Abstract

An investigation has been made of the degree to which the invariance of the relative dispersion of the atmosphere will permit an interferometric separation between geometric path differences and path differences due to atmospheric inhomogeneities. Humidity variations are the most serious. A difference in average humidity of 1% of saturation at 15°C would affect the comparison of two paths by approximately 2 parts in 108. The feasibility of photographing interference for long paths through an uncontrolled atmosphere has been investigated. Photographs of channel spectrum interference have been readily obtained for path lengths of 115 m near ground level.

© 1962 Optical Society of America

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References

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  1. Y. Väisälä, Veröff. Finn. Geod. Inst. No. 2 (1923); Veröff. Finn. Geod. Inst. No. 14 (1930); Veröff. Finn. Geod. Inst. No. 47 (1955). See also No. 37 by T. Honkasalo.
  2. N. Watanabe, Trav. Assn. Int. de Geod. 13, 2 (1936).
  3. N. Watanabe, K. Muraoka, and K. Kitada, J. Geod. Soc. Japan 4, No. 3, 76 (1958) and No. 4, 97 (1958).
  4. F. Mühlig, Veröff. Geod. Inst. Potsdam (1949).
  5. K. E. Erickson, J. Opt. Soc. Am. 52, 777 (1962).
    [Crossref]
  6. K. E. Erickson, dissertation, The Johns Hopkins University (1961).
  7. Bengt Edlén, J. Opt. Soc. Am. 43, 339 (1953).
    [Crossref]
  8. Karl-Filip Svensson, Arkiv Fysik 16, 361 (1960).
  9. N. K. Johnson, Geophys. Mem. 46 (1929).
  10. E. Inoue, On the Smallest Scale Turbulence in the Atmosphere (The A. & M. College of Texas. Department of Oceanography, 54-21T, 1954).
  11. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, New York, 1960), p. 210.
  12. J. A. Fejer, Proc. Roy. Soc. (London) A220, 455 (1953).
    [Crossref]
  13. See reference 11, Chap. 7. In Soviet Phys.—Acoustics 6, 81 (1960), V. Pisareva has questioned the validity of formulas for rms phase fluctuations based on the method of “smooth” perturba tions (used by Tatarski and others) for the case where these fluctuations are notmuch smaller than unity. Investigations in the optical region might therefore be useful.
  14. A. A. Michelson and G. Hale, Astrophys. J. 61, 137 (1925).
    [Crossref]
  15. K. B. Newbound, J. Opt. Soc. Am. 39, 835 (1949).
    [Crossref]
  16. For a discussion of other effects see W. F. Brown, Dielectrics, volume 17 of Handbook of Physics (Springer-Verlag, Berlin, 1956).
    [Crossref]

1962 (1)

1960 (1)

Karl-Filip Svensson, Arkiv Fysik 16, 361 (1960).

1958 (1)

N. Watanabe, K. Muraoka, and K. Kitada, J. Geod. Soc. Japan 4, No. 3, 76 (1958) and No. 4, 97 (1958).

1953 (2)

Bengt Edlén, J. Opt. Soc. Am. 43, 339 (1953).
[Crossref]

J. A. Fejer, Proc. Roy. Soc. (London) A220, 455 (1953).
[Crossref]

1949 (2)

K. B. Newbound, J. Opt. Soc. Am. 39, 835 (1949).
[Crossref]

F. Mühlig, Veröff. Geod. Inst. Potsdam (1949).

1936 (1)

N. Watanabe, Trav. Assn. Int. de Geod. 13, 2 (1936).

1929 (1)

N. K. Johnson, Geophys. Mem. 46 (1929).

1925 (1)

A. A. Michelson and G. Hale, Astrophys. J. 61, 137 (1925).
[Crossref]

1923 (1)

Y. Väisälä, Veröff. Finn. Geod. Inst. No. 2 (1923); Veröff. Finn. Geod. Inst. No. 14 (1930); Veröff. Finn. Geod. Inst. No. 47 (1955). See also No. 37 by T. Honkasalo.

Brown, W. F.

For a discussion of other effects see W. F. Brown, Dielectrics, volume 17 of Handbook of Physics (Springer-Verlag, Berlin, 1956).
[Crossref]

Edlén, Bengt

Erickson, K. E.

K. E. Erickson, J. Opt. Soc. Am. 52, 777 (1962).
[Crossref]

K. E. Erickson, dissertation, The Johns Hopkins University (1961).

Fejer, J. A.

J. A. Fejer, Proc. Roy. Soc. (London) A220, 455 (1953).
[Crossref]

Hale, G.

A. A. Michelson and G. Hale, Astrophys. J. 61, 137 (1925).
[Crossref]

Inoue, E.

E. Inoue, On the Smallest Scale Turbulence in the Atmosphere (The A. & M. College of Texas. Department of Oceanography, 54-21T, 1954).

Johnson, N. K.

N. K. Johnson, Geophys. Mem. 46 (1929).

Kitada, K.

N. Watanabe, K. Muraoka, and K. Kitada, J. Geod. Soc. Japan 4, No. 3, 76 (1958) and No. 4, 97 (1958).

Michelson, A. A.

A. A. Michelson and G. Hale, Astrophys. J. 61, 137 (1925).
[Crossref]

Mühlig, F.

F. Mühlig, Veröff. Geod. Inst. Potsdam (1949).

Muraoka, K.

N. Watanabe, K. Muraoka, and K. Kitada, J. Geod. Soc. Japan 4, No. 3, 76 (1958) and No. 4, 97 (1958).

Newbound, K. B.

Svensson, Karl-Filip

Karl-Filip Svensson, Arkiv Fysik 16, 361 (1960).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, New York, 1960), p. 210.

Väisälä, Y.

Y. Väisälä, Veröff. Finn. Geod. Inst. No. 2 (1923); Veröff. Finn. Geod. Inst. No. 14 (1930); Veröff. Finn. Geod. Inst. No. 47 (1955). See also No. 37 by T. Honkasalo.

Watanabe, N.

N. Watanabe, K. Muraoka, and K. Kitada, J. Geod. Soc. Japan 4, No. 3, 76 (1958) and No. 4, 97 (1958).

N. Watanabe, Trav. Assn. Int. de Geod. 13, 2 (1936).

Arkiv Fysik (1)

Karl-Filip Svensson, Arkiv Fysik 16, 361 (1960).

Astrophys. J. (1)

A. A. Michelson and G. Hale, Astrophys. J. 61, 137 (1925).
[Crossref]

Geophys. Mem. (1)

N. K. Johnson, Geophys. Mem. 46 (1929).

J. Geod. Soc. Japan (1)

N. Watanabe, K. Muraoka, and K. Kitada, J. Geod. Soc. Japan 4, No. 3, 76 (1958) and No. 4, 97 (1958).

J. Opt. Soc. Am. (3)

Proc. Roy. Soc. (London) (1)

J. A. Fejer, Proc. Roy. Soc. (London) A220, 455 (1953).
[Crossref]

Trav. Assn. Int. de Geod. (1)

N. Watanabe, Trav. Assn. Int. de Geod. 13, 2 (1936).

Veröff. Finn. Geod. Inst. (1)

Y. Väisälä, Veröff. Finn. Geod. Inst. No. 2 (1923); Veröff. Finn. Geod. Inst. No. 14 (1930); Veröff. Finn. Geod. Inst. No. 47 (1955). See also No. 37 by T. Honkasalo.

Veröff. Geod. Inst. Potsdam (1)

F. Mühlig, Veröff. Geod. Inst. Potsdam (1949).

Other (5)

E. Inoue, On the Smallest Scale Turbulence in the Atmosphere (The A. & M. College of Texas. Department of Oceanography, 54-21T, 1954).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, New York, 1960), p. 210.

See reference 11, Chap. 7. In Soviet Phys.—Acoustics 6, 81 (1960), V. Pisareva has questioned the validity of formulas for rms phase fluctuations based on the method of “smooth” perturba tions (used by Tatarski and others) for the case where these fluctuations are notmuch smaller than unity. Investigations in the optical region might therefore be useful.

K. E. Erickson, dissertation, The Johns Hopkins University (1961).

For a discussion of other effects see W. F. Brown, Dielectrics, volume 17 of Handbook of Physics (Springer-Verlag, Berlin, 1956).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Corner-cube interferometer, virtual arrangement. Beams are shown as passing through all plane reflecting surfaces into the virtual spaces beyond. Beams penetrate beamsplitter at B, B1, B2. Optical centers of corner cubes are at P1 and P2. Lateral refraction is illustrated for one beam.

Fig. 2
Fig. 2

Experimental arrangement for photographing channel spectrum interference between beams following separate outdoor paths.

Fig. 3
Fig. 3

Monochromatic fringes over entire field of view (slit removed). Two frames at 64 frames/sec; 115-m paths; λ = 5461 A.

Fig. 4
Fig. 4

Continuous strip photograph of channel spectrum interference. Xenon arc source; 115-m paths.

Fig. 5
Fig. 5

Continuous strip photograph of channel spectrum interference. Mercury source; 115-m paths. The periodicity in the intensity is from a periodicity in the camera drive.

Fig. 6
Fig. 6

Rapid disappearance and reappearance of channel spectrum interference. Four frames at 64 frames/sec; xenon arc source; 115-m paths.

Equations (58)

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m ( k ) = k D + k [ 0 L 1 δ ( k , T 1 , P 1 , ρ 1 ) d x 1 0 L 2 δ ( k , T 2 , P 2 , ρ 2 ) d x 2 ] + m I ( k ) ,
δ ˜ ( k , k 0 , T , P , ρ ) δ ( k , T , P , ρ ) / δ ( k 0 , T , P , ρ )
m ( k ) = k D + k [ 0 L 1 δ ˜ ( k , k 0 , T 1 , P 1 , ρ 1 ) δ ( k 0 , T 1 , P 1 , ρ 1 ) d x 1 0 L 2 δ ˜ ( k , k 0 , T 2 , P 2 , ρ 2 ) δ ( k 0 , T 2 , P 2 , ρ 2 ) d x 2 ] + m I ( k ) .
δ ˜ ( k , k 0 , T , P , ρ ) = δ ˜ ( k , k 0 ) + ( T T 0 ) α ( k , k 0 ) + ( P P 0 ) β ( k , k 0 ) + ( ρ ρ 0 ) γ ( k , k 0 )
α ( k , k 0 ) δ ˜ ( k , k 0 , T , P , ρ ) T ; β ( k , k 0 ) δ ˜ ( k , k 0 , T , P , ρ ) P ; γ ( k , k 0 ) δ ˜ ( k , k 0 , T , P , ρ ) ρ .
m ( k ) = k D k δ ˜ ( k , k 0 ) Q ( k 0 ) + m I ( k ) + m I I ( k , k 0 ) ,
Q ( k 0 ) = 0 L 2 δ ( k 0 , T 2 , P 2 , ρ 2 ) d x 2 0 L 1 δ ( k 0 , T 1 , P 1 , ρ 1 ) d x 1
m II ( k , k 0 ) = k 0 L 1 [ ( T 1 T 0 ) α ( k , k 0 ) + ( P 1 P 0 ) β ( k , k 0 ) + ( ρ 1 ρ 0 ) γ ( k , k 0 ) ] d x 1 k 0 L 2 [ ( T 2 T 0 ) α ( k , k 0 ) + ( P 2 P 0 ) β ( k , k 0 ) + ( ρ 2 ρ 0 ) γ ( k , k 0 ) ] d x 2 .
L 1 L 2 L
δ ( k 0 , T 1 , P 1 , ρ 1 ) δ ( k 0 , T 2 , P 2 , ρ 2 ) δ ( k 0 , T 0 , P 0 , ρ 0 ) , m II ( k , k 0 ) = k L δ ( k 0 , T 0 , P 0 , ρ 0 ) [ Δ T α ( k , k 0 ) + Δ P β ( k , k 0 ) + Δ ρ γ ( k , k 0 ) ]
m 2 m 2 , 1 = k 1 D k 1 δ ˜ 1 Q + m 1 I + m 1 II ,
m 2 = k 2 D k 2 δ ˜ 2 Q + m 2 I + m 2 II ,
m 2 + m 3 , 2 = k 3 D k 3 δ ˜ 3 Q + m 3 I + m 3 II .
D = [ ( k 3 δ ˜ 3 k 2 δ ˜ 2 ) A ( k 3 δ ˜ 3 k 1 δ ˜ 1 ) B + ( k 2 δ ˜ 2 k 1 δ ˜ 1 ) C ] / Δ ,
Q ( k 0 ) = [ ( k 3 k 2 ) A ( k 3 k 1 ) B + ( k 2 k 1 ) C ] / Δ ,
m 2 = [ k 2 k 3 ( δ ˜ 3 δ ˜ 2 ) A k 1 k 3 ( δ ˜ 3 δ ˜ 1 ) B + k 1 k 2 ( δ ˜ 2 δ ˜ 1 ) C ] / Δ ,
Δ k 2 k 3 ( δ ˜ 3 δ ˜ 2 ) k 1 k 3 ( δ ˜ 3 δ ˜ 1 ) + k 1 k 2 ( δ ˜ 2 δ ˜ 1 )
A m 2 , 1 + m 1 I + m 1 II ,
B m 2 I + m 2 II ,
C m 3 , 2 + m 3 I + m 3 II .
k 1 = 1.54000 μ 1 ( λ 1 = 0.64935 μ ) , k 2 = 2.15000 μ 1 ( λ 2 = 0.46512 μ ) , k 3 = 2.74000 μ 1 ( λ 2 = 0.36496 μ ) .
k 0 = 1.83074 μ 1 ( λ 0 = 0.54623 μ )
δ ˜ 1 = 0.994303 , δ ˜ 2 = 1.007542 , δ ˜ 3 = 1.025359.
D = ( 36.2 μ ) A ( 72.0 μ ) B + ( 35.8 μ ) C ,
Q ( k 0 ) = ( 33.2 μ ) A ( 67.6 μ ) B + ( 34.4 μ ) C ,
m 2 = 5.91 A 7.38 B + 2.47 C ,
D = 36.2 μ ( m 2 , 1 + m 1 I + m 1 II ) 72.0 μ ( m 2 I + m 2 II ) + 35.8 μ ( m 3 , 2 + m 3 I + m 3 II ) .
( 36.2 μ ) m 1 I ( 72.0 μ ) m 2 I + ( 35.8 μ ) m 3 I .
Δ II D = ( 36.2 μ ) m 1 II ( 72.0 μ ) m 2 II + ( 35.8 μ ) m 3 II .
Δ II D = ( 36.2 μ ) m 1 II + ( 35.8 μ ) m 3 II .
Δ II D T = [ 0.0156 α 1 + 0.275 α 3 ] Δ T L , Δ II D P = [ 0.0156 β 1 + 0.275 β 3 ] Δ P L , Δ II D ρ = [ 0.0156 γ 1 + 0.275 γ 3 ] Δ ρ L .
γ ( k 1 , k 2 ) = 0.0062 m 3 / kg , γ ( k 3 , k 2 ) = 0.0087 m 3 / kg .
Δ II D T < ( 4 × 10 8 / ° C ) Δ T L , Δ II D P < ( 4 × 10 10 / mm ) Δ P L , Δ II D ρ ( 1.4 × 10 4 m 3 / kg ) Δ ρ L .
| | < λ / 4 ϕ x .
| | < λ / 4 ϕ y .
| ( k 3 ) ( k 1 ) | < λ / 2 ϕ .
| ( k 3 ) ( k 1 ) | = 1 4 [ δ ˜ ( k 3 , k 0 ) δ ˜ ( k 1 , k 0 ) ] | δ ( k 0 ) | L 2 .
1 4 [ δ ˜ ( k 3 , k 0 ) δ ˜ ( k 1 , k 0 ) ] | δ ( k 0 ) | L 2 < λ / 2 ϕ .
| δ ( k 0 ) | L < 2 λ / [ δ ˜ ( k 3 , k 0 ) δ ˜ ( k 1 , k 0 ) ] a .
| δ ( k 0 ) | L < 0.0008.
n 1 [ sec θ 1 ( k ) 1 ] d x 1 and n 2 [ sec θ 2 ( k ) 1 ] d x 2 .
m θ = k 0 L 1 n 1 [ sec θ 1 ( k ) 1 ] d x 1 k 0 L 2 n 2 [ sec θ 2 ( k ) 1 ] d x 2 .
n 1 n 2 1 , L 1 L 2 L , sec θ ( k ) 1 1 2 θ 2 ( k ) m θ 1 2 k L Δ θ 2 ( k )
m ( k ) = k D k δ ˜ ( k , k 0 ) Q ( k 0 ) + 1 2 k L Δ θ 2 ( k ) + m I ( k ) + m I I ( k , k 0 ) .
m ( k ) = k D k δ ˜ ( k , k 0 ) Q ( k 0 ) + m I ( k ) + m II ( k , k 0 ) + m III ( k , k 0 ) ,
Q ( k 0 ) Q ( k 0 ) 1 2 L Δ θ 2 ( k 0 )
m III ( k , k 0 ) 1 2 k L Δ θ 2 ( k 0 ) [ Δ θ 2 ( k ) Δ θ 2 ( k 0 ) δ ˜ ( k , k 0 ) ] .
Δ θ 2 ( k ) = | δ ( k ) | 2 L 2 / 48 .
| δ ( k ) | / δ ( k ) | T | / T .
m I I I ( k , k 0 ) δ ˜ ( k , k 0 ) [ δ ˜ ( k , k 0 ) 1 ] k L 3 × | T | 2 δ 2 ( k 0 ) / 96 T 2 .
m 1 III = 0.20 , m 2 III = 0 , m 3 III = 0.50.
Δ III D = ( 36.2 μ ) m 1 III ( 72.0 μ ) m 2 III + ( 35.8 μ ) m 3 III .
m IV ( k , k 0 ) = 1 2 k L [ Δ ϕ 2 ( k 0 ) ] av { [ Δ ϕ 2 ( k ) ] av [ Δ ϕ 2 ( k 0 ) ] av δ ˜ ( k , k 0 ) } ,
Δ II D ρ ( 1.4 × 10 4 m 3 / kg ) Δ ρ L .
Δ II D ρ 1.8 × 10 8 L .
Δ II D P < ( 4 × 10 10 / mm ) Δ P L ,
Δ II D T < ( 4 × 10 8 / ° C ) Δ T L .
Δ II D T ( 4 × 10 8 / ° C ) Δ T L .