Abstract

Adaptive correction for thermal blooming by multidither and phase-conjugation algorithms is analyzed with the use of numerical models of beams propagating in a nonlinear medium. Methods to increase the stability of these algorithms are proposed. The influence of an adaptive mirror on the efficiency and the divergence of correction algorithms is considered. The feasibility of amplitude-phase control with a two-mirror adaptive optics system is also analyzed.

© 1998 Optical Society of America

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References

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  1. J. L. Walsh, P. B. Ulrich, “Thermal blooming in the atmosphere,” in Laser Beam Propagation in the Atmosphere, J. W. Strohben, ed. (Springer-Verlag, New York, 1978), pp. 223–320.
    [CrossRef]
  2. J. E. Pearson, “Thermal blooming compensation with adaptive optics,” Opt. Lett. 2, 7–9 (1978).
    [CrossRef] [PubMed]
  3. D. E. Novoseller, “Zernike-ordered adaptive-optics correction of thermal blooming,” J. Opt. Soc. Am. A 5, 1937–1942 (1988).
    [CrossRef]
  4. B. Johnson, C. A. Primmerman, “Experimental observation of thermal-blooming phase-compensation instability,” Opt. Lett. 14, 639–641 (1989).
    [CrossRef] [PubMed]
  5. J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high-energy laser beam through the atmosphere,” Appl. Phys. 10, 129–139 (1976).
    [CrossRef]
  6. M. A. Vorontsov, V. I. Shmalhausen, Principles of Adaptive Optics (Nauka, Moscow, 1986).
  7. S. A. Akhmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Sukhorukov, S. S. Chesnokov, “Thermal blooming of laser beams and methods of its compensation,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 23, 1–37 (1980).
  8. F. Yu. Kanev, S. S. Chesnokov, “Deformable mirror in algorithms of thermal blooming correction,” Atmos. Opt. 2, 1015–1019 (1989).
  9. F. Yu. Kanev, V. P. Lukin, “Algorithms of compensation for thermal blooming,” Atmos. Opt. 6, 856–803 (1993).
  10. F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Quality of wavefront reproduction by an adaptive mirror vs. number of its actuators,” Atmos. Opt. 6, 555–558 (1991).
  11. M. P. Ogibalov, Deformations, Stability, and Oscillations of Plates (Nauka, Moscow, 1958).
  12. V. P. Kandidov, S. S. Chesnokov, V. A. Visloukh, Finite-Element Method in the Problem of Mechanics (Moscow State University, Moscow, 1976).
  13. J. F. Schonfeld, “Instability in saturated full-field compensation for thermal blooming,” J. Opt. Soc. Am. B 9, 1794–1799 (1992).
    [CrossRef]
  14. N. V. Visotina, N. N. Rosanov, V. E. Semenov, V. A. Smirnov, “Amplitude - phase adaptation with deformable mirrors on long inhomogeneous paths,” Izv. Vyssh. Uchebn. Zaved. Fiz. 28, 42–50 (1985).
  15. M. C. Roggemann, 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]

1998

1993

F. Yu. Kanev, V. P. Lukin, “Algorithms of compensation for thermal blooming,” Atmos. Opt. 6, 856–803 (1993).

1992

1991

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Quality of wavefront reproduction by an adaptive mirror vs. number of its actuators,” Atmos. Opt. 6, 555–558 (1991).

1989

F. Yu. Kanev, S. S. Chesnokov, “Deformable mirror in algorithms of thermal blooming correction,” Atmos. Opt. 2, 1015–1019 (1989).

B. Johnson, C. A. Primmerman, “Experimental observation of thermal-blooming phase-compensation instability,” Opt. Lett. 14, 639–641 (1989).
[CrossRef] [PubMed]

1988

1985

N. V. Visotina, N. N. Rosanov, V. E. Semenov, V. A. Smirnov, “Amplitude - phase adaptation with deformable mirrors on long inhomogeneous paths,” Izv. Vyssh. Uchebn. Zaved. Fiz. 28, 42–50 (1985).

1980

S. A. Akhmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Sukhorukov, S. S. Chesnokov, “Thermal blooming of laser beams and methods of its compensation,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 23, 1–37 (1980).

1978

1976

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high-energy laser beam through the atmosphere,” Appl. Phys. 10, 129–139 (1976).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Sukhorukov, S. S. Chesnokov, “Thermal blooming of laser beams and methods of its compensation,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 23, 1–37 (1980).

Chesnokov, S. S.

F. Yu. Kanev, S. S. Chesnokov, “Deformable mirror in algorithms of thermal blooming correction,” Atmos. Opt. 2, 1015–1019 (1989).

S. A. Akhmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Sukhorukov, S. S. Chesnokov, “Thermal blooming of laser beams and methods of its compensation,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 23, 1–37 (1980).

V. P. Kandidov, S. S. Chesnokov, V. A. Visloukh, Finite-Element Method in the Problem of Mechanics (Moscow State University, Moscow, 1976).

Feit, M. D.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high-energy laser beam through the atmosphere,” Appl. Phys. 10, 129–139 (1976).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high-energy laser beam through the atmosphere,” Appl. Phys. 10, 129–139 (1976).
[CrossRef]

Johnson, B.

Kandidov, V. P.

S. A. Akhmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Sukhorukov, S. S. Chesnokov, “Thermal blooming of laser beams and methods of its compensation,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 23, 1–37 (1980).

V. P. Kandidov, S. S. Chesnokov, V. A. Visloukh, Finite-Element Method in the Problem of Mechanics (Moscow State University, Moscow, 1976).

Kanev, F. Yu.

F. Yu. Kanev, V. P. Lukin, “Algorithms of compensation for thermal blooming,” Atmos. Opt. 6, 856–803 (1993).

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Quality of wavefront reproduction by an adaptive mirror vs. number of its actuators,” Atmos. Opt. 6, 555–558 (1991).

F. Yu. Kanev, S. S. Chesnokov, “Deformable mirror in algorithms of thermal blooming correction,” Atmos. Opt. 2, 1015–1019 (1989).

Lavrinova, L. N.

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Quality of wavefront reproduction by an adaptive mirror vs. number of its actuators,” Atmos. Opt. 6, 555–558 (1991).

Lee, D. J.

Lukin, V. P.

F. Yu. Kanev, V. P. Lukin, “Algorithms of compensation for thermal blooming,” Atmos. Opt. 6, 856–803 (1993).

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Quality of wavefront reproduction by an adaptive mirror vs. number of its actuators,” Atmos. Opt. 6, 555–558 (1991).

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high-energy laser beam through the atmosphere,” Appl. Phys. 10, 129–139 (1976).
[CrossRef]

Novoseller, D. E.

Ogibalov, M. P.

M. P. Ogibalov, Deformations, Stability, and Oscillations of Plates (Nauka, Moscow, 1958).

Pearson, J. E.

Primmerman, C. A.

Roggemann, M. C.

Rosanov, N. N.

N. V. Visotina, N. N. Rosanov, V. E. Semenov, V. A. Smirnov, “Amplitude - phase adaptation with deformable mirrors on long inhomogeneous paths,” Izv. Vyssh. Uchebn. Zaved. Fiz. 28, 42–50 (1985).

Schonfeld, J. F.

Semenov, V. E.

N. V. Visotina, N. N. Rosanov, V. E. Semenov, V. A. Smirnov, “Amplitude - phase adaptation with deformable mirrors on long inhomogeneous paths,” Izv. Vyssh. Uchebn. Zaved. Fiz. 28, 42–50 (1985).

Shmalhausen, V. I.

M. A. Vorontsov, V. I. Shmalhausen, Principles of Adaptive Optics (Nauka, Moscow, 1986).

Smirnov, V. A.

N. V. Visotina, N. N. Rosanov, V. E. Semenov, V. A. Smirnov, “Amplitude - phase adaptation with deformable mirrors on long inhomogeneous paths,” Izv. Vyssh. Uchebn. Zaved. Fiz. 28, 42–50 (1985).

Sukhorukov, A. P.

S. A. Akhmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Sukhorukov, S. S. Chesnokov, “Thermal blooming of laser beams and methods of its compensation,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 23, 1–37 (1980).

Ulrich, P. B.

J. L. Walsh, P. B. Ulrich, “Thermal blooming in the atmosphere,” in Laser Beam Propagation in the Atmosphere, J. W. Strohben, ed. (Springer-Verlag, New York, 1978), pp. 223–320.
[CrossRef]

Visloukh, V. A.

V. P. Kandidov, S. S. Chesnokov, V. A. Visloukh, Finite-Element Method in the Problem of Mechanics (Moscow State University, Moscow, 1976).

Visotina, N. V.

N. V. Visotina, N. N. Rosanov, V. E. Semenov, V. A. Smirnov, “Amplitude - phase adaptation with deformable mirrors on long inhomogeneous paths,” Izv. Vyssh. Uchebn. Zaved. Fiz. 28, 42–50 (1985).

Vorontsov, M. A.

S. A. Akhmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Sukhorukov, S. S. Chesnokov, “Thermal blooming of laser beams and methods of its compensation,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 23, 1–37 (1980).

M. A. Vorontsov, V. I. Shmalhausen, Principles of Adaptive Optics (Nauka, Moscow, 1986).

Walsh, J. L.

J. L. Walsh, P. B. Ulrich, “Thermal blooming in the atmosphere,” in Laser Beam Propagation in the Atmosphere, J. W. Strohben, ed. (Springer-Verlag, New York, 1978), pp. 223–320.
[CrossRef]

Appl. Opt.

Appl. Phys.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high-energy laser beam through the atmosphere,” Appl. Phys. 10, 129–139 (1976).
[CrossRef]

Atmos. Opt.

F. Yu. Kanev, S. S. Chesnokov, “Deformable mirror in algorithms of thermal blooming correction,” Atmos. Opt. 2, 1015–1019 (1989).

F. Yu. Kanev, V. P. Lukin, “Algorithms of compensation for thermal blooming,” Atmos. Opt. 6, 856–803 (1993).

F. Yu. Kanev, V. P. Lukin, L. N. Lavrinova, “Quality of wavefront reproduction by an adaptive mirror vs. number of its actuators,” Atmos. Opt. 6, 555–558 (1991).

Izv. Vyssh. Uchebn. Zaved. Fiz.

N. V. Visotina, N. N. Rosanov, V. E. Semenov, V. A. Smirnov, “Amplitude - phase adaptation with deformable mirrors on long inhomogeneous paths,” Izv. Vyssh. Uchebn. Zaved. Fiz. 28, 42–50 (1985).

Izv. Vyssh. Uchebn. Zaved. Radiofiz.

S. A. Akhmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Sukhorukov, S. S. Chesnokov, “Thermal blooming of laser beams and methods of its compensation,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 23, 1–37 (1980).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Lett.

Other

J. L. Walsh, P. B. Ulrich, “Thermal blooming in the atmosphere,” in Laser Beam Propagation in the Atmosphere, J. W. Strohben, ed. (Springer-Verlag, New York, 1978), pp. 223–320.
[CrossRef]

M. P. Ogibalov, Deformations, Stability, and Oscillations of Plates (Nauka, Moscow, 1958).

V. P. Kandidov, S. S. Chesnokov, V. A. Visloukh, Finite-Element Method in the Problem of Mechanics (Moscow State University, Moscow, 1976).

M. A. Vorontsov, V. I. Shmalhausen, Principles of Adaptive Optics (Nauka, Moscow, 1986).

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Figures (8)

Fig. 1
Fig. 1

Adaptive control by the modified phase-conjugation algorithm [Eq. (5)]: Z = 0.5Z d , R v = -20.

Fig. 2
Fig. 2

Criterion J [Eq. (3)] as a function of two coordinates (tilt–defocusing): Z = 0.5Z d , R v = -100, and the receiving aperture S t = a 0/4.

Fig. 3
Fig. 3

Same as in Fig. 2 but for S t = a 0/2.

Fig. 4
Fig. 4

Schematic of adaptive mirrors used in numerical experiments.

Fig. 5
Fig. 5

Oscillations of J due to oscillations of the reflecting surface: Z = 0.5Z d , R v = -20.

Fig. 6
Fig. 6

Adaptive control by the multidither algorithm in the presence of oscillations of the adaptive mirror (curve 1). Curve 2 is for the flat mirror (results obtained without correction). Z = 0.5Z d , R v = -20.

Fig. 7
Fig. 7

Schematic of a two-mirror adaptive optics system: L, laser; M1 and M2, deformable mirrors; S, screen where the laser beam parameters are detected. The reference beam is opposite the main beam.

Fig. 8
Fig. 8

Results of thermal-blooming correction with the two-mirror adaptive optics system: N z = 0 corresponds to flat mirror M1; N z = 1, … , 4 indicates the increase of the number of Zernike polynomials reproduced by the first mirror; N z = 5 corresponds to the ideal full-field conjugation.

Tables (1)

Tables Icon

Table 1 Results of Adaptive Correction for Thermal Distortions with Different Mirrorsa

Equations (9)

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2 ik   E z = Δ E + 2   k 2 n 0   n NL E ,
T t + V x T x + V y T y = α ρ 0 C p   I ,
x = x / a 0 ,     y = y / a 0 ,     z = z / z d ,
2 i   E z = Δ E + R v TE , T t + V x T x + V y T y = | E | 2 .
R v = 2 ka 0 2 α I n 0 ρ 0 C p V n T .
J t = 1 P     exp - x 2 + y 2 / S t 2 I x ,   y ,   z 0 ,   t d x d y
U x ,   y ,   t = - ϕ x ,   y ,   t - τ d ,
U x ,   y ,   t = 1 - β t - τ d U max x ,   y - β t - τ d ϕ x ,   y ,   t - τ d .
F t = F t - τ d + β t - τ d grad   J t - τ d ,

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