Abstract

A heterodyne technique is presented for the independent, direct measurement of the amplitude and phase of photorefractive space-charge fields during uninterrupted buildup and photoinduced decay. The technique is based on using a probe beam with a frequency slightly different from that of the two recording beams to continuously read photorefractive phase gratings during all stages of formation and decay. The probe beam is virtually collinear with one of the recording beams. The beat between the diffracted component of the frequency-shifted probe beam and the transmitted component of the recording beam produces a heterodyne beam component. This heterodyne component contains the photorefractive grating information and is monitored to yield the amplitude and phase of the photorefractive fields. This nondestructive characterization technique exhibits excellent sensitivity and permits photorefractive phase measurements to within 1.5°.

© 1994 Optical Society of America

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References

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  1. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I, II (Springer-Verlag, Berlin, 1988, 1989).
    [Crossref]
  2. P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
    [Crossref]
  3. D. Makgerefteh and J. Feinburg, “Erasure rate and coasting in photorefractive barium titanate at high optical power,” Opt. Lett. 13, 1111–1113 (1988).
    [Crossref]
  4. R. A. Mullen, “Photorefractive measurements of physical parameters,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 175–189.
  5. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electro-optic crystals,” Ferroelectrics 22, 949–960 (1979).
    [Crossref]
  6. R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sub-linear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259–269 (1989).
    [Crossref]
  7. C. Medrano, E. Voit, P. Amrhien, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
    [Crossref]
  8. F. P. Stohkendl, J. M. C. Johnathon, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
    [Crossref]
  9. M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
    [Crossref]
  10. M. Z. Zha, P. Amrhein, and P. Günter, “Measurement of phase shift of photorefractive gratings by a novel method,” IEEE J. Quantum Electron. 26, 788–792 (1990).
    [Crossref]
  11. M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 217–273.
  12. J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
    [Crossref]
  13. G. C. Valley, “Two-wave mixing with an applied field and moving grating,” J. Opt. Soc. Am. B 1, 868–873 (1984).
    [Crossref]
  14. P. H. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
    [Crossref]
  15. B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J.-P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals,” Opt. Lett. 13, 327–329 (1988).
    [Crossref] [PubMed]
  16. R. Hofmeister, A. Yariv, A. Kewitsch, and S. Yagi, “Simple methods of measuring the net photorefractive phase shift and coupling constant,” Opt. Lett. 18, 488–490 (1993).
    [Crossref]
  17. R. M. Montgomery and M. R. Lange, “Amplitude and phase measurement technique for photorefractive gratings,” J. Appl. Phys. 68, 4782–4787 (1990).
    [Crossref]
  18. W. B. Lawler, C. J. Sherman, and M. G. Moharam, “Direct measurement of the amplitude and the phase of photorefractive fields in KNbO3:Ta and BaTiO3,” J. Opt. Soc. Am. A 8, 2190–2195 (1991).
    [Crossref]
  19. R. M. Montgomery and M. R. Lange, “Development of a photorefractive grating via temporally modulated photoconductivity and a correlated ac bias,” J. Appl. Phys. 66, 1915–1919 (1989).
    [Crossref]
  20. A. Korpel, Acousto-Optics, Optical Engineering Series, (Dekker, New York, 1988), pp. 174–179.
  21. D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrasonics SU-24, 7–18 (1977).
    [Crossref]

1993 (1)

1991 (1)

W. B. Lawler, C. J. Sherman, and M. G. Moharam, “Direct measurement of the amplitude and the phase of photorefractive fields in KNbO3:Ta and BaTiO3,” J. Opt. Soc. Am. A 8, 2190–2195 (1991).
[Crossref]

1990 (2)

R. M. Montgomery and M. R. Lange, “Amplitude and phase measurement technique for photorefractive gratings,” J. Appl. Phys. 68, 4782–4787 (1990).
[Crossref]

M. Z. Zha, P. Amrhein, and P. Günter, “Measurement of phase shift of photorefractive gratings by a novel method,” IEEE J. Quantum Electron. 26, 788–792 (1990).
[Crossref]

1989 (2)

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sub-linear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259–269 (1989).
[Crossref]

R. M. Montgomery and M. R. Lange, “Development of a photorefractive grating via temporally modulated photoconductivity and a correlated ac bias,” J. Appl. Phys. 66, 1915–1919 (1989).
[Crossref]

1988 (3)

1986 (1)

1985 (2)

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
[Crossref]

P. H. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[Crossref]

1984 (1)

1982 (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

1980 (1)

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[Crossref]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electro-optic crystals,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

1977 (1)

D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrasonics SU-24, 7–18 (1977).
[Crossref]

Amrhein, P.

M. Z. Zha, P. Amrhein, and P. Günter, “Measurement of phase shift of photorefractive gratings by a novel method,” IEEE J. Quantum Electron. 26, 788–792 (1990).
[Crossref]

Amrhien, P.

C. Medrano, E. Voit, P. Amrhien, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[Crossref]

Feinberg, J.

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[Crossref]

Feinburg, J.

Günter, P.

M. Z. Zha, P. Amrhein, and P. Günter, “Measurement of phase shift of photorefractive gratings by a novel method,” IEEE J. Quantum Electron. 26, 788–792 (1990).
[Crossref]

C. Medrano, E. Voit, P. Amrhien, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[Crossref]

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

Hecht, D. L.

D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrasonics SU-24, 7–18 (1977).
[Crossref]

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[Crossref]

Hellwarth, R. W.

F. P. Stohkendl, J. M. C. Johnathon, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
[Crossref]

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[Crossref]

Herriau, J. P.

Hofmeister, R.

Huignard, J.-P.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J.-P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals,” Opt. Lett. 13, 327–329 (1988).
[Crossref] [PubMed]

P. H. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[Crossref]

Imbert, B.

Johnathon, J. M. C.

Kewitsch, A.

Klein, M. B.

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
[Crossref]

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 217–273.

Korpel, A.

A. Korpel, Acousto-Optics, Optical Engineering Series, (Dekker, New York, 1988), pp. 174–179.

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electro-optic crystals,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Lange, M. R.

R. M. Montgomery and M. R. Lange, “Amplitude and phase measurement technique for photorefractive gratings,” J. Appl. Phys. 68, 4782–4787 (1990).
[Crossref]

R. M. Montgomery and M. R. Lange, “Development of a photorefractive grating via temporally modulated photoconductivity and a correlated ac bias,” J. Appl. Phys. 66, 1915–1919 (1989).
[Crossref]

Lawler, W. B.

W. B. Lawler, C. J. Sherman, and M. G. Moharam, “Direct measurement of the amplitude and the phase of photorefractive fields in KNbO3:Ta and BaTiO3,” J. Opt. Soc. Am. A 8, 2190–2195 (1991).
[Crossref]

Maillard, A.

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sub-linear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259–269 (1989).
[Crossref]

Makgerefteh, D.

Mallick, S.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electro-optic crystals,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Medrano, C.

C. Medrano, E. Voit, P. Amrhien, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[Crossref]

Moharam, M. G.

W. B. Lawler, C. J. Sherman, and M. G. Moharam, “Direct measurement of the amplitude and the phase of photorefractive fields in KNbO3:Ta and BaTiO3,” J. Opt. Soc. Am. A 8, 2190–2195 (1991).
[Crossref]

Montgomery, R. M.

R. M. Montgomery and M. R. Lange, “Amplitude and phase measurement technique for photorefractive gratings,” J. Appl. Phys. 68, 4782–4787 (1990).
[Crossref]

R. M. Montgomery and M. R. Lange, “Development of a photorefractive grating via temporally modulated photoconductivity and a correlated ac bias,” J. Appl. Phys. 66, 1915–1919 (1989).
[Crossref]

Mullen, R. A.

R. A. Mullen, “Photorefractive measurements of physical parameters,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 175–189.

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electro-optic crystals,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Rajbenbach, H.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J.-P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals,” Opt. Lett. 13, 327–329 (1988).
[Crossref] [PubMed]

P. H. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[Crossref]

Réfrégier, P. H.

P. H. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[Crossref]

Rupp, R. A.

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sub-linear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259–269 (1989).
[Crossref]

Sherman, C. J.

W. B. Lawler, C. J. Sherman, and M. G. Moharam, “Direct measurement of the amplitude and the phase of photorefractive fields in KNbO3:Ta and BaTiO3,” J. Opt. Soc. Am. A 8, 2190–2195 (1991).
[Crossref]

Solymar, L.

P. H. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[Crossref]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electro-optic crystals,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Stohkendl, F. P.

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[Crossref]

Valley, G. C.

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
[Crossref]

G. C. Valley, “Two-wave mixing with an applied field and moving grating,” J. Opt. Soc. Am. B 1, 868–873 (1984).
[Crossref]

Vinetski, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electro-optic crystals,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Voit, E.

C. Medrano, E. Voit, P. Amrhien, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[Crossref]

Walter, J.

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sub-linear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259–269 (1989).
[Crossref]

Yagi, S.

Yariv, A.

Zha, M. Z.

M. Z. Zha, P. Amrhein, and P. Günter, “Measurement of phase shift of photorefractive gratings by a novel method,” IEEE J. Quantum Electron. 26, 788–792 (1990).
[Crossref]

Appl. Phys. A (1)

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sub-linear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259–269 (1989).
[Crossref]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electro-optic crystals,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Z. Zha, P. Amrhein, and P. Günter, “Measurement of phase shift of photorefractive gratings by a novel method,” IEEE J. Quantum Electron. 26, 788–792 (1990).
[Crossref]

IEEE Trans. Sonics Ultrasonics (1)

D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrasonics SU-24, 7–18 (1977).
[Crossref]

J. Appl. Phys. (6)

R. M. Montgomery and M. R. Lange, “Development of a photorefractive grating via temporally modulated photoconductivity and a correlated ac bias,” J. Appl. Phys. 66, 1915–1919 (1989).
[Crossref]

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[Crossref]

P. H. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[Crossref]

R. M. Montgomery and M. R. Lange, “Amplitude and phase measurement technique for photorefractive gratings,” J. Appl. Phys. 68, 4782–4787 (1990).
[Crossref]

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
[Crossref]

C. Medrano, E. Voit, P. Amrhien, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[Crossref]

J. Opt. Soc. Am. A (1)

W. B. Lawler, C. J. Sherman, and M. G. Moharam, “Direct measurement of the amplitude and the phase of photorefractive fields in KNbO3:Ta and BaTiO3,” J. Opt. Soc. Am. A 8, 2190–2195 (1991).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

Phys. Rep. (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

Other (4)

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I, II (Springer-Verlag, Berlin, 1988, 1989).
[Crossref]

R. A. Mullen, “Photorefractive measurements of physical parameters,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 175–189.

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 217–273.

A. Korpel, Acousto-Optics, Optical Engineering Series, (Dekker, New York, 1988), pp. 174–179.

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Figures (2)

Fig. 1
Fig. 1

Characterization-system configuration.

Fig. 2
Fig. 2

Space-charge field for KINbO3:Ta for grating spacings of 2.5, 5.5, and 7.5 μm.

Equations (15)

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

E 1 = I 1 exp ( - j k 1 · r ) exp [ j 2 π ( f L + f 1 ) t ] ,
E 2 = { I 2 + I p exp [ j ( 2 π Δ f t + ψ p ) ] } exp [ - j ( k 2 · r - ψ ) ] × exp [ j 2 π ( f L + f 1 ) t ] ,
I ( t ) = I 2 + I p + 2 I 2 I p cos ( 2 π Δ f t + ψ p ) .
I c ( t ) = I 1 + I 2 + I p + 2 I 2 I p cos ( 2 π Δ f t + ψ p ) + 2 I 1 I p cos ( 2 π Δ f t + ψ - K · r + ψ p ) + 2 I 1 I 2 cos ( K · r - ψ ) .
E sc ( t ) = E 1 ( t ) cos [ K · r - ψ + ϕ ph ( t ) ] ,
Δ n ( t ) = ( 1 / 2 ) n 3 r E sc ( t ) cos [ K · r - ψ + ϕ ph ( t ) ] ,
E k 1 = ( I 1 cos γ ph - j sin γ ph exp ( j ϕ ph ) × { I 2 + I p exp [ j ( 2 π Δ f t + ψ p ) ] } ) exp ( - j k 1 · r ) ,
γ ph ( t ) = π Δ n d λ cos θ .
I k 1 ( t ) = I 1 cos 2 γ ph + ( I 2 + I p ) sin 2 γ ph + I 1 I 2 sin ( 2 γ ph ) sin ϕ ph + 2 I 2 I p sin 2 γ ph cos ( 2 π Δ f t + ψ p ) + I 1 I p sin ( 2 γ ph ) × cos [ 2 π Δ f t + ψ p + ϕ ph - ( π / 2 ) ] ,
E k 2 = ( cos γ ph { I 2 + I p exp [ j ( 2 π Δ f t + ψ p ) ] } - j I 1 sin γ ph exp ( - j ϕ ph ) ) exp [ - j ( k 2 · r - ψ ) ] ,
I k 2 ( t ) = ( I 1 + I p ) cos 2 γ ph + I 2 sin 2 γ ph - I 1 I 2 sin ( 2 γ ph ) sin ϕ ph + 2 I 2 I p cos 2 γ ph cos ( 2 π Δ f t + ψ p ) + I 1 I p sin ( 2 γ ph ) cos [ 2 π Δ f t + ψ p + ϕ ph + ( π / 2 ) ]
S ( t ) = A ( t ) I 1 I p sin [ 2 γ ph ( t ) ] cos [ 2 π Δ f t + ψ p + ϕ ph ( t ) - ( π / 2 ) + Δ ϕ ( t ) ] ,
A = 1 + ( I 2 / I 1 ) tan 2 γ ph + 2 I 2 / I 1 tan γ ph sin ϕ ph ,
Δ ϕ = tan - 1 ( I 2 / I 1 tan γ ph cos ϕ ph 1 + I 2 / I 2 tan γ ph sin ϕ ph ) .
I decay = I 1 I p sin ( 2 γ ph ) cos [ ( 2 π Δ f t + ψ p + ϕ ph - ( π / 2 ) ] ,

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