Abstract

We have constructed an image-stabilization system that measures wave-front tilt over a telescope aperture that is due to atmospheric turbulence. This system uses small features on the Sun as point sources. The wave-front tilt power spectral density has been measured with this system out to more than 500 Hz. The spectra show three distinct asymptotic slopes that do not, in general, agree with theoretical predictions based on the Kolmogorov model.

© 1992 Optical Society of America

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References

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  1. C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wave-front distortions due to atmospheric turbulence,” IEEE Trans Antennas Propag. AP-24, 144–154 (1976).
    [Crossref]
  2. O. von der Luhe, “Measurements of characteristics of image motion with a solar image stabilization device,” Astron. Astrophys. 205, 354–360 (1988).
  3. B. Carlson, Communication Systems Analysis (McGraw-Hill, New York, 1986), p. 76.
  4. F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
    [Crossref]
  5. Ref. 1, p. 148.
  6. V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).
  7. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 389.

1988 (1)

O. von der Luhe, “Measurements of characteristics of image motion with a solar image stabilization device,” Astron. Astrophys. 205, 354–360 (1988).

1978 (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[Crossref]

1976 (1)

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wave-front distortions due to atmospheric turbulence,” IEEE Trans Antennas Propag. AP-24, 144–154 (1976).
[Crossref]

Butts, R. R.

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wave-front distortions due to atmospheric turbulence,” IEEE Trans Antennas Propag. AP-24, 144–154 (1976).
[Crossref]

Carlson, B.

B. Carlson, Communication Systems Analysis (McGraw-Hill, New York, 1986), p. 76.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 389.

Harris, F. J.

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[Crossref]

Hogge, C. B.

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wave-front distortions due to atmospheric turbulence,” IEEE Trans Antennas Propag. AP-24, 144–154 (1976).
[Crossref]

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).

von der Luhe, O.

O. von der Luhe, “Measurements of characteristics of image motion with a solar image stabilization device,” Astron. Astrophys. 205, 354–360 (1988).

Astron. Astrophys. (1)

O. von der Luhe, “Measurements of characteristics of image motion with a solar image stabilization device,” Astron. Astrophys. 205, 354–360 (1988).

IEEE Trans Antennas Propag. (1)

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wave-front distortions due to atmospheric turbulence,” IEEE Trans Antennas Propag. AP-24, 144–154 (1976).
[Crossref]

Proc. IEEE (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[Crossref]

Other (4)

Ref. 1, p. 148.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 389.

B. Carlson, Communication Systems Analysis (McGraw-Hill, New York, 1986), p. 76.

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Figures (6)

Fig. 1
Fig. 1

Optical layout. Specific components are described in the text.

Fig. 2
Fig. 2

Servo system diagram.

Fig. 3
Fig. 3

Typical recorded tilt signal.

Fig. 4
Fig. 4

Raw PSD (dashed curve), PSD after subtracting noise spectrum (dotted line), resultant PSD after correcting for system bandpass and RC circuit (solid curve). This run was taken with a 22-cm aperture.

Fig. 5
Fig. 5

Tilt PSD in the X and Y directions for a 22-cm aperture.

Fig. 6
Fig. 6

Tilt PSD in the X and Y directions for a 76-cm aperture. The solid straight lines represent the theoretical slopes of −2/3 and −11/3.

Equations (3)

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f 0 = ( 1 - R 2 ) 1 / 2 f c R ,
T ( f ) = f 0 ( f 0 2 + f 2 ) 1 / 2 .
T ( f ) = f ( f RC 2 + f 2 ) 1 / 2 .

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