Abstract

To implement adaptive optics compensation for propagation through deep turbulence, the concept of gradient descent tomography has been developed. Here two or more deformable mirrors are controlled by an efficient iterative algorithm that optimizes the integral I2 image-sharpening metric. In this work a difficult case involving imaging over a 2km path with a Cn2 of 2×1013m23 is considered. For a wavelength of 1.06μm and a 10-cm-diameter aperture, λD is seven times the isoplanatic angle (ϑ0=1.54μrad), and the Rytov number is 5.5. For three points placed along a line spanning approximately 70 isoplanatic patch sizes all three points are compensated somewhat, illustrating that anisoplanatism is addressed. The fact that the corresponding performance improvement ratios are 1.20, 1.34, and 3.26 in the presence of such strong scintillation and anisoplanatism is quite significant.

© 2006 Optical Society of America

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References

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  1. P. H. Roberts, "Expected performance of a wavefront compensation experiment using a fat spot with a Hartmann sensor," Rep. TR-1281 (the Optical Sciences Company, Anaheim, California, 1994).
  2. D. L. Fried, "Fat spot AGS focus anisoplanatism: Zernike-mode analysis," Rep. TR-1337 (the Optical Sciences Company, Anaheim, California, 1995).
  3. J. L. Vaughn, "Wavefront error for an extended beacon," Rep. TR-1342 (the Optical Sciences Company, Anaheim, California, 1995).
  4. P. H. Roberts, R. H. Dueck, S. L. Browne, G. A. Tyler, and J. L. Vaughn, "Experimental comparison of wavefront measurements of a star and an extended guide star," Rep. TR-1346 (the Optical Sciences Company, Anaheim, California, 1995).
  5. M. Belen'kii and K. Hughes, "Beacon anisoplanatism," in Proc. SPIE 5087, 69-82 (2003).
    [CrossRef]
  6. B. L. Ellerbroek, "First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes," J. Opt. Soc. Am. A 11, 783-805 (1994).
    [CrossRef]
  7. R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron. Astrophys. 342, L53-L56 (1999).
  8. R. Flicker, F. J. Rigaut, and B. L. Ellerbroek, "Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope," Proc. SPIE 4007, 1032-1043 (2000).
    [CrossRef]
  9. M. Lloyd-Hart and N. M. Milton, "Fundamental limits on isoplanatic correction with multiconjugate adaptive optics," J. Opt. Soc. Am. A 20, 1949-1956 (2003).
    [CrossRef]
  10. M. C. Roggemann and D. J. Lee, "Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere," Appl. Opt. 37, 4577-4585 (1998).
    [CrossRef]
  11. J. D. Barchers and B. L. Ellerbroek, "Improved compensation of turbulence-induced amplitude and phase distortions by means of multiple near-field phase measurements," J. Opt. Soc. Am. A 18, 399-411 (2001).
    [CrossRef]
  12. J. D. Barchers, "Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations," J. Opt. Soc. Am. A 19, 926-945 (2002).
    [CrossRef]
  13. A. Tokovinin and E. Viard, "Limiting precision of tomographic phase estimation," J. Opt. Soc. Am. A 18, 873-881 (2001).
    [CrossRef]
  14. J. B. Shellan, "Evaluation of multi-conjugate adaptive optics for exact compensation in multiple directions," Rep. TR-1599 (the Optical Sciences Company, Anaheim, California, 2003).
  15. M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, "Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration," J. Opt. Soc. Am. A 17, 1440-1453 (2000).
    [CrossRef]
  16. D. L. Fried, "Branch point problem in adaptive optics," J. Opt. Soc. Am. A 15, 2759-2768 (1998).
    [CrossRef]
  17. G. A. Tyler, "Reconstruction and assessment of the least-squares and slope discrepancy components of the phase," J. Opt. Soc. Am. A 17, 1828-1839 (2000).
    [CrossRef]
  18. D. L. Fried and J. L. Vaughn, "Branch cuts in the phase function," Appl. Opt. 31, 2865-2882 (1992).
    [CrossRef] [PubMed]

2003 (2)

2002 (1)

2001 (2)

2000 (3)

1999 (1)

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron. Astrophys. 342, L53-L56 (1999).

1998 (2)

1994 (1)

1992 (1)

Barchers, J. D.

Belen'kii, M.

M. Belen'kii and K. Hughes, "Beacon anisoplanatism," in Proc. SPIE 5087, 69-82 (2003).
[CrossRef]

Browne, S. L.

P. H. Roberts, R. H. Dueck, S. L. Browne, G. A. Tyler, and J. L. Vaughn, "Experimental comparison of wavefront measurements of a star and an extended guide star," Rep. TR-1346 (the Optical Sciences Company, Anaheim, California, 1995).

Carhart, G. W.

Cauwenberghs, G.

Cohen, M.

Dueck, R. H.

P. H. Roberts, R. H. Dueck, S. L. Browne, G. A. Tyler, and J. L. Vaughn, "Experimental comparison of wavefront measurements of a star and an extended guide star," Rep. TR-1346 (the Optical Sciences Company, Anaheim, California, 1995).

Ellerbroek, B. L.

Flicker, R.

R. Flicker, F. J. Rigaut, and B. L. Ellerbroek, "Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope," Proc. SPIE 4007, 1032-1043 (2000).
[CrossRef]

Fried, D. L.

Hughes, K.

M. Belen'kii and K. Hughes, "Beacon anisoplanatism," in Proc. SPIE 5087, 69-82 (2003).
[CrossRef]

Lee, D. J.

Lloyd-Hart, M.

Marchetti, E.

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron. Astrophys. 342, L53-L56 (1999).

Milton, N. M.

Ragazzoni, R.

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron. Astrophys. 342, L53-L56 (1999).

Rigaut, F.

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron. Astrophys. 342, L53-L56 (1999).

Rigaut, F. J.

R. Flicker, F. J. Rigaut, and B. L. Ellerbroek, "Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope," Proc. SPIE 4007, 1032-1043 (2000).
[CrossRef]

Roberts, P. H.

P. H. Roberts, "Expected performance of a wavefront compensation experiment using a fat spot with a Hartmann sensor," Rep. TR-1281 (the Optical Sciences Company, Anaheim, California, 1994).

P. H. Roberts, R. H. Dueck, S. L. Browne, G. A. Tyler, and J. L. Vaughn, "Experimental comparison of wavefront measurements of a star and an extended guide star," Rep. TR-1346 (the Optical Sciences Company, Anaheim, California, 1995).

Roggemann, M. C.

Shellan, J. B.

J. B. Shellan, "Evaluation of multi-conjugate adaptive optics for exact compensation in multiple directions," Rep. TR-1599 (the Optical Sciences Company, Anaheim, California, 2003).

Tokovinin, A.

Tyler, G. A.

G. A. Tyler, "Reconstruction and assessment of the least-squares and slope discrepancy components of the phase," J. Opt. Soc. Am. A 17, 1828-1839 (2000).
[CrossRef]

P. H. Roberts, R. H. Dueck, S. L. Browne, G. A. Tyler, and J. L. Vaughn, "Experimental comparison of wavefront measurements of a star and an extended guide star," Rep. TR-1346 (the Optical Sciences Company, Anaheim, California, 1995).

Vaughn, J. L.

D. L. Fried and J. L. Vaughn, "Branch cuts in the phase function," Appl. Opt. 31, 2865-2882 (1992).
[CrossRef] [PubMed]

P. H. Roberts, R. H. Dueck, S. L. Browne, G. A. Tyler, and J. L. Vaughn, "Experimental comparison of wavefront measurements of a star and an extended guide star," Rep. TR-1346 (the Optical Sciences Company, Anaheim, California, 1995).

J. L. Vaughn, "Wavefront error for an extended beacon," Rep. TR-1342 (the Optical Sciences Company, Anaheim, California, 1995).

Viard, E.

Vorontsov, M. A.

Appl. Opt. (2)

Astron. Astrophys. (1)

R. Ragazzoni, E. Marchetti, and F. Rigaut, "Modal tomography for adaptive optics," Astron. Astrophys. 342, L53-L56 (1999).

J. Opt. Soc. Am. A (8)

Proc. SPIE (2)

R. Flicker, F. J. Rigaut, and B. L. Ellerbroek, "Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope," Proc. SPIE 4007, 1032-1043 (2000).
[CrossRef]

M. Belen'kii and K. Hughes, "Beacon anisoplanatism," in Proc. SPIE 5087, 69-82 (2003).
[CrossRef]

Other (5)

J. B. Shellan, "Evaluation of multi-conjugate adaptive optics for exact compensation in multiple directions," Rep. TR-1599 (the Optical Sciences Company, Anaheim, California, 2003).

P. H. Roberts, "Expected performance of a wavefront compensation experiment using a fat spot with a Hartmann sensor," Rep. TR-1281 (the Optical Sciences Company, Anaheim, California, 1994).

D. L. Fried, "Fat spot AGS focus anisoplanatism: Zernike-mode analysis," Rep. TR-1337 (the Optical Sciences Company, Anaheim, California, 1995).

J. L. Vaughn, "Wavefront error for an extended beacon," Rep. TR-1342 (the Optical Sciences Company, Anaheim, California, 1995).

P. H. Roberts, R. H. Dueck, S. L. Browne, G. A. Tyler, and J. L. Vaughn, "Experimental comparison of wavefront measurements of a star and an extended guide star," Rep. TR-1346 (the Optical Sciences Company, Anaheim, California, 1995).

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Figures (6)

Fig. 1
Fig. 1

Results correspond to the 2000-m-deep turbulence case summarized in Table 1. Left figure corresponds to a point beacon, the right figure to a 20-cm-diameter beacon.

Fig. 2
Fig. 2

Top panel illustrates the far-field patterns that were obtained from a wave-optics simulation of the deep turbulence configuration. The six rows of far-field patterns from top to bottom correspond, respectively, to the following cases: diffraction-limited, point beacon, 5-cm beacon, 10-cm beacon, 20-cm beacon, uncompensated. In each case the far-field patterns from left to right correspond to an extended beacon at various positions off axis that include zero, one, two, four, eight and 16 times ϑ 0 . These qualitative results are enhanced by the quantitative data presented in the bottom panel. Here the Strehl ratios for all cases are plotted for various field angles.

Fig. 3
Fig. 3

Top panel illustrates an array of far-field patterns. From top to bottom, each row corresponds, respectively, to the following different wavefront reconstructor–beacon configurations: diffraction limited, point source branch cut, 20-cm beacon branch cut, point source least-squares, 20-cm beacon least-squares. Each column of the figure corresponds left to right to the following different off-axis locations: on-axis, one, two, four, eight, sixteen times ϑ 0 . Quantitative results are illustrated in the bottom panel.

Fig. 4
Fig. 4

Seven far-field patterns are shown. The far-field pattern in the upper right represents the diffraction-limited result. The remaining six far-field patterns contain three pairs. From left to right each pair corresponds to uncompensated, one DM using GDT, and two DMs driven by the GDT algorithm. The Strehl ratios in each case are illustrated.

Fig. 5
Fig. 5

Left figures illustrate beacon irradiance and estimated irradiance. Right figure illustrates performance for a variety of techniques as a function of turbulence strength.

Fig. 6
Fig. 6

Two-km case presented in Table 1 is evaluated with the Optical Sciences Company’s wave-optics simulation to obtain these results, which illustrate that not only are the point sources compensated for, but anisoplanatism is reduced. The Strehl ratios are 0.0081, 0.0252, and 0.0304 for uncompensated and 0.0097, 0.0337, and 0.0992 for the corresponding compensated cases. The performance improvement ratios are 1.20, 1.34, and 3.26. The spots in the left set are uncompensated, and those in the right set are compensated.

Tables (2)

Tables Icon

Table 1 Plane-Wave Turbulence Parameters

Tables Icon

Table 2 Anisoplanatism Reduction Obtained with Zernike Tomography for Uniform Turbulence along a Path of Length L

Equations (13)

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ϕ 1 [ ( 1 z 1 R 1 ) r R ] + ϕ 2 [ ( 1 z 2 R 1 ) r R ] = ψ 1 ( r ) ,
ϕ 1 [ ( 1 z 1 R 2 ) r R ] + ϕ 2 [ ( 1 z 2 R 2 ) r R ] = ψ 2 ( r ) .
ψ n ( r ) = p a p ( n ) Z p ( r R ) ,
ϕ m [ ( 1 z m R j ) r R ] = p c p ( m ) Z p [ ( 1 z m R j ) r R ] ,
Z p [ ( 1 z m R j ) r R ] = p B p q ( m j ) Z q ( r R ) .
ϕ m [ ( 1 z m R j ) r R ] = p q c p ( m ) B p q ( m j ) Z q ( r R ) .
p q [ c p ( 1 ) B p q ( 1 , 1 ) + c p ( 2 ) B p q ( 2 , 1 ) ] Z q ( r R ) = p a p ( 1 ) Z p ( r R ) ,
p q [ c p ( 1 ) B p q ( 1 , 2 ) + c p ( 2 ) B p q ( 2 , 2 ) ] Z q ( r R ) = p a p ( 2 ) Z p ( r R ) .
a = B c .
c = B 1 a .
s = d r I 2 ( r ) ,
g n = s a n ,
δ a = β g ,

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