Abstract

Based on the concept of common-path/common-mode adaptive optics, the time-sharing wave-front-sensing adaptive optics system contains only one Hartmann–Shack (H–S) wave-front sensor, which detects two aberrations in the beam path alternately. After data fusion of the two aberrations, the actuator voltage of the deformable mirror (DM) is obtained. Four different data fusion methods are developed. How the disturbances of the slope data and the response matrix influence the DM’s actuator voltage in the data fusion methods is discussed, and the effective upper limits are given. Feasible data fusion methods are tested, and experiments verify that the performance of the system is good. The time-sharing technique is limited in sampling rate and is suitable only for corrections of slowly changing phases, because the H–S wave-front sensor’s sampling frequency must be adequate for the alternate detection of two aberrations.

© 2004 Optical Society of America

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References

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  1. K. W. Billman, J. A. Breakwell, R. B. Holmes, “Airborne laser system common path/common mode design approach,” in SPIE Conference on Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds, Proc. SPIE3706, 196–203 (1999).
    [CrossRef]
  2. A. J. MacGovern, “Discrete phase conjugate technique for precompensation of laser beams transmitted through turbulence,” U.S. Patent4,635,299 (January6, 1987).
  3. H. H. Barrett, S. F. Jacobs, “Retro reflective arrays as approximate phase conjugators,” Opt. Lett. 4, 190–192 (1979).
    [CrossRef] [PubMed]
  4. S. F. Jacobs, “Experiments with retro directive arrays,” Opt. Eng. (Bellingham) 21, 281–283 (1982).
    [CrossRef]
  5. R. A. Chipman, J. Shamir, “Wave-front correcting properties of corner-cube arrays,” Appl. Opt. 27, 3203–3209 (1988).
    [CrossRef] [PubMed]
  6. J. Hou, W.-H. Jiang, N. Ling, “Pseudo conjugator in common path/common mode adaptive optical system,” Acta Opt. Sin. 21, 1326–1330 (2001) (in Chinese).
  7. J. Hou, W.-H. Jiang, N. Ling, “Pseudo phase conjugate fidelity analysis of retro-reflector array,” High Power Laser Particle Beams 13, 287–290 (2001) (in Chinese).
  8. W.-H. Jiang, N. Ling, “Data fusion of the two Hartman–Shack wave-front Sensors in the common path/common mode adaptive optics system,” Acta Opt. Sin. (in Chinese, to be published).

2001 (2)

J. Hou, W.-H. Jiang, N. Ling, “Pseudo conjugator in common path/common mode adaptive optical system,” Acta Opt. Sin. 21, 1326–1330 (2001) (in Chinese).

J. Hou, W.-H. Jiang, N. Ling, “Pseudo phase conjugate fidelity analysis of retro-reflector array,” High Power Laser Particle Beams 13, 287–290 (2001) (in Chinese).

1988 (1)

1982 (1)

S. F. Jacobs, “Experiments with retro directive arrays,” Opt. Eng. (Bellingham) 21, 281–283 (1982).
[CrossRef]

1979 (1)

Barrett, H. H.

Billman, K. W.

K. W. Billman, J. A. Breakwell, R. B. Holmes, “Airborne laser system common path/common mode design approach,” in SPIE Conference on Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds, Proc. SPIE3706, 196–203 (1999).
[CrossRef]

Breakwell, J. A.

K. W. Billman, J. A. Breakwell, R. B. Holmes, “Airborne laser system common path/common mode design approach,” in SPIE Conference on Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds, Proc. SPIE3706, 196–203 (1999).
[CrossRef]

Chipman, R. A.

Holmes, R. B.

K. W. Billman, J. A. Breakwell, R. B. Holmes, “Airborne laser system common path/common mode design approach,” in SPIE Conference on Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds, Proc. SPIE3706, 196–203 (1999).
[CrossRef]

Hou, J.

J. Hou, W.-H. Jiang, N. Ling, “Pseudo phase conjugate fidelity analysis of retro-reflector array,” High Power Laser Particle Beams 13, 287–290 (2001) (in Chinese).

J. Hou, W.-H. Jiang, N. Ling, “Pseudo conjugator in common path/common mode adaptive optical system,” Acta Opt. Sin. 21, 1326–1330 (2001) (in Chinese).

Jacobs, S. F.

S. F. Jacobs, “Experiments with retro directive arrays,” Opt. Eng. (Bellingham) 21, 281–283 (1982).
[CrossRef]

H. H. Barrett, S. F. Jacobs, “Retro reflective arrays as approximate phase conjugators,” Opt. Lett. 4, 190–192 (1979).
[CrossRef] [PubMed]

Jiang, W.-H.

J. Hou, W.-H. Jiang, N. Ling, “Pseudo conjugator in common path/common mode adaptive optical system,” Acta Opt. Sin. 21, 1326–1330 (2001) (in Chinese).

J. Hou, W.-H. Jiang, N. Ling, “Pseudo phase conjugate fidelity analysis of retro-reflector array,” High Power Laser Particle Beams 13, 287–290 (2001) (in Chinese).

W.-H. Jiang, N. Ling, “Data fusion of the two Hartman–Shack wave-front Sensors in the common path/common mode adaptive optics system,” Acta Opt. Sin. (in Chinese, to be published).

Ling, N.

J. Hou, W.-H. Jiang, N. Ling, “Pseudo phase conjugate fidelity analysis of retro-reflector array,” High Power Laser Particle Beams 13, 287–290 (2001) (in Chinese).

J. Hou, W.-H. Jiang, N. Ling, “Pseudo conjugator in common path/common mode adaptive optical system,” Acta Opt. Sin. 21, 1326–1330 (2001) (in Chinese).

W.-H. Jiang, N. Ling, “Data fusion of the two Hartman–Shack wave-front Sensors in the common path/common mode adaptive optics system,” Acta Opt. Sin. (in Chinese, to be published).

MacGovern, A. J.

A. J. MacGovern, “Discrete phase conjugate technique for precompensation of laser beams transmitted through turbulence,” U.S. Patent4,635,299 (January6, 1987).

Shamir, J.

Acta Opt. Sin. (1)

J. Hou, W.-H. Jiang, N. Ling, “Pseudo conjugator in common path/common mode adaptive optical system,” Acta Opt. Sin. 21, 1326–1330 (2001) (in Chinese).

Appl. Opt. (1)

High Power Laser Particle Beams (1)

J. Hou, W.-H. Jiang, N. Ling, “Pseudo phase conjugate fidelity analysis of retro-reflector array,” High Power Laser Particle Beams 13, 287–290 (2001) (in Chinese).

Opt. Eng. (Bellingham) (1)

S. F. Jacobs, “Experiments with retro directive arrays,” Opt. Eng. (Bellingham) 21, 281–283 (1982).
[CrossRef]

Opt. Lett. (1)

Other (3)

W.-H. Jiang, N. Ling, “Data fusion of the two Hartman–Shack wave-front Sensors in the common path/common mode adaptive optics system,” Acta Opt. Sin. (in Chinese, to be published).

K. W. Billman, J. A. Breakwell, R. B. Holmes, “Airborne laser system common path/common mode design approach,” in SPIE Conference on Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds, Proc. SPIE3706, 196–203 (1999).
[CrossRef]

A. J. MacGovern, “Discrete phase conjugate technique for precompensation of laser beams transmitted through turbulence,” U.S. Patent4,635,299 (January6, 1987).

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Figures (8)

Fig. 1
Fig. 1

Common-path/common-mode AO system design.1

Fig. 2
Fig. 2

Optical configuration of time-sharing wave-front-sensing AO with one wave-front corrector. If the flat mirror is replaced by a wave-front corrector, the system will work with two wave-front correctors.

Fig. 3
Fig. 3

Time sequence working map of the time-sharing wave-front sensing AO system.

Fig. 4
Fig. 4

Configuration of the subapertures of the H–S WFS and the DM in a 37-element AO system. Hexagons represent the subapertures of the H–S WFS, and circles represent the actuators of the deformable mirror. (b) Photograph of the retroreflector array. The retroreflector array has the same arrangement as the subapertures of the H–S WFS.

Fig. 5
Fig. 5

Layout of the experiment to test the validity of phase detection with the retroreflector array.

Fig. 6
Fig. 6

Zernike coefficients of phase dtections. Data1 are obtained directly by the H–S WFS, and data2 multiplied by -1 are from measurement with the retroreflector array placed before the H–S WFS.

Fig. 7
Fig. 7

Far-field spots of the laser beam (a) without correction and (b) with correction by the time-sharing AO system, which works with the direct Slope data fusion method. The Strehl ratio is (a) 0.048 and (b) 0.240.

Fig. 8
Fig. 8

Far-field spots of the laser beam with correction by the time-sharing AO system, which works with the (a) modified slope, (b) voltage and (c) wave-front data fusion method, respectively. The Strehl ratio is (a) 0.695, (b) 0.682, and (c) 0.623.

Tables (1)

Tables Icon

Table 1 Comparison of the Lower-Order Zernike Coefficients in the Experiment Reported in Fig. 6

Equations (15)

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V=V1+V2=D1+G1+D2+G2=D1+(G1+D1D2+G2)=D1+(G1+TG2)=D1+G.
Cond(D)=DD+
ΔVVCond(D)ΔGG,
δV1+δV2V1+V2D1+δG1+D2+δGD1+G1+D2+G2=D1D1+δG1D1D1+G1+D2+G2+D2D2+δG2D2D1+G1+D2+G2Cond(D1)δG1G1+D1D2+G2+Cond(D2)δG2D2D1+G1+G2,
δV1+δV2=D1+δG1+D2+δG2D1+δG1+D2+δG.
δV1+δV2V1+V2Cond(D1)δG1GT1+Cond(D2)δG2GT2,
δV1+δV2V1+V2Cond(D1)δG1+δG2G.
δVi=-Di+δDiVi-Di+δDiδVi,
δV1+δV2V1+δV1+V2+δV2=-D1+δD1V1-D1+δD1δV1-D2+δD2V2-D2+δD2δV2V1+δV1+V2+δV2V1+δV1V1+δV1+V2+δV2D1+δD1+V1+δV1V1+δV1+V2+δV2D2+δD2M1Cond(D1)δD1D1+M2Cond(D2)δD2D2,
Mi=Vi+δViV1+δV1+V2+δV2,
δV1+δV2V1+δV1+V2+δV2Cond(D1)δD1D1,
Gi=DiVii=1,2,
V1=D1+G1,
V2=D2+G2.
G1=D1D2+G2.

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