Abstract

We describe a self-referencing interferometer in which the wavefront and its complex conjugate are generated in a Fabry–Perot cavity having one phase conjugate mirror (PCM). The finite response time of the PCM allows one to display momentarily the moiré between old and new interferograms after a sudden change has affected the input wavefront. Results using an externally pumped BaTiO3 crystal as a PCM are analyzed.

© 1989 Optical Society of America

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References

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  1. Y. Fainman, E. Lenz, J. Shamir, “Contouring by Phase Conjugation,” Appl. Opt. 20, 158–163 (1981).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [PubMed]
  4. O. Ikeda, T. Suzuki, T. Sako, “High-accuracy Surface Profile Measuring System Using a BSO Phase Conjugating Mirror,” Appl. Opt. 21, 4468–4472 (1982).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. D. Z. Anderson, D. M. Lininger, J. Feinberg, “Optical Tracking Novelty Filter,” Opt. Lett. 12, 123–125 (1987).
    [CrossRef] [PubMed]
  7. S. Chang, M. Isono, T. Sako, “Dynamic Interferometry Using Two Phase Conjugate Waves,” Appl. Opt. 27, 4735–4738 (1988).
    [CrossRef] [PubMed]
  8. N. Tan-no, K. Kawauchi, K. Yokoto, “Self-interferometry by Dual-wave-front Generation in Degerate Four-wave Mixing,” J. Opt. Soc. Am. B 3, 60–64 (1986).
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    [CrossRef]
  11. I. Lindsay, J. C. Dainty, “Partial Cancellation of Specular Reflection in the Presence of a Phase Conjugate Mirror,” Opt. Commun. 59, 405–410 (1986).
    [CrossRef]
  12. A. T. Friberg, M. Kauranen, R. Salomaa, “Dynamics of Fabry–Perot Resonators with a Phase-conjugate Mirror,” J. Opt. Soc. Am. B 3, 1656–1672 (1986).
    [CrossRef]

1988

1987

1986

1983

1982

G. S. Agarwal, A. T. Friberg, E. Wolf, “Elimination of Distorsion by Phase Conjugation Without Losses or Gains,” Opt. Commun. 43, 446–450 (1982).
[CrossRef]

O. Ikeda, T. Suzuki, T. Sako, “High-accuracy Surface Profile Measuring System Using a BSO Phase Conjugating Mirror,” Appl. Opt. 21, 4468–4472 (1982).
[CrossRef] [PubMed]

1981

1980

F. A. Hopf, “Interferometry Using Conjugate-wave Generation,” J. Opt. Soc. Am,. 70, 1320–1323 (1980).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, A. T. Friberg, E. Wolf, “Elimination of Distorsion by Phase Conjugation Without Losses or Gains,” Opt. Commun. 43, 446–450 (1982).
[CrossRef]

Anderson, D. Z.

Bar-Joseph, I.

Belanger, P. A.

A. E. Siegman, P. A. Belanger, A. Hardy, Ch. 13 “Optical Resonators Using Phase-conjugate Mirrors,” in Optical Phase Conjugation, R. A. Fisher, Ed. (Academic, New York, 1983).

Chang, S.

Dainty, J. C.

I. Lindsay, J. C. Dainty, “Partial Cancellation of Specular Reflection in the Presence of a Phase Conjugate Mirror,” Opt. Commun. 59, 405–410 (1986).
[CrossRef]

Fainman, Y.

Feinberg, J.

Friberg, A. T.

A. T. Friberg, M. Kauranen, R. Salomaa, “Dynamics of Fabry–Perot Resonators with a Phase-conjugate Mirror,” J. Opt. Soc. Am. B 3, 1656–1672 (1986).
[CrossRef]

G. S. Agarwal, A. T. Friberg, E. Wolf, “Elimination of Distorsion by Phase Conjugation Without Losses or Gains,” Opt. Commun. 43, 446–450 (1982).
[CrossRef]

Hardy, A.

I. Bar-Joseph, A. Hardy, Y. Katzir, Y. Silberberg, “Low-power Phase-Conjugate Interferometry,” Opt. Lett. 6, 414–416 (1981).
[PubMed]

A. E. Siegman, P. A. Belanger, A. Hardy, Ch. 13 “Optical Resonators Using Phase-conjugate Mirrors,” in Optical Phase Conjugation, R. A. Fisher, Ed. (Academic, New York, 1983).

Hopf, F. A.

F. A. Hopf, “Interferometry Using Conjugate-wave Generation,” J. Opt. Soc. Am,. 70, 1320–1323 (1980).
[CrossRef]

Ikeda, O.

Isono, M.

Katzir, Y.

Kauranen, M.

Kawauchi, K.

Lenz, E.

Lindsay, I.

I. Lindsay, J. C. Dainty, “Partial Cancellation of Specular Reflection in the Presence of a Phase Conjugate Mirror,” Opt. Commun. 59, 405–410 (1986).
[CrossRef]

Lininger, D. M.

Sako, T.

Salomaa, R.

Shamir, J.

Siegman, A. E.

A. E. Siegman, P. A. Belanger, A. Hardy, Ch. 13 “Optical Resonators Using Phase-conjugate Mirrors,” in Optical Phase Conjugation, R. A. Fisher, Ed. (Academic, New York, 1983).

Silberberg, Y.

Suzuki, T.

Tan-no, N.

Wolf, E.

G. S. Agarwal, A. T. Friberg, E. Wolf, “Elimination of Distorsion by Phase Conjugation Without Losses or Gains,” Opt. Commun. 43, 446–450 (1982).
[CrossRef]

Yokoto, K.

Appl. Opt.

J. Opt. Soc. Am

F. A. Hopf, “Interferometry Using Conjugate-wave Generation,” J. Opt. Soc. Am,. 70, 1320–1323 (1980).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

G. S. Agarwal, A. T. Friberg, E. Wolf, “Elimination of Distorsion by Phase Conjugation Without Losses or Gains,” Opt. Commun. 43, 446–450 (1982).
[CrossRef]

I. Lindsay, J. C. Dainty, “Partial Cancellation of Specular Reflection in the Presence of a Phase Conjugate Mirror,” Opt. Commun. 59, 405–410 (1986).
[CrossRef]

Opt. Lett.

Other

A. E. Siegman, P. A. Belanger, A. Hardy, Ch. 13 “Optical Resonators Using Phase-conjugate Mirrors,” in Optical Phase Conjugation, R. A. Fisher, Ed. (Academic, New York, 1983).

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Figures (5)

Fig. 1
Fig. 1

Fabry–Perot cavity with a phase conjugate mirror (PCM). The output of the self-referencing interferometer is EO1.

Fig. 2
Fig. 2

Setup of the self-referencing interferometer. (BS beam splitter, M mirrors, BE beam expander, PBS pellicle beam splitter, PCM phase conjugate mirror).

Fig. 3
Fig. 3

(A) Initial interferogram of a spherical wavefront. (B) Momentary moiré between inital and final interferogram when the incident wavefront is suddenly translated. (C) Final interferogram of the translated spherical wavefront.

Fig. 4
Fig. 4

(A) Initial interferogram of spherical wavefront. (B) Momentary moiré after a sudden change of the curvature of the incident wavefront. (C) Final interferogram.

Fig. 5
Fig. 5

(A) Initial interferogram of a plane wave with added background fringes. (B) Momentary moiré after the sudden introduction of a transplant plastic box in the test area. (C) Steady-state interferogram of the stationary box.

Equations (8)

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r * t + r t * = 0 ,
t * t = 1 | r | 2 .
E O 1 = ρ τ * μ ( 1 | α | 2 ) 1 ( t α * E i + t * E i * ) ,
α = r τ τ * μ = r μ ( 1 | ρ | 2 )
E O 2 = ρ ( 1 | α | 2 ) 1 ( t E i + t * α E i * ) .
E O 4 = ( 1 | μ r | 2 ) 1 [ ( 1 | μ | 2 ) r E i + ( 1 | r | 2 ) μ E i * ] .
E O 1 ( t ) ( α * E i 1 + E i 1 * ) e t / τ + ( α * E i 2 + E i 2 * ) ( 1 e t / τ ) ,
E O 1 ( t ) cos ( ϕ 1 + / 2 ) e t / τ + cos ( ϕ 2 + / 2 ) ( 1 e t / τ ) .

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