Force Research Laboratory, San Antonio, 2008).

Kojima, M.

T. Okuno, M. Kojima, I. Hata, and D. H. Sliney, “Temperature rises in the crystalline lens from focal irradiation,” Health Phys. 88, 214-222 (2005).
[CrossRef] [PubMed]

Kovsh, D.

Kovsh, D. I.

Kruse, A.

W. Wagner and A. Kruse, Properties of Water and Steam: The Industrial Standard IAPWS-IF97 for the Thermodynamic Properties and Supplementary Equations for Other Properties (Springer-Verlag, 1998), p. 150.

Leite, R. C.

J. P. Gordon, R. C. Leite, R. S. Moore, S. P. Porto, and J. R. Whinnery, “Long transient effects of lasers with inserted liquid samples,” J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

Levelt Sengers, J. M. H.

A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761-774 (1998).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

Li, G.

G. Li, H. Zwick, B. Stuck, and D. J. Lund, “On the use of schematic eye models to estimate retinal image quality,” J. Biomed. Opt. 5, 307-314 (2000).
[CrossRef] [PubMed]

Lin, W. C.

W. C. Lin, “Dynamics of tissue optics during laser heating,” Ph.D. dissertation (University of Texas, Austin, Texas, 1997).

Litkouhi, B.

J. V. Beck, K. D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat Conduction Using Green's Functions (Hemisphere Publishing Corp., 1992), pp. 201-216.

Lund, D. J.

R. L. Vincelette, B. A. Rockwell, R. J. Thomas, D. J. Lund, and A. J. Welch, “Thermal lensing in ocular media exposed to continuous-wave near-infrared radiation: 1150-1350 nm region,” J. Biomed. Opt. 13, 054005 (2008).
[CrossRef] [PubMed]

J. A. Zuclich, D. J. Lund, and B. E. Stuck, “Wavelength dependence of ocular damage thresholds in the near-IR to far-IR transition region: Proposed revisions to MPEs,” Health Phys. 92, 15-23 (2007).
[CrossRef]

D. J. Lund, P. Edsall, and B. E. Stuck, “Spectral dependence of retinal thermal injury,” Proc. SPIE 3902, 22-34 (2000).
[CrossRef]

G. Li, H. Zwick, B. Stuck, and D. J. Lund, “On the use of schematic eye models to estimate retinal image quality,” J. Biomed. Opt. 5, 307-314 (2000).
[CrossRef] [PubMed]

D. J. Lund and P. Edsall, “Action spectrum for retinal thermal injury,” Proc. SPIE 3591, 324-334 (1999).
[CrossRef]

J. A. Zuclich, D. J. Lund, B. E. Stuck, and P. R. Edsall, “Ocular effects and safety standard implications for high-power lasers in the 1.3-1.4 μm wavelength range,” (Air Force Research Laboratory, Laser Radiation Branch, San Antonio, Texas, 2004).

Maher, E. F.

E. F. Maher, “Transmission and absorption coefficients for the ocular media of the Rhesus monkey,” Tech. Rep. SAM-TR-78-32 (USAF School of Aerospace Medicine, 1978).

Maseberg, P. D. S.

C. D. Clark, L. J. Irvin, P. D. S. Maseberg, G. D. Buffington, R. J. Thomas, M. L. Edwards, and J. Stolarski, “BTEC Thermal Model,” Report AFRL-RH-BR-TR-2008-0006 (Air Force Research Laboratory, San Antonio, 2008).

Moore, R. S.

J. P. Gordon, R. C. Leite, R. S. Moore, S. P. Porto, and J. R. Whinnery, “Long transient effects of lasers with inserted liquid samples,” J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

Morrell, J.

R. L. Swofford and J. Morrell, “Analysis of the repetitively pulsed dual-beam thermo-optical absorption spectrometer,” J. Appl. Phys. 49, 3667-3674 (1978).
[CrossRef]

Morris, M. D.

Motamedi, M.

M. Motamedi, A. J. Welch, W. F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biological medium,” IEEE J. Quantum Electron. 24, 693-696 (1988).
[CrossRef]

Okuno, T.

T. Okuno, M. Kojima, I. Hata, and D. H. Sliney, “Temperature rises in the crystalline lens from focal irradiation,” Health Phys. 88, 214-222 (2005).
[CrossRef] [PubMed]

Piers, P.

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLS to correct spherical aberration,” Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

Porras, M. A.

Porto, S. P.

J. P. Gordon, R. C. Leite, R. S. Moore, S. P. Porto, and J. R. Whinnery, “Long transient effects of lasers with inserted liquid samples,” J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

Povazay, B.

Powell, R. C.

Prieto, P. M.

Querry, M. R.

Ramos, G. R.

Redondo, M.

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLS to correct spherical aberration,” Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

Revert, M. A. R.

Rockwell, B. A.

R. L. Vincelette, B. A. Rockwell, R. J. Thomas, D. J. Lund, and A. J. Welch, “Thermal lensing in ocular media exposed to continuous-wave near-infrared radiation: 1150-1350 nm region,” J. Biomed. Opt. 13, 054005 (2008).
[CrossRef] [PubMed]

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “Thermal lensing in the ocular media,” Proc. SPIE 6435, 0C1-7 (2007).

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “A comparison of a first-order thermal lensing model to a closed aperture Z-scan for the propagation of light in ocular media,” Proc. SPIE 6084, 0G1-0G9 (2006).

R. J. Thomas, R. L. Vincelette, G. D. Buffington, A. D. Strunk, M. A. Edwards, B. A. Rockwell, and A. J. Welch, “A first order model of thermal lensing of laser propagation in the eye and implications for laser safety,” in International Laser Safety Conference (Laser Institute of America, 2005), 147-154.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Schiebener, P.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Sliney, D. H.

T. Okuno, M. Kojima, I. Hata, and D. H. Sliney, “Temperature rises in the crystalline lens from focal irradiation,” Health Phys. 88, 214-222 (2005).
[CrossRef] [PubMed]

Smith, G.

D. A. Atchison and G. Smith, Optics of the Human Eye (Elsevier, 2002).

St. John, W. D

Stolarski, J.

R. J. Thomas, R. L. Vincelette, C. D. Clark, III, J. Stolarski, L. J. Irvin, and G. D. Buffington, “Propagation effects in the assessment of laser damage thresholds to the eye and skin,” Proc. SPIE 6435, A1-12 (2007).

C. D. Clark, L. J. Irvin, P. D. S. Maseberg, G. D. Buffington, R. J. Thomas, M. L. Edwards, and J. Stolarski, “BTEC Thermal Model,” Report AFRL-RH-BR-TR-2008-0006 (Air Force Research Laboratory, San Antonio, 2008).

Straub, J.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

Strunk, A. D.

R. J. Thomas, R. L. Vincelette, G. D. Buffington, A. D. Strunk, M. A. Edwards, B. A. Rockwell, and A. J. Welch, “A first order model of thermal lensing of laser propagation in the eye and implications for laser safety,” in International Laser Safety Conference (Laser Institute of America, 2005), 147-154.

Stuck, B.

G. Li, H. Zwick, B. Stuck, and D. J. Lund, “On the use of schematic eye models to estimate retinal image quality,” J. Biomed. Opt. 5, 307-314 (2000).
[CrossRef] [PubMed]

Stuck, B. E.

J. A. Zuclich, D. J. Lund, and B. E. Stuck, “Wavelength dependence of ocular damage thresholds in the near-IR to far-IR transition region: Proposed revisions to MPEs,” Health Phys. 92, 15-23 (2007).
[CrossRef]

D. J. Lund, P. Edsall, and B. E. Stuck, “Spectral dependence of retinal thermal injury,” Proc. SPIE 3902, 22-34 (2000).
[CrossRef]

J. A. Zuclich, D. J. Lund, B. E. Stuck, and P. R. Edsall, “Ocular effects and safety standard implications for high-power lasers in the 1.3-1.4 μm wavelength range,” (Air Force Research Laboratory, Laser Radiation Branch, San Antonio, Texas, 2004).

Swofford, R.

H. L. Fang and R. Swofford, “Analysis of the thermal lensing effect for an optically thick sample-A revised model,” J. Appl. Phys. 50, 6609-6615 (1979).
[CrossRef]

Swofford, R. L.

R. L. Swofford and J. Morrell, “Analysis of the repetitively pulsed dual-beam thermo-optical absorption spectrometer,” J. Appl. Phys. 49, 3667-3674 (1978).
[CrossRef]

Tabernero, J.

P. Artal, A. Benito, and J. Tabernero, “The human eye is an example of robust optical design,” J. Vision 6, 1-7 (2006).
[CrossRef]

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLS to correct spherical aberration,” Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

Taheri, B.

Tan, O. T.

M. Motamedi, A. J. Welch, W. F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biological medium,” IEEE J. Quantum Electron. 24, 693-696 (1988).
[CrossRef]

Thomas, R. J.

R. L. Vincelette, B. A. Rockwell, R. J. Thomas, D. J. Lund, and A. J. Welch, “Thermal lensing in ocular media exposed to continuous-wave near-infrared radiation: 1150-1350 nm region,” J. Biomed. Opt. 13, 054005 (2008).
[CrossRef] [PubMed]

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “Thermal lensing in the ocular media,” Proc. SPIE 6435, 0C1-7 (2007).

R. J. Thomas, R. L. Vincelette, C. D. Clark, III, J. Stolarski, L. J. Irvin, and G. D. Buffington, “Propagation effects in the assessment of laser damage thresholds to the eye and skin,” Proc. SPIE 6435, A1-12 (2007).

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “A comparison of a first-order thermal lensing model to a closed aperture Z-scan for the propagation of light in ocular media,” Proc. SPIE 6084, 0G1-0G9 (2006).

C. D. Clark, L. J. Irvin, P. D. S. Maseberg, G. D. Buffington, R. J. Thomas, M. L. Edwards, and J. Stolarski, “BTEC Thermal Model,” Report AFRL-RH-BR-TR-2008-0006 (Air Force Research Laboratory, San Antonio, 2008).

R. J. Thomas, R. L. Vincelette, G. D. Buffington, A. D. Strunk, M. A. Edwards, B. A. Rockwell, and A. J. Welch, “A first order model of thermal lensing of laser propagation in the eye and implications for laser safety,” in International Laser Safety Conference (Laser Institute of America, 2005), 147-154.

Tran, C. D.

M. Franko and C. D. Tran, “Analytical thermal lens instrumentation,” Rev. Sci. Instrum. 67, 1-18 (1996).
[CrossRef]

Unterhuber, A.

Van Stryland, E. W.

Vincelette, R. L.

R. L. Vincelette, B. A. Rockwell, R. J. Thomas, D. J. Lund, and A. J. Welch, “Thermal lensing in ocular media exposed to continuous-wave near-infrared radiation: 1150-1350 nm region,” J. Biomed. Opt. 13, 054005 (2008).
[CrossRef] [PubMed]

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “Thermal lensing in the ocular media,” Proc. SPIE 6435, 0C1-7 (2007).

R. J. Thomas, R. L. Vincelette, C. D. Clark, III, J. Stolarski, L. J. Irvin, and G. D. Buffington, “Propagation effects in the assessment of laser damage thresholds to the eye and skin,” Proc. SPIE 6435, A1-12 (2007).

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “A comparison of a first-order thermal lensing model to a closed aperture Z-scan for the propagation of light in ocular media,” Proc. SPIE 6084, 0G1-0G9 (2006).

R. J. Thomas, R. L. Vincelette, G. D. Buffington, A. D. Strunk, M. A. Edwards, B. A. Rockwell, and A. J. Welch, “A first order model of thermal lensing of laser propagation in the eye and implications for laser safety,” in International Laser Safety Conference (Laser Institute of America, 2005), 147-154.

Wagner, W.

W. Wagner and A. Kruse, Properties of Water and Steam: The Industrial Standard IAPWS-IF97 for the Thermodynamic Properties and Supplementary Equations for Other Properties (Springer-Verlag, 1998), p. 150.

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Welch, A. J.

R. L. Vincelette, B. A. Rockwell, R. J. Thomas, D. J. Lund, and A. J. Welch, “Thermal lensing in ocular media exposed to continuous-wave near-infrared radiation: 1150-1350 nm region,” J. Biomed. Opt. 13, 054005 (2008).
[CrossRef] [PubMed]

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “Thermal lensing in the ocular media,” Proc. SPIE 6435, 0C1-7 (2007).

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “A comparison of a first-order thermal lensing model to a closed aperture Z-scan for the propagation of light in ocular media,” Proc. SPIE 6084, 0G1-0G9 (2006).

M. Motamedi, A. J. Welch, W. F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biological medium,” IEEE J. Quantum Electron. 24, 693-696 (1988).
[CrossRef]

R. J. Thomas, R. L. Vincelette, G. D. Buffington, A. D. Strunk, M. A. Edwards, B. A. Rockwell, and A. J. Welch, “A first order model of thermal lensing of laser propagation in the eye and implications for laser safety,” in International Laser Safety Conference (Laser Institute of America, 2005), 147-154.

Westheimer, G.

G. Westheimer, “The Eye: Including Central Nervous System Control of Eye Movements,” in Medical Physiology, Vol. 1, V.B.Mountcastle, ed., 14th ed. (C. V. Mosby Company, 1980), pp. 482-503.

Whinnery, J. R.

J. P. Gordon, R. C. Leite, R. S. Moore, S. P. Porto, and J. R. Whinnery, “Long transient effects of lasers with inserted liquid samples,” J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

Wicksted, J. P.

Wyld, H. A.

H. A. Wyld, Mathematical Methods for Physics (W. A. Benjamin, 1976), pp. 319-326.

Yang, S.

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989), pp. 106-123.

Zuclich, J. A.

J. A. Zuclich, D. J. Lund, and B. E. Stuck, “Wavelength dependence of ocular damage thresholds in the near-IR to far-IR transition region: Proposed revisions to MPEs,” Health Phys. 92, 15-23 (2007).
[CrossRef]

J. A. Zuclich, D. J. Lund, B. E. Stuck, and P. R. Edsall, “Ocular effects and safety standard implications for high-power lasers in the 1.3-1.4 μm wavelength range,” (Air Force Research Laboratory, Laser Radiation Branch, San Antonio, Texas, 2004).

Zwick, H.

G. Li, H. Zwick, B. Stuck, and D. J. Lund, “On the use of schematic eye models to estimate retinal image quality,” J. Biomed. Opt. 5, 307-314 (2000).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Spectrosc.

Health Phys.

T. Okuno, M. Kojima, I. Hata, and D. H. Sliney, “Temperature rises in the crystalline lens from focal irradiation,” Health Phys. 88, 214-222 (2005).
[CrossRef] [PubMed]

J. A. Zuclich, D. J. Lund, and B. E. Stuck, “Wavelength dependence of ocular damage thresholds in the near-IR to far-IR transition region: Proposed revisions to MPEs,” Health Phys. 92, 15-23 (2007).
[CrossRef]

IEEE J. Quantum Electron.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

M. Motamedi, A. J. Welch, W. F. Cheong, S. A. Ghaffari, and O. T. Tan, “Thermal lensing in biological medium,” IEEE J. Quantum Electron. 24, 693-696 (1988).
[CrossRef]

Invest. Ophthalmol. Visual Sci.

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLS to correct spherical aberration,” Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

J. Appl. Phys.

R. L. Swofford and J. Morrell, “Analysis of the repetitively pulsed dual-beam thermo-optical absorption spectrometer,” J. Appl. Phys. 49, 3667-3674 (1978).
[CrossRef]

H. L. Fang and R. Swofford, “Analysis of the thermal lensing effect for an optically thick sample-A revised model,” J. Appl. Phys. 50, 6609-6615 (1979).
[CrossRef]

J. P. Gordon, R. C. Leite, R. S. Moore, S. P. Porto, and J. R. Whinnery, “Long transient effects of lasers with inserted liquid samples,” J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

J. Biomed. Opt.

R. L. Vincelette, B. A. Rockwell, R. J. Thomas, D. J. Lund, and A. J. Welch, “Thermal lensing in ocular media exposed to continuous-wave near-infrared radiation: 1150-1350 nm region,” J. Biomed. Opt. 13, 054005 (2008).
[CrossRef] [PubMed]

G. Li, H. Zwick, B. Stuck, and D. J. Lund, “On the use of schematic eye models to estimate retinal image quality,” J. Biomed. Opt. 5, 307-314 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

J. Phys. Chem. Ref. Data

A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761-774 (1998).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

J. Vision

P. Artal, A. Benito, and J. Tabernero, “The human eye is an example of robust optical design,” J. Vision 6, 1-7 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

D. J. Lund, P. Edsall, and B. E. Stuck, “Spectral dependence of retinal thermal injury,” Proc. SPIE 3902, 22-34 (2000).
[CrossRef]

D. J. Lund and P. Edsall, “Action spectrum for retinal thermal injury,” Proc. SPIE 3591, 324-334 (1999).
[CrossRef]

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “A comparison of a first-order thermal lensing model to a closed aperture Z-scan for the propagation of light in ocular media,” Proc. SPIE 6084, 0G1-0G9 (2006).

R. L. Vincelette, R. J. Thomas, B. A. Rockwell, and A. J. Welch, “Thermal lensing in the ocular media,” Proc. SPIE 6435, 0C1-7 (2007).

R. J. Thomas, R. L. Vincelette, C. D. Clark, III, J. Stolarski, L. J. Irvin, and G. D. Buffington, “Propagation effects in the assessment of laser damage thresholds to the eye and skin,” Proc. SPIE 6435, A1-12 (2007).

Rev. Sci. Instrum.

M. Franko and C. D. Tran, “Analytical thermal lens instrumentation,” Rev. Sci. Instrum. 67, 1-18 (1996).
[CrossRef]

Other

J. A. Zuclich, D. J. Lund, B. E. Stuck, and P. R. Edsall, “Ocular effects and safety standard implications for high-power lasers in the 1.3-1.4 μm wavelength range,” (Air Force Research Laboratory, Laser Radiation Branch, San Antonio, Texas, 2004).

G. Westheimer, “The Eye: Including Central Nervous System Control of Eye Movements,” in Medical Physiology, Vol. 1, V.B.Mountcastle, ed., 14th ed. (C. V. Mosby Company, 1980), pp. 482-503.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989), pp. 106-123.

W. C. Lin, “Dynamics of tissue optics during laser heating,” Ph.D. dissertation (University of Texas, Austin, Texas, 1997).

H. A. Wyld, Mathematical Methods for Physics (W. A. Benjamin, 1976), pp. 319-326.

J. V. Beck, K. D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat Conduction Using Green's Functions (Hemisphere Publishing Corp., 1992), pp. 201-216.

R. J. Thomas, R. L. Vincelette, G. D. Buffington, A. D. Strunk, M. A. Edwards, B. A. Rockwell, and A. J. Welch, “A first order model of thermal lensing of laser propagation in the eye and implications for laser safety,” in International Laser Safety Conference (Laser Institute of America, 2005), 147-154.

D. A. Atchison and G. Smith, Optics of the Human Eye (Elsevier, 2002).

C. D. Clark, L. J. Irvin, P. D. S. Maseberg, G. D. Buffington, R. J. Thomas, M. L. Edwards, and J. Stolarski, “BTEC Thermal Model,” Report AFRL-RH-BR-TR-2008-0006 (Air Force Research Laboratory, San Antonio, 2008).

E. F. Maher, “Transmission and absorption coefficients for the ocular media of the Rhesus monkey,” Tech. Rep. SAM-TR-78-32 (USAF School of Aerospace Medicine, 1978).

W. Wagner and A. Kruse, Properties of Water and Steam: The Industrial Standard IAPWS-IF97 for the Thermodynamic Properties and Supplementary Equations for Other Properties (Springer-Verlag, 1998), p. 150.

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Figures (11)

Fig. 1
Fig. 1

Example of a negative thermal lens z-scan. The cases for the samples exposed at the z positions: (a) very far from the focus of the lens and very near or at the focus resulting in unity normalized irradiance, (b) before the focus resulting in an increase in normalized signal irradiance, and (c) after the focus resulting in a decrease in signal irradiance. (d) Resulting z-scan data set.

Fig. 2
Fig. 2

Closed-aperture, single-beam z-scan set up. The z axis is referenced to the focal position of the lens found using a knife-edge technique in air, with no cuvette in the beam path. The laser was a 1313 nm CrystaLaser IRCL-150-1313-P-L. M1–M4, IR-coated mirrors; L1 and L2, IR-coated lenses created a beam expander of 1.5 × ; L3, 400 mm ThorLabs planoconvex 1 in. lens; SW, 1 cm diameter Uniblitz shutter; Quartz cuvette from Starna Cells; A, Aperture set to 2.5 mm diameter; D, 818-IR Newport detector.

Fig. 3
Fig. 3

Simple eye model with a radius of curvature of 0.61 cm on the front surface of the cornea brings a collimated 589 nm beam to a minimum at the virtual retinal plane 2.44 cm after the front surface of the eye. The vitreous layer is infinitely long, with beam trend observations made at the position of the virtual retina.

Fig. 4
Fig. 4

Values of d n d T (in K 1 ) as a function of temperature for water in the liquid phase for five different wavelengths. Values here were based on taking the derivative of n ( T ) P at each of the five wavelengths as reported by Schiebener et al. at 0.1 MPa [16].

Fig. 5
Fig. 5

Z-scan data for a 10 mm water-filled cuvette exposed to 1313 nm CW laser source for 1 s at (a) 2.6 mW and (b) 48 mW . The time response for the maxima and minima from each peak can be found in Fig. 6.

Fig. 6
Fig. 6

Transient response for the z scan peaks from Fig. 5 for 2.6 mW (a) maximum and (b) minimum and 48 mW (c) maximum and (d) minimum.

Fig. 7
Fig. 7

Increase in the beam radius at the retina as a function of time for selected powers delivered to the cornea. Parameters were for 1318 nm CW laser radiation into a human eye, with a 1 e 2 Gaussian beam radius of 2.12 mm at the virtual cornea. The y axis was normalized to 98 μ m , which was the beam radius at the virtual retina determined at time zero.

Fig. 8
Fig. 8

Increase in the beam radius at the retina as a function of time for selected input beam radii at the cornea.

Fig. 9
Fig. 9

Increase in the beam radius for 1318 nm laser radiation at the retina as a function of input power at the cornea for (a) short time ( t 1 ms ) and (b) long time ( 1 ms < t 250 ms ) . Note the 340 W power at 0.350 ms approximates the ED 50 threshold level reported in Zuclich et al. [34] for the equivalent wavelength. The y axis was normalized to the initial beam radius of 98 μ m .

Fig. 10
Fig. 10

Increase in the beam radius for 1150 nm laser radiation at the retina as a function of input power at the cornea for (a) short time ( t 1 ms ) and (b) long time ( 1 ms < t 250 ms ) . The y axis was normalized to the initial beam radius of 82 μ m .

Fig. 11
Fig. 11

Increase in the beam radius for 1318 nm laser radiation at the retina as a function of input power at the cornea for (a) short time ( t 1 ms ) and (b) long time ( 1 ms < t 250 ms ) having doubled the value of d n d T to 8.92 × 10 5 K 1 . The y axis was normalized to the initial beam radius of 98 μ m .

Tables (2)

Tables Icon

Table 1 Thermal Couductivity κ, Density ρ, Specific Heat at Constant Pressure c p , and Thermal Diffusivity η, As a Function of Temperature T Found to Fit Data for Liquid Water a for 0.1 MPa between 283.15 and 363.15 K

Tables Icon

Table 2 Linear Absorption Coefficients for Ocular Media and Water at 1150 and 1318 nm a

Equations (18)

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

T S 1 3 2 π ω min 2 λ ,
n ( r , T ) = n o + r ( n r ) r = 0 + r 2 2 ! ( 2 n r 2 ) r = 0 .
n ( r , T ) = n 0 + r ( n T T r ) r = 0 + r 2 2 r ( n T T r ) r = 0 .
n ( r , T ) = n 0 + r 2 2 [ r ( n T ) ] T r r = 0 + r 2 2 [ r ( T r ) ] n T r = 0 ,
n ( r , T ) = n 0 + r 2 2 2 T r 2 n T r = 0 .
n = n 0 ( 1 X r 2 2 ) .
X = 1 n 0 d n d T 2 T r 2 .
[ A B C D ] = [ cosh ( X 1 2 Δ z ) X 1 2 sinh ( X 1 2 Δ z ) X 1 2 sinh ( X 1 2 Δ z ) cosh ( X 1 2 Δ z ) ]
q ( z ) new = A q ( z ) old + B C q ( z ) old + D .
1 q ( z ) = 1 R ( z ) i m 2 λ π ω ( z ) 2 ,
1 r r [ κ r T r ] + S ( z ) = ρ c p T t ,
2 T r 2 + 1 r T r + 1 κ S ( z ) = 1 η T t .
G ( r , t ; r , t ) = 1 4 π η ( t t ) exp [ ( r 2 + r 2 ) 4 η ( t t ) ] I 0 [ r r 2 η ( t t ) ] ,
T ( z , r , t ) = 1 ρ c p 0 t d t 0 2 π d θ 0 r d r S ( z , r ) G ( r , t ; r ) .
S ( z , r ) = 2 μ a P z π ω 2 exp [ 2 ( r ) 2 ω 2 ]
2 T r 2 = η 8 μ α P z π κ ω 2 [ t 8 η t + ω 2 ] .
2 T r 2 = μ a P z π ω 2 κ [ 1 1 + t c t ] .
( T t ) r = 0 = η ( 2 2 T r 2 + 1 κ S ( z ) ) r = 0 .

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