Abstract

The phase conjugate COAT (coherent optical adaptive technique) is investigated for thin, nonlinear lenses, simulating thermal blooming. The iteration scheme applied has convergent and divergent regimes.

© 1977 Optical Society of America

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References

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  1. W. T. Cathey, C. L. Hayes, W. C. Davis, and V. F. Pizzuro, Appl. Opt. 9, 701 (1970).
    [Crossref] [PubMed]
  2. W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O’Meara, J. A. Sanguinet, and W. P. Brown, Appl. Opt. 13, 291 (1974).
    [Crossref] [PubMed]
  3. W. P. Brown, (August1973); J. Winocur, Rockwell International (private communication).
  4. H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
    [Crossref] [PubMed]

1974 (1)

1970 (1)

1966 (1)

Bridges, W. B.

Brown, W. P.

Brunner, P. T.

Cathey, W. T.

Davis, W. C.

Hayes, C. L.

Kogelnik, H.

Lazzara, S. P.

Li, T.

Nussmeier, T. A.

O’Meara, T. R.

Pizzuro, V. F.

Sanguinet, J. A.

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Figures (10)

FIG. 1
FIG. 1

Notation used in the phase conjugate COAT calculations for geometric beam.

FIG. 2
FIG. 2

Beam with corrected radius of curvature at the transmitter.

FIG. 3
FIG. 3

Beam radius at the target as a function of iteration for different values of the initial curvature K0 = S/L2. The two dashed curves use an iteration with half the gain.

FIG. 4
FIG. 4

Schematic representation of phase conjugate COAT systems with an atmospheric time constant tat. For the cw case, the iteration time is tit. For the MP case, the pulse length is tp, the pulse spacing is Tp, and the time between the sensing of the atmosphere by a glint return and the next pulse is tg. Standard multipulse conditions require tptatTp.

FIG. 5
FIG. 5

Radius of beam in the target plane as a function of iteration number for some values of the time constants described by the coefficient f = exp(− tit/tat).

FIG. 6
FIG. 6

Limits to phase correction for Gaussian beam for single constant lens inserted at distance z between transmitter and target.

FIG. 7
FIG. 7

Beam radius at target vs curvature at transmitter for five-lens system with geometrical beam.

FIG. 8
FIG. 8

Beam radius at target vs iteration for cases of Fig. 7.

FIG. 9
FIG. 9

Beam radius at target vs curvature at transmitter for five-lens system with Gaussian beam.

FIG. 10
FIG. 10

Beam radius at target vs iteration for the cases of Fig. 9.

Equations (15)

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K ( z ) = S [ a t / a ( z ) ] Q ,
Δ n α P v 1 a y ( 1 + erf x a x ) exp ( - y 2 a y 2 ) ,
1 L + D = 1 L + R T - R - K ,
R T C = R - L 2 / ( L + 1 / K ) .
K = S ( a t / a ) 2 ,
a t / a = R T / ( L + R T - R ) .
1 L + D = 1 L + R T - R - S R T 2 ( L + R T - R ) 2 .
1 - 4 S R ( R - L ) / L 0.
R T ( n + 1 ) = R - L 2 / ( L + 1 / K n ) ,
K n = S R T n 2 / ( R T n + L - R ) 2
R T n = 0.5 ( R T n + R T ( n - 1 ) ) ,
R T 0 = R ,             K - 1 = 0 with n = 0 , 1 , 2 , , K n = S [ R T n / ( L - R + R T n ) ] Q , K n = f K n - 1 + ( 1 - f ) K n , R T ( n + 1 ) = R - L 2 ( L + 1 / K n ) - 1 ,
a f 2 = a t 2 [ 1 + C R + K R ( 1 - z ) + K R C R z ( 1 - z ) ] 2 + a t 2 [ 1 + K R z ( 1 - z ) ] 2 / N F 2 ,
a f , min = a t [ 1 + K R z ( 1 - z ) ] / N F ;
C min R = - [ 1 + K R ( 1 - z ) ] / [ 1 + K R z ( 1 - z ) ] .