Abstract

We present results of numerical simulations of incomplete phase conjugation of a beam aberrated by a thin phase screen. We find good agreement with a previously developed theory for phase screens with Gaussian autocorrelation functions and investigate some regimes in which the theory is not valid. We show that when the phase conjugation is incomplete, introduction of an aberrator can lead to an improvement in the system resolution.

© 1996 Optical Society of America

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References

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  1. E. Jakeman, K. D. Ridley, “Incomplete phase conjugation through a random-phase screen: I. Theory,” J. Opt. Soc. Am. A 13, 2279–2287 (1996).
    [CrossRef]
  2. C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
    [CrossRef]
  3. D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).
    [CrossRef]
  4. J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
    [CrossRef] [PubMed]
  5. E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
    [CrossRef]

1996 (1)

1994 (1)

C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

1988 (1)

1984 (1)

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
[CrossRef]

1983 (1)

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).
[CrossRef]

Flatté, S. M.

Gu, C.

C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

Jakeman, E.

Knepp, D. L.

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).
[CrossRef]

Martin, J. M.

Ridley, K. D.

Yeh, P.

C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

Appl. Opt. (1)

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

Opt. Commun. (1)

C. Gu, P. Yeh, “Partial phase conjugation, fidelity, and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

Opt. Eng. (1)

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
[CrossRef]

Proc. IEEE (1)

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Geometry for incomplete phase conjugation through a random-phase screen.

Fig. 2
Fig. 2

Example of the phase structure of a phase screen with a Gaussian autocorrelation function.

Fig. 3
Fig. 3

(a) Intensity profile after a single pass through a phase screen in the focusing regime at z = 5000 (note that a saturated intensity scale is used here), (b) central part of the intensity profile in the speckle regime at z = 50,000 (here the scale is linear).

Fig. 4
Fig. 4

Intensity profiles of the beam reflected from the PCM and propagated back to the phase screen for different PCM aperture sizes W, including one for the ideal phase conjugate.

Fig. 5
Fig. 5

Intensity profiles in the far field after passing back through the phase screen. The far-field profile is obtained by focusing with an f = 50,000 lens.

Fig. 6
Fig. 6

Cross section through the averaged far-field intensity pattern for two different scalings: (a) f = 50,000, (b) f = 25,600. The solid curves are the theoretical predictions.

Fig. 7
Fig. 7

Three plots showing averaged intensity along with theoretical prediction for different distances of the PCM from the phase screens and with a fixed PCM aperture size of W = 10.

Fig. 8
Fig. 8

Comparisons of theory and simulation for the power in the coherent part of the reflected beam.

Fig. 9
Fig. 9

Correlation between the fraction in the far-field spot for a number of phase screens (measured by the fitting of a Gaussian) and the parameter F defined by Eq. (4) for W = 15.

Fig. 10
Fig. 10

Plot of the phase profile for a phase screen with a negative exponential correlation function with an inner scale.

Fig. 11
Fig. 11

Comparison of the fraction in the central spot of the intensity profile averaged over a number of phase screens with the predictions based on Eq. (4).

Fig. 12
Fig. 12

Far-field profile for a single Gaussian phase screen with W = 10 and z = 5000.

Equations (5)

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E c = E i * exp ( | r | 2 W 2 ) ,
x y 2 E 2 i k E z = 0 ,
e ( k , z 1 ) = e ( k , z 0 ) exp [ i | k | 2 ( z 1 z 0 ) 2 k ] ,
F = | | E | 2 a ( r 3 ) d 2 r 3 | 2 | E | 2 d 2 r 3 | E | 2 | a ( r 3 ) | 2 d 2 r 3 .
Φ ( k ) = 1 1 + ξ 2 | k | 2 exp ( | k | 2 k i 2 ) .

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