Abstract

Compensation of extended (deep) turbulence effects is one of the most challenging problems in adaptive optics (AO). In the AO approach described, the deep turbulence wave propagation regime was achieved by imaging stars at low elevation angles when image quality improvement with conventional AO was poor. These experiments were conducted at the U.S. Air Force Maui Optical and Supercomputing Site (AMOS) by using the 3.63m telescope located on Haleakala, Maui. To enhance compensation performance we used a cascaded AO system composed of a conventional AO system based on a Shack–Hartmann wavefront sensor and a deformable mirror with 941 actuators, and an AO system based on stochastic parallel gradient descent optimization with four deformable mirrors (75 control channels). This first-time field demonstration of a cascaded AO system achieved considerably improved performance of wavefront phase aberration compensation. Image quality was improved in a repeatable way in the presence of stressing atmospheric conditions obtained by using stars at elevation angles as low as 15°.

© 2008 Optical Society of America

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2007 (1)

2006 (1)

2005 (1)

2002 (3)

2001 (1)

2000 (2)

1998 (2)

1997 (1)

1994 (1)

1992 (1)

1982 (1)

1974 (1)

Aksenov, V. P.

Barchers, J. D.

Beresnev, L.

M. A. Vorontsov, J. F. Riker, G. Carhart, V. S. Gudimetla, L. Beresnev, and T. Weyrauch “Atmospheric turbulence compensation of point source images using asynchronous stochastic parallel gradient descent technique on AMOS 3.6 m telescope,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2007). pp. 658-668.

Beresnev, L. A.

L. A. Beresnev, M. A. Vorontsov, and P. Wangsness, “Pocket deformable mirror for adaptive optics applications,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2006), pp. 568-575.

L. A. Beresnev and M. A. Vorontsov, “Scalable-size deformable pocket mirror with on-pockets bimorph actuators,” provisional U.S. patent application 60/984,799 filed 2 November, 2007.

Bifano, T. G.

Buffington, A.

Carhart, G.

M. A. Vorontsov and G. Carhart, “Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters,” J. Opt. Soc. Am. A 23, 2613-2622 (2006).
[CrossRef]

M. A. Vorontsov, J. F. Riker, G. Carhart, V. S. Gudimetla, L. Beresnev, and T. Weyrauch “Atmospheric turbulence compensation of point source images using asynchronous stochastic parallel gradient descent technique on AMOS 3.6 m telescope,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2007). pp. 658-668.

Carhart, G. W.

Cauwenberghs, G.

Chen, M.

Cohen, M.

Fried, D. L.

Gudimetla, V. S.

M. A. Vorontsov, J. F. Riker, G. Carhart, V. S. Gudimetla, L. Beresnev, and T. Weyrauch “Atmospheric turbulence compensation of point source images using asynchronous stochastic parallel gradient descent technique on AMOS 3.6 m telescope,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2007). pp. 658-668.

Hammer, J.

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).

Kireev, S. V.

Kravtsov, Yu A.

M. C. Rytov, Yu A. Kravtsov, and V. I. Tatarskii, Wave Propagation through Random Media, Vol. 4 of Principles of Statistical Radiophysics (Springer-Verlag, 1989).

Link, D. J.

Muller, R. A.

Neyman, C. R.

L. C. Roberts, Jr., and C. R. Neyman, “Characterization of the AMOS adaptive optics system,” Pub. Astron. Soc. Pacific 114, 1260-1266 (2002).
[CrossRef]

Olivier, J. C.

Ricklin, J. C.

Riker, J. F.

M. A. Vorontsov, J. F. Riker, G. Carhart, V. S. Gudimetla, L. Beresnev, and T. Weyrauch “Atmospheric turbulence compensation of point source images using asynchronous stochastic parallel gradient descent technique on AMOS 3.6 m telescope,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2007). pp. 658-668.

Roberts, L. C.

L. C. Roberts, Jr., and C. R. Neyman, “Characterization of the AMOS adaptive optics system,” Pub. Astron. Soc. Pacific 114, 1260-1266 (2002).
[CrossRef]

Roddier, F.

F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).
[CrossRef]

Roux, F. S.

Rytov, M. C.

M. C. Rytov, Yu A. Kravtsov, and V. I. Tatarskii, Wave Propagation through Random Media, Vol. 4 of Principles of Statistical Radiophysics (Springer-Verlag, 1989).

Sasiela, R. J.

Sivokon, V. P.

Sokolovskiy, S. V.

Tatarskii, V. I.

M. C. Rytov, Yu A. Kravtsov, and V. I. Tatarskii, Wave Propagation through Random Media, Vol. 4 of Principles of Statistical Radiophysics (Springer-Verlag, 1989).

Tikhomirova, O. V.

Tyler, G. A.

Vorontsov, M. A.

M. A. Vorontsov and G. Carhart, “Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters,” J. Opt. Soc. Am. A 23, 2613-2622 (2006).
[CrossRef]

T. Weyrauch and M. A. Vorontsov, “Atmospheric compensation with a speckle beacon under strong scintillation conditions: directed energy and laser communication applications,” Appl. Opt. 44, 6388-6401 (2005).
[CrossRef] [PubMed]

T. Weyrauch, M. A. Vorontsov, T. G. Bifano, J. Hammer, M. Cohen, and G. Cauwenberghs, “Micro-scale adaptive optics: wavefront control with μ mirror array and VLSI stochastic gradient descent controller,” Appl. Opt. 40, 4243-4253(2001).
[CrossRef]

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]

M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel gradient descent technique for high-resolution wavefront phase distortion correction,” J. Opt. Soc. Am. A 15, 2745-2758(1998).
[CrossRef]

M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22, 907-909 (1997).
[CrossRef] [PubMed]

M. A. Vorontsov, J. F. Riker, G. Carhart, V. S. Gudimetla, L. Beresnev, and T. Weyrauch “Atmospheric turbulence compensation of point source images using asynchronous stochastic parallel gradient descent technique on AMOS 3.6 m telescope,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2007). pp. 658-668.

L. A. Beresnev and M. A. Vorontsov, “Scalable-size deformable pocket mirror with on-pockets bimorph actuators,” provisional U.S. patent application 60/984,799 filed 2 November, 2007.

L. A. Beresnev, M. A. Vorontsov, and P. Wangsness, “Pocket deformable mirror for adaptive optics applications,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2006), pp. 568-575.

Wangsness, P.

L. A. Beresnev, M. A. Vorontsov, and P. Wangsness, “Pocket deformable mirror for adaptive optics applications,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2006), pp. 568-575.

Weyrauch, T.

T. Weyrauch and M. A. Vorontsov, “Atmospheric compensation with a speckle beacon under strong scintillation conditions: directed energy and laser communication applications,” Appl. Opt. 44, 6388-6401 (2005).
[CrossRef] [PubMed]

T. Weyrauch, M. A. Vorontsov, T. G. Bifano, J. Hammer, M. Cohen, and G. Cauwenberghs, “Micro-scale adaptive optics: wavefront control with μ mirror array and VLSI stochastic gradient descent controller,” Appl. Opt. 40, 4243-4253(2001).
[CrossRef]

M. A. Vorontsov, J. F. Riker, G. Carhart, V. S. Gudimetla, L. Beresnev, and T. Weyrauch “Atmospheric turbulence compensation of point source images using asynchronous stochastic parallel gradient descent technique on AMOS 3.6 m telescope,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2007). pp. 658-668.

Appl. Opt. (4)

J. Opt. Soc. Am. (2)

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

Opt. Lett. (1)

Pub. Astron. Soc. Pacific (1)

L. C. Roberts, Jr., and C. R. Neyman, “Characterization of the AMOS adaptive optics system,” Pub. Astron. Soc. Pacific 114, 1260-1266 (2002).
[CrossRef]

Other (6)

L. A. Beresnev, M. A. Vorontsov, and P. Wangsness, “Pocket deformable mirror for adaptive optics applications,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2006), pp. 568-575.

L. A. Beresnev and M. A. Vorontsov, “Scalable-size deformable pocket mirror with on-pockets bimorph actuators,” provisional U.S. patent application 60/984,799 filed 2 November, 2007.

M. A. Vorontsov, J. F. Riker, G. Carhart, V. S. Gudimetla, L. Beresnev, and T. Weyrauch “Atmospheric turbulence compensation of point source images using asynchronous stochastic parallel gradient descent technique on AMOS 3.6 m telescope,” in Proceedings of AMOS Technologies Conference (Maui Economic Development Board, 2007). pp. 658-668.

M. C. Rytov, Yu A. Kravtsov, and V. I. Tatarskii, Wave Propagation through Random Media, Vol. 4 of Principles of Statistical Radiophysics (Springer-Verlag, 1989).

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).

F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Notional schematic of the cascaded AO imaging system composed of the conventional adaptive system (C_AO) and the SPGD system (SPGD_AO). The residual wavefront phase δ A in the C_AO system is analyzed by the Shack–Hartmann wavefront sensor (WFS), and the sensor’s output signals { S l } are sent to the controller (C_AO controller) that provides control voltages { c j } applied to the actuators of the deformable mirror DM COA . In the SPGD_AO system the corrected optical wave with residual phase aberration δ S is focused into a pinhole. The SPGD controller (SPGD_AO controller) uses the measurement of the signal J received through the pinhole as an input to compute control voltages { a j } applied to the deformable mirrors shown as a single transmissive optical element DM SPGD . The perturbation generator (PG) supplies small amplitude control voltages { δ a j } to both deformable mirrors DM SPGD and the SPGD controller.

Fig. 2
Fig. 2

Schematic of the SPGD adaptive system. The system is composed of the pocket mirror PM, two deformable mirrors DM 1 and DM 1 , tip–tilt (beam steering) mirror TTM, off-axis parabolic mirrors OAP 1 OAP 3 , beam splitter BS, pinhole D, photodetector PD, and a NIR CCD camera. The SPGD control system includes personal computers PC 1 PC 3 and high-voltage amplifiers HVA (number of control channels is indicated in parentheses).

Fig. 3
Fig. 3

Pocket deformable mirror (PM): (a) photograph of the back side of PM with seven machined pockets, (b) geometry of seven electrodes inside each pocket, (c) an interference pattern, (d) the 3D phase pattern reconstructed from the interferogram in (c). In (c) and (d) static control signals with the amplitude 90   V were applied to the electrodes indicated by the stars in (b), and zero control signals to the remaining electrodes.

Fig. 4
Fig. 4

Deformable mirror (DM): (a) photograph of the front side of DM with aperture 25 mm , (b) geometry of 13 electrodes, (c) an interference pattern, (d) the 3D phase pattern reconstructed from the interferogram in (c). The patterns in (c) and (d) illustrate the phase aberration introduced by the deformable mirror corresponding to a static control signal with an amplitude of 90   V applied to the electrode indicated by the star in (b), and zero control signals to the remaining electrodes.

Fig. 5
Fig. 5

Characteristic examples of metric J time dependence corresponding to single (a) and averaged (b) adaptation trials composed of the following four adaptation phases: the SPGD AO system turned off (SPGD_OFF), the SPGD system operating with only deformable mirror DM 2 active (DM_ONLY), with the corresponding system operating with both the PM and DM 2 mirrors active (PM&DM), and with only the PM (PM_ONLY) active. The pinhole size is equal to 150   μm . The light source was Antares at elevation angle 16 ° . The C_AO system (AEOS) was on for all cases. In all four adaptation phases the control voltages applied to the deformable mirror DM 1 were fixed.

Fig. 6
Fig. 6

Probability distributions p J versus metric J in arbitrary units (a.u.) obtained by averaging 50 adaptation trials for different adaptation phases: (a) without and (b) with quasi-static (atmospheric averaged) phase aberration compensation. The corresponding data were recorded with the C_AO system off, using Antares as a light source at an elevation angle between 16 ° and 18 ° . The SPGD adaptation rate was about 6000 iterations per second. The pinhole size for metric measurements was 200   μm . Note that compensation of quasi-static aberration in (b) resulted in a noticeable shift toward bigger metric values (to the right) in the probability distribution curve, corresponding to the SPGD OFF regime.

Fig. 7
Fig. 7

Probability distributions p J versus metric J in arbitrary units (a.u.) obtained by averaging 50 adaptation trials with one (a) and with two (b) SPGD controllers. In (a) the SPGD controller PC 1 was used to control the deformable mirror DM 1 (DM ONLY), or PM (PM ONLY), or DM 1 and PM (DM&PM) with the iteration rate 6000 iterations per second. In (b) the SPGD controller PC 2 was used to control the deformable mirror DM 2 with the iteration rate 8000 iterations per second (DM ONLY), and both PC 2 and PC 1 SPGD controllers were used to asynchronously control two deformable mirrors DM 2 and DM 1 with the iteration rates 8000 and 6000 iterations per second, correspondingly (2DMs). The corresponding data were recorded with the C_AO system off, using Antares as a light source at an elevation angle between 16 ° and 18 ° (between 9:09 p.m. and 9:30 p.m.) on (a) 18 May and (b) 17 May 2007. The pinhole size for metric measurements was 200   μm .

Fig. 8
Fig. 8

Temporal dependences of the image quality metrics calculated based on postprocessing of a video-sequence (movie) containing 500 short-exposure NIR images of the third magnitude star Delta Ophiuchi at an ~45° elevation angle for the following operational regimes: ON / ON , feedback control is on for both the C_AO system and SPGD AO system with DM 1 and PM deformable mirrors both operating; OFF / ON , feedback control is on for only the SPGD AO system; and OFF / ON , feedback control is on for only the C_AO system. The image quality metrics are: (a) sharpness function J 2 , (b) star image width w in micrometers; (c) power-in-the-bucket metric J PIB (received light power inside a circular area of 200   μm ) in arbitrary units (a.u.), and (d) maximum focal plane intensity I max . The SPGD adaptation rate was 4600 iterations per second. The pinhole size was 200   μm .

Fig. 9
Fig. 9

Short exposure images of the star Antares at low elevation angles (between 11° and 13°) obtained on 18 May 2007 in the cascaded adaptive optical system with the operational regimes (a)  OFF / OFF (no AO control, (b)  ON / OFF (control is on for only C_AO), and (c)  OFF / ON (control is on for only SPGD AO with DM 1 ). The diffraction-limited image and the pinhole sizes are shown in the bottom left by the white circle and ring, respectively.

Fig. 10
Fig. 10

Short exposure images of the star Antares at low elevation angles (between 22° and 25°) obtained on 18 May 2007 in the cascade adaptive optical system with the operational regimes (a)  OFF / OFF (no AO control), (b)  ON / OFF (control of only C_AO), (c) OFF/ON (control of only SPGD AO with DM 1 ), (d)  ON / ON (cascaded AO).

Equations (3)

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a j ( n + 1 ) = a j ( n ) + γ ( n ) δ a j ( n ) δ J ( n ) ( J = 1 , , N ) , n = 1 , ,
γ ( n ) = γ 0 ( J opt J opt + J ( n ) ) , κ ( n ) = κ 0 ( J opt J opt + J ( n ) ) q ,
w 2 = 1 P 0 s | r r c | 2 I ( r ) d 2 r , where     r c = 1 P 0 s r I ( r ) d 2 r

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