Abstract

We have developed an active optical imaging system capable of correcting optical wave-front errors in real time at frequencies in the kilohertz range. Wave-front errors due to atmospheric turbulence in the propagation path, as well as optical figure aberrations and wave-front errors due to mechanical and thermal changes may be compensated. The system used an ac shearing interferometer, a parallel analog data processor, and a monolithic piezoelectric active mirror arranged in a closed-loop configuration. This compensation system can be applied to apertures of any size; experimental results are shown for a system with 21 correction zones.

© 1977 Optical Society of America

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  1. H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
    [CrossRef]
  2. Restoration of Atmospherically Degraded Images, Woods Hole Summer Study, July1966. .
  3. B. L. McGlamery, “Restoration of turbulence degraded images,” J. Opt. Soc. Am. 57, 293–297 (1967).
    [CrossRef]
  4. J. W. Goodman and J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).
  5. J. R. Breedlove “Digital image processing of simulated turbulence and photon noise degraded images of extended objects,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 155–162 (1976).
  6. J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real time phase correction of optical imaging systems,” Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by Opt. Soc. of America, Boulder, Colo., July1974, Paper ThB1.
  7. J. W. Hardy, “Real-time wavefront correction system,” U. S. Patent3, 923, 400, filed Jan. 3, 1974, issued Dec2, 1975.
  8. J. C. Wyant, “White light extended source shearing interferometer,” Appl. Opt. 13, 200–202 (1974).
    [CrossRef] [PubMed]
  9. J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems,” Appl. Opt. 14, 2622–2626 (1975).
    [CrossRef] [PubMed]
  10. J. W. Hardy, “Analog Data Processor,” U. S. Patent3, 921, 080, filed Jan. 3, 1974, issued Nov.18, 1975.
  11. J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, No. 6 (1974).
    [CrossRef]
  12. R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
    [CrossRef]
  13. L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging through turbulence with coherent optical adaptive techniques,” Ref. 6, paper ThB2.
  14. R. H. Dicke “Real time correction of telescope ‘seeing’,” J. Opt. Soc. Am. 65, 1206 (1975).
  15. V. N. Mahajan, “Optical wavefront correction in real time,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 109–118 (1976).
  16. F. J. Dyson, “Photon noise and atmospheric noise in active optical systems,” J. Opt. Soc. Am. 65, 551–558 (1975).
    [CrossRef]
  17. M. P. Rimmer, “Method for evaluating lateral shearing interferograms,” Appl. Opt. 13, 623–629 (1974).
    [CrossRef] [PubMed]
  18. D. P. Greenwood and D. L. Fried, “Power spectra requirements for wavefront-compensation systems,” J. Opt. Soc. Am. 66, 193–206 (1976).
    [CrossRef]
  19. R. Hudgin, “Wave-front compensation error due to finite corrector element size,” J. Opt. Soc. Am. 67, 393–395 (1977) (this issue).
    [CrossRef]
  20. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977) (this issue).
    [CrossRef]
  21. J. Vernon and F. Roddier, “Experimental determination of two-dimensional spatio temporal power spectra of stellar light scintillation: Evidence for a multilayer structure of the air turbulence in the upper atmosphere,” J. Opt. Soc. Am. 63, 270–273 (1973).
    [CrossRef]

1977 (2)

1976 (4)

D. P. Greenwood and D. L. Fried, “Power spectra requirements for wavefront-compensation systems,” J. Opt. Soc. Am. 66, 193–206 (1976).
[CrossRef]

J. W. Goodman and J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).

J. R. Breedlove “Digital image processing of simulated turbulence and photon noise degraded images of extended objects,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 155–162 (1976).

V. N. Mahajan, “Optical wavefront correction in real time,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 109–118 (1976).

1975 (3)

1974 (4)

1973 (1)

1967 (1)

1953 (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Belsher, J. F.

J. W. Goodman and J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).

Breedlove, J. R.

J. R. Breedlove “Digital image processing of simulated turbulence and photon noise degraded images of extended objects,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 155–162 (1976).

Brown, W. P.

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging through turbulence with coherent optical adaptive techniques,” Ref. 6, paper ThB2.

Buffington, A.

Cone, P. F.

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, No. 6 (1974).
[CrossRef]

Dicke, R. H.

R. H. Dicke “Real time correction of telescope ‘seeing’,” J. Opt. Soc. Am. 65, 1206 (1975).

Dyson, F. J.

Feinleib, J.

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, No. 6 (1974).
[CrossRef]

J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real time phase correction of optical imaging systems,” Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by Opt. Soc. of America, Boulder, Colo., July1974, Paper ThB1.

Fried, D. L.

Goodman, J. W.

J. W. Goodman and J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).

Greenwood, D. P.

Hardy, J. W.

J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real time phase correction of optical imaging systems,” Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by Opt. Soc. of America, Boulder, Colo., July1974, Paper ThB1.

J. W. Hardy, “Real-time wavefront correction system,” U. S. Patent3, 923, 400, filed Jan. 3, 1974, issued Dec2, 1975.

J. W. Hardy, “Analog Data Processor,” U. S. Patent3, 921, 080, filed Jan. 3, 1974, issued Nov.18, 1975.

Hudgin, R.

Hudgin, R. H.

Jenney, J. A.

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging through turbulence with coherent optical adaptive techniques,” Ref. 6, paper ThB2.

Lipson, S. G.

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, No. 6 (1974).
[CrossRef]

Mahajan, V. N.

V. N. Mahajan, “Optical wavefront correction in real time,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 109–118 (1976).

McGlamery, B. L.

Miller, L.

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging through turbulence with coherent optical adaptive techniques,” Ref. 6, paper ThB2.

Muller, R. A.

O’Meara, T. R.

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging through turbulence with coherent optical adaptive techniques,” Ref. 6, paper ThB2.

Rimmer, M. P.

Roddier, F.

Vernon, J.

Wyant, J. C.

J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems,” Appl. Opt. 14, 2622–2626 (1975).
[CrossRef] [PubMed]

J. C. Wyant, “White light extended source shearing interferometer,” Appl. Opt. 13, 200–202 (1974).
[CrossRef] [PubMed]

J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real time phase correction of optical imaging systems,” Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by Opt. Soc. of America, Boulder, Colo., July1974, Paper ThB1.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, No. 6 (1974).
[CrossRef]

J. Opt. Soc. Am. (8)

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

J. W. Goodman and J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).

J. R. Breedlove “Digital image processing of simulated turbulence and photon noise degraded images of extended objects,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 155–162 (1976).

V. N. Mahajan, “Optical wavefront correction in real time,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 109–118 (1976).

Publ. Astron. Soc. Pac. (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Other (5)

Restoration of Atmospherically Degraded Images, Woods Hole Summer Study, July1966. .

J. W. Hardy, “Analog Data Processor,” U. S. Patent3, 921, 080, filed Jan. 3, 1974, issued Nov.18, 1975.

J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real time phase correction of optical imaging systems,” Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by Opt. Soc. of America, Boulder, Colo., July1974, Paper ThB1.

J. W. Hardy, “Real-time wavefront correction system,” U. S. Patent3, 923, 400, filed Jan. 3, 1974, issued Dec2, 1975.

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging through turbulence with coherent optical adaptive techniques,” Ref. 6, paper ThB2.

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Figures (10)

FIG. 1
FIG. 1

Optical imaging relationships in a real-time atmospheric compensation system. Light from the reference source S passes through the optical path disturbance OPD and is collected by telescope aperture A to form an uncorrected image of the reference source at the focal plane FP. Lens L1 collimates the light and directs it to the wave-front corrector WFC which is located at an image plane of OPD, and which corrects the optical path disturbance. Lens L2 forms a (corrected) image of the source at the interferometer grating G. Lens L3 forms an image of the wave-front corrector at the detector plane.

FIG. 2
FIG. 2

Block diagram of a real-time atmospheric compensation system. The interferometer measures the wave-front error in real time and provides electrical feedback through the wave-front computer to the wave-front corrector, thereby forming a closed-loop control system.

FIG. 3
FIG. 3

Operation of a grating interferometer. (a) Wave-front deformation W is imaged on to the detector plane D so that each detector location corresponds to a specific zone of the wave front. (b) Reference source focused on to the grating produces multiple images of the input aperture at the detector plane due to diffraction. (c) Representation of lateral sheared images at the detector plane, showing zero order, +1 order, and −1 order sidebands which produce interference over the shaded area.

FIG. 4
FIG. 4

Location of X and Y detector arrays in relation to wave-front correction zone centers. Wave-front correction zone centers are numbered 1 through 9. (a) and (b) show the location of the detector subapertures in the Y-shear and X-shear arrays, respectively.

FIG. 5
FIG. 5

Wave-front reconstruction. (a) Algorithm for determination of wave-front value at zone N, using the sum of the values at the adjoining points and the sum of the path length differences measured by the interferometer. (b) Complete matrix for reconstruction of 21 wave-front zones using 16 X path differences and 16 Y path differences.

FIG. 6
FIG. 6

Monolithic piezoelectric mirror. Cross section and top view of a 21-element MPM showing configuration of separately addressable electrodes.

FIG. 7
FIG. 7

Interferograms showing controlled surface deformation of a monolithic piezoelectric mirror. Each fringe represents 1 wavelength (0.633 μm) of wave-front deformation.

FIG. 8
FIG. 8

Test data from experimental RTAC system. The contour plots were made from interferograms of actual wave fronts at λ = 0.633 μm with contour spacings of 0.05λ. The corresponding point-spread functions were computed from these contour plots. (a) Residual wave-front error of the RTAC with a plane-wave input, 0.04λ, rms, 0.21λ peak to peak. (b) Input wave-front distortion producing 0.27λ rms, 1.28λ peak to peak at system output with RTAC off. (c) Same input as (b) with RTAC on. Residual wave-front distortion has been reduced to 0.06λ rms, 0.35λ peak to peak.

FIG. 9
FIG. 9

Operation of RTAC with He-Ne laser reference over a 300 m turbulent path. Two frames from a 16 mm movie made at RADC’s Advanced Optical Test Facility, using a 30 cm aperture corrected by the 21-zone RTAC. (a) Typical uncorrected point-spread function. (b) Typical point-spread function corrected by RTAC.

FIG. 10
FIG. 10

RTAC performance with a 3-bar resolution target. The resolution target was illuminated with white light and located in the same isoplanatic patch as the He-Ne laser reference source, which is masked out. (a) Shows baseline RTAC resolution with no added wave-front distortion. The diffraction limit of the system is 130 cycles/mm (target group 6-6 is 114 cycles/mm). (b) Shows degradation due to 1.5 waves peak to peak wave-front distortion, RTAC off. (c) Shows resolution under same conditions, with RTAC on. Target group 6-6 is just resolvable on the original negative.

Equations (7)

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I ( x , t ) 1 2 + γ ( 2 / π ) cos ( ω t + ϕ ( x ) ) ,
ϕ ( x ) = α ( x ) S / λ ,
OPD = ϕ λ L / S .
N = ( 1 / G ) [ A + B + C + D + a - b - c + d ] ,
σ FIT 2 = K 1 ( L / r 0 ) 5 / 3 ,
σ PH 2 = ( K 2 / γ 2 M ) ( L 2 / s 2 ) ,
σ PRED 2 = K 3 T s n C n 2 ν n 5 / 3 ,