Abstract

The turbulent superresolution effect of a telescope, caused by the focusing properties of a distant turbulent layer, is discussed theoretically and experimentally. This effect is described as follows. Under certain observational conditions the energy-spectrum components of the instantaneous image correspond to the energy-spectrum components of the object that lie beyond the cutoff diffraction limits of the telescope resolution. The analytical expression for the instantaneous image spectrum of an extended incoherent object is found. This expression shows under what conditions the superresolution effect is observed. Short-exposure photographs of a rectangular grating observed through a turbulent layer are obtained. They demonstrate the existence of this effect.

© 1990 Optical Society of America

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References

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  1. A. Labeyrie, “Attainment of diffraction-limited resolution in large telescope by Fourier analyzing speckle pattern in stars images,” Astron. Astrophys. 6, 85–87 (1970).
  2. 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]
  3. J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984).
  4. J. C. Dainty, J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.
  5. A. A. Tokovinin, Stellar Interferometers (Nauka, Moscow, 1988).
  6. V. U. Zavorotnyy, M. I. Charnotskii, “The effect of the telescope resolution increasing due to turbulent inhomogeneities of the atmosphere,” Sov. Astron. Lett. 15, 1058–1065 (1989).
  7. B. S. Agrovskii, A. S. Gurvich, M. A. Kallistratova, “Light intensity fluctuations at focusing in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radifiz. 21, 212–216 (1978).

1989

V. U. Zavorotnyy, M. I. Charnotskii, “The effect of the telescope resolution increasing due to turbulent inhomogeneities of the atmosphere,” Sov. Astron. Lett. 15, 1058–1065 (1989).

1978

B. S. Agrovskii, A. S. Gurvich, M. A. Kallistratova, “Light intensity fluctuations at focusing in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radifiz. 21, 212–216 (1978).

1970

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescope by Fourier analyzing speckle pattern in stars images,” Astron. Astrophys. 6, 85–87 (1970).

Agrovskii, B. S.

B. S. Agrovskii, A. S. Gurvich, M. A. Kallistratova, “Light intensity fluctuations at focusing in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radifiz. 21, 212–216 (1978).

Charnotskii, M. I.

V. U. Zavorotnyy, M. I. Charnotskii, “The effect of the telescope resolution increasing due to turbulent inhomogeneities of the atmosphere,” Sov. Astron. Lett. 15, 1058–1065 (1989).

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984).

J. C. Dainty, J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.

Fienup, J. R.

J. C. Dainty, J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.

Gurvich, A. S.

B. S. Agrovskii, A. S. Gurvich, M. A. Kallistratova, “Light intensity fluctuations at focusing in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radifiz. 21, 212–216 (1978).

Kallistratova, M. A.

B. S. Agrovskii, A. S. Gurvich, M. A. Kallistratova, “Light intensity fluctuations at focusing in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radifiz. 21, 212–216 (1978).

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescope by Fourier analyzing speckle pattern in stars images,” Astron. Astrophys. 6, 85–87 (1970).

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]

Tokovinin, A. A.

A. A. Tokovinin, Stellar Interferometers (Nauka, Moscow, 1988).

Zavorotnyy, V. U.

V. U. Zavorotnyy, M. I. Charnotskii, “The effect of the telescope resolution increasing due to turbulent inhomogeneities of the atmosphere,” Sov. Astron. Lett. 15, 1058–1065 (1989).

Astron. Astrophys.

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescope by Fourier analyzing speckle pattern in stars images,” Astron. Astrophys. 6, 85–87 (1970).

Izv. Vyssh. Uchebn. Zaved. Radifiz.

B. S. Agrovskii, A. S. Gurvich, M. A. Kallistratova, “Light intensity fluctuations at focusing in a turbulent medium,” Izv. Vyssh. Uchebn. Zaved. Radifiz. 21, 212–216 (1978).

Sov. Astron. Lett.

V. U. Zavorotnyy, M. I. Charnotskii, “The effect of the telescope resolution increasing due to turbulent inhomogeneities of the atmosphere,” Sov. Astron. Lett. 15, 1058–1065 (1989).

Other

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]

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984).

J. C. Dainty, J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.

A. A. Tokovinin, Stellar Interferometers (Nauka, Moscow, 1988).

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Figures (4)

Fig. 1
Fig. 1

Geometry of the problem.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Images obtained with the use of the larger aperture (D = 0.8 cm): A, in the conjugate plane; B, 1.5 cm nearer the lens.

Fig. 4
Fig. 4

Images obtained with the use of the smaller aperture (D = 0.3 cm): A, in the conjugate plane; B, 1.5 cm nearer the lens.

Equations (23)

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I ( ρ 3 ) = d ρ 1 O ( ρ 1 ) P ( ρ 3 + z L ρ 1 , ρ 1 ) ,
I ˜ ( q ) = d ρ 3 I ( ρ 3 ) exp ( i q ρ 3 ) ,
P ˜ ( q , ρ 1 ) = d ρ 3 P ( ρ 3 = ρ 3 + z L ρ 1 , ρ 1 ) exp ( i q ρ 3 ) .
I ˜ ( q ) = d ρ 1 O ( ρ 1 ) P ˜ ( q , ρ 1 ) exp ( i q ρ 1 z / L ) .
I ˜ ( q ) = P ˜ ( q ) O ˜ ( z L q ) ,
O ˜ ( p ) = d ρ 1 O ( ρ 1 ) exp ( i p ρ 1 )
E ( q , p + z L q ) = ( 2 π ) 2 d ρ 1 P ˜ ( q , ρ 1 ) exp [ i ρ 1 ( p + z L q ) ] .
I ˜ ( q ) = d p O ˜ ( p ) E ( q , p + z L q ) .
E ( q , p + z L q ) = ( 2 π ) 2 δ ( p + z L q ) P ˜ ( q ) .
P ˜ ( q , ρ 1 ) = P ˜ 0 d ρ 2 M ( ρ 2 ) M * ( ρ 2 + z k q ) × g ( ρ 1 , ρ 2 ) g * ( ρ 1 , ρ 2 + z k q ) ,
E ( q , p + z L q ) = ( 2 π ) 2 P ˜ 0 d ρ 2 M ( ρ 2 ) M * ( ρ 2 + z k q ) × γ 2 ( q , p , ρ 2 ) ,
γ 2 ( q , p , ρ 2 ) = d ρ 1 g ( ρ 1 , ρ 2 ) g * ( ρ 1 , ρ 2 + z k q ) × exp [ i ρ 1 ( p + z L q ) ] .
g ( ρ 1 , ρ 2 ) = [ k L / 2 π i ( L L s ) L s ] d ρ s exp { i k 2 [ ( ρ 1 ρ 2 ) 2 / L s + ( ρ s ρ 2 ) 2 / ( L L s ) ( ρ 1 ρ 2 ) 2 / L ] + i S ( ρ s ) } ,
E ( q , p + z L q ) = ( 2 π L / ( L L s ) ) 2 P ˜ 0 F ( q , p ) T ( q , p ) f ( q , p ) ,
F ( q , p ) = exp [ i L L s 2 ( L L s ) k ( p + z L q ) 2 ] ,
T ( q , p ) = d ρ 2 M ( ρ 2 ) M * ( ρ 2 + z k q ) × exp [ i L s ( L L s ) ( p + z L q ) ρ 2 ] ,
f ( q , p ) = d ρ s exp { i L ( L L s ) ( p + z L q ) ρ s + i [ S ( ρ 3 ) S ( ρ s L s k p ) ] } .
M ( ρ 2 ) = exp [ ρ 2 2 ( a 2 i k / Δ F ) / 2 ]
F 0 1 = L 1 + z 1 ,
Δ F = F F 0 / ( F F 0 ) .
E ( q , p + z L q ) = π a 2 ( L / 2 π ( L L s ) ) 2 P ˜ 0 × h DIF ( q ) h P ( p , q ) h s ( p , q ) f ( p , q ) ,
h DIF = exp [ ( q z / k a ) 2 / 4 ] , h P ( p , q ) = exp [ L L s p ( p + z L q ) / 2 k ( L L s ) ] , h s = exp [ [ a L s / 2 ( L L s ) ] 2 ( p + z L q N ) 2 ] , N = 1 + ( L L s ) L / L s Δ F .
f ( q , p ) δ ( p + q z / L ) ,

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