Abstract

Fast-Fourier-transform-based simulators of atmospheric wave fronts with a von Kármán turbulence spectrum were tested with reference to the phase-structure function and phase variance over a pupil on large square and rectangular formats. The symmetry and the accuracy of the phase-structure function were found to be limited by the aspect ratio and the size of the phase screen. The phase variance over a pupil is less sensitive to the aspect ratio than the phase-structure function and is dependent mainly on the size of the phase screen. Several tests are reported and discussed together with a method of compensation for the negative effects of rectangular formats.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. H. Jakobsson, “Simulations of time series of atmospherically distorted wave fronts,” Appl. Opt. 35, 1561–1565 (1996).
    [CrossRef] [PubMed]
  3. M. C. Roggemann, B. M. Welsh, D. Montera, T. A. Rhoadamer, “Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions,” Appl. Opt. 34, 4037–4051 (1995).
    [CrossRef] [PubMed]
  4. B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating nonisoplanatic geometries and temporal evolution,” in Propagation and Imaging through the Atmosphere, L. R. Bissonnette, J. C. Dainty, eds., Proc. SPIE3125, 327–338 (1997).
    [CrossRef]
  5. D. F. Buscher, J. T. Armstrong, C. A. Hummel, A. Quirrenbach, D. Mozurkewich, K. J. Johnston, C. S. Denison, M. M. Colavita, M. Shao, “Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales,” Appl. Opt. 34, 1081–1096 (1995).
    [CrossRef] [PubMed]
  6. E. M. Johansson, D. T. Gavel, “Simulation of stellar speckle imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 372–383 (1994).
    [CrossRef]
  7. A. Glindemann, R. G. Lane, J. C. Dainty, “Simulations of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
    [CrossRef]
  8. F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 281–376.
    [CrossRef]
  9. A. Glindemann, N. Rees, “Photon counting vs. CCD sensors for wavefront sensing—performance comparison in the presence of noise,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 824–834 (1994).
    [CrossRef]
  10. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
    [CrossRef]
  11. R. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  12. B. J. Herman, L. A. Strugala, “Method for inclusion of low frequency contributions in numerical representation of atmospheric turbulence,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, E. Wilson, eds., Proc. SPIE1221, 183–192 (1990).
    [CrossRef]
  13. R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random Media 2, 202–304 (1992).
    [CrossRef]
  14. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [CrossRef]

1996 (1)

1995 (2)

1993 (1)

A. Glindemann, R. G. Lane, J. C. Dainty, “Simulations of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[CrossRef]

1992 (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random Media 2, 202–304 (1992).
[CrossRef]

1990 (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

1976 (1)

1965 (1)

Armstrong, J. T.

Buscher, D. F.

Colavita, M. M.

Dainty, J. C.

A. Glindemann, R. G. Lane, J. C. Dainty, “Simulations of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random Media 2, 202–304 (1992).
[CrossRef]

Denison, C. S.

Fried, D. L.

Gavel, D. T.

E. M. Johansson, D. T. Gavel, “Simulation of stellar speckle imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 372–383 (1994).
[CrossRef]

Glindemann, A.

A. Glindemann, R. G. Lane, J. C. Dainty, “Simulations of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random Media 2, 202–304 (1992).
[CrossRef]

A. Glindemann, N. Rees, “Photon counting vs. CCD sensors for wavefront sensing—performance comparison in the presence of noise,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 824–834 (1994).
[CrossRef]

Herman, B. J.

B. J. Herman, L. A. Strugala, “Method for inclusion of low frequency contributions in numerical representation of atmospheric turbulence,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, E. Wilson, eds., Proc. SPIE1221, 183–192 (1990).
[CrossRef]

Hummel, C. A.

Jakobsson, H.

Johansson, E. M.

E. M. Johansson, D. T. Gavel, “Simulation of stellar speckle imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 372–383 (1994).
[CrossRef]

Johnston, K. J.

Lane, R. G.

A. Glindemann, R. G. Lane, J. C. Dainty, “Simulations of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random Media 2, 202–304 (1992).
[CrossRef]

McGlamery, B. L.

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]

Montera, D.

Mozurkewich, D.

Noll, R.

Quirrenbach, A.

Rees, N.

A. Glindemann, N. Rees, “Photon counting vs. CCD sensors for wavefront sensing—performance comparison in the presence of noise,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 824–834 (1994).
[CrossRef]

Rhoadamer, T. A.

Roddier, F.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 281–376.
[CrossRef]

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Roggemann, M. C.

Shao, M.

Strugala, L. A.

B. J. Herman, L. A. Strugala, “Method for inclusion of low frequency contributions in numerical representation of atmospheric turbulence,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, E. Wilson, eds., Proc. SPIE1221, 183–192 (1990).
[CrossRef]

Welsh, B. M.

M. C. Roggemann, B. M. Welsh, D. Montera, T. A. Rhoadamer, “Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions,” Appl. Opt. 34, 4037–4051 (1995).
[CrossRef] [PubMed]

B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating nonisoplanatic geometries and temporal evolution,” in Propagation and Imaging through the Atmosphere, L. R. Bissonnette, J. C. Dainty, eds., Proc. SPIE3125, 327–338 (1997).
[CrossRef]

Appl. Opt. (3)

J. Mod. Opt. (1)

A. Glindemann, R. G. Lane, J. C. Dainty, “Simulations of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Eng. (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Waves in Random Media (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random Media 2, 202–304 (1992).
[CrossRef]

Other (6)

B. J. Herman, L. A. Strugala, “Method for inclusion of low frequency contributions in numerical representation of atmospheric turbulence,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, E. Wilson, eds., Proc. SPIE1221, 183–192 (1990).
[CrossRef]

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 281–376.
[CrossRef]

A. Glindemann, N. Rees, “Photon counting vs. CCD sensors for wavefront sensing—performance comparison in the presence of noise,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 824–834 (1994).
[CrossRef]

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]

B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating nonisoplanatic geometries and temporal evolution,” in Propagation and Imaging through the Atmosphere, L. R. Bissonnette, J. C. Dainty, eds., Proc. SPIE3125, 327–338 (1997).
[CrossRef]

E. M. Johansson, D. T. Gavel, “Simulation of stellar speckle imaging,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 372–383 (1994).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Phase-structure functions of FFT-based phase-screen simulations for square formats with additional subharmonic phase screens: DFFT is the radial section from the center of the phase-structure function of the FFT-based phase screen, DLF is the same for the subharmonic phase screen, and D Von Karman the theoretical phase structure functions (thick curve). (a) Phase screen of 20 m × 20 m and 128 × 128 pixels, r 0 = 0.1 m, L 0 = 30 m, three subharmonics; (b) phase screen of 40 m × 40 m and 128 × 128 pixels, r 0 = 0.1 m, L 0 = 30 m, no subharmonics.

Fig. 2
Fig. 2

Phase-structure functions of FFT-based phase-screen simulations for rectangular formats with additional subharmonic phase screens: Phase-structure function image of (a) the FFT-based phase screen (DFFT); (b) the subharmonic phase screen (DLF), rebinned to 128 × 64 pixels in the reproduction. (c) X and Y sections from the center of the phase-structure function. DFFT(x) and DFFT(y) are the X and the Y sections of the phase-structure function of the FFT-based phase screen, respectively, DLF(x) and DLF(y) are the same for the subharmonic phase screen, D(x) is the X section of the overall phase-structure function sum of DFFT(x) and DLF(x), D(y) is the Y-section sum of DFFT(y) and DLF(y), and D Von Karman is the theoretical phase structure function (thick curve). The phase screen is 8 m × 4 m and 512 × 256 pixels, r 0 = 0.1 m, L 0 = 10 m, three subharmonics.

Fig. 3
Fig. 3

Normalized phase variance over circular pupils of 100 FFT-based phase-screen simulations for square formats with additional subharmonic phase screens. There is one sigma error bars. All phase screens are 10 m × 10 m and 128 × 128 pixels, with r 0 = 0.1 m: (a) L 0 = 10 m, three subharmonics; (b) L 0 = 30 m, five subharmonics; (c) L 0 = 100 m, five subharmonics; (d) infinite L 0, ten subharmonics. Case (d) used 200 simulations. The theoretical values are plotted by continuous curves.

Fig. 4
Fig. 4

Normalized phase variance over circular pupils of 200 FFT-based phase-screen simulations for square formats with additional subharmonic phase screens and tip–tilt removal. There is one sigma error bar, and the phase screen is 10 m × 10 m and 128 × 128 pixels, with r 0 = 0.1 m, infinite L 0, and ten subharmonics. The theoretical values are plotted by the solid line.

Fig. 5
Fig. 5

Normalized phase variance over circular pupils of 100 FFT-based phase-screen simulations for rectangular formats with additional subharmonic phase screens. There is one sigma error bar. The phase screens have (1024 × 128) pixels, with r 0 = 0.1 m, L 0 = 10 m, three subharmonics, and a size of (a) 16 m × 2 m, (b) 80 m × 10 m. The theoretical values are plotted by continuous curves.

Fig. 6
Fig. 6

Symmeterized phase-structure functions of FFT-based phase-screen simulations for rectangular formats with additional subharmonic phase screens and compensation for the aspect-ratio effects on the FFT-based phase-structure function. W x and W y are the X and the Y square-root spectral weights used for the compensation. The phase screens are (a), (b) 4 m × 2 m and 256 × 128 pixels, with three subharmonics; (c), (d) 64 m × 16 m and 512 × 128 pixels, with no subharmonics; (e), (f) 256 m × 16 m and 2048 × 128 pixels, with no subharmonics; (g), (h) 512 m × 16 m and 4096 × 128 pixels, with no subharmonics. In all cases r 0 = 0.1 m, L 0 = 30 m, and N G = 8. All images show the central region of 256 × 128 pixels rebinned to 128 × 64 pixels in the reproduction. DFFT marks the FFT-based phase-structure function image and DFFT(x) and DFFT(y) are its X and Y sections, respectively, DLF, DLF(x), and DLF(y) do the same for the subharmonic phase screen, D(x) is the X section of the overall phase structure function sum of DFFT(x) and DLF(x), D(y) is the Y-section sum of DFFT(y) and DLF(y), and D Von Karman is the theoretical phase-structure function (thick curve).

Fig. 7
Fig. 7

Symmetrized phase-structure function of the subharmonic phase screen with compensation for the aspect-ratio effects. The phase screen is 8 m × 4 m and 512 × 256 pixels, with r 0 = 0.1 m, L 0 = 10 m, three subharmonics, and N G = 8. (a) Phase-structure function image (DLF) of the subharmonic phase screen rebinned to 128 × 64 pixels in the reproduction, (b) X and Y sections form the center of the phase-structure function of the subharmonic phase screen. DLF(x) and DLF(y) are the X and Y sections of DLF, which overlap in the figure. The radial section of the phase-structure function of the subharmonic phase screen at nominal FFT resolution is plotted by the dotted curve.

Fig. 8
Fig. 8

Normalized phase variance over circular pupils of 100 FFT-based phase-screen simulations for rectangular formats with additional subharmonic phase screens and compensation for the aspect-ratio effects on the phase-structure function. There is one sigma error bar. W x and W y are the X and the Y square-root spectral weights used for the compensation. The phase screens are (a) 16 m × 2 m and 1024 × 128 pixels, with r 0 = 0.1 m, L 0 = 10 m, three subharmonics, and N G = 8; (b) 32 m × 4 m and 1024 × 128 pixels, with r 0 = 0.1 m, L 0 = 10 m, one subharmonic, and N G = 8. The theoretical values are plotted by the continuous curves.

Equations (13)

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

ϕ mn = m = - N x / 2 N x / 2 - 1 n = - N y / 2 N y / 2 - 1   h m n f m n × exp i 2 π m m / N x + n n / N y ,
f m n = 0.15132 G x G y - 1 / 2 r 0 - 5 / 6 × m / G x 2 + n / G y 2 + L 0 - 2 - 11 / 12 ,
ϕ mn LF = p = 1 N p m = - 1 1 n = - 1 1   h m n LF   f m n LF × exp i 2 π 3 - p m m / N x + n n / N y ,
f m n LF = 0.15132 G x G y - 1 / 2 r 0 - 5 / 6 3 - p 3 - p m / G x 2 + 3 - p n / G y 2 + L 0 - 2 - 11 / 12 ,
D ϕ m ,   n = 2 B ϕ 0 ,   0 - B ϕ m ,   n ,
B ϕ m ,   n = m = - N x / 2 N x / 2 - 1 n = - N y / 2 N y / 2 - 1   f m n 2 × exp i 2 π m m / N x + n n / N y ,
B mn LF = p = 1 N p m = - 1 1 n = - 1 1 f m n LF 2 × exp i 2 π 3 - p m m / N x + n n / N y .
D r = 6.16 r 0 - 5 / 3 3 / 5 L 0 / 2 π 5 / 3 - rL 0 / 4 π 5 / 6 K 5 / 6 2 π r / L 0 / Γ 11 / 6 ,
σ ϕ 2 d = 4 d - 2 0 d   rF C r ,   d D r d r ,
F C r ,   d = π - 1 2   arccos r / d - 2 r / d 1 - r / d 2 1 / 2 ,
F L r ,   d = π - 1 6   arccos r / d - 14 r / d - 8 r / d 3 × 1 - r / d 2 1 / 2 ,
ϕ rs LFG = p = 1 N p m = - 1 1 n = - 1 1   h m n LF f m n LFG × exp i 2 π 3 - p m i / N x + n j / N x ,
f m n LFG = 0.15132 G x - 1 r 0 - 5 / 6 3 - p 3 - p m / G x 2 + 3 - p n / G x 2 + L 0 - 2 - 11 / 12 ,

Metrics