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Applied Optics

Applied Optics


  • Vol. 40, Iss. 4 — Feb. 1, 2001
  • pp: 544–552

Measurement of telescope aberrations through atmospheric turbulence by use of phase diversity

Naoshi Baba and Kohta Mutoh  »View Author Affiliations

Applied Optics, Vol. 40, Issue 4, pp. 544-552 (2001)

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We conduct computer simulations of the reconstruction of a wave front at a telescope pupil with the phase-diversity method. An instantaneous wave front is reconstructed from focused and defocused specklegrams of a point star. In the wave-front reconstruction we do not fit the wave front to Zernike polynomials but retrieve the phase with a phase-unwrapping procedure. Averaging over many atmospherically perturbed wave fronts leads to the residual phase error, namely, the aberration of the telescope. The scintillation effect, nonuniformity of amplitude on a telescope pupil, is also discussed.

© 2001 Optical Society of America

OCIS Codes
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(030.6610) Coherence and statistical optics : Stellar speckle interferometry
(100.5070) Image processing : Phase retrieval
(110.6770) Imaging systems : Telescopes
(350.1260) Other areas of optics : Astronomical optics

Original Manuscript: May 30, 2000
Revised Manuscript: October 23, 2000
Published: February 1, 2001

Naoshi Baba and Kohta Mutoh, "Measurement of telescope aberrations through atmospheric turbulence by use of phase diversity," Appl. Opt. 40, 544-552 (2001)

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  1. R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).
  2. L. Noethe, F. Franza, P. Giordano, R. N. Wilson, O. Citterio, G. Conti, E. Mattaini, “Active optics II. Results of an experiment with a thin 1 m test mirror,” J. Mod. Opt. 35, 1427–1457 (1988). [CrossRef]
  3. C. Roddier, F. Roddier, “Wave-front reconstruction from defocused images and the testing of ground-based optical telescopes,” J. Opt. Soc. Am. A 10, 2277–2287 (1993). [CrossRef]
  4. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
  5. M. G. Loefdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).
  6. R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, C. U. Keller, “Evaluation of phase-diverse techniques for solar-image restoration,” Astrophys. J. 466, 1087–1099 (1996). [CrossRef]
  7. M. G. Löfdahl, R. L. Kendrick, A. Harwit, K. E. Mitchell, A. L. Duncan, J. H. Seldin, R. G. Paxman, D. S. Acton, “A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II Telescope,” in Space Telescopes and Instruments V, P. V. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 1190–1201 (1998). [CrossRef]
  8. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  9. R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992). [CrossRef]
  10. N. Baba, H. Tomita, N. Miura, “Iterative reconstruction method in phase-diversity imaging,” Appl. Opt. 33, 4428–4433 (1994). [CrossRef] [PubMed]
  11. J. Strand, T. Taxt, “Performance evaluation of two-dimensional phase unwrapping algorithms,” Appl. Opt. 38, 4333–4344 (1999). [CrossRef]
  12. D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107–117 (1994). [CrossRef]
  13. D. C. Ghiglia, M. D. Pratt, Two-dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, 1998).
  14. W. H. Press, B. D. Flanmery, S. A. Tenkolsky, W. T. Vallerling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1986).
  15. B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Urbach, ed., Proc. SPIE74, 225–233 (1976). [CrossRef]
  16. L. Meynadier, V. Michan, M.-T. Velluet, J.-M. Conan, L. M. Mugnier, G. Rousset, “Noise propagation in wave-front sensing with phase diversity,” Appl. Opt. 38, 4967–4979 (1999). [CrossRef]
  17. F. Roddier, “The effect of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19. [CrossRef]
  18. R. Avila, J. Vermin, E. Masciadri, “Whole atmospheric-turbulence profiling with generalized SCIDAR,” Appl. Opt. 36, 7898–7905 (1997). [CrossRef]
  19. R. A. Johnston, R. G. Lane, “Modeling scintillation from a periodic Kolmogorov phase screen,” Appl. Opt. 39, 4761–4769 (2000). [CrossRef]
  20. N. Baba, E. Kenmochi, “Wavefront retrieval with use of defocused PSF data,” Optik 84, 70–72 (1990).
  21. D. J. Lee, M. C. Roggemann, B. M. Welsh, “Cramer–Rao analysis of phase-diverse wave-front sensing,” J. Opt. Soc. Am. A 16, 1005–1015 (1999). [CrossRef]
  22. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998). [CrossRef]

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