Abstract

Measurements using an experimental, visible wavelength, eighteen-element, multidither, self-adaptive, planar, optical phased array have been made on a well-characterized outdoor 100-m propagation range. The measurements have proved that this type of coat system can remove most of the beam distortions produced by atmospheric turbulence and by fixed optical system errors. The system has demonstrated the ability to form a beam with a nearly diffraction-limited peak intensity for turbulence levels characterized by structure constants (CN2) ranging from 1 × 10−16 cm−2/3 to 6 × 10−14 cm−2/3. Convergence times for the coat system range from 1.5 msec to 3.0 msec for a servo system with a 500-Hz unity gain bandwidth. Spectral analysis of the coat correction signals indicates, however, that only a 50-Hz bandwidth is required for correction to within tenth-wave residual wavefront errors for static targets, even in strong turbulence. The experimental phase error spectra agree well with theoretical calculations that use a Von Karman spectrum for the refractive index fluctuations. Multiple glint discrimination and tracking of the strongest glint in a multiple glint target are demonstrated in high turbulence. Good target tracking is observed at rates up to 14 mrad/sec. The convergence stability of the coat system is good, limited only by the inability of planar, stepwise phase control to remove atmospheric beam wander and scintillation effects. Receiver aperture size has had no appreciable effect on system performance except in multiple glint cases where the glints are within 2–3 dB in net reflectance.

© 1976 Optical Society of America

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References

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  1. coat is the term generally applied to optical phased arrays that derive their phasing information from target returns.
  2. W. B. Bridges, J. E. Pearson, Appl. Phys. Lett. 26, 539 (1975).
    [CrossRef]
  3. T. R. O’Meara, Hughes Research Laboratories, “Classification of Adaptive Arrays,” unpublished.
  4. W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O’Meara, J. A. Sanguinet, W. P. Brown, Appl. Opt. 13, 291 (1974).
    [CrossRef] [PubMed]
  5. J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, M. E. Pedinoff, Appl. Opt. 15, 611 (1976).
    [CrossRef] [PubMed]
  6. W. B. Bridges, J. E. Pearson, S. Hansen, L. S. Horwitz, R. M. Kubo, S. P. Lazzara, T. J. Walsh, “C.O.A.T.,” RADC Technical Reports RADC-TR-74-38, October1973; RADC-TR-74-108, January1974; RADC-TR-74-187, April1974 (available from RADC or through NTIS).
  7. J. E. Pearson, RADC Technical Report RADC-TR-75-46, January1975 (available from RADC or through NTIS).
  8. J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, R. F. Ogrodnik, Paper ThB5, OSA Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, July 1974.
  9. Strehl ratio is the ratio of the peak beam irradiance to the diffraction-limited irradiance.
  10. J. E. Pearson, J. Opt. Soc. Am. 65, 938 (1975).
    [CrossRef]
  11. J. R. Dunphy, J. R. Kerr, J. Opt. Soc. Am. 64, 1015 (1974).
    [CrossRef]
  12. J. Feinleib, S. G. Lipson, P. F. Cone, Appl. Phys. Lett. 25, 311 (1974).
    [CrossRef]
  13. W. P. Brown, Hughes Research Laboratories, unpublished.
  14. N. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  15. D. L. Fried, J. Opt. Soc. Am. 55, 1427 (1965).
    [CrossRef]
  16. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [CrossRef]
  17. The author is grateful to a reviewer for pointing this out.
  18. D. M. Chase, J. Opt. Soc. Am. 56, 33 (1966).
    [CrossRef]
  19. W. P. Brown, Hughes Research Laboratories, unpublished.
  20. G. W. Reinhardt, S. A. Collins, J. Opt. Soc. Am. 62, 1526 (1972).
    [CrossRef]
  21. A. J. Huber, “Measurements of the Temporal Power Spectra of a Propagating 10.6 Micron Wave Front,” RADC Rep. RADC-TR-74-44, February1974.
  22. R. L. Fante, J. Opt. Soc. Am. 64, 592 (1974).
    [CrossRef]
  23. This condition is strictly applicable only for stepwise phase correction across an aperture. The condition for a deformable mirror is less stringent. (Fewer elements are required for the same degree of correction.)
  24. L. C. Bradley, M. G. Cheifetz, J. Opt. Soc. Am. 65, 1212 (1975).

1976 (1)

1975 (3)

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

L. C. Bradley, M. G. Cheifetz, J. Opt. Soc. Am. 65, 1212 (1975).

J. E. Pearson, J. Opt. Soc. Am. 65, 938 (1975).
[CrossRef]

1974 (4)

1972 (1)

1966 (2)

1965 (1)

Bradley, L. C.

L. C. Bradley, M. G. Cheifetz, J. Opt. Soc. Am. 65, 1212 (1975).

Bridges, W. B.

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, M. E. Pedinoff, Appl. Opt. 15, 611 (1976).
[CrossRef] [PubMed]

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

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O’Meara, J. A. Sanguinet, W. P. Brown, Appl. Opt. 13, 291 (1974).
[CrossRef] [PubMed]

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, R. F. Ogrodnik, Paper ThB5, OSA Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, July 1974.

W. B. Bridges, J. E. Pearson, S. Hansen, L. S. Horwitz, R. M. Kubo, S. P. Lazzara, T. J. Walsh, “C.O.A.T.,” RADC Technical Reports RADC-TR-74-38, October1973; RADC-TR-74-108, January1974; RADC-TR-74-187, April1974 (available from RADC or through NTIS).

Brown, W. P.

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O’Meara, J. A. Sanguinet, W. P. Brown, Appl. Opt. 13, 291 (1974).
[CrossRef] [PubMed]

W. P. Brown, Hughes Research Laboratories, unpublished.

W. P. Brown, Hughes Research Laboratories, unpublished.

Brunner, P. T.

Chase, D. M.

Cheifetz, M. G.

L. C. Bradley, M. G. Cheifetz, J. Opt. Soc. Am. 65, 1212 (1975).

Collins, S. A.

Cone, P. F.

J. Feinleib, S. G. Lipson, P. F. Cone, Appl. Phys. Lett. 25, 311 (1974).
[CrossRef]

Dunphy, J. R.

Fante, R. L.

Feinleib, J.

J. Feinleib, S. G. Lipson, P. F. Cone, Appl. Phys. Lett. 25, 311 (1974).
[CrossRef]

Fried, D. L.

Hansen, S.

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, M. E. Pedinoff, Appl. Opt. 15, 611 (1976).
[CrossRef] [PubMed]

W. B. Bridges, J. E. Pearson, S. Hansen, L. S. Horwitz, R. M. Kubo, S. P. Lazzara, T. J. Walsh, “C.O.A.T.,” RADC Technical Reports RADC-TR-74-38, October1973; RADC-TR-74-108, January1974; RADC-TR-74-187, April1974 (available from RADC or through NTIS).

Horwitz, L. S.

W. B. Bridges, J. E. Pearson, S. Hansen, L. S. Horwitz, R. M. Kubo, S. P. Lazzara, T. J. Walsh, “C.O.A.T.,” RADC Technical Reports RADC-TR-74-38, October1973; RADC-TR-74-108, January1974; RADC-TR-74-187, April1974 (available from RADC or through NTIS).

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, R. F. Ogrodnik, Paper ThB5, OSA Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, July 1974.

Huber, A. J.

A. J. Huber, “Measurements of the Temporal Power Spectra of a Propagating 10.6 Micron Wave Front,” RADC Rep. RADC-TR-74-44, February1974.

Kerr, J. R.

Kubo, R. M.

W. B. Bridges, J. E. Pearson, S. Hansen, L. S. Horwitz, R. M. Kubo, S. P. Lazzara, T. J. Walsh, “C.O.A.T.,” RADC Technical Reports RADC-TR-74-38, October1973; RADC-TR-74-108, January1974; RADC-TR-74-187, April1974 (available from RADC or through NTIS).

Lazzara, S. P.

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O’Meara, J. A. Sanguinet, W. P. Brown, Appl. Opt. 13, 291 (1974).
[CrossRef] [PubMed]

W. B. Bridges, J. E. Pearson, S. Hansen, L. S. Horwitz, R. M. Kubo, S. P. Lazzara, T. J. Walsh, “C.O.A.T.,” RADC Technical Reports RADC-TR-74-38, October1973; RADC-TR-74-108, January1974; RADC-TR-74-187, April1974 (available from RADC or through NTIS).

Lipson, S. G.

J. Feinleib, S. G. Lipson, P. F. Cone, Appl. Phys. Lett. 25, 311 (1974).
[CrossRef]

Nussmeier, T. A.

O’Meara, T. R.

Ogrodnik, R. F.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, R. F. Ogrodnik, Paper ThB5, OSA Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, July 1974.

Pearson, J. E.

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, M. E. Pedinoff, Appl. Opt. 15, 611 (1976).
[CrossRef] [PubMed]

J. E. Pearson, J. Opt. Soc. Am. 65, 938 (1975).
[CrossRef]

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

W. B. Bridges, J. E. Pearson, S. Hansen, L. S. Horwitz, R. M. Kubo, S. P. Lazzara, T. J. Walsh, “C.O.A.T.,” RADC Technical Reports RADC-TR-74-38, October1973; RADC-TR-74-108, January1974; RADC-TR-74-187, April1974 (available from RADC or through NTIS).

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, R. F. Ogrodnik, Paper ThB5, OSA Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, July 1974.

J. E. Pearson, RADC Technical Report RADC-TR-75-46, January1975 (available from RADC or through NTIS).

Pedinoff, M. E.

Reinhardt, G. W.

Sanguinet, J. A.

Tatarski, N. I.

N. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

Walsh, T. J.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, R. F. Ogrodnik, Paper ThB5, OSA Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, July 1974.

W. B. Bridges, J. E. Pearson, S. Hansen, L. S. Horwitz, R. M. Kubo, S. P. Lazzara, T. J. Walsh, “C.O.A.T.,” RADC Technical Reports RADC-TR-74-38, October1973; RADC-TR-74-108, January1974; RADC-TR-74-187, April1974 (available from RADC or through NTIS).

Appl. Opt. (2)

Appl. Phys. Lett. (2)

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

J. Feinleib, S. G. Lipson, P. F. Cone, Appl. Phys. Lett. 25, 311 (1974).
[CrossRef]

J. Opt. Soc. Am. (8)

Other (12)

coat is the term generally applied to optical phased arrays that derive their phasing information from target returns.

W. P. Brown, Hughes Research Laboratories, unpublished.

N. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

The author is grateful to a reviewer for pointing this out.

W. P. Brown, Hughes Research Laboratories, unpublished.

A. J. Huber, “Measurements of the Temporal Power Spectra of a Propagating 10.6 Micron Wave Front,” RADC Rep. RADC-TR-74-44, February1974.

This condition is strictly applicable only for stepwise phase correction across an aperture. The condition for a deformable mirror is less stringent. (Fewer elements are required for the same degree of correction.)

T. R. O’Meara, Hughes Research Laboratories, “Classification of Adaptive Arrays,” unpublished.

W. B. Bridges, J. E. Pearson, S. Hansen, L. S. Horwitz, R. M. Kubo, S. P. Lazzara, T. J. Walsh, “C.O.A.T.,” RADC Technical Reports RADC-TR-74-38, October1973; RADC-TR-74-108, January1974; RADC-TR-74-187, April1974 (available from RADC or through NTIS).

J. E. Pearson, RADC Technical Report RADC-TR-75-46, January1975 (available from RADC or through NTIS).

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, R. F. Ogrodnik, Paper ThB5, OSA Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, July 1974.

Strehl ratio is the ratio of the peak beam irradiance to the diffraction-limited irradiance.

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Figures (10)

Fig. 1
Fig. 1

Block diagram of eighteen-element, visible wavelength, multidither coat system.

Fig. 2
Fig. 2

Atmospheric correlation length ρc as a function of CN2 for conditions appropriate to the range measurements [Eq. (3)].

Fig. 3
Fig. 3

Schematic of target configuration used in range measurements.

Fig. 4
Fig. 4

Single frame TV monitor pictures illustrating a typical data sequence of a strong glint moving near a weaker glint as the moving glint comes into the transmitted beam pattern: (a) beam locked on stationary boresight glint; (b) and (c) coat system selects the stronger, moving glint and maintains a beam maximum on it; (d) moving glint passes out of transmitter field of view; beam reforms on stationary glint.

Fig. 5
Fig. 5

coat convergence in high turbulence (CN2 = 6 × 10−14 cm−2/3). Each beam profile picture contains three traces, 30 msec apart: (a) single element profile; (b) eighteen-element array, coat servo loop open; (c) coat on (servo loop closed); array beamwidth compared to element width in (a) gives ratio of 5.4 ± 0.4.

Fig. 6
Fig. 6

Fluctuations in the power on a single boresight glint for various turbulence conditions: (a) low turbulence, CN2 = 2 × 10−15 cm−2/3; (b) high turbulence, CN2 = 6.1 × 10−14 cm−2/3; (c) high turbulence, but different amount of fluctuations; CN2 = 4.2 × 10−14 cm−2/3.

Fig. 7
Fig. 7

Frequency spectra of control channel 15 error voltage for high and low turbulence conditions. Also shown is the theoretical frequency spectrum [Eq. (10)].

Fig. 8
Fig. 8

Frequency spectrum of a single control channel (15) error voltage compared to the spectrum of the difference in the error voltages for two channels (12 and 15) on opposite sides of the transmitter array (see Fig. 1). High turbulence conditions.

Fig. 9
Fig. 9

Power on each of two glints when one is stationary and one is moving: (a) moving glint angular velocity is θ ˙ = 0.85 mrad/sec; (b) θ ˙ = 1.4 mrad/sec. Turbulence level is CN2 (opt) = 4.4 × 10−14 cm−2/3. The moving glint is 3 dB larger in reflectivity.

Fig. 10
Fig. 10

Computer simulation results showing maximum power density on a strong glint moving near a fixed, weaker glint. Experimental points are also shown.

Tables (2)

Tables Icon

Table I coat Turbulence Compensation Performance

Tables Icon

Table II Visible Experiment Parameters Scaled to 10.6 μm and 3.8 μm

Equations (14)

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D T ρ c D e ,
ϕ 2 = 2.91 C 1 k 2 R C N 2 ρ c 5 / 3 ,
ρ c = 0.105 ( λ 2 R C N 2 ) 3 / 5 = 2.79 × 10 - 9 ( C N 2 ) - 3 / 5 cm .
R s = ( I ) COAT - formed beam ( m = 1 18 I m 1 / 2 ) 2 ,
α = ϕ rms θ D L = 1 ( 4 λ / π D T ) [ 2.06 k 2 D T 2 ( D T ρ c ) 5 / 3 ] 1 / 2 = 0.18 ( D T ρ c ) 5 / 6 ,
I rms I D L = R ¯ s sin 2 ( α π / 5 ) ( α π / 5 ) 2 .
1 R ¯ s exp ( - 4 σ x 2 ) ,
ϕ n ( K ) = ( constant ) × [ 1 + ( K / K 0 ) 2 ] - 11 / 6 ,
S ϕ = ( constant ) × [ 1 + ( f V / L 0 ) 2 ] - 4 / 3 ,
S ϕ 1 / 2 = ( constant ) × [ 1 + ( f V / L 0 ) 2 ] - 2 / 3 .
Δ f = 0.69 ( V T / ρ c ) ,
α F = ( k D T 2 ) / R ,
α S = C N 2 k 7 / 6 R 11 / 6 ,
N 2 > 1.1 α F α S 6 / 5 .

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