Abstract

The use of femtosecond lasers requires accurate measurements of the dispersive properties of media. Here we measure the second- and third-order dispersion of water, seawater, and ocular components in the range of 660930nm using a new method known as multiphoton intrapulse interference phase scan. Our direct dispersion measurements of water have the highest precision and accuracy to date. We found that the dispersion for seawater increases proportionally to the concentration of salt. The dispersion of the vitreous humor was found to be close to that of water. The chromatic dispersion of the cornea–lens complex was measured to obtain the full dispersive properties of the eye.

© 2007 Optical Society of America

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  1. S. Toyran, Y. M. Liu, S. Singha, S. Shan, M. R. Cho, R. J. Gordon, and D. P. Edward, "Femtosecond laser photodisruption of human trabecular meshwork: an in vitro study," Exp. Eye Res. 81, 298-305 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. B. G. Wang, I. Riemann, H. Schubert, K. J. Halbhuber, and K. Koenig, "In-vivo intratissue ablation by nanojoule near-infrared femtosecond laser pulses," Cell Tissue Res. 328, 515-520 (2007).
    [CrossRef] [PubMed]
  4. M. Blum, K. Kunert, S. Nolte, S. Riehemann, M. Palme, T. Peschel, M. Dick, and H. B. Dick, "Presbyopia treatment using a femtosecond laser," Ophthalmologe 103, 1014-1019 (2006).
    [CrossRef] [PubMed]
  5. G. Gerten, T. Ripken, P. Breitenfeld, R. R. Krueger, O. Kermani, H. Lubatschowski, and U. Oberheide, "In vitro and in vivo investigations on the treatment of presbyopia using femtosecond lasers," Ophthalmologe 104, 40-46 (2007).
    [CrossRef]
  6. C. P. Cain, R. J. Thomas, G. D. Noojin, D. J. Stolarski, P. K. Kennedy, G. D. Buffington, and B. A. Rockwell, "Sub-50-fs laser retinal damage thresholds in primate eyes with group velocity dispersion, self-focusing and low-density plasmas," Graefes Arch. Ophthalmol. 243, 101-112 (2005).
    [CrossRef]
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    [CrossRef]
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  23. D. A. Atchison and G. Smith, "Chromatic dispersions of the ocular media of human eyes," J. Opt. Soc. Am. A 22, 29-37 (2005).
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2007 (4)

B. G. Wang, I. Riemann, H. Schubert, K. J. Halbhuber, and K. Koenig, "In-vivo intratissue ablation by nanojoule near-infrared femtosecond laser pulses," Cell Tissue Res. 328, 515-520 (2007).
[CrossRef] [PubMed]

G. Gerten, T. Ripken, P. Breitenfeld, R. R. Krueger, O. Kermani, H. Lubatschowski, and U. Oberheide, "In vitro and in vivo investigations on the treatment of presbyopia using femtosecond lasers," Ophthalmologe 104, 40-46 (2007).
[CrossRef]

M. Dantus, V. V. Lozovoy, and I. Pastirk, "MIIPS characterizes and corrects femtosecond pulses," Laser Focus World 43, 101-104 (2007).

M. Daimon and A. Masumura, "Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region," Appl. Opt. 46, 3811-3820 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (5)

S. Toyran, Y. M. Liu, S. Singha, S. Shan, M. R. Cho, R. J. Gordon, and D. P. Edward, "Femtosecond laser photodisruption of human trabecular meshwork: an in vitro study," Exp. Eye Res. 81, 298-305 (2005).
[CrossRef] [PubMed]

T. M. Johnson and B. M. Glaser, "Micropulse laser treatment of retinal-choroidal anastomoses in age-related macular degeneration," Graefes Arch. Ophthalmol. 243, 570-575 (2005).
[CrossRef]

C. P. Cain, R. J. Thomas, G. D. Noojin, D. J. Stolarski, P. K. Kennedy, G. D. Buffington, and B. A. Rockwell, "Sub-50-fs laser retinal damage thresholds in primate eyes with group velocity dispersion, self-focusing and low-density plasmas," Graefes Arch. Ophthalmol. 243, 101-112 (2005).
[CrossRef]

V. V. Lozovoy and M. Dantus, "Coherent control in femtochemistry," Chem. PhysChem. 6, 1970-2000 (2005).
[CrossRef]

D. A. Atchison and G. Smith, "Chromatic dispersions of the ocular media of human eyes," J. Opt. Soc. Am. A 22, 29-37 (2005).
[CrossRef]

2004 (1)

2002 (1)

K. A. Walowicz, I. Pastirk, V. V. Lozovoy, and M. Dantus, "Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases," J. Phys. Chem. A 106, 9369-9373 (2002).
[CrossRef]

2000 (1)

I. G. Cormack, F. Baumann, and D. T. Reid, "Measurement of group velocity dispersion using white light interferometry: a teaching laboratory experiment," Am. J. Phys. 68, 1146-1150 (2000).
[CrossRef]

1999 (1)

1998 (2)

A. H. Harvey, J. S. Gallagher, and J. 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]

A. G. Van Engen, S. A. Diddams, and T. S. Clement, "Dispersion measurements of water with white-light interferometry," Appl. Opt. 37, 5679-5686 (1998).
[CrossRef]

1996 (1)

1995 (1)

1986 (1)

A. E. Siegman, Lasers (University Science Books, 1986).

1985 (2)

L. G. Cohen, "Comparison of single-mode fiber dispersion measurement techniques," J. Lightwave Technol. 3, 958-966 (1985).
[CrossRef]

R. Navarro, J. Santamaria, and J. Bescos, "Accommodation-dependent model of the human-eye with aspherics," J. Opt. Soc. Am. A 2, 1273-1281 (1985).
[CrossRef] [PubMed]

1976 (1)

R. W. Austin and G. Halikas, "The index of refraction of seawater, Report SIO Reference 76-1" (Scripps Institution of Oceanography, San Diego, 1976).

1967 (1)

Y. Le Grand, Form and Space Vision (Indiana U. Press, 1967).

Atchison, D. A.

Austin, R. W.

R. W. Austin and G. Halikas, "The index of refraction of seawater, Report SIO Reference 76-1" (Scripps Institution of Oceanography, San Diego, 1976).

Baumann, F.

I. G. Cormack, F. Baumann, and D. T. Reid, "Measurement of group velocity dispersion using white light interferometry: a teaching laboratory experiment," Am. J. Phys. 68, 1146-1150 (2000).
[CrossRef]

Bescos, J.

Blum, M.

M. Blum, K. Kunert, S. Nolte, S. Riehemann, M. Palme, T. Peschel, M. Dick, and H. B. Dick, "Presbyopia treatment using a femtosecond laser," Ophthalmologe 103, 1014-1019 (2006).
[CrossRef] [PubMed]

Breitenfeld, P.

G. Gerten, T. Ripken, P. Breitenfeld, R. R. Krueger, O. Kermani, H. Lubatschowski, and U. Oberheide, "In vitro and in vivo investigations on the treatment of presbyopia using femtosecond lasers," Ophthalmologe 104, 40-46 (2007).
[CrossRef]

Buffington, G. D.

C. P. Cain, R. J. Thomas, G. D. Noojin, D. J. Stolarski, P. K. Kennedy, G. D. Buffington, and B. A. Rockwell, "Sub-50-fs laser retinal damage thresholds in primate eyes with group velocity dispersion, self-focusing and low-density plasmas," Graefes Arch. Ophthalmol. 243, 101-112 (2005).
[CrossRef]

Cain, C. P.

C. P. Cain, R. J. Thomas, G. D. Noojin, D. J. Stolarski, P. K. Kennedy, G. D. Buffington, and B. A. Rockwell, "Sub-50-fs laser retinal damage thresholds in primate eyes with group velocity dispersion, self-focusing and low-density plasmas," Graefes Arch. Ophthalmol. 243, 101-112 (2005).
[CrossRef]

Cho, M. R.

S. Toyran, Y. M. Liu, S. Singha, S. Shan, M. R. Cho, R. J. Gordon, and D. P. Edward, "Femtosecond laser photodisruption of human trabecular meshwork: an in vitro study," Exp. Eye Res. 81, 298-305 (2005).
[CrossRef] [PubMed]

Clement, T. S.

Coello, Y.

Cohen, L. G.

L. G. Cohen, "Comparison of single-mode fiber dispersion measurement techniques," J. Lightwave Technol. 3, 958-966 (1985).
[CrossRef]

Cormack, I. G.

I. G. Cormack, F. Baumann, and D. T. Reid, "Measurement of group velocity dispersion using white light interferometry: a teaching laboratory experiment," Am. J. Phys. 68, 1146-1150 (2000).
[CrossRef]

Daimon, M.

Dantus, M.

Dela Cruz, J. M.

Dick, H. B.

M. Blum, K. Kunert, S. Nolte, S. Riehemann, M. Palme, T. Peschel, M. Dick, and H. B. Dick, "Presbyopia treatment using a femtosecond laser," Ophthalmologe 103, 1014-1019 (2006).
[CrossRef] [PubMed]

Dick, M.

M. Blum, K. Kunert, S. Nolte, S. Riehemann, M. Palme, T. Peschel, M. Dick, and H. B. Dick, "Presbyopia treatment using a femtosecond laser," Ophthalmologe 103, 1014-1019 (2006).
[CrossRef] [PubMed]

Diddams, S.

Diddams, S. A.

Diels, J. C.

Edward, D. P.

S. Toyran, Y. M. Liu, S. Singha, S. Shan, M. R. Cho, R. J. Gordon, and D. P. Edward, "Femtosecond laser photodisruption of human trabecular meshwork: an in vitro study," Exp. Eye Res. 81, 298-305 (2005).
[CrossRef] [PubMed]

Fry, E. S.

Gallagher, J. S.

A. H. Harvey, J. S. Gallagher, and J. 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]

Gerten, G.

G. Gerten, T. Ripken, P. Breitenfeld, R. R. Krueger, O. Kermani, H. Lubatschowski, and U. Oberheide, "In vitro and in vivo investigations on the treatment of presbyopia using femtosecond lasers," Ophthalmologe 104, 40-46 (2007).
[CrossRef]

Glaser, B. M.

T. M. Johnson and B. M. Glaser, "Micropulse laser treatment of retinal-choroidal anastomoses in age-related macular degeneration," Graefes Arch. Ophthalmol. 243, 570-575 (2005).
[CrossRef]

Gordon, R. J.

S. Toyran, Y. M. Liu, S. Singha, S. Shan, M. R. Cho, R. J. Gordon, and D. P. Edward, "Femtosecond laser photodisruption of human trabecular meshwork: an in vitro study," Exp. Eye Res. 81, 298-305 (2005).
[CrossRef] [PubMed]

Gunn, J. M.

Halbhuber, K. J.

B. G. Wang, I. Riemann, H. Schubert, K. J. Halbhuber, and K. Koenig, "In-vivo intratissue ablation by nanojoule near-infrared femtosecond laser pulses," Cell Tissue Res. 328, 515-520 (2007).
[CrossRef] [PubMed]

Halikas, G.

R. W. Austin and G. Halikas, "The index of refraction of seawater, Report SIO Reference 76-1" (Scripps Institution of Oceanography, San Diego, 1976).

Hammer, D. X.

Harris, D. A.

Harvey, A. H.

A. H. Harvey, J. S. Gallagher, and J. 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]

Johnson, T. M.

T. M. Johnson and B. M. Glaser, "Micropulse laser treatment of retinal-choroidal anastomoses in age-related macular degeneration," Graefes Arch. Ophthalmol. 243, 570-575 (2005).
[CrossRef]

Kennedy, P. K.

C. P. Cain, R. J. Thomas, G. D. Noojin, D. J. Stolarski, P. K. Kennedy, G. D. Buffington, and B. A. Rockwell, "Sub-50-fs laser retinal damage thresholds in primate eyes with group velocity dispersion, self-focusing and low-density plasmas," Graefes Arch. Ophthalmol. 243, 101-112 (2005).
[CrossRef]

Kermani, O.

G. Gerten, T. Ripken, P. Breitenfeld, R. R. Krueger, O. Kermani, H. Lubatschowski, and U. Oberheide, "In vitro and in vivo investigations on the treatment of presbyopia using femtosecond lasers," Ophthalmologe 104, 40-46 (2007).
[CrossRef]

Koenig, K.

B. G. Wang, I. Riemann, H. Schubert, K. J. Halbhuber, and K. Koenig, "In-vivo intratissue ablation by nanojoule near-infrared femtosecond laser pulses," Cell Tissue Res. 328, 515-520 (2007).
[CrossRef] [PubMed]

Krueger, R. R.

G. Gerten, T. Ripken, P. Breitenfeld, R. R. Krueger, O. Kermani, H. Lubatschowski, and U. Oberheide, "In vitro and in vivo investigations on the treatment of presbyopia using femtosecond lasers," Ophthalmologe 104, 40-46 (2007).
[CrossRef]

Kunert, K.

M. Blum, K. Kunert, S. Nolte, S. Riehemann, M. Palme, T. Peschel, M. Dick, and H. B. Dick, "Presbyopia treatment using a femtosecond laser," Ophthalmologe 103, 1014-1019 (2006).
[CrossRef] [PubMed]

Le Grand, Y.

Y. Le Grand, Form and Space Vision (Indiana U. Press, 1967).

Liu, Y. M.

S. Toyran, Y. M. Liu, S. Singha, S. Shan, M. R. Cho, R. J. Gordon, and D. P. Edward, "Femtosecond laser photodisruption of human trabecular meshwork: an in vitro study," Exp. Eye Res. 81, 298-305 (2005).
[CrossRef] [PubMed]

Lozovoy, V. V.

Lubatschowski, H.

G. Gerten, T. Ripken, P. Breitenfeld, R. R. Krueger, O. Kermani, H. Lubatschowski, and U. Oberheide, "In vitro and in vivo investigations on the treatment of presbyopia using femtosecond lasers," Ophthalmologe 104, 40-46 (2007).
[CrossRef]

Masumura, A.

Navarro, R.

Nolte, S.

M. Blum, K. Kunert, S. Nolte, S. Riehemann, M. Palme, T. Peschel, M. Dick, and H. B. Dick, "Presbyopia treatment using a femtosecond laser," Ophthalmologe 103, 1014-1019 (2006).
[CrossRef] [PubMed]

Noojin, G. D.

C. P. Cain, R. J. Thomas, G. D. Noojin, D. J. Stolarski, P. K. Kennedy, G. D. Buffington, and B. A. Rockwell, "Sub-50-fs laser retinal damage thresholds in primate eyes with group velocity dispersion, self-focusing and low-density plasmas," Graefes Arch. Ophthalmol. 243, 101-112 (2005).
[CrossRef]

D. X. Hammer, A. J. Welch, G. D. Noojin, R. J. Thomas, D. J. Stolarski, and B. A. Rockwell, "Spectrally resolved white-light interferometry for measurement of ocular dispersion," J. Opt. Soc. Am. A 16, 2092-2102 (1999).
[CrossRef]

Oberheide, U.

G. Gerten, T. Ripken, P. Breitenfeld, R. R. Krueger, O. Kermani, H. Lubatschowski, and U. Oberheide, "In vitro and in vivo investigations on the treatment of presbyopia using femtosecond lasers," Ophthalmologe 104, 40-46 (2007).
[CrossRef]

Palme, M.

M. Blum, K. Kunert, S. Nolte, S. Riehemann, M. Palme, T. Peschel, M. Dick, and H. B. Dick, "Presbyopia treatment using a femtosecond laser," Ophthalmologe 103, 1014-1019 (2006).
[CrossRef] [PubMed]

Pastirk, I.

M. Dantus, V. V. Lozovoy, and I. Pastirk, "MIIPS characterizes and corrects femtosecond pulses," Laser Focus World 43, 101-104 (2007).

V. V. Lozovoy, I. Pastirk, and M. Dantus, "Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation," Opt. Lett. 29, 775-777 (2004).
[CrossRef] [PubMed]

K. A. Walowicz, I. Pastirk, V. V. Lozovoy, and M. Dantus, "Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases," J. Phys. Chem. A 106, 9369-9373 (2002).
[CrossRef]

Peschel, T.

M. Blum, K. Kunert, S. Nolte, S. Riehemann, M. Palme, T. Peschel, M. Dick, and H. B. Dick, "Presbyopia treatment using a femtosecond laser," Ophthalmologe 103, 1014-1019 (2006).
[CrossRef] [PubMed]

Quan, X. H.

Reid, D. T.

I. G. Cormack, F. Baumann, and D. T. Reid, "Measurement of group velocity dispersion using white light interferometry: a teaching laboratory experiment," Am. J. Phys. 68, 1146-1150 (2000).
[CrossRef]

Riehemann, S.

M. Blum, K. Kunert, S. Nolte, S. Riehemann, M. Palme, T. Peschel, M. Dick, and H. B. Dick, "Presbyopia treatment using a femtosecond laser," Ophthalmologe 103, 1014-1019 (2006).
[CrossRef] [PubMed]

Riemann, I.

B. G. Wang, I. Riemann, H. Schubert, K. J. Halbhuber, and K. Koenig, "In-vivo intratissue ablation by nanojoule near-infrared femtosecond laser pulses," Cell Tissue Res. 328, 515-520 (2007).
[CrossRef] [PubMed]

Ripken, T.

G. Gerten, T. Ripken, P. Breitenfeld, R. R. Krueger, O. Kermani, H. Lubatschowski, and U. Oberheide, "In vitro and in vivo investigations on the treatment of presbyopia using femtosecond lasers," Ophthalmologe 104, 40-46 (2007).
[CrossRef]

Rockwell, B. A.

C. P. Cain, R. J. Thomas, G. D. Noojin, D. J. Stolarski, P. K. Kennedy, G. D. Buffington, and B. A. Rockwell, "Sub-50-fs laser retinal damage thresholds in primate eyes with group velocity dispersion, self-focusing and low-density plasmas," Graefes Arch. Ophthalmol. 243, 101-112 (2005).
[CrossRef]

D. X. Hammer, A. J. Welch, G. D. Noojin, R. J. Thomas, D. J. Stolarski, and B. A. Rockwell, "Spectrally resolved white-light interferometry for measurement of ocular dispersion," J. Opt. Soc. Am. A 16, 2092-2102 (1999).
[CrossRef]

Santamaria, J.

Schubert, H.

B. G. Wang, I. Riemann, H. Schubert, K. J. Halbhuber, and K. Koenig, "In-vivo intratissue ablation by nanojoule near-infrared femtosecond laser pulses," Cell Tissue Res. 328, 515-520 (2007).
[CrossRef] [PubMed]

Sengers, J.

A. H. Harvey, J. S. Gallagher, and J. 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]

Shan, S.

S. Toyran, Y. M. Liu, S. Singha, S. Shan, M. R. Cho, R. J. Gordon, and D. P. Edward, "Femtosecond laser photodisruption of human trabecular meshwork: an in vitro study," Exp. Eye Res. 81, 298-305 (2005).
[CrossRef] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Singha, S.

S. Toyran, Y. M. Liu, S. Singha, S. Shan, M. R. Cho, R. J. Gordon, and D. P. Edward, "Femtosecond laser photodisruption of human trabecular meshwork: an in vitro study," Exp. Eye Res. 81, 298-305 (2005).
[CrossRef] [PubMed]

Smith, G.

Stolarski, D. J.

C. P. Cain, R. J. Thomas, G. D. Noojin, D. J. Stolarski, P. K. Kennedy, G. D. Buffington, and B. A. Rockwell, "Sub-50-fs laser retinal damage thresholds in primate eyes with group velocity dispersion, self-focusing and low-density plasmas," Graefes Arch. Ophthalmol. 243, 101-112 (2005).
[CrossRef]

D. X. Hammer, A. J. Welch, G. D. Noojin, R. J. Thomas, D. J. Stolarski, and B. A. Rockwell, "Spectrally resolved white-light interferometry for measurement of ocular dispersion," J. Opt. Soc. Am. A 16, 2092-2102 (1999).
[CrossRef]

Thomas, R. J.

C. P. Cain, R. J. Thomas, G. D. Noojin, D. J. Stolarski, P. K. Kennedy, G. D. Buffington, and B. A. Rockwell, "Sub-50-fs laser retinal damage thresholds in primate eyes with group velocity dispersion, self-focusing and low-density plasmas," Graefes Arch. Ophthalmol. 243, 101-112 (2005).
[CrossRef]

D. X. Hammer, A. J. Welch, G. D. Noojin, R. J. Thomas, D. J. Stolarski, and B. A. Rockwell, "Spectrally resolved white-light interferometry for measurement of ocular dispersion," J. Opt. Soc. Am. A 16, 2092-2102 (1999).
[CrossRef]

Toyran, S.

S. Toyran, Y. M. Liu, S. Singha, S. Shan, M. R. Cho, R. J. Gordon, and D. P. Edward, "Femtosecond laser photodisruption of human trabecular meshwork: an in vitro study," Exp. Eye Res. 81, 298-305 (2005).
[CrossRef] [PubMed]

Van Engen, A. G.

Walowicz, K. A.

K. A. Walowicz, I. Pastirk, V. V. Lozovoy, and M. Dantus, "Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases," J. Phys. Chem. A 106, 9369-9373 (2002).
[CrossRef]

Wang, B. G.

B. G. Wang, I. Riemann, H. Schubert, K. J. Halbhuber, and K. Koenig, "In-vivo intratissue ablation by nanojoule near-infrared femtosecond laser pulses," Cell Tissue Res. 328, 515-520 (2007).
[CrossRef] [PubMed]

Welch, A. J.

Xu, B. W.

Am. J. Phys. (1)

I. G. Cormack, F. Baumann, and D. T. Reid, "Measurement of group velocity dispersion using white light interferometry: a teaching laboratory experiment," Am. J. Phys. 68, 1146-1150 (2000).
[CrossRef]

Appl. Opt. (3)

Cell Tissue Res. (1)

B. G. Wang, I. Riemann, H. Schubert, K. J. Halbhuber, and K. Koenig, "In-vivo intratissue ablation by nanojoule near-infrared femtosecond laser pulses," Cell Tissue Res. 328, 515-520 (2007).
[CrossRef] [PubMed]

Chem. PhysChem. (1)

V. V. Lozovoy and M. Dantus, "Coherent control in femtochemistry," Chem. PhysChem. 6, 1970-2000 (2005).
[CrossRef]

Exp. Eye Res. (1)

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Figures (11)

Fig. 1
Fig. 1

Sinusoidal spectral phase function in the frequency domain produces a maximum in the SHG spectrum at the frequency corresponding to the point of inflection of the spectral phase. (b) Spectrum of the ultrabroad-bandwidth femtosecond laser used for this work. (a) The experimental SHG spectrum obtained when the sinusoidal spectral phase shown in (b) (top) is applied to the laser pulses.

Fig. 2
Fig. 2

(a) Experimental MIIPS traces for TL pulses. Diagonal features are equally spaced and have the same slope. (b) Experimental MIIPS traces showing the change in spacing between the diagonal features caused by a ϕ = 120 fs 2 quadratic phase distortion in the frequency domain. (c) Experimental MIIPS traces showing the slope change caused by a ϕ = 336 fs 3 cubic phase distortion in the frequency domain.

Fig. 3
Fig. 3

Block diagram of the experimental setup. The arrows indicate the propagation of the laser beam, the dashed lines indicate computer communication.

Fig. 4
Fig. 4

Chromatic dispersion as a function of medium thickness. (a) ϕ ( λ ) data points measured by MIIPS and second-order polynomial fits for water samples of 5, 10, 20, and 30 mm thickness (ascending order). (b) Linear regression of ϕ ( λ ) at 800 nm .

Fig. 5
Fig. 5

Comparison of k for water measured by MIIPS and white-light interferometry and calculated using the Sellmeier and NIST dispersion formulas. The upper graph shows the difference of the corresponding values with respect to those calculated using the Sellmeier dispersion formula. For both calculations a temperature of 21.5 ° C was used.

Fig. 6
Fig. 6

Comparison of water third-order dispersion calculated from our measurements, the Sellmeier and NIST dispersion formulas, and obtained using white-light interferometry.

Fig. 7
Fig. 7

Experimental measurements of k of water, seawater, and water with three times the concentration of salt in seawater ( 3 × ) . Only a few experimental points were plotted for clarity.

Fig. 8
Fig. 8

Increase in k of seawater with respect to de-ionized water as a function of the concentration of sea salt. The symbols correspond to MIIPS measurements and the line to a calculation based on the refractive index formula for seawater proposed by Quan and Fry [20]. For the calculation the temperature was set at 21.5 ° C . Note that the calculation has been extended beyond the original range of validity for S ( 35 g / l ) .

Fig. 9
Fig. 9

Diagram of an eye. The dashed square corresponds to the cornea–lens complex.

Fig. 10
Fig. 10

Comparison of k for the vitreous humor measured by MIIPS and k for water calculated using the Sellmeier dispersion formula for distilled water. The upper graph shows the deviation of the vitreous humor measurements with respect to the calculated values for water.

Fig. 11
Fig. 11

Measured chromatic dispersion ϕ of a cornea–lens complex. The dots correspond to the experimental points. The curve corresponds to a third-order polynomial fit of the data.

Tables (4)

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Table 1 Parameters of the Sellmeier Formula for Water at 21.5 °C

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Table 2 Seawater Parameters for Eq. (6) in the 660–930 nm Range

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Table 3 Vitreous Humor Parameters for Eq. (7) in the 660–930 nm Range

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Table 4 Experimental Dispersion Measurements for Water, Seawater, and Eye Components

Equations (9)

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k ( λ ) = λ 3 2 π c 2 d 2 n ( λ ) d λ 2 .
SHG ( 2 ω ) | E ( ω + Ω ) E ( ω Ω ) d Ω | 2
| e i ϕ ( ω + Ω ) + i ϕ ( ω Ω ) d Ω | 2 ,
SHG ( 2 ω ) | e i ϕ ( ω ) Ω 2 d Ω | 2 ,
ϕ ( ω ) = f ( ω , δ max ) = α γ 2 sin [ γ ( ω ω 0 ) δ max ( ω ) ] .
n 2 1 = l = 1 4 A i 1 ( λ 1 / λ ) 2 ,
k ( λ ) = C 0 + C 1 λ + C 2 λ 2 + C S S ,
k ( λ ) = C 0 + C 1 λ + C 2 λ 2 .
τ = τ 0 [ 1 + ( 4 ϕ τ 0 2 ln 2 ) 2 ] 0.5 .

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