Abstract

We introduce image quality criteria for organizing feedback control in adaptive imaging systems. These image quality criteria are dependent on the Fourier spectrum of the image and can be obtained optically with a coherent optical system. Digital processing of the image plane intensity distribution is not required. We present experimental results, along with corresponding numerical simulations, that demonstrate the potential effectiveness of these criteria for adaptive correction of phase-distorted extended-source images.

© 1996 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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1995 (2)

M. A. Vorontsov, J. C. Ricklin, G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. 34, 3229–3238 (1995).
[CrossRef]

J. C. Ricklin, M. A. Vorontsov, G. W. Carhart, D. Gose, W. B. Miller, “Turbulent phase screen for study of imaging system performance,” J. Mod. Opt. 42, 13–17 (1995).
[CrossRef]

1994 (8)

1993 (1)

1992 (1)

1984 (1)

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, V. I. Shmalhausen, “Flexible mirror for adaptive light-beam formation systems,” Sov. J. Quantum Electron. 14, 839–841 (1984).
[CrossRef]

1977 (2)

1975 (1)

R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
[CrossRef]

1974 (1)

1970 (1)

V. V. Anisimov, S. M. Kozel, G. P. Lakshin, “Spectral properties of a random intensity field produced by coherent radiation scattering on a moving rough surface,” Radiotek. Elektron. 15, 539–545 (1970).

1965 (1)

Akhmanov, S. A.

S. A. Akhmanov, Y. E. D’jakov, A. S. Chirkin, Introduction to Statistical Radiophysics and Optics (Nauka, Moscow, 1981).

Anisimov, V. V.

V. V. Anisimov, S. M. Kozel, G. P. Lakshin, “Spectral properties of a random intensity field produced by coherent radiation scattering on a moving rough surface,” Radiotek. Elektron. 15, 539–545 (1970).

Belsher, J. F.

Buffington, A.

Carhart, G. W.

M. A. Vorontsov, J. C. Ricklin, G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. 34, 3229–3238 (1995).
[CrossRef]

J. C. Ricklin, M. A. Vorontsov, G. W. Carhart, D. Gose, W. B. Miller, “Turbulent phase screen for study of imaging system performance,” J. Mod. Opt. 42, 13–17 (1995).
[CrossRef]

Caudill, E. L.

Chirkin, A. S.

S. A. Akhmanov, Y. E. D’jakov, A. S. Chirkin, Introduction to Statistical Radiophysics and Optics (Nauka, Moscow, 1981).

Crawford, F. S.

D’jakov, Y. E.

S. A. Akhmanov, Y. E. D’jakov, A. S. Chirkin, Introduction to Statistical Radiophysics and Optics (Nauka, Moscow, 1981).

Dicke, R. H.

R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
[CrossRef]

Fienup, J. R.

Fox, M. J.

Fried, D. L.

Fugate, R. Q.

R. Q. Fugate, “Laser beacon adaptive optics,” Opt. Photon. News 5, 14–19 (June1994).

Goldfischer, L. I.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

Gose, D.

J. C. Ricklin, M. A. Vorontsov, G. W. Carhart, D. Gose, W. B. Miller, “Turbulent phase screen for study of imaging system performance,” J. Mod. Opt. 42, 13–17 (1995).
[CrossRef]

Hu, P. H.

Ivanov, V. Yu.

Johnston, D. C.

Koriabin, A. V.

M. A. Vorontsov, A. V. Koriabin, V. I. Shmalhausen, Controlling Optical Systems (Nauka, Moscow, 1988).

Kozel, S. M.

V. V. Anisimov, S. M. Kozel, G. P. Lakshin, “Spectral properties of a random intensity field produced by coherent radiation scattering on a moving rough surface,” Radiotek. Elektron. 15, 539–545 (1970).

Kudryashov, A. V.

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, V. I. Shmalhausen, “Flexible mirror for adaptive light-beam formation systems,” Sov. J. Quantum Electron. 14, 839–841 (1984).
[CrossRef]

Lakshin, G. P.

V. V. Anisimov, S. M. Kozel, G. P. Lakshin, “Spectral properties of a random intensity field produced by coherent radiation scattering on a moving rough surface,” Radiotek. Elektron. 15, 539–545 (1970).

Lipson, S. G.

Ma, S.

Matson, L. C.

Miller, W. B.

J. C. Ricklin, M. A. Vorontsov, G. W. Carhart, D. Gose, W. B. Miller, “Turbulent phase screen for study of imaging system performance,” J. Mod. Opt. 42, 13–17 (1995).
[CrossRef]

Mills, S. P.

Muller, R. A.

Nazarkin, S. I.

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, V. I. Shmalhausen, “Flexible mirror for adaptive light-beam formation systems,” Sov. J. Quantum Electron. 14, 839–841 (1984).
[CrossRef]

O’Meara, T. R.

Ribak, E.

Ricklin, J. C.

M. A. Vorontsov, J. C. Ricklin, G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. 34, 3229–3238 (1995).
[CrossRef]

J. C. Ricklin, M. A. Vorontsov, G. W. Carhart, D. Gose, W. B. Miller, “Turbulent phase screen for study of imaging system performance,” J. Mod. Opt. 42, 13–17 (1995).
[CrossRef]

Roggemann, M. C.

M. C. Roggemann, E. L. Caudill, D. W. Tylper, M. J. Fox, M. A. Von Bokern, L. C. Matson, “Compensated speckle imaging: theory and experimental results,” Appl. Opt. 33, 3099–3110 (1994).
[CrossRef] [PubMed]

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 67, 3254–3264 (1994).
[CrossRef]

Schwartz, C.

Schwemin, A. J.

Shmalhausen, V. I.

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, V. I. Shmalhausen, “Flexible mirror for adaptive light-beam formation systems,” Sov. J. Quantum Electron. 14, 839–841 (1984).
[CrossRef]

M. A. Vorontsov, A. V. Koriabin, V. I. Shmalhausen, Controlling Optical Systems (Nauka, Moscow, 1988).

M. A. Vorontsov, V. I. Shmalhausen, Principles of Adaptive Optics (Nauka, Moscow, 1988).

Sivokon, V. P.

Smits, R. G.

Stone, J.

Stoudt, C. A.

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 67, 3254–3264 (1994).
[CrossRef]

Tylper, D. W.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).

Von Bokern, M. A.

Vorontsov, M. A.

J. C. Ricklin, M. A. Vorontsov, G. W. Carhart, D. Gose, W. B. Miller, “Turbulent phase screen for study of imaging system performance,” J. Mod. Opt. 42, 13–17 (1995).
[CrossRef]

M. A. Vorontsov, J. C. Ricklin, G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. 34, 3229–3238 (1995).
[CrossRef]

V. Yu. Ivanov, V. P. Sivokon, M. A. Vorontsov, “Phase retrieval from a set of intensity measurements: theory and experiment,” J. Opt. Soc. Am. A 9, 1515–1524 (1992).
[CrossRef]

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, V. I. Shmalhausen, “Flexible mirror for adaptive light-beam formation systems,” Sov. J. Quantum Electron. 14, 839–841 (1984).
[CrossRef]

M. A. Vorontsov, A. V. Koriabin, V. I. Shmalhausen, Controlling Optical Systems (Nauka, Moscow, 1988).

M. A. Vorontsov, V. I. Shmalhausen, Principles of Adaptive Optics (Nauka, Moscow, 1988).

Welsh, B. M.

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 67, 3254–3264 (1994).
[CrossRef]

D. C. Johnston, B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994).
[CrossRef]

Appl. Opt. (2)

Astrophys. J. (1)

R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
[CrossRef]

J. Mod. Opt. (1)

J. C. Ricklin, M. A. Vorontsov, G. W. Carhart, D. Gose, W. B. Miller, “Turbulent phase screen for study of imaging system performance,” J. Mod. Opt. 42, 13–17 (1995).
[CrossRef]

J. Opt. Soc. Am A (1)

Special Issue: Atmospheric-Compensation Technology, J. Opt. Soc. Am A 2(1994).

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (5)

Opt. Eng. (2)

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 67, 3254–3264 (1994).
[CrossRef]

M. A. Vorontsov, J. C. Ricklin, G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. 34, 3229–3238 (1995).
[CrossRef]

Opt. Photon. News (1)

R. Q. Fugate, “Laser beacon adaptive optics,” Opt. Photon. News 5, 14–19 (June1994).

Radiotek. Elektron. (1)

V. V. Anisimov, S. M. Kozel, G. P. Lakshin, “Spectral properties of a random intensity field produced by coherent radiation scattering on a moving rough surface,” Radiotek. Elektron. 15, 539–545 (1970).

Sov. J. Quantum Electron. (1)

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, V. I. Shmalhausen, “Flexible mirror for adaptive light-beam formation systems,” Sov. J. Quantum Electron. 14, 839–841 (1984).
[CrossRef]

Other (7)

M. A. Vorontsov, V. I. Shmalhausen, Principles of Adaptive Optics (Nauka, Moscow, 1988).

S. A. Akhmanov, Y. E. D’jakov, A. S. Chirkin, Introduction to Statistical Radiophysics and Optics (Nauka, Moscow, 1981).

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

M. A. Vorontsov, A. V. Koriabin, V. I. Shmalhausen, Controlling Optical Systems (Nauka, Moscow, 1988).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

H. P. Baltes, ed., Inverse Problems in Optics (Springer-Verlag, New York, 1978).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Adaptive imaging system block diagram.

Fig. 2
Fig. 2

Optical scheme for image quality analyzer.

Fig. 3
Fig. 3

Experimental setup for investigating image quality criteria.

Fig. 4
Fig. 4

Normalized imaging system MTF’s with phase distortions introduced by a deformable mirror for different voltages u applied to all mirror electrodes: a: u = 0 V; b: u = 30 V; c: u = −60 V; d: u = 90 V; e: u = −150 V. The resulting images (a–e) correspond to given voltages.

Fig. 5
Fig. 5

Normalized photocurrent fluctuation power spectra: a: undistorted image (u = 0 V); b: distorted image (u = 90 V). The images in a and b correspond to Figs. 4(a) and 4(d), respectively.

Fig. 6
Fig. 6

Normalized discrimination curves for the spectral criterion J Δ ph measured in different spectral bands f ∈ [f0 − Δ/2, f0 + Δ/2]: 1: f0 = 30 kHz, Δ = 6 kHz; 2: f0 = 30 kHz, Δ = 24 kHz; 3: f0 = 0, Δ = 60 kHz (criterion J σ ph); 4: f0 = 47 kHz, Δ = 10 kHz.

Fig. 7
Fig. 7

Normalized discrimination curves J Δ ph ( u ): a: full-frame image; b: image fragment. The images correspond to u = 0 V.

Fig. 8
Fig. 8

Normalized discrimination curves J Δ ph in an imaging system: a: with defocus; b: with astigmatism wave-front distortion. The undistorted image (u = 0) is shown on the left, astigmatism-type aberration corresponding to curve b is shown in the center [200 V applied to deformable mirror electrodes 1, 2, 5, and 6; −200 V applied to electrodes 3, 4, 7, and 8 (u9 = 0)], and defocus-type aberration corresponding to curve a is shown on the right (−200 V applied to all nine mirror electrodes).

Fig. 9
Fig. 9

Normalized discrimination curves J σ ph ( u ) in an imaging system with large- and small-scale aberrations: 1: without small-scale phase distortions; 2: with small-scale phase distortions, phase distortion standard deviation of 0.6π; 3: with small-scale phase distortions, phase distortion standard deviation of 1.5π. Picture a shows an undistorted image (u = 0), and pictures b and c correspond to curve 3. Picture b depicts the effects of only small-scale phase aberrations (u = 0), while picture c demonstrates the combined effects of small-and large-scale aberrations (u = 100 V applied to all mirror electrodes).

Fig. 10
Fig. 10

Normalized discrimination curves J σ ph for different LCLV voltages v: 1: v = 12 V; 2: v = 12.5 V; 3: v = 14 V; 4: v = 22.5 V.

Fig. 11
Fig. 11

Numerical calculation of the spatial spectra characteristic width bph for phase images (curves 1–3) compared with spatial spectra characteristic width b (dashed curve) for an intensity plane image as a function of the voltage controlling the imaging system defocus aberration. For curves 1, 2, and 3 α = π, 2π, and 2.5π, respectively.

Fig. 12
Fig. 12

Numerical simulation of the normalized image quality criterion J as a function of the voltage controlling imaging system defocus aberration for different values of the phase modulation parameter α: 1: α = 0.5π; 2: α = π; 3: α = 2π; 4: α = 2.5π [the image used was the space station image shown in Fig 13(a)].

Fig. 13
Fig. 13

Dependence of the phase image zero-order spectral component on phase modulation depth α for three images obtained in a system with defocus-type wave-front aberration: a: undistorted image (u = 0); b: distorted image (u = 100 V); c: distorted image (u = 200 V).

Equations (16)

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J 1 = M ( r ) I ( r , t ) d 2 r , J 2 = I 2 ( r , t ) d 2 r , J 3 = | m + n I ( r , t ) x m y n | 2 d 2 r .
I s ( r F ) = γ I 0 F { I ( r ) } 2 ,             I 0 = A 0 2 ,
I ph ( r F ) = γ I 0 F { exp [ i α I ( r ) ] } 2 .
b = ( k x 2 + k y 2 ) 1 / 2 I s ( k ) d 2 k / I s ( k ) d 2 k ,
b ph = ( k x 2 + k y 2 ) 1 / 2 I ph ( k ) d 2 k / I ph ( k ) d 2 k .
B i ( τ ) = I s ( r F ) I s ( r F + v τ ) d 2 r F .
G ( ω ) = 1 π 0 B i ( τ ) cos ( ω τ ) d τ = 1 π 0 cos ( ω τ ) I s ( r F ) I s ( r F + v τ ) d 2 r F d τ ,
J σ σ i 2 = ( i - i ) 2 = B i ( 0 ) = 0 G ( ω ) d ω = I s 2 ( r F ) d 2 r F ,
J σ ph = σ i 2 = I ph 2 ( r F ) d 2 r F .
J 2 = I 2 ( r ) d 2 r = F { I } 2 d 2 r F = 1 γ I 0 I s ( r F ) d 2 r F .
J 2 = σ i 2 = I 2 ( r ) d 2 r .
J σ = σ i 2 = 1 T t t + T [ i ( ξ ) - i ¯ ] 2 d ξ ,
T 2 1 T 0 G ( ω ) [ sin ( ω T / 2 ) ω T / 2 ] 2 d ω .
J Δ ω 0 - Δ / 2 ω 0 + Δ / 2 G ( ω ) d ω = 1 π ω 0 - Δ / 2 ω 0 + Δ / 2 0 cos ( ω τ ) I s ( r F ) × I s ( r F + v τ ) d 2 r F d τ d ω ,
J Δ ph = 1 π ω 0 - Δ / 2 ω 0 + Δ / 2 0 cos ( ω τ ) I ph ( r F ) × I ph ( r F + v τ ) d 2 r F d τ d ω .
J = J σ ph / J 0 = I ph 2 ( k ) d 2 k / I ph ( k ) d 2 k .

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