Abstract

It is considered how the source spectrum influences the measurement accuracy of optical wave arrival angles, as well as the estimation of the path-averaged structure parameter of the refractive index fluctuations. Two reasons that can cause the wavelength dependence of the variance of fluctuations of wave arrival angles are analyzed. The first one is connected with the fact that phases depend on a wavelength in the approximation of smooth perturbations. The second reason is associated with the wavelength dependence of the refractive index and, consequently, its fluctuations. Strict equations are obtained to take into account the influence of the source spectrum on the measurement accuracy of the variance of arrival angle fluctuations and, indirectly, on the estimation accuracy of the path-averaged refractive index structure parameter. It can be stated that for most radiation sources (even nonmonochromatic) the influence of the source spectral composition can be neglected.

© 2008 Optical Society of America

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  1. G. R. Ochs, I. W. Ting, R. W. Lawrence, and S. F. Clifford, “Refractive-turbulence profiles measured by one-dimensional spatial filtering of scintillations,” Appl. Opt. 15, 2504-2510(1976).
    [CrossRef] [PubMed]
  2. Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
    [CrossRef]
  3. S. F. Clifford and J. H. Churnside, “Refractive turbulence profiling using synthetic aperture spatial filtering of scintillation,” Appl. Opt. 26, 1295-1303 (1987).
    [CrossRef] [PubMed]
  4. R. Johnston, C. Dainty, N. Wooder, and R. Lane, “Generalized scintillation detection and ranging results obtained by use of a modified inversion technique,” Appl. Opt. 41, 6768-6772(2002).
    [CrossRef] [PubMed]
  5. A. Tokovinin, “From differential image motion to seeing,” Publ. Astron. Soc. Pac. 114, 1156 (2002).
    [CrossRef]
  6. V. Kornilov, A. Tokovinin, N. Shatsky, O. Voziakova, S. Potatin, and B. Safonov, “Combined MASS-DIMM instrument from atmospheric turbulence studies,” Mon. Not. R. Astron. Soc. (2007).
    [CrossRef]
  7. V. A. Banakh, I. N. Smalkho, and B. N. Chen, “Shift of the image of incoherent light source in turbulent atmosphere,” Opt. Spectrosc. 61, 582-586 (1986).
  8. A. S. Gurvich, V. L. Mironov, A. I. Kon, and S. S. Khmelevtsov, Propagation of Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).
  9. L. V. Antoshkin, N. N. Botugina, O. N. Emaleev, L. N. Lavrinova, and V. P. Lukin, “Differential optical monitor of atmospheric turbulence parameters,” Atmos. Oceanic Opt. 11, 1219 (1998).
  10. B. S. Haugstad and V. R. Eshleman, “On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres,” Astrophys. J. 229, 393-398 (1979).
    [CrossRef]
  11. W. B. Hubbard and J. R. Jokipi, “Comment of the paper 'On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres' by Haugstad and Eshleman,” Astrophys. J. 229, 399-401 (1977).
    [CrossRef]
  12. I. S. Gragshteyn and I. M. Ryzhik, Tabicy Integralov, Summ, Riyadov i Proizvedenii (Fiziko-Mathematik, 1964).

2007

V. Kornilov, A. Tokovinin, N. Shatsky, O. Voziakova, S. Potatin, and B. Safonov, “Combined MASS-DIMM instrument from atmospheric turbulence studies,” Mon. Not. R. Astron. Soc. (2007).
[CrossRef]

2002

1998

L. V. Antoshkin, N. N. Botugina, O. N. Emaleev, L. N. Lavrinova, and V. P. Lukin, “Differential optical monitor of atmospheric turbulence parameters,” Atmos. Oceanic Opt. 11, 1219 (1998).

1987

S. F. Clifford and J. H. Churnside, “Refractive turbulence profiling using synthetic aperture spatial filtering of scintillation,” Appl. Opt. 26, 1295-1303 (1987).
[CrossRef] [PubMed]

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

1986

V. A. Banakh, I. N. Smalkho, and B. N. Chen, “Shift of the image of incoherent light source in turbulent atmosphere,” Opt. Spectrosc. 61, 582-586 (1986).

1979

B. S. Haugstad and V. R. Eshleman, “On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres,” Astrophys. J. 229, 393-398 (1979).
[CrossRef]

1977

W. B. Hubbard and J. R. Jokipi, “Comment of the paper 'On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres' by Haugstad and Eshleman,” Astrophys. J. 229, 399-401 (1977).
[CrossRef]

1976

Mironov, V. L.

A. S. Gurvich, V. L. Mironov, A. I. Kon, and S. S. Khmelevtsov, Propagation of Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

Ochs, G. R.

Antoshkin, L. V.

L. V. Antoshkin, N. N. Botugina, O. N. Emaleev, L. N. Lavrinova, and V. P. Lukin, “Differential optical monitor of atmospheric turbulence parameters,” Atmos. Oceanic Opt. 11, 1219 (1998).

Balin, Yu. S.

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

Banakh, V. A.

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

V. A. Banakh, I. N. Smalkho, and B. N. Chen, “Shift of the image of incoherent light source in turbulent atmosphere,” Opt. Spectrosc. 61, 582-586 (1986).

Botugina, N. N.

L. V. Antoshkin, N. N. Botugina, O. N. Emaleev, L. N. Lavrinova, and V. P. Lukin, “Differential optical monitor of atmospheric turbulence parameters,” Atmos. Oceanic Opt. 11, 1219 (1998).

Chen, B. N.

V. A. Banakh, I. N. Smalkho, and B. N. Chen, “Shift of the image of incoherent light source in turbulent atmosphere,” Opt. Spectrosc. 61, 582-586 (1986).

Churnside, J. H.

Clifford, S. F.

Dainty, C.

Emaleev, O. N.

L. V. Antoshkin, N. N. Botugina, O. N. Emaleev, L. N. Lavrinova, and V. P. Lukin, “Differential optical monitor of atmospheric turbulence parameters,” Atmos. Oceanic Opt. 11, 1219 (1998).

Eshleman, V. R.

B. S. Haugstad and V. R. Eshleman, “On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres,” Astrophys. J. 229, 393-398 (1979).
[CrossRef]

Gragshteyn, I. S.

I. S. Gragshteyn and I. M. Ryzhik, Tabicy Integralov, Summ, Riyadov i Proizvedenii (Fiziko-Mathematik, 1964).

Gurvich, A. S.

A. S. Gurvich, V. L. Mironov, A. I. Kon, and S. S. Khmelevtsov, Propagation of Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

Haugstad, B. S.

B. S. Haugstad and V. R. Eshleman, “On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres,” Astrophys. J. 229, 393-398 (1979).
[CrossRef]

Hubbard, W. B.

W. B. Hubbard and J. R. Jokipi, “Comment of the paper 'On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres' by Haugstad and Eshleman,” Astrophys. J. 229, 399-401 (1977).
[CrossRef]

Johnston, R.

Jokipi, J. R.

W. B. Hubbard and J. R. Jokipi, “Comment of the paper 'On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres' by Haugstad and Eshleman,” Astrophys. J. 229, 399-401 (1977).
[CrossRef]

Khmelevtsov, S. S.

A. S. Gurvich, V. L. Mironov, A. I. Kon, and S. S. Khmelevtsov, Propagation of Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

Kon, A. I.

A. S. Gurvich, V. L. Mironov, A. I. Kon, and S. S. Khmelevtsov, Propagation of Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

Kopytin, Yu. D.

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

Kornilov, V.

V. Kornilov, A. Tokovinin, N. Shatsky, O. Voziakova, S. Potatin, and B. Safonov, “Combined MASS-DIMM instrument from atmospheric turbulence studies,” Mon. Not. R. Astron. Soc. (2007).
[CrossRef]

Krekov, G. M.

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

Lane, R.

Lavrinova, L. N.

L. V. Antoshkin, N. N. Botugina, O. N. Emaleev, L. N. Lavrinova, and V. P. Lukin, “Differential optical monitor of atmospheric turbulence parameters,” Atmos. Oceanic Opt. 11, 1219 (1998).

Lawrence, R. W.

Lukin, V. P.

L. V. Antoshkin, N. N. Botugina, O. N. Emaleev, L. N. Lavrinova, and V. P. Lukin, “Differential optical monitor of atmospheric turbulence parameters,” Atmos. Oceanic Opt. 11, 1219 (1998).

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

Mironov, V. L.

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

Orlov, V. M.

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

Potatin, S.

V. Kornilov, A. Tokovinin, N. Shatsky, O. Voziakova, S. Potatin, and B. Safonov, “Combined MASS-DIMM instrument from atmospheric turbulence studies,” Mon. Not. R. Astron. Soc. (2007).
[CrossRef]

Ryzhik, I. M.

I. S. Gragshteyn and I. M. Ryzhik, Tabicy Integralov, Summ, Riyadov i Proizvedenii (Fiziko-Mathematik, 1964).

Safonov, B.

V. Kornilov, A. Tokovinin, N. Shatsky, O. Voziakova, S. Potatin, and B. Safonov, “Combined MASS-DIMM instrument from atmospheric turbulence studies,” Mon. Not. R. Astron. Soc. (2007).
[CrossRef]

Samokhvalov, I. V.

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

Shatsky, N.

V. Kornilov, A. Tokovinin, N. Shatsky, O. Voziakova, S. Potatin, and B. Safonov, “Combined MASS-DIMM instrument from atmospheric turbulence studies,” Mon. Not. R. Astron. Soc. (2007).
[CrossRef]

Smalkho, I. N.

V. A. Banakh, I. N. Smalkho, and B. N. Chen, “Shift of the image of incoherent light source in turbulent atmosphere,” Opt. Spectrosc. 61, 582-586 (1986).

Ting, I. W.

Tokovinin, A.

V. Kornilov, A. Tokovinin, N. Shatsky, O. Voziakova, S. Potatin, and B. Safonov, “Combined MASS-DIMM instrument from atmospheric turbulence studies,” Mon. Not. R. Astron. Soc. (2007).
[CrossRef]

A. Tokovinin, “From differential image motion to seeing,” Publ. Astron. Soc. Pac. 114, 1156 (2002).
[CrossRef]

Voziakova, O.

V. Kornilov, A. Tokovinin, N. Shatsky, O. Voziakova, S. Potatin, and B. Safonov, “Combined MASS-DIMM instrument from atmospheric turbulence studies,” Mon. Not. R. Astron. Soc. (2007).
[CrossRef]

Wooder, N.

Zuev, V. E.

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

Appl. Opt.

Astrophys. J.

B. S. Haugstad and V. R. Eshleman, “On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres,” Astrophys. J. 229, 393-398 (1979).
[CrossRef]

W. B. Hubbard and J. R. Jokipi, “Comment of the paper 'On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres' by Haugstad and Eshleman,” Astrophys. J. 229, 399-401 (1977).
[CrossRef]

Atmos. Oceanic Opt.

L. V. Antoshkin, N. N. Botugina, O. N. Emaleev, L. N. Lavrinova, and V. P. Lukin, “Differential optical monitor of atmospheric turbulence parameters,” Atmos. Oceanic Opt. 11, 1219 (1998).

J. Sov. Laser Res.

Yu. S. Balin, V. A. Banakh, G. M. Krekov, Yu. D. Kopytin, V. P. Lukin, V. L. Mironov, V. M. Orlov, I. V. Samokhvalov, and V. E. Zuev, “Signal and noise in laser ranging,” J. Sov. Laser Res. 8, 283-426 (1987).
[CrossRef]

Mon. Not. R. Astron. Soc.

V. Kornilov, A. Tokovinin, N. Shatsky, O. Voziakova, S. Potatin, and B. Safonov, “Combined MASS-DIMM instrument from atmospheric turbulence studies,” Mon. Not. R. Astron. Soc. (2007).
[CrossRef]

Opt. Spectrosc.

V. A. Banakh, I. N. Smalkho, and B. N. Chen, “Shift of the image of incoherent light source in turbulent atmosphere,” Opt. Spectrosc. 61, 582-586 (1986).

Publ. Astron. Soc. Pac.

A. Tokovinin, “From differential image motion to seeing,” Publ. Astron. Soc. Pac. 114, 1156 (2002).
[CrossRef]

Other

A. S. Gurvich, V. L. Mironov, A. I. Kon, and S. S. Khmelevtsov, Propagation of Laser Radiation in the Turbulent Atmosphere (Nauka, 1976).

I. S. Gragshteyn and I. M. Ryzhik, Tabicy Integralov, Summ, Riyadov i Proizvedenii (Fiziko-Mathematik, 1964).

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Equations (24)

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Θ ( ρ , k ) = 0 x d ξ d 2 n ( κ , ξ ) exp ( i κ ρ γ ) cos ( κ 2 ( x ξ ) γ / 2 k ) ,
n 1 ( r ) = d 2 n ( κ , ξ ) exp ( i κ ρ ) ,
ρ θ ( ρ , k ) = i 0 x d ξ γ ( ξ ) d 2 n ( κ , ξ ) exp ( i κ ρ γ ) κ γ cos ( κ 2 ( x ξ ) γ / 2 k ) .
φ = 1 d 2 ρ W ( ρ ) ρ Θ ( ρ , k ) = i 0 x d ξ γ ( ξ ) d 2 n ( κ , ξ ) κ exp ( κ 2 d 2 γ 2 / 4 ) cos ( κ 2 ( x ξ ) γ / 2 k ) .
φ 2 = φ φ * = 0 x d ξ 1 γ ( ξ 1 ) 0 x d ξ 2 γ ( ξ 2 ) d 2 n ( κ 1 , ξ 1 ) d 2 * n ( κ 2 , ξ 2 ) κ 1 κ 2 × exp ( κ 1 2 d 2 γ 2 ( ξ 1 ) / 4 ) exp ( κ 2 2 d 2 γ 2 ( ξ 2 ) / 4 ) cos ( κ 1 2 ( x ξ 1 ) γ ( ξ 1 ) / 2 k ) cos ( κ 2 2 ( x ξ 2 ) γ ( ξ 2 ) / 2 k ) ,
d 2 n ( κ 1 , ξ 1 ) d 2 * n ( κ 2 , ξ 2 ) = 2 π δ ( ξ 1 ξ 2 ) δ ( κ 1 + κ 2 ) Φ n ( κ 1 , ξ 1 ) d κ 1 d κ 2 ,
φ 2 = 2 π 0 x d ξ γ 2 ( ξ ) d 2 κ κ 2 Φ n ( κ , ξ ) exp ( κ 2 d 2 γ 2 ( ξ ) / 2 ) cos 2 ( κ 2 ( x ξ ) γ ( ξ ) 2 k ) ,
Φ n ( κ , ξ ) = 0.033 C n 2 ( ξ ) κ 11 / 3 .
0 d κ κ 3 11 / 3 exp ( κ 2 d 2 γ 2 ( ξ ) / 2 ) cos 2 [ κ 2 ( x ξ ) γ ( ξ ) / 2 k ] = Γ ( 1 / 6 ) 2 5 / 6 γ 1 / 3 ( ξ ) d 1 / 3 [ 1 + ( 1 + ( x ξ ) 2 k 2 d 4 γ 2 ( ξ ) ) 1 / 12 cos { 1 6 arctan ( 2 ( x ξ ) / k d 2 γ ( ξ ) ) } ] .
φ 2 = 2 7 / 6 π 2 0.033 Γ ( 1 6 ) d 1 / 3 0 x d ξ γ 5 / 3 ( ξ ) C n 2 ( ξ ) { 1 + [ 1 + ( x ξ ) 2 k 2 d 4 γ 2 ( ξ ) ] 1 / 12 cos [ 1 6 arctan ( 2 ( x ξ ) / k d 2 γ ( ξ ) ] } .
φ 2 sph = 2 7 / 6 π 2 3 8 0.033 Γ ( 1 6 ) C n 2 ( 0 ) d 1 / 3 × 0 x ( ξ / x ) 5 / 3 d ξ { 1 + [ 1 + ( x ξ ) 2 k 2 d 4 ( ξ / x ) 2 ] 1 / 12 cos [ 1 6 arctan ( 2 ( x ξ ) k d 2 ( ξ / x ) ) ] } .
φ 2 sph = 4 π 2 Γ ( 1 / 6 ) 2 5 / 6 0 , 033 C n 2 ( 0 ) d 1 / 3 ( 3 4 x 1 12 Γ ( 3 ) Γ ( 2 / 3 ) Γ ( 3 + 2 / 3 ) x Ω 2 ) = 3 π 2 Γ ( 1 / 6 ) 2 5 / 6 0 , 033 C n 2 ( 0 ) d 1 / 3 x ( 1 0 , 075 Ω 2 ) ,
φ 2 = 3 2 11 / 6 π 2 Γ ( 1 / 6 ) C n 2 ( 0 ) x [ 1 + 1 , 23 × cos ( π / 12 ) Ω 1 / 6 ] .
φ 2 pl = 2 7 / 6 π 2 0.033 Γ ( 1 6 ) d 1 / 3 C n 2 ( 0 ) 0 x d ξ { 1 + ( 1 + ( x ξ ) 2 k 2 d 4 ) 1 / 12 × cos [ 1 6 arctan ( 2 ( x ξ ) / k d 2 ) ] } .
φ 2 pl = 2 7 / 6 π 2 0.033 Γ ( 1 6 ) d 1 / 3 C n 2 ( 0 ) x [ 1 1 72 ( x 2 k 2 d 4 ) ] = 2 7 / 6 π 2 0.033 Γ ( 1 6 ) d 1 / 3 C n 2 ( 0 ) x ( 1 0.013 Ω 2 ) ,
φ 2 pl 2 1 / 6 π 2 0.033 Γ ( 1 6 ) d 1 / 3 C n 2 ( 0 ) 0 2 d ξ [ 1 + cos ( π / 12 ) ( x ξ k d 2 ) 1 / 6 ] = 2 1 / 6 π 2 0.033 Γ ( 1 6 ) d 1 / 3 C n 2 ( 0 ) x [ 1 + 6 5 cos ( π / 12 ) Ω 1 / 6 ] .
φ 2 sph = 2 7 / 6 π 2 3 8 0.033 Γ ( 1 6 ) d 1 / 3 C n 2 ( 0 ) x [ 1 0.075 Ω 2 ] .
φ 2 sph = 2 7 / 6 3 8 π 2 0.033 Γ ( 1 6 ) d 1 / 3 C n 2 ( 0 ) x .
( λ 1 λ 2 d λ K ( λ ) ) 1 λ 1 λ 2 d λ K ( λ ) C n 2 ( λ ) C n a v 2 ,
λ 1 λ 2 d λ C n 2 ( λ ) / ( λ 2 λ 1 ) C n a v 2 .
N λ = ( n λ 1 ) · 10 6 = 77.6 P T + 0.584 P T λ 2 - 0.06 P w . v .
N λ = N λ ( 1 + 0.584 77.6 λ 2 ) ,
C n 2 ( λ ) = C n 2 ( λ ) ( 1 + 0.584 77.6 λ 2 ) 2 .
λ 1 λ 2 d λ C n 2 ( λ ) / | λ 2 λ 1 | = C n 2 ( λ ) / | λ 2 λ 1 | · λ 1 λ 2 d λ ( 1 + 0.0075 λ 2 ) 2 C n 2 ( λ ) ( 1 + 0.015 / λ 1 λ 2 ) .

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