Abstract

New results in spectral interferometry are presented. The effect of imperfect calibration of the optical spectrometer is demonstrated both theoretically and experimentally. It is shown in particular that slight calibration imperfections can lead to mistakes because of the principle of spectral interferometry itself. Efficient methods are demonstrated to overcome this problem and to provide spectrometer calibration with a precision far superior to the instrument’s optical resolution. Results for spectral phase interferometry for direct electric-field reconstruction are also demonstrated.

© 1999 Optical Society of America

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References

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  1. I. Walmsley and V. Wong, “Characterization of the electric field of ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 2453–2463 (1996).
    [CrossRef]
  2. R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
    [CrossRef]
  3. H. Lange, M. Franco, J. Ripoche, B. Prade, P. Rousseau, and A. Mysyrowicz, “Measurement of the time profile of femtosecond laser pulses through cross-phase modulation,” IEEE J. Sel. Topics Quantum Electron. 4, 295–300 (1998).
    [CrossRef]
  4. J. Rhee, T. Sosnowski, A. Tien, and T. Norris, “Real-time dispersion analyzer of femtosecond laser pulses with use of a spectrally and temporally resolved upconversion technique,” J. Opt. Soc. Am. B 13, 1780–1785 (1996).
    [CrossRef]
  5. J. Chilla and O. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
    [CrossRef]
  6. K. Chu, J. Heritage, R. Grant, and W. White, “Temporal interferometric measurement of femtosecond spectral phase,” Opt. Lett. 21, 1842–1844 (1996).
    [CrossRef] [PubMed]
  7. C. Iaconis and I. Walmsley, “Spectral phase interferometry for direct electric field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
    [CrossRef]
  8. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995).
    [CrossRef]
  9. C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183–196 (1973).
  10. M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. Robertson and G. Reid, eds. (Institute of Physics, Philadelphia, Pa., 1993), pp. 141–193.
  11. E. Tokunaga, A. Terasaki and T. Kobayashi, “Femtosecond phase spectroscopy by use of frequency-domain interference,” J. Opt. Soc. Am. B 12, 753–771 (1995).
    [CrossRef]
  12. J. Geindre, P. Audebert, A. Rousse, F. Falliès, J. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, “Frequency-domain interferometer for measuring the phase and amplitude of a femtosecond pulse probing a laser-produced plasma,” Opt. Lett. 19, 1997–1999 (1994).
    [CrossRef] [PubMed]
  13. C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
    [CrossRef]
  14. C. Dorrer and F. Salin, “Characterization of spectral phase modulation using classical and polarization spectral interferometry,” J. Opt. Soc. Am. B 15, 2331–2337 (1998).
    [CrossRef]
  15. D. Meshulach, D. Yelin, and Y. Siberberg, “White light dispersion measurements by one- and two-dimensional spectral interference,” IEEE J. Quantum Electron. 33, 1969–1974 (1997).
    [CrossRef]
  16. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
    [CrossRef] [PubMed]
  17. L. Lepetit and M. Joffre, “Two-dimensional nonlinear optics using Fourier transform spectral interferometry,” Opt. Lett. 21, 564–566 (1996).
    [CrossRef] [PubMed]
  18. F. Reynaud, F. Salin, and A. Barthelemy, “Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,” Opt. Lett. 14, 275–277 (1989).
    [CrossRef] [PubMed]
  19. L. Zheng, O. Konoplev, and D. Meyerhofer, “Determination of the optical-axis orientation of a uniaxial crystal by frequency-domain interferometry,” Opt. Lett. 22, 931–933 (1997).
    [CrossRef] [PubMed]
  20. J. P. Likforman, M. Joffre, and V. Thierry-Mieg, “Measurement of photon echoes by use of femtosecond Fourier transform spectral interferometry,” Opt. Lett. 22, 1104–1106 (1997).
    [CrossRef] [PubMed]
  21. S. Gallagher, A. Albrecht, J. Hybl, B. Landin, B. Rajaram, and D. Jonas, “Heterodyne detection of the complete electric field of femtosecond four-wave mixing signals,” J. Opt. Soc. Am. B 15, 2338–2345 (1998).
    [CrossRef]
  22. V. Wong and I. Walmsley, “Analysis of ultrashort pulse-shape measurement using linear interferometers,” Opt. Lett. 15, 287–289 (1994).
    [CrossRef]
  23. C. Iaconis and I. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
    [CrossRef]
  24. V. Kumar and D. Rao, “Using interference in the frequency domain for precise determination of thickness and refractive indices of normal dispersive materials,” J. Opt. Soc. Am. B 12, 1559–1563 (1995).
    [CrossRef]
  25. M. Beck and I. Walmsley, “Measurement of group delay with high temporal and spectral resolution,” Opt. Lett. 15, 492–494 (1990).
    [CrossRef] [PubMed]
  26. S. Brodersen, “Interferometric frequency calibration of infrared spectrometers,” J. Opt. Soc. Am. 46, 255–258 (1956).
    [CrossRef]

1998 (5)

1997 (4)

L. Zheng, O. Konoplev, and D. Meyerhofer, “Determination of the optical-axis orientation of a uniaxial crystal by frequency-domain interferometry,” Opt. Lett. 22, 931–933 (1997).
[CrossRef] [PubMed]

J. P. Likforman, M. Joffre, and V. Thierry-Mieg, “Measurement of photon echoes by use of femtosecond Fourier transform spectral interferometry,” Opt. Lett. 22, 1104–1106 (1997).
[CrossRef] [PubMed]

D. Meshulach, D. Yelin, and Y. Siberberg, “White light dispersion measurements by one- and two-dimensional spectral interference,” IEEE J. Quantum Electron. 33, 1969–1974 (1997).
[CrossRef]

R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

1996 (5)

1995 (3)

1994 (3)

J. Geindre, P. Audebert, A. Rousse, F. Falliès, J. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, “Frequency-domain interferometer for measuring the phase and amplitude of a femtosecond pulse probing a laser-produced plasma,” Opt. Lett. 19, 1997–1999 (1994).
[CrossRef] [PubMed]

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

V. Wong and I. Walmsley, “Analysis of ultrashort pulse-shape measurement using linear interferometers,” Opt. Lett. 15, 287–289 (1994).
[CrossRef]

1991 (1)

J. Chilla and O. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

1990 (1)

1989 (1)

1973 (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183–196 (1973).

1956 (1)

Albrecht, A.

Antonetti, A.

Audebert, P.

Barthelemy, A.

Beck, M.

Bowie, J. L.

Brodersen, S.

Calatroni, J.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

Chériaux, G.

Chilla, J.

J. Chilla and O. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

Chu, K.

DeLong, K.

R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

DeLong, K. W.

Dorrer, C.

Dos Santos, A.

Escalona, R.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

Falliès, F.

Fittinghoff, D.

R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Fittinghoff, D. N.

Franco, M.

H. Lange, M. Franco, J. Ripoche, B. Prade, P. Rousseau, and A. Mysyrowicz, “Measurement of the time profile of femtosecond laser pulses through cross-phase modulation,” IEEE J. Sel. Topics Quantum Electron. 4, 295–300 (1998).
[CrossRef]

Froehly, C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183–196 (1973).

Gallagher, S.

Gauthier, J.

Geindre, J.

Grant, R.

Hamoniaux, G.

Heritage, J.

Hybl, J.

Iaconis, C.

Jennings, R. T.

Joffre, M.

Jonas, D.

Jourdain, P.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

Kane, D.

R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Kobayashi, T.

Konoplev, O.

Krumbügel, M.

R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Krumbügel, M. A.

Kumar, V.

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183–196 (1973).

Landin, B.

Lange, H.

H. Lange, M. Franco, J. Ripoche, B. Prade, P. Rousseau, and A. Mysyrowicz, “Measurement of the time profile of femtosecond laser pulses through cross-phase modulation,” IEEE J. Sel. Topics Quantum Electron. 4, 295–300 (1998).
[CrossRef]

Lepetit, L.

Likforman, J. P.

Martinez, O.

J. Chilla and O. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

Meshulach, D.

D. Meshulach, D. Yelin, and Y. Siberberg, “White light dispersion measurements by one- and two-dimensional spectral interference,” IEEE J. Quantum Electron. 33, 1969–1974 (1997).
[CrossRef]

Meyerhofer, D.

Mysyrowicz, A.

H. Lange, M. Franco, J. Ripoche, B. Prade, P. Rousseau, and A. Mysyrowicz, “Measurement of the time profile of femtosecond laser pulses through cross-phase modulation,” IEEE J. Sel. Topics Quantum Electron. 4, 295–300 (1998).
[CrossRef]

J. Geindre, P. Audebert, A. Rousse, F. Falliès, J. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, “Frequency-domain interferometer for measuring the phase and amplitude of a femtosecond pulse probing a laser-produced plasma,” Opt. Lett. 19, 1997–1999 (1994).
[CrossRef] [PubMed]

Norris, T.

Prade, B.

H. Lange, M. Franco, J. Ripoche, B. Prade, P. Rousseau, and A. Mysyrowicz, “Measurement of the time profile of femtosecond laser pulses through cross-phase modulation,” IEEE J. Sel. Topics Quantum Electron. 4, 295–300 (1998).
[CrossRef]

Rajaram, B.

Rao, D.

Reynaud, F.

Rhee, J.

Richman, B.

R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Ripoche, J.

H. Lange, M. Franco, J. Ripoche, B. Prade, P. Rousseau, and A. Mysyrowicz, “Measurement of the time profile of femtosecond laser pulses through cross-phase modulation,” IEEE J. Sel. Topics Quantum Electron. 4, 295–300 (1998).
[CrossRef]

Rousse, A.

Rousseau, P.

H. Lange, M. Franco, J. Ripoche, B. Prade, P. Rousseau, and A. Mysyrowicz, “Measurement of the time profile of femtosecond laser pulses through cross-phase modulation,” IEEE J. Sel. Topics Quantum Electron. 4, 295–300 (1998).
[CrossRef]

Sainz, C.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

Salin, F.

Siberberg, Y.

D. Meshulach, D. Yelin, and Y. Siberberg, “White light dispersion measurements by one- and two-dimensional spectral interference,” IEEE J. Quantum Electron. 33, 1969–1974 (1997).
[CrossRef]

Sosnowski, T.

Sweester, J.

R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Sweetser, J. N.

Terasaki, A.

Thierry-Mieg, V.

Tien, A.

Tokunaga, E.

Trebino, R.

R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183–196 (1973).

Walmsley, I.

Walmsley, I. A.

White, W.

Wong, V.

I. Walmsley and V. Wong, “Characterization of the electric field of ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 2453–2463 (1996).
[CrossRef]

V. Wong and I. Walmsley, “Analysis of ultrashort pulse-shape measurement using linear interferometers,” Opt. Lett. 15, 287–289 (1994).
[CrossRef]

Yelin, D.

D. Meshulach, D. Yelin, and Y. Siberberg, “White light dispersion measurements by one- and two-dimensional spectral interference,” IEEE J. Quantum Electron. 33, 1969–1974 (1997).
[CrossRef]

Zheng, L.

IEEE J. Quantum Electron. (2)

J. Chilla and O. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

D. Meshulach, D. Yelin, and Y. Siberberg, “White light dispersion measurements by one- and two-dimensional spectral interference,” IEEE J. Quantum Electron. 33, 1969–1974 (1997).
[CrossRef]

IEEE J. Sel. Topics Quantum Electron. (1)

H. Lange, M. Franco, J. Ripoche, B. Prade, P. Rousseau, and A. Mysyrowicz, “Measurement of the time profile of femtosecond laser pulses through cross-phase modulation,” IEEE J. Sel. Topics Quantum Electron. 4, 295–300 (1998).
[CrossRef]

J. Opt. (Paris) (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183–196 (1973).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (7)

Opt. Commun. (1)

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Real-time interferometric measurements of dispersion curves,” Opt. Commun. 111, 632–641 (1994).
[CrossRef]

Opt. Lett. (11)

J. Geindre, P. Audebert, A. Rousse, F. Falliès, J. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, “Frequency-domain interferometer for measuring the phase and amplitude of a femtosecond pulse probing a laser-produced plasma,” Opt. Lett. 19, 1997–1999 (1994).
[CrossRef] [PubMed]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

L. Lepetit and M. Joffre, “Two-dimensional nonlinear optics using Fourier transform spectral interferometry,” Opt. Lett. 21, 564–566 (1996).
[CrossRef] [PubMed]

F. Reynaud, F. Salin, and A. Barthelemy, “Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,” Opt. Lett. 14, 275–277 (1989).
[CrossRef] [PubMed]

L. Zheng, O. Konoplev, and D. Meyerhofer, “Determination of the optical-axis orientation of a uniaxial crystal by frequency-domain interferometry,” Opt. Lett. 22, 931–933 (1997).
[CrossRef] [PubMed]

J. P. Likforman, M. Joffre, and V. Thierry-Mieg, “Measurement of photon echoes by use of femtosecond Fourier transform spectral interferometry,” Opt. Lett. 22, 1104–1106 (1997).
[CrossRef] [PubMed]

K. Chu, J. Heritage, R. Grant, and W. White, “Temporal interferometric measurement of femtosecond spectral phase,” Opt. Lett. 21, 1842–1844 (1996).
[CrossRef] [PubMed]

C. Iaconis and I. Walmsley, “Spectral phase interferometry for direct electric field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
[CrossRef]

M. Beck and I. Walmsley, “Measurement of group delay with high temporal and spectral resolution,” Opt. Lett. 15, 492–494 (1990).
[CrossRef] [PubMed]

V. Wong and I. Walmsley, “Analysis of ultrashort pulse-shape measurement using linear interferometers,” Opt. Lett. 15, 287–289 (1994).
[CrossRef]

C. Iaconis and I. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Trebino, K. DeLong, D. Fittinghoff, J. Sweester, M. Krumbügel, B. Richman, and D. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Other (1)

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. Robertson and G. Reid, eds. (Institute of Physics, Philadelphia, Pa., 1993), pp. 141–193.

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Figures (9)

Fig. 1
Fig. 1

Main steps in the Fourier treatment for spectral interferometry: (a) Interferogram. (b) Amplitude of the Fourier transform of the channeled spectrum. The filter is plotted about the t=+τ component. (c) Retrieved amplitude |E1(ω)||E2(ω)| and phase ψ(ω)+ωτ.

Fig. 2
Fig. 2

Symmetric Michelson interferometer for measurement of the dispersion of a glass plate.

Fig. 3
Fig. 3

Spectral phase differences for the compensated Michelson interferometer for eight delays from -2 to 2 ps.

Fig. 4
Fig. 4

Measured group-velocity dispersion versus delay before correction for (a) an empty Michelson interferometer and (b) a fused-silica plate inserted into one arm of the interferometer.

Fig. 5
Fig. 5

Two experimental determinations of the nonlinear part of the error r(ω) without the fused-silica plate (squares) and with the fused-silica plate (circles) in the interferometer. For clarity, only 50 experimental points have been plotted.

Fig. 6
Fig. 6

Measured group-velocity dispersion at 800 nm versus delay after correction for (a) an empty Michelson interferometer and (b) a fused-silica plate inserted into one arm of the interferometer.

Fig. 7
Fig. 7

Spectral phase differences for the compensated Michelson interferometer after correction of the calibration, for eight delays from -2 to 2 ps.

Fig. 8
Fig. 8

Experimental determination of the nonlinear part of the error r(ω) after the first correction.

Fig. 9
Fig. 9

Experimental determination of the nonlinear part of the error r(ω) at 400 nm after correction at 800 nm.

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