D. Dravins, L. Lindegren, E. Mezey, A. T. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).

[CrossRef]

S. M. Flatté, C. Bracher, G.-Y. Wang, “Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation,” J. Opt. Soc. Am. A 11, 2080–2092 (1994);R. Hill, R. G. Frehlich, “Probability distribution of irradiance for the onset of strong scintillation,” J. Opt. Soc. Am. A 14, 1530–1540 (1997).

[CrossRef]

S. E. Troxel, R. 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]

A. Consortini, F. Cochetti, J. H. Churnside, R. J. Hill, “Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation,” J. Opt. Soc. Am. A 10, 2354–2362 (1993).

[CrossRef]

S. M. Flatté, G.-Y. Wang, J. Martin, “Irradiance variance of optical waves through atmospheric turbulence by numerical simulation and comparison with experiment,” J. Opt. Soc. Am. A 10, 2363–2370 (1993).

[CrossRef]

J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988);W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).

[CrossRef]
[PubMed]

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).

[CrossRef]

H. A. Whale, “Diffraction of a plane wave by a random phase screen,” J. Atmos. Terr. Phys. 35, 263–274 (1973);R. Buckley, “Diffraction by a random phase-changing screen: a numerical experiment,” J. Atmos. Terr. Phys. 37, 1431–1446 (1975);W. P. Brown, “Computer simulation of adaptive optical systems,” Hughes Research Laboratories Report, contract N60921–74–C–0249, 1975; 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]

J. Bufton, S. H. Genatt, “Simultaneous observations of atmospheric turbulence effects on stellar irradiance and phase,” Astron. J. 76, 378–386 (1971); see also G. Parry, J. G. Walker, R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).

[CrossRef]

M. J. Levin, “Generation of a sampled Gaussian time series having a specified correlation function,” IRE Trans. Inf. Theory IT-6, 545–548 (1960);J. C. Camparo, P. Lambropoulos, “Monte Carlo simulations of field fluctuations in strongly driven resonant transitions,” Phys. Rev. A 47, 480–494 (1993).

[CrossRef]
[PubMed]

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, (Dover, New York, 1972), Chap. 25.

R. R. Beland, “Propagation through atmospheric optical turbulence,” in Atmospheric Propagation of Radiation, F. G. Smith, ed. (SPIE Press, Bellingham, Wash., 1993), Chap. 2.

J. Bufton, S. H. Genatt, “Simultaneous observations of atmospheric turbulence effects on stellar irradiance and phase,” Astron. J. 76, 378–386 (1971); see also G. Parry, J. G. Walker, R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).

[CrossRef]

D. Dravins, L. Lindegren, E. Mezey, A. T. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).

[CrossRef]

S. M. Flatté, C. Bracher, G.-Y. Wang, “Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation,” J. Opt. Soc. Am. A 11, 2080–2092 (1994);R. Hill, R. G. Frehlich, “Probability distribution of irradiance for the onset of strong scintillation,” J. Opt. Soc. Am. A 14, 1530–1540 (1997).

[CrossRef]

S. M. Flatté, G.-Y. Wang, J. Martin, “Irradiance variance of optical waves through atmospheric turbulence by numerical simulation and comparison with experiment,” J. Opt. Soc. Am. A 10, 2363–2370 (1993).

[CrossRef]

J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988);W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).

[CrossRef]
[PubMed]

The author received the text of D. Fried’s phase-screen generation algorithm from D. L. Fried, 14671 Tumbleweed Lane, Monterey County, Calif. 95076 (private communication).

C-E. Fröberg, Introduction to Numerical Analysis (Addison–Wesley, Reading, Mass., 1965), Chap. 10.

J. Bufton, S. H. Genatt, “Simultaneous observations of atmospheric turbulence effects on stellar irradiance and phase,” Astron. J. 76, 378–386 (1971); see also G. Parry, J. G. Walker, R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).

[CrossRef]

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

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, Vl. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978), Chap. 4.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, Vl. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978), Chap. 4.

William L. Hays, Statistics (Holt, Rinehart & Winston, New York, 1988), Chap. 5.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, Vl. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978), Chap. 4.

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).

[CrossRef]

M. J. Levin, “Generation of a sampled Gaussian time series having a specified correlation function,” IRE Trans. Inf. Theory IT-6, 545–548 (1960);J. C. Camparo, P. Lambropoulos, “Monte Carlo simulations of field fluctuations in strongly driven resonant transitions,” Phys. Rev. A 47, 480–494 (1993).

[CrossRef]
[PubMed]

D. Dravins, L. Lindegren, E. Mezey, A. T. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).

[CrossRef]

J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988);W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).

[CrossRef]
[PubMed]

D. Dravins, L. Lindegren, E. Mezey, A. T. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).

[CrossRef]

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, Vl. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978), Chap. 4.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, (Dover, New York, 1972), Chap. 25.

J. W. Strohbehn, “Modern theories in the propagation of optical waves in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn ed. (Springer–Verlag, Berlin, 1978), Chap. 3.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 8.

S. M. Flatté, C. Bracher, G.-Y. Wang, “Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation,” J. Opt. Soc. Am. A 11, 2080–2092 (1994);R. Hill, R. G. Frehlich, “Probability distribution of irradiance for the onset of strong scintillation,” J. Opt. Soc. Am. A 14, 1530–1540 (1997).

[CrossRef]

S. M. Flatté, G.-Y. Wang, J. Martin, “Irradiance variance of optical waves through atmospheric turbulence by numerical simulation and comparison with experiment,” J. Opt. Soc. Am. A 10, 2363–2370 (1993).

[CrossRef]

H. A. Whale, “Diffraction of a plane wave by a random phase screen,” J. Atmos. Terr. Phys. 35, 263–274 (1973);R. Buckley, “Diffraction by a random phase-changing screen: a numerical experiment,” J. Atmos. Terr. Phys. 37, 1431–1446 (1975);W. P. Brown, “Computer simulation of adaptive optical systems,” Hughes Research Laboratories Report, contract N60921–74–C–0249, 1975; 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]

D. Dravins, L. Lindegren, E. Mezey, A. T. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).

[CrossRef]

J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988);W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).

[CrossRef]
[PubMed]

J. Bufton, S. H. Genatt, “Simultaneous observations of atmospheric turbulence effects on stellar irradiance and phase,” Astron. J. 76, 378–386 (1971); see also G. Parry, J. G. Walker, R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).

[CrossRef]

M. J. Levin, “Generation of a sampled Gaussian time series having a specified correlation function,” IRE Trans. Inf. Theory IT-6, 545–548 (1960);J. C. Camparo, P. Lambropoulos, “Monte Carlo simulations of field fluctuations in strongly driven resonant transitions,” Phys. Rev. A 47, 480–494 (1993).

[CrossRef]
[PubMed]

H. A. Whale, “Diffraction of a plane wave by a random phase screen,” J. Atmos. Terr. Phys. 35, 263–274 (1973);R. Buckley, “Diffraction by a random phase-changing screen: a numerical experiment,” J. Atmos. Terr. Phys. 37, 1431–1446 (1975);W. P. Brown, “Computer simulation of adaptive optical systems,” Hughes Research Laboratories Report, contract N60921–74–C–0249, 1975; 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]

H. T. Yura, “Physical model for strong optical-amplitude fluctuations in a turbulent medium,” J. Opt. Soc. Am. 64, 59 (1974).

[CrossRef]

S. F. Clifford, G. R. Ochs, R. S. Lawrence, “Saturation of optical scintillation by strong turbulence,” J. Opt. Soc. Am. 64, 148–154 (1974).

[CrossRef]

R. E. Hufnagel, N. R. Stanley, “Modulation transfer function associated with image transmission through turbulent media,” J. Opt. Soc. Am. 54, 52–61 (1964).

[CrossRef]

S. E. Troxel, R. 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]

A. Consortini, F. Cochetti, J. H. Churnside, R. J. Hill, “Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation,” J. Opt. Soc. Am. A 10, 2354–2362 (1993).

[CrossRef]

S. M. Flatté, G.-Y. Wang, J. Martin, “Irradiance variance of optical waves through atmospheric turbulence by numerical simulation and comparison with experiment,” J. Opt. Soc. Am. A 10, 2363–2370 (1993).

[CrossRef]

S. M. Flatté, C. Bracher, G.-Y. Wang, “Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation,” J. Opt. Soc. Am. A 11, 2080–2092 (1994);R. Hill, R. G. Frehlich, “Probability distribution of irradiance for the onset of strong scintillation,” J. Opt. Soc. Am. A 14, 1530–1540 (1997).

[CrossRef]

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” Proc. IEEE 71, 722–737 (1983).

[CrossRef]

D. Dravins, L. Lindegren, E. Mezey, A. T. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).

[CrossRef]

In the following, we refer to the lower 9 km of atmosphere as the troposphere, the 9–12-km region as the tropopause, and the 12–20-km region as the lower stratosphere.

R. R. Beland, “Propagation through atmospheric optical turbulence,” in Atmospheric Propagation of Radiation, F. G. Smith, ed. (SPIE Press, Bellingham, Wash., 1993), Chap. 2.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 8.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, Vl. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978), Chap. 4.

C-E. Fröberg, Introduction to Numerical Analysis (Addison–Wesley, Reading, Mass., 1965), Chap. 10.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, (Dover, New York, 1972), Chap. 25.

The author received the text of D. Fried’s phase-screen generation algorithm from D. L. Fried, 14671 Tumbleweed Lane, Monterey County, Calif. 95076 (private communication).

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

For completeness, we note that the pixel size of ∼0.3 cm–0.4 cm introduces an inner scale of turbulence into the simulations. This is an unavoidable consequence of all finite element numerical simulations.

In principle, a telescope of any diameter may be simulated. However, for larger-aperture telescopes to be considered, the phase-screen length must also become larger, which in turn requires a larger number of pixels to span the screen’s length. (As discussed in Appendix A, the pixel size is bounded by considerations related to the strength of turbulence and the interscreen spacing.) The computational requirements for dealing with phase screens that have large numbers of pixels can quickly become prohibitive.

William L. Hays, Statistics (Holt, Rinehart & Winston, New York, 1988), Chap. 5.

J. W. Strohbehn, “Modern theories in the propagation of optical waves in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn ed. (Springer–Verlag, Berlin, 1978), Chap. 3.