Abstract

Analytical and computer simulation results are presented which show that both multidither and phase conjugate COAT (coherent optical adaptive techniques) performance for extended dynamic targets will be degraded relative to that achievable for point targets. System parameters, target properties, and interaction geometry all strongly influence the degree to which performance will be influenced by target effects. In general, large targets (relative to diffraction pattern dimensions) and those with dynamic rates which cause the power spectrum of the target backscatter to overlap the sensing bands will significantly degrade both dither and conjugate COAT system performance.

© 1977 Optical Society of America

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References

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  1. J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeir, and M. E. Pedinoff, “Coherent optical adaptive techniques: design and performance of an 18-element visible multidither COAT system,” Appl. Opt. 15, 611–621 (1976).
    [Crossref] [PubMed]
  2. M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, “A visible wavelength COAT array”, Opt. Eng. 15, 56–60 (1976).
    [Crossref]
  3. S. A. Kokorowski, M. E. Pedinoff, and J. E. Pearson, lytical, experimental, and computer simulation results on the interactive effects of speckle with multidither adaptive optics systems,” J. Opt. Soc. Am. 67, 333–345 (1977) (preceding paper).
    [Crossref]
  4. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Topics in Applied Physics, Vol. 9, edited by J. C. Dainty (Springer-Verlag, New York, 1975).
    [Crossref]
  5. A. Papoulis, The Fourier Integral and Its Application (McGraw-Hill, New York, 1962).

1977 (1)

1976 (2)

Bridges, W. B.

Cadwallender, W. K.

M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, “A visible wavelength COAT array”, Opt. Eng. 15, 56–60 (1976).
[Crossref]

DeYoung, T. F.

M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, “A visible wavelength COAT array”, Opt. Eng. 15, 56–60 (1976).
[Crossref]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Topics in Applied Physics, Vol. 9, edited by J. C. Dainty (Springer-Verlag, New York, 1975).
[Crossref]

Hansen, S.

Kokorowski, S. A.

Lavan, M. J.

M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, “A visible wavelength COAT array”, Opt. Eng. 15, 56–60 (1976).
[Crossref]

Nussmeir, T. A.

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Application (McGraw-Hill, New York, 1962).

Pearson, J. E.

Pedinoff, M. E.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, “A visible wavelength COAT array”, Opt. Eng. 15, 56–60 (1976).
[Crossref]

Other (2)

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Topics in Applied Physics, Vol. 9, edited by J. C. Dainty (Springer-Verlag, New York, 1975).
[Crossref]

A. Papoulis, The Fourier Integral and Its Application (McGraw-Hill, New York, 1962).

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Figures (6)

FIG. 1
FIG. 1

Block diagram of baseline multidither (MD) COAT system: β = dither modulation (± 20°), LPF = low-pass filters, HPF = high-pass filters, ϕi = phase shifters, fi = dither frequencies, GE, GD = electronic, detector gains, Ω = target rotation rate.

FIG. 2
FIG. 2

Strehl ratio (I/I0) vs maximum target modulation frequency (fmax) for MD system with uniform square target. System noise equivalent bandwidth (Δf) is varied, and gain is adjusted to give constant convergence time (~ 1 ms). (a) Δf = 5π Hz; (b) Δf = 10π Hz; (c) Δf = 30π Hz. Minimum dither and interdither spacing = 8 and 1.5 kHz, respectively.

FIG. 3
FIG. 3

Seven-channel MD simulations with a small (≪λR/D) square target. Parameters: dither frequencies (fD) = 8–17 kHz, point receiver (a) fmax = 1 kHz; (b) fmax = 10 kHz; (c) fmax = 30 kHz; (d) fmax = 100 kHz.

FIG. 4
FIG. 4

Block diagram of baseline phase conjugate (PC) COAT system. Ideal optical heterodyne receivers and phase comparators are assumed. Δf = system noise–equivalent bandwidth.

FIG. 5
FIG. 5

Strehl ratio (I/I0) vs normalized maximum target modulation frequency (fmax/fc) for a 19-channel PC system. (a) System gain (G) = 1; (b) G = 10; (c) G = 100. Parameterized by single subaperture beam size with respect to target size (θb/θt).

FIG. 6
FIG. 6

19-channel PC simulations with uniform square targets. Parameterized by single subaperture beam size with respect to target size (θb/θt). System gain (G) = 4. Two target rotation rates are shown corresponding to fmax~ 1 and 38 kHz.

Equations (11)

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S I ( f x , f y ) = I 2 [ δ ( f x , f y ) + Γ I ( λ R f x , λ R f y ) ] ,
S 0 ( f x , f y ) = S I ( f x , f y ) H ( f x , f y ) 2 ,
S 0 ( f ) = ( v x ) - 1 ( - S 0 ( f x , f y ) d f y ) f x = f / v x ,
I I 0 = 1 M 2 ( m = 1 M exp j ϕ m ) ( n = 1 M exp - j ϕ n ) ,
I / I 0 = exp ( - σ ϕ 2 ) + ( 1 / M ) [ 1 - exp ( - σ ϕ 2 ) ] .
σ ϕ i 2 β 2 2 + σ i 2 G L 2 + S 0 ( f i ) ( M β ) 2 ( I I 0 ) Δ f ,
S c β 2 e / ( M 2 Δ f ) .
σ ϕ 2 = - f c f c G 2 S ( f ) d f ,
σ ϕ 2 = π 2 G 2 3 ( 2 - θ b θ t )             if f c f max 2
= π 2 G 2 3 ( 2 f c f max - θ b θ t )             if 1 2 > f c f max > θ b θ t
= π 2 G 2 3 [ ( f c f max ) 2 · θ t θ b ]             if f c f max < θ b θ t