Abstract

We discuss the use of a physically constrained iterative deconvolution algorithm to combine and deconvolve images taken with interferometric imaging arrays. To demonstrate this method we have simulated imaging with the Large Binocular Telescope [Proc. SPIE 3352, 23 (1998)]. This is a two-element interferometer in which each element is under adaptive-optics control for atmospheric compensation and in which the fixed baseline is maintained by active control to compensate for elastic flexure of steel under variable gravitational loading. We show how images taken at different position angles, by means of the two 8.4-m apertures, co-phased across the 14.6-m center-to-center separation, can be used to tomographically reconstruct an astronomical object at the full-aperture (23-m) diffraction limit of the Large Binocular Telescope.

© 1999 Optical Society of America

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References

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  1. E. Hege, J. Beckers, P. Strittmatter, D. McCarthy, “Multiple mirror telescope as a phased array telescope,” Appl. Opt. 24, 2565–2576 (1984).
    [CrossRef]
  2. J. M. Hill, P. Salinari, “The Large Binocular Telescope project,” in Advanced Technology Optical/IR Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 23–33 (1998).
    [CrossRef]
  3. D. Sandler, S. Stahl, J. Angel, M. Lloyd-Hart, D. McCarthy, “Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes,” J. Opt. Soc. Am. A 11, 925–945 (1994).
    [CrossRef]
  4. F. Roddier, C. Roddier, J. Graves, M. Northcott, “Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle,” Astrophys. J. 443, 249–260 (1995).
    [CrossRef]
  5. L. Close, F. Roddier, M. Northcott, C. Roddier, J. Graves, “Adaptive optics 0″.2 resolution infrared images of HL Tauri: direct images of an active accretion disk around a protostar,” Astrophys. J. 478, 766–777 (1997).
    [CrossRef]
  6. M. Lloyd-Hart, R. Dekany, D. Sandler, D. Wittmann, R. Angel, D. McCarthy, “Progress in diffraction-limited imaging at the Multiple Mirror Telescope with adaptive optics,” J. Opt. Soc. Am. A 11, 846–857 (1994).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 167 et seq.
  8. W. Traub, “Combining beams from separated telescopes,” Appl. Opt. 25, 528–532 (1986).
    [CrossRef] [PubMed]
  9. J. Hill, “Strategy for interferometry with the Large Binocular Telescope,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 248–259 (1994).
    [CrossRef]
  10. S. Jefferies, J. Christou, “Restoration of astronomical images by iterative deconvolution,” Astrophys. J. 415, 862–874 (1993).
    [CrossRef]
  11. J. Christou, E. K. Hege, S. M. Jefferies, C. Keller, “Application of multiframe iterative blind deconvolution for diverse astronomical imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 433–444 (1994).
    [CrossRef]
  12. J. Christou, E. Hege, S. Jefferies, “Speckle deconvolution imaging using an iterative algorithm,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 134–143 (1995).
    [CrossRef]
  13. E. K. Hege, “Psf calibration in astronomical imaging—physical constraints for a noisy problem,” in Signal Recovery and Synthesis, Vol. 11 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 2–4.
  14. E. K. Hege, “Super-resolved point-spread-function calibration for astronomical imaging,” in Time-Frequency and Time-Scale Analysis: Proceedings of the IEEE Signal Processing International Symposium (IEEE Service Center, Piscataway, N.J., 1998), pp. 477–480.
  15. E. Thiébaut, J.-M. Conan, “Strict a priori constraints for maximum-likelihood blind deconvolution,” J. Opt. Soc. Am. A 12, 485–492 (1995).
    [CrossRef]
  16. R. Dekany, K. Hege, D. Wittman, “Searching for planets by differential astrometry with large telescopes,” Astrophys. Space Sci. 212, 299–319 (1994).
    [CrossRef]
  17. Skylight, the atmospheric imaging software program, is available bookm Twinklesoft, P.O. Box 92838, Pasadena, Calif. 91103 [telephone: (626) 793-1015, e-mail: http://www.twinklesoft.com ].
  18. IRAF is the Image Reduction and Analysis Facility developed at the National Astronomical Observatories. From the IRAF command-line prompt cl>, the galaxy image is dev$pix.
  19. D. Sheppard, B. Hunt, M. Marcellin, “Iterative multiframe superresolution algorithms for atmospheric-turbulence-degraded imagery,” J. Opt. Soc. Am. A 15, 978–992 (1998).
    [CrossRef]
  20. E. Hege, J. Angel, A. Gleckler, K. Pflibsen, B. Ulich, “An adaptive steerable imaging array,” in Digital Image Recovery and Synthesis II, P. Idell, ed., Proc. SPIE2029, 354–368 (1993).
    [CrossRef]

1998

1997

L. Close, F. Roddier, M. Northcott, C. Roddier, J. Graves, “Adaptive optics 0″.2 resolution infrared images of HL Tauri: direct images of an active accretion disk around a protostar,” Astrophys. J. 478, 766–777 (1997).
[CrossRef]

1995

F. Roddier, C. Roddier, J. Graves, M. Northcott, “Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle,” Astrophys. J. 443, 249–260 (1995).
[CrossRef]

E. Thiébaut, J.-M. Conan, “Strict a priori constraints for maximum-likelihood blind deconvolution,” J. Opt. Soc. Am. A 12, 485–492 (1995).
[CrossRef]

1994

1993

S. Jefferies, J. Christou, “Restoration of astronomical images by iterative deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

1986

1984

Angel, J.

D. Sandler, S. Stahl, J. Angel, M. Lloyd-Hart, D. McCarthy, “Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes,” J. Opt. Soc. Am. A 11, 925–945 (1994).
[CrossRef]

E. Hege, J. Angel, A. Gleckler, K. Pflibsen, B. Ulich, “An adaptive steerable imaging array,” in Digital Image Recovery and Synthesis II, P. Idell, ed., Proc. SPIE2029, 354–368 (1993).
[CrossRef]

Angel, R.

Beckers, J.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 167 et seq.

Christou, J.

S. Jefferies, J. Christou, “Restoration of astronomical images by iterative deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

J. Christou, E. Hege, S. Jefferies, “Speckle deconvolution imaging using an iterative algorithm,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 134–143 (1995).
[CrossRef]

J. Christou, E. K. Hege, S. M. Jefferies, C. Keller, “Application of multiframe iterative blind deconvolution for diverse astronomical imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 433–444 (1994).
[CrossRef]

Close, L.

L. Close, F. Roddier, M. Northcott, C. Roddier, J. Graves, “Adaptive optics 0″.2 resolution infrared images of HL Tauri: direct images of an active accretion disk around a protostar,” Astrophys. J. 478, 766–777 (1997).
[CrossRef]

Conan, J.-M.

Dekany, R.

Gleckler, A.

E. Hege, J. Angel, A. Gleckler, K. Pflibsen, B. Ulich, “An adaptive steerable imaging array,” in Digital Image Recovery and Synthesis II, P. Idell, ed., Proc. SPIE2029, 354–368 (1993).
[CrossRef]

Graves, J.

L. Close, F. Roddier, M. Northcott, C. Roddier, J. Graves, “Adaptive optics 0″.2 resolution infrared images of HL Tauri: direct images of an active accretion disk around a protostar,” Astrophys. J. 478, 766–777 (1997).
[CrossRef]

F. Roddier, C. Roddier, J. Graves, M. Northcott, “Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle,” Astrophys. J. 443, 249–260 (1995).
[CrossRef]

Hege, E.

E. Hege, J. Beckers, P. Strittmatter, D. McCarthy, “Multiple mirror telescope as a phased array telescope,” Appl. Opt. 24, 2565–2576 (1984).
[CrossRef]

J. Christou, E. Hege, S. Jefferies, “Speckle deconvolution imaging using an iterative algorithm,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 134–143 (1995).
[CrossRef]

E. Hege, J. Angel, A. Gleckler, K. Pflibsen, B. Ulich, “An adaptive steerable imaging array,” in Digital Image Recovery and Synthesis II, P. Idell, ed., Proc. SPIE2029, 354–368 (1993).
[CrossRef]

Hege, E. K.

E. K. Hege, “Psf calibration in astronomical imaging—physical constraints for a noisy problem,” in Signal Recovery and Synthesis, Vol. 11 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 2–4.

E. K. Hege, “Super-resolved point-spread-function calibration for astronomical imaging,” in Time-Frequency and Time-Scale Analysis: Proceedings of the IEEE Signal Processing International Symposium (IEEE Service Center, Piscataway, N.J., 1998), pp. 477–480.

J. Christou, E. K. Hege, S. M. Jefferies, C. Keller, “Application of multiframe iterative blind deconvolution for diverse astronomical imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 433–444 (1994).
[CrossRef]

Hege, K.

R. Dekany, K. Hege, D. Wittman, “Searching for planets by differential astrometry with large telescopes,” Astrophys. Space Sci. 212, 299–319 (1994).
[CrossRef]

Hill, J.

J. Hill, “Strategy for interferometry with the Large Binocular Telescope,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 248–259 (1994).
[CrossRef]

Hill, J. M.

J. M. Hill, P. Salinari, “The Large Binocular Telescope project,” in Advanced Technology Optical/IR Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 23–33 (1998).
[CrossRef]

Hunt, B.

Jefferies, S.

S. Jefferies, J. Christou, “Restoration of astronomical images by iterative deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

J. Christou, E. Hege, S. Jefferies, “Speckle deconvolution imaging using an iterative algorithm,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 134–143 (1995).
[CrossRef]

Jefferies, S. M.

J. Christou, E. K. Hege, S. M. Jefferies, C. Keller, “Application of multiframe iterative blind deconvolution for diverse astronomical imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 433–444 (1994).
[CrossRef]

Keller, C.

J. Christou, E. K. Hege, S. M. Jefferies, C. Keller, “Application of multiframe iterative blind deconvolution for diverse astronomical imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 433–444 (1994).
[CrossRef]

Lloyd-Hart, M.

Marcellin, M.

McCarthy, D.

Northcott, M.

L. Close, F. Roddier, M. Northcott, C. Roddier, J. Graves, “Adaptive optics 0″.2 resolution infrared images of HL Tauri: direct images of an active accretion disk around a protostar,” Astrophys. J. 478, 766–777 (1997).
[CrossRef]

F. Roddier, C. Roddier, J. Graves, M. Northcott, “Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle,” Astrophys. J. 443, 249–260 (1995).
[CrossRef]

Pflibsen, K.

E. Hege, J. Angel, A. Gleckler, K. Pflibsen, B. Ulich, “An adaptive steerable imaging array,” in Digital Image Recovery and Synthesis II, P. Idell, ed., Proc. SPIE2029, 354–368 (1993).
[CrossRef]

Roddier, C.

L. Close, F. Roddier, M. Northcott, C. Roddier, J. Graves, “Adaptive optics 0″.2 resolution infrared images of HL Tauri: direct images of an active accretion disk around a protostar,” Astrophys. J. 478, 766–777 (1997).
[CrossRef]

F. Roddier, C. Roddier, J. Graves, M. Northcott, “Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle,” Astrophys. J. 443, 249–260 (1995).
[CrossRef]

Roddier, F.

L. Close, F. Roddier, M. Northcott, C. Roddier, J. Graves, “Adaptive optics 0″.2 resolution infrared images of HL Tauri: direct images of an active accretion disk around a protostar,” Astrophys. J. 478, 766–777 (1997).
[CrossRef]

F. Roddier, C. Roddier, J. Graves, M. Northcott, “Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle,” Astrophys. J. 443, 249–260 (1995).
[CrossRef]

Salinari, P.

J. M. Hill, P. Salinari, “The Large Binocular Telescope project,” in Advanced Technology Optical/IR Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 23–33 (1998).
[CrossRef]

Sandler, D.

Sheppard, D.

Stahl, S.

Strittmatter, P.

Thiébaut, E.

Traub, W.

Ulich, B.

E. Hege, J. Angel, A. Gleckler, K. Pflibsen, B. Ulich, “An adaptive steerable imaging array,” in Digital Image Recovery and Synthesis II, P. Idell, ed., Proc. SPIE2029, 354–368 (1993).
[CrossRef]

Wittman, D.

R. Dekany, K. Hege, D. Wittman, “Searching for planets by differential astrometry with large telescopes,” Astrophys. Space Sci. 212, 299–319 (1994).
[CrossRef]

Wittmann, D.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 167 et seq.

Appl. Opt.

Astrophys. J.

F. Roddier, C. Roddier, J. Graves, M. Northcott, “Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle,” Astrophys. J. 443, 249–260 (1995).
[CrossRef]

L. Close, F. Roddier, M. Northcott, C. Roddier, J. Graves, “Adaptive optics 0″.2 resolution infrared images of HL Tauri: direct images of an active accretion disk around a protostar,” Astrophys. J. 478, 766–777 (1997).
[CrossRef]

S. Jefferies, J. Christou, “Restoration of astronomical images by iterative deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

Astrophys. Space Sci.

R. Dekany, K. Hege, D. Wittman, “Searching for planets by differential astrometry with large telescopes,” Astrophys. Space Sci. 212, 299–319 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Other

J. M. Hill, P. Salinari, “The Large Binocular Telescope project,” in Advanced Technology Optical/IR Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 23–33 (1998).
[CrossRef]

J. Hill, “Strategy for interferometry with the Large Binocular Telescope,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 248–259 (1994).
[CrossRef]

Skylight, the atmospheric imaging software program, is available bookm Twinklesoft, P.O. Box 92838, Pasadena, Calif. 91103 [telephone: (626) 793-1015, e-mail: http://www.twinklesoft.com ].

IRAF is the Image Reduction and Analysis Facility developed at the National Astronomical Observatories. From the IRAF command-line prompt cl>, the galaxy image is dev$pix.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 167 et seq.

E. Hege, J. Angel, A. Gleckler, K. Pflibsen, B. Ulich, “An adaptive steerable imaging array,” in Digital Image Recovery and Synthesis II, P. Idell, ed., Proc. SPIE2029, 354–368 (1993).
[CrossRef]

J. Christou, E. K. Hege, S. M. Jefferies, C. Keller, “Application of multiframe iterative blind deconvolution for diverse astronomical imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 433–444 (1994).
[CrossRef]

J. Christou, E. Hege, S. Jefferies, “Speckle deconvolution imaging using an iterative algorithm,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 134–143 (1995).
[CrossRef]

E. K. Hege, “Psf calibration in astronomical imaging—physical constraints for a noisy problem,” in Signal Recovery and Synthesis, Vol. 11 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 2–4.

E. K. Hege, “Super-resolved point-spread-function calibration for astronomical imaging,” in Time-Frequency and Time-Scale Analysis: Proceedings of the IEEE Signal Processing International Symposium (IEEE Service Center, Piscataway, N.J., 1998), pp. 477–480.

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Figures (4)

Fig. 1
Fig. 1

Simulated LBT PSF’s at parallactic angles -45° (top), 0° (middle), and 45° (bottom). The 8.4-m Airy response is crossed by Young’s fringes owing to the binocular pupil. The Strehl ratio of these PSF’s is ≈0.1. The square root of the image intensity is shown.

Fig. 2
Fig. 2

Simulations of photon-statistics-limited (Strehl ratio, ≈0.1) imaging with the LBT. Exposures were made at each of three parallactic angles (same as in Fig. 1), -45° (left), 0° (middle), and 45° (right), with 105 (top row), 106 (middle row), and 107 (bottom row) photons per long-exposure image. The loge of the image intensity is shown.

Fig. 3
Fig. 3

Fourier moduli showing the SNR problem. The Fourier moduli of the coadded long-exposure images (left) compared with the reconstructed moduli (right). The two highest-SNR cases, 3×106 photons integrated with reconstruction at SNR=1730 (top) and 3×107 photons integrated with reconstruction at SNR=5500 (middle), are displayed loge for comparison with the noise-free target moduli (bottom). At 3×105 photons integrated, the SNR=550 image-visibility fringes do not reconstruct for baselines longer than 8.4 m.

Fig. 4
Fig. 4

Noise-limited LBT imagery. Coadded exposures are shown (left) compared with the corresponding PCID results (right) for SNR=550 (top), SNR=1750 (upper middle), and SNR=5500 (lower middle). The bottom row shows the reference galaxy target, the ideal target (left), and the bandpass limited response of a 22.8-m perfectly circular aperture (right) corresponding to the visibility moduli displayed in the bottom row of Fig. 3. All the images are displayed as the square root of the image intensity. The FOV is 0.64 arc sec with 0.01-arc sec pixels.

Tables (1)

Tables Icon

Table 1 Integration Time for a Given Dynamic Range DR

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

g˜k(r)=gk(r)+nk(r)=f(r)*hk(r)+nk(r),
=krSg,h,k[g˜k(r)-fˆ (r)*h^k(r)-ηks˜k(r)]2+k|f|>(D/λ)|H(f)|2,
R=|G(0)|2-Nb2|G(f )|2f>fc1/2,
R=N0Nd=Φ0t(Φ0t+Φbt)1/2,
t=R2(Φ0+Φb)Φ02=σ2(ϕ0+ϕbFA)ηϕ02A,

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