Abstract

The effect of image compensation in viewing extended targets through thermal blooming is discussed. A wave-optics propagation code simulating multiple point sources and a low-bandwidth return-wave adaptive optics system is used to determine the steady-state thermally induced phase distortions and wave-front correction through various Zernike modes. Incoherent point spread functions for the isoplanatic regions are generated and convolved with the appropriate object field to reconstruct the extended target image. Image distortion, degradation in peak irradiance, and adaptive optics loop stability are discussed with respect to degree of correction and wavelength sensitivity.

© 1983 Optical Society of America

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References

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  1. L. C. Bradley, J. Herrmann, Appl. Opt. 13, 331 (1974).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. D. C. Smith, Proc. IEEE 65, 651 (1978).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

1982

1981

1978

J. E. Pearson, Opt. Lett. 2, 7 (1978).
[CrossRef] [PubMed]

C. A. Primmerman, F. B. Johnson, I. Wigdor, Appl. Opt. 17, 2909 (1978).
[CrossRef] [PubMed]

See, for example, J. W. Hardy, Proc. IEEE 66, 651 (1978); C. B. Hogge, “Adaptive Optics in High Energy Laser Systems,” in Adaptive Optics and Short Wavelength Sources, S. Jacobs, Ed. (Addison-Wesley, Reading, Mass., 1978), pp. 55–120.
[CrossRef]

D. C. Smith, Proc. IEEE 65, 651 (1978).

1977

1976

1975

W. B. Bridges, J. E. Pearson, Appl. Phys. Lett. 26, 539 (1975).
[CrossRef]

1974

1972

Akkapeddi, P. R.

Baker, J.

Bradley, L. C.

Bridges, W. B.

W. B. Bridges, J. E. Pearson, Appl. Phys. Lett. 26, 539 (1975).
[CrossRef]

Butts, R. R.

Fouche, D. G.

Gebhardt, F. G.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 113.

Greenwood, D. P.

Gurski, G. F.

Hardy, J. W.

See, for example, J. W. Hardy, Proc. IEEE 66, 651 (1978); C. B. Hogge, “Adaptive Optics in High Energy Laser Systems,” in Adaptive Optics and Short Wavelength Sources, S. Jacobs, Ed. (Addison-Wesley, Reading, Mass., 1978), pp. 55–120.
[CrossRef]

Herrmann, J.

Hogge, C. B.

Johnson, F. B.

Nahrstedt, D. A.

Nomiyama, N. T.

Pearson, J. E.

J. E. Pearson, Opt. Lett. 2, 7 (1978).
[CrossRef] [PubMed]

W. B. Bridges, J. E. Pearson, Appl. Phys. Lett. 26, 539 (1975).
[CrossRef]

Primmerman, C. A.

Radley, R. J.

Robertson, H. J.

Seibert, E. T.

Smith, D. C.

D. C. Smith, Proc. IEEE 65, 651 (1978).

D. C. Smith, United Technologies Research Center, private communication.

Volpe, G. T.

Wigdor, I.

Wilson, J.

Appl. Opt.

Appl. Phys. Lett.

W. B. Bridges, J. E. Pearson, Appl. Phys. Lett. 26, 539 (1975).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Proc. IEEE

See, for example, J. W. Hardy, Proc. IEEE 66, 651 (1978); C. B. Hogge, “Adaptive Optics in High Energy Laser Systems,” in Adaptive Optics and Short Wavelength Sources, S. Jacobs, Ed. (Addison-Wesley, Reading, Mass., 1978), pp. 55–120.
[CrossRef]

D. C. Smith, Proc. IEEE 65, 651 (1978).

Other

D. C. Smith, United Technologies Research Center, private communication.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 113.

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Figures (10)

Fig. 1
Fig. 1

Multiple-source return-wave algorithm.

Fig. 2
Fig. 2

Uncorrected far-field irradiance and typical PSFs (10-μm sensing).

Fig. 3
Fig. 3

Baseline case: uncorrected far-field thermal blooming.

Fig. 4
Fig. 4

Percent composition through Zernike mode Zi.

Fig. 5
Fig. 5

Object (target) and diffraction-limited image (10-μm back propagation).

Fig. 6
Fig. 6

Effect of phase compensation on far-field and extended target image (through Zernike mode Zi).

Fig. 7
Fig. 7

Far-field and target image improvement as a function of degree of correction.

Fig. 8
Fig. 8

Closed-loop stability of adaptive optics improvement (through Zernike mode Zi).

Fig. 9
Fig. 9

Wavelength sensitivity: Extended target image reconstruction (through Z10 correction).

Fig. 10
Fig. 10

Wavelength sensitivity: Effect on PSF distortion.

Tables (1)

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Table I Baseline Example

Equations (19)

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Δ ϑ ( x , y ; Δ z ) = 2 π ( n 0 1 ) λ F c p ρ 0 z z + Δ z x α ( ξ ) I ( β , y , ξ ) T ( ξ ) [ υ 0 ( ξ ) + θ ˙ ξ ] d β d ξ ,
z n ( n 1 ) N path α ( z ) ( υ + θ ˙ z ) r ( z ) T ( z ) d z ; 1 n N ,
r ( z ) = ( 1 z f ) D 2 + ( z f ) ( λ F f D ) ; 0 z f ,
ϑ a υ e ( x , y ) = 1 N i = 1 N [ I i ( x , y ) / I p k , i ] ϑ i ( x , y ) ,
I i ( x , y ) = K I g ( x ˜ 0 , y ˜ 0 ) h ˜ ( x x ˜ 0 , y y ˜ 0 ) d x ˜ 0 d y ˜ 0 ,
I T O T ( x , y ) = i = 1 N I i ( x + Δ x , y + Δ y ) ,
Δ x = x ¯ υ + Δ x T B ,
Δ y = y ¯ υ + Δ y T B ,
I rel I p k ( bloomed ) I p k ( vacuum ) exp ( α R ) ,
N D N 0 q ( N F ) f ( N s ) g ( N α ) ,
N 0 ( n / T ) I 0 α R 2 n 0 ρ 0 c p υ 0 a 0 ,
q ( N F ) 2 N F 2 N F 1 1 ln N F N F 1 ,
f ( N s ) 2 N s 2 [ ( N s + 1 ) ln ( N s + 1 ) N s ] ,
g ( N α ) 2 N α 2 [ N α 1 + exp ( N α ) ] ,
N F 2 π a 0 2 λ R ,
N S θ ˙ R / υ 0 ,
N α α R .
% composition n ( 1 i = n + 1 n a i 2 i = 1 n a i 2 ) × 100 % ,
AOI I p k ( corrected ) I p k ( uncorrected ) .

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