OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 34, Iss. 20 — Jul. 10, 1995
  • pp: 4037–4051

Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions

Michael C. Roggemann, Byron M. Welsh, Dennis Montera, and Troy A. Rhoadarmer  »View Author Affiliations

Applied Optics, Vol. 34, Issue 20, pp. 4037-4051 (1995)

View Full Text Article

Enhanced HTML    Acrobat PDF (1586 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Simulating the effects of atmospheric turbulence on optical imaging systems is an important aspect of understanding the performance of these systems. Simulations are particularly important for understanding the statistics of some adaptive-optics system performance measures, such as the mean and variance of the compensated optical transfer function, and for understanding the statistics of estimators used to reconstruct intensity distributions from turbulence-corrupted image measurements. Current methods of simulating the performance of these systems typically make use of random phase screens placed in the system pupil. Methods exist for making random draws of phase screens that have the correct spatial statistics. However, simulating temporal effects and anisoplanatism requires one or more phase screens at different distances from the aperture, possibly moving with different velocities. We describe and demonstrate a method for creating random draws of phase screens with the correct space–time statistics for arbitrary turbulence and wind-velocity profiles, which can be placed in the telescope pupil in simulations. Results are provided for both the von Kármán and the Kolmogorov turbulence spectra. We also show how to simulate anisoplanatic effects with this technique.

© 1995 Optical Society of America

Original Manuscript: October 4, 1994
Revised Manuscript: January 3, 1995
Published: July 10, 1995

Michael C. Roggemann, Byron M. Welsh, Dennis Montera, and Troy A. Rhoadarmer, "Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions," Appl. Opt. 34, 4037-4051 (1995)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. XIX, pp. 281–376. [CrossRef]
  2. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  3. A. W. Lohmann, G. Weigelt, B. Wirnitzer, “Speckle masking in astronomy: triple correlation theory and applications,” Appl. Opt. 22, 4028–4037 (1983). [CrossRef] [PubMed]
  4. D. L. Fried, “Postdetection wave-front compensation,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 127–133 (1987).
  5. J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990). [CrossRef]
  6. J. D. Gonglewski, D. G. Voelz, J. S. Fender, D. C. Dayton, B. K. Spielbusch, R. E. Pierson, “First astronomical application of postdetection turbulence compensation: images of a Aurigae, n Ursae Majoris, and a Geminorum using self-referenced speckle holography,” Appl. Opt. 29, 4527–4529 (1990). [CrossRef] [PubMed]
  7. B. M. Welsh, R. N. V. Niederhausern, “Performance analysis of the self-referenced speckle holography image reconstruction technique,” Appl. Opt. 32, 5071–5078 (1993). [CrossRef] [PubMed]
  8. E. P. Wallner, “Optimal wave-front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983). [CrossRef]
  9. B. M. Welsh, C. S. Gardner, “Performance analysis of adaptive optics systems using slope sensors,” J. Opt. Soc. Am. A 6, 1913–1923 (1989). [CrossRef]
  10. R. Q. Fugate, B. L. Ellerbroek, C. H. Higgins, M. P. Jelonek, W. J. Lange, A. C. Slavin, W. J. Wild, D. M. Winker, J. M. Wynia, J. M. Spinhirne, B. R. Boeke, R. E. Ruane, J. F. Moroney, M. D. Oliker, D. W. Sindle, R. A. Cleis, “Two generations of laser-guide-star adaptive-optics experiments at the Starfire Optical Range,” J. Opt. Soc. Am. A 11, 310–314 (1994). [CrossRef]
  11. B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric turbulence compensation in extended field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783–805 (1994). [CrossRef]
  12. P. Nisenson, R. Barakat, “Partial atmospheric correction with adaptive optics,” J. Opt. Soc. Am. A 4, 2249–2253 (1987). [CrossRef]
  13. R. C. Smithson, M. L. Peri, “Partial correction of astronomical images with active mirrors,” J. Opt. Soc. Am. A 6, 92–97 (1989). [CrossRef]
  14. M. C. Roggemann, “Limited degree-of-freedom adaptive-optics and image reconstruction,” Appl. Opt. 30, 4227–4233 (1991). [CrossRef] [PubMed]
  15. M. C. Roggemann, C. L. Matson, “Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive-optics and bispectrum postprocessing,” J. Opt. Soc. Am. A 9, 1525–1535 (1992). [CrossRef]
  16. M. C. Roggemann, J. A. Meinhardt, “Image reconstruction by means of wave-front sensor measurements in closed-loop adaptive-optics systems,” J. Opt. Soc. Am. A 10, 1996–2007 (1993). [CrossRef]
  17. J. C. Dainty, A. H. Greenaway, “Estimation of spatial power spectra in speckle imaging,” J. Opt. Soc. Am. 69, 786–790 (1979). [CrossRef]
  18. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  19. G. Cochran, “Phase screen generation,” Tech. Rep. TR-663 (Optical Sciences Company, Placentia, Calif., 1985).
  20. N. Roddier, “Atmospheric wave-front simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990). [CrossRef]
  21. T. Goldring, L. Carlson, “Analysis and implementation of non-Kolmogorov phase screens appropriate to structured environments,” in Nonlinear Optical Beam Manipulation and High Energy Beam Propagation through the Atmosphere, R. A. Fisher, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1060, 244–264 (1989).
  22. R. G. Paxman, B. J. Thelen, J. H. Seldin, “Phase diversity correction of turbulence-induced space variant blur,” Opt. Lett. 19, 1231–1233 (1994). [CrossRef] [PubMed]
  23. A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), Vol. 25, pp. 129–170. [CrossRef]
  24. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  25. S. E. Troxel, B. M. Welsh, M. C. Roggemann, “Off-axis optical transfer function calculations in an adaptive-optics system by means of a diffraction calculation for weak index fluctuations,” J. Opt. Soc. Am. A 11, 2100–2111 (1994). [CrossRef]
  26. R. J. Sasiela, J. D. Shelton, “Transverse spectral filtering and Mellin-transform techniques applied to the effect of outer scale on tilt and tilt anisoplanatism,” J. Opt. Soc. Am. A 10, 646–660 (1993). [CrossRef]
  27. R. J. Sasiela, J. D. Shelton, “Mellin transform methods applied to integral evaluation: Taylor series and asymptotic approximations,” J. Math. Phys. N.Y. 34, 2572–2619 (1993). [CrossRef]
  28. R. J. Sasiela, “A unified approach to electromagnetic wave propagation in turbulence and the evaluation of multiparameter integrals,” Tech. Rep. TR 807 (Lincoln Laboratory, MIT, Cambridge, Mass., 1988).
  29. IMSL “Math/library: special functions,” in IMSL Fortran Subroutines for Mathematical Applications (IMSL, 2500 Permian Tower, 2500 City West Boulevard, Houston, Tex. 77042-3020, 1991), pp. 97–142.
  30. G. A. Tyler, “Merging: a new method for tomography through random media,” J. Opt. Soc. Am. A 10, 409–425 (1993).
  31. D. P. Greenwood, “Bandwidth specification for adaptive-optics systems,” J. Opt. Soc. Am. 67, 390–393 (1977). [CrossRef]
  32. M. Miller, P. Zieske, D. Hanson, “Characterization of atmospheric turbulence,” in Imaging Through The Atmosphere, J. C. Wyant, ed., Proc. Soc. Photo-Opt. Instrum. Eng.75, 30–38 (1976).
  33. R. E. Hufnagel, “Variations of atmospheric turbulence,” in Optical Propagation through Turbulence, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1974), paper WA1.
  34. M. C. Roggemann, B. L. Ellerbroek, T. A. Rhoadarmer, “Widening the effective field-of-view of adaptive-optics telescopes using deconvolution from wave-front sensing: average and signal-to-noise ratio performance,” Appl. Opt. (to be published).
  35. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).
  36. G. Strang, Linear Algebra and its Applications (Academic, New York, 1980).
  37. W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes—The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1986).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited