Abstract

Holmes and Rao Gudimetla [ J. Opt. Soc. Am. 73, 1119– 1122 ( 1983)] analyze the performance of an adaptive optical system in which the optical path differences caused by atmospheric turbulence are measured at one wavelength and used to compensate an outgoing laser beam of a different wavelength. The wavelength dependence of diffraction is shown to lead to imperfect correction. Earlier work [ E. P. Wallner, Proc. Soc. Photo-Opt. Instrum. Eng. 75, 119– 125 ( 1976); J. Opt. Soc. Am. 67, 407– 409 ( 1977)] shows that the wavelength dependence of the index of refraction of air also leads to imperfect correction for beams not directed vertically. In this Communication I compare the refractive and diffractive effects and show that either may be more important, depending on the geometry of the case and the wavelengths used.

© 1984 Optical Society of America

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References

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  1. J. F. Holmes, V. S. Rao Gudimetla, “Strehl’s ratio for a two-wavelength continuously deformable optical adaptive transmitter,” J. Opt. Soc. Am. 73, 1119–1122 (1983).
    [CrossRef]
  2. E. P. Wallner, “The effects of atmospheric refraction on compensated imaging,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 119–125 (1976).
  3. E. P. Wallner, “Minimizing atmospheric dispersion effects in compensated imaging,” J. Opt. Soc. Am. 67, 407–409 (1977).
    [CrossRef]
  4. R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 56, 1523–1545 (1970).
    [CrossRef]
  5. National Advisory Committee for Aeronautics, “Manual of the ICAO standard atmosphere,” NACA Tech. Note 3182, Washington, D.C., 1954.
  6. J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature, and composition,” Appl. Opt. 6, 51–59 (1967).
    [CrossRef] [PubMed]

1983 (1)

1977 (1)

1976 (1)

E. P. Wallner, “The effects of atmospheric refraction on compensated imaging,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 119–125 (1976).

1970 (1)

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 56, 1523–1545 (1970).
[CrossRef]

1967 (1)

Holmes, J. F.

Lawrence, R. S.

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 56, 1523–1545 (1970).
[CrossRef]

Owens, J. C.

Rao Gudimetla, V. S.

Strohbehn, J. W.

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 56, 1523–1545 (1970).
[CrossRef]

Wallner, E. P.

E. P. Wallner, “Minimizing atmospheric dispersion effects in compensated imaging,” J. Opt. Soc. Am. 67, 407–409 (1977).
[CrossRef]

E. P. Wallner, “The effects of atmospheric refraction on compensated imaging,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 119–125 (1976).

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Proc. IEEE (1)

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 56, 1523–1545 (1970).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

E. P. Wallner, “The effects of atmospheric refraction on compensated imaging,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 119–125 (1976).

Other (1)

National Advisory Committee for Aeronautics, “Manual of the ICAO standard atmosphere,” NACA Tech. Note 3182, Washington, D.C., 1954.

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Figures (2)

Fig. 1
Fig. 1

Comparison of refractive and diffractive dispersion.

Fig. 2
Fig. 2

Refractive dispersion for distant beacon.

Equations (16)

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S exp ( - k 1 2 σ OPD 2 ) ,
δ ( x ) = θ ( x , λ 1 ) - θ ( x , λ 2 ) ,
( x ) = δ ( x ) - - d x 1 W ( x 1 ) δ ( x 1 ) = - d x 1 W ( x 1 ) [ δ ( x ) - δ ( x 1 ) ] ,
σ OPD 2 = - d x 3 W ( x 3 ) ( x 3 ) 2 = - d x 1 - d x 2 - d x 3 W ( x 1 ) W ( x 2 ) W ( x 3 ) × [ δ ( x 1 ) - ( δ ( x 2 ) ] [ δ ( x 1 ) - δ ( x 3 ) ] ,
D ( x 1 - x 2 , λ 1 , λ 2 ) = [ θ ( x 1 , λ 1 ) - θ ( x 2 , λ 2 ) ] 2 ,
σ OPD 2 = D ( 0 , λ 1 , λ 2 ) - - d x 1 - d x 2 W ( x 1 ) W ( x 2 ) × [ ½ D ( x 1 - x 2 , λ 1 , λ 2 ) + ½ D ( x 1 - x 2 , λ 2 , λ 1 ) - D ( x 1 - x 2 , λ 1 , λ 1 ) ] .
0 ( y ) = - d x W ( x + y / 2 ) W ( x - y / 2 ) = { 2 R 2 { cos - 1 ( y / 2 R ) - ( y / 2 R ) [ 1 - ( y / 2 R ) 2 ] 1 / 2 } , 0 < 2 < y 0 , y 2 ,
σ OPD 2 = D ( 0 , λ 1 , λ 2 ) - - d y 0 ( y ) [ ½ D ( y , λ 1 , λ 2 ) + ½ D ( y , λ 2 , λ 1 ) - D ( y , λ 1 , λ 1 ) ] .
D ( y , λ 1 , λ 2 ) = 2.914 sec z 0 H d h C n 2 ( h ) s ( y , λ 1 , λ 2 , h ) 5 / 3 ,
σ OPD 2 = 2.914 sec z 0 H d h C n 2 ( h ) { s ( 0 , λ 1 , λ 2 , h 5 / 3 - - d y 0 ( y ) [ ½ s ( y , λ 1 , λ 2 , h ) 5 / 3 + ½ s ( y , λ 2 , λ 1 , h ) 5 / 3 - s ( y , λ 1 , λ 1 , h ) 5 / 3 ] } .
s 1 ( y , h ) = ( 1 - h / H ) y .
b ( h , λ ) = N s ( λ ) sec ( z ) tan ( z ) [ P ( h ) / g ρ s ] = b 0 ( λ ) P ( λ ) / P 0 ,
s 2 ( λ 1 , λ 2 , h ) = { y + h δ z sec ( z ) + [ b 0 ( λ 1 ) - b 0 ( λ 2 ) ] P ( h ) / P 0 } u v ,
s 2 ( λ 1 , λ 2 , h ) = [ b 0 ( λ 1 ) - b 0 ( λ 2 ) ] × { 1 - P ( h ) / P 0 - [ 1 - P ( H ) / P 0 ] h / H } u v .
s ( y , λ 1 , λ 2 , h ) = s 1 ( y , h ) + s 2 ( λ 1 , λ 2 , h ) = ( 1 - h / H ) y 1 + [ 1 - P ( h ) / P ( H ) ] y 2 ,
y 1 = [ b 0 ( λ 1 ) - b 0 ( λ 2 ) ] [ 1 - P ( H ) / P 0 ] u v + y , y 2 = [ b 0 ( λ 1 ) - b 0 ( λ 2 ) ] [ P ( h ) / P 0 ] u v .

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