Abstract

An extension of the two-wavelength interferogram technique is proposed that will enable selective measurements to be made of the variation in the density of a specific atomic population. One wavelength should be chosen to closely coincide with the wavelength associated with an absorption line of the species of interest, whereas the other wavelength should be displaced by several angstroms from the line. The difference between the fringe shifts on the two interferograms would then enable the density variation of the specific atomic population of interest to be measured with high sensitivity. Two criteria are established that ascertain for any system the minimum density that could be detected, and the range in density variation for which the interferograms should be discernible.

© 1970 Optical Society of America

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References

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  1. R. A. Alpher, R. White, Phys. Fluids 2, 111 (1959).
  2. H. Samelson, Electronics 41, 142 (1968).
  3. M. D. Martin, E. L. Thomas, Phys. Lett. 25A, 637 (1967).
  4. K. E. Harnwell, R. O. Jahn, Phys. Fluids 7, 214 (1964).
    [CrossRef]
  5. A. K. Belozerov, R. M. Measures, J. Fluid Mech. 36, 695 (1969).
    [CrossRef]
  6. R. W. Ditchburn, Light (John Wiley & Sons, New York, 1963).
  7. L. H. Aller, Astrophysics: Atmosphere of the Sun and Stars (Ronald Press, New York, 1963).

1969 (1)

A. K. Belozerov, R. M. Measures, J. Fluid Mech. 36, 695 (1969).
[CrossRef]

1968 (1)

H. Samelson, Electronics 41, 142 (1968).

1967 (1)

M. D. Martin, E. L. Thomas, Phys. Lett. 25A, 637 (1967).

1964 (1)

K. E. Harnwell, R. O. Jahn, Phys. Fluids 7, 214 (1964).
[CrossRef]

1959 (1)

R. A. Alpher, R. White, Phys. Fluids 2, 111 (1959).

Aller, L. H.

L. H. Aller, Astrophysics: Atmosphere of the Sun and Stars (Ronald Press, New York, 1963).

Alpher, R. A.

R. A. Alpher, R. White, Phys. Fluids 2, 111 (1959).

Belozerov, A. K.

A. K. Belozerov, R. M. Measures, J. Fluid Mech. 36, 695 (1969).
[CrossRef]

Ditchburn, R. W.

R. W. Ditchburn, Light (John Wiley & Sons, New York, 1963).

Harnwell, K. E.

K. E. Harnwell, R. O. Jahn, Phys. Fluids 7, 214 (1964).
[CrossRef]

Jahn, R. O.

K. E. Harnwell, R. O. Jahn, Phys. Fluids 7, 214 (1964).
[CrossRef]

Martin, M. D.

M. D. Martin, E. L. Thomas, Phys. Lett. 25A, 637 (1967).

Measures, R. M.

A. K. Belozerov, R. M. Measures, J. Fluid Mech. 36, 695 (1969).
[CrossRef]

Samelson, H.

H. Samelson, Electronics 41, 142 (1968).

Thomas, E. L.

M. D. Martin, E. L. Thomas, Phys. Lett. 25A, 637 (1967).

White, R.

R. A. Alpher, R. White, Phys. Fluids 2, 111 (1959).

Electronics (1)

H. Samelson, Electronics 41, 142 (1968).

J. Fluid Mech. (1)

A. K. Belozerov, R. M. Measures, J. Fluid Mech. 36, 695 (1969).
[CrossRef]

Phys. Fluids (2)

R. A. Alpher, R. White, Phys. Fluids 2, 111 (1959).

K. E. Harnwell, R. O. Jahn, Phys. Fluids 7, 214 (1964).
[CrossRef]

Phys. Lett. (1)

M. D. Martin, E. L. Thomas, Phys. Lett. 25A, 637 (1967).

Other (2)

R. W. Ditchburn, Light (John Wiley & Sons, New York, 1963).

L. H. Aller, Astrophysics: Atmosphere of the Sun and Stars (Ronald Press, New York, 1963).

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Figures (4)

Fig. 1
Fig. 1

Normalized attenuation coefficient H(u,α) and normalized phase change P(u,α) as functions of u for several values of α.

Fig. 2
Fig. 2

Ratio of the normalized attenuation coefficient to the normalized phase change as a function of u for several values of α.

Fig. 3
Fig. 3

Normalized attenuation coefficient H ( μ , α ) and normalized phase change P ( μ , α ) as a function of μ for several values of α.

Fig. 4
Fig. 4

Ratio of the normalized attenuation coefficient to the normalized phase change as a function of μ for several values of α.

Equations (40)

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E ω = 1 2 E 0 { e K I / 2 exp [ i ( ω t ϕ I ) ] + e K II / 2 exp [ i ( ω t ϕ II ) ] } ,
K I I k ( ω ) d z , ϕ I ω c I n ( ω ) d z , K II II k ( ω ) d z ,
ϕ II ω c II n ( ω ) d z .
I = I [ e 0 K I + e K II + 2 e ( K I + K II ) / 2 cos ( ϕ I ϕ II ) ] ,
ϕ I ϕ II = 2 m π , m = 0,1,2 ,
V = ( I max I min ) / ( I max + I min ) ,
I * = I 0 [ e ( K I + Δ K ) + e K II + 2 exp ( K I + K II + Δ K ) / 2 × cos ( ϕ I ϕ II + Δ ϕ ) ] ,
V χ , 0 < χ < 1 ,
2 exp ( K I + K II + Δ K ) / 2 e ( K I + Δ K ) + e K II χ ,
Δ K 2 cos h 1 ( 1 / χ )
Δ ϕ 1 = ( ω 1 / c ) Δ n 1 D and Δ ϕ 2 = ( ω 2 / c ) Δ n 2 D ,
Δ ϕ 1 Δ ϕ 2 2 π ξ ,
Δ n ( ω ) = n * n + Δ η ( ω ) ,
Δ η ( ω ) = N f r 0 c 2 ( π ) 1 2 ω 0 β ( y u ) e y 2 d y ( y u ) 2 + α 2 ,
Δ η ( ω 1 ) = ( N f c / ω 0 β ) P ( u 1 , α )
Δ η ( ω 2 ) = ( N f c / ω 0 β ) P ( u 2 , α ) ,
P ( u , α ) = r 0 c ( π ) 1 2 ( y u ) e y 2 d y ( y u ) 2 + α 2
Δ ϕ 1 = ( ω 1 / c ) ( n * n ) D + ( ω 1 / c ) Δ η ( ω 1 ) D ,
Δ ϕ 2 = ( ω 2 / c ) ( n * n ) D + ( ω 2 / c ) Δ η ( ω 2 ) D .
Δ ϕ 2 Δ ϕ 1 ( ω 0 / c ) [ Δ η ( ω 2 ) Δ η ( ω 1 ) ] D ,
Δ ϕ 1 Δ ϕ 2 ( N f D / β ) [ P ( u 2 , α ) P ( u 1 , α ) ] ,
P ( u , α ) = Δ ϕ ( u , α ) ( N f D / β ) ,
P ( u , α ) π r 0 c / u .
Δ ϕ 2 Δ ϕ 1 ( N f D / β ) P ( u 2 , α )
N f 2 π β ξ / [ D | P ( u 2 , α ) | ] .
Δ K ( ω ) = ( k * k ) D + Δ k ( ω ) D ,
Δ k ( ω ) = ( N f / β ) H ( u , α ) ,
H ( u , α ) = r 0 c α ( π ) 1 2 e y 2 d y ( y u ) 2 + α 2 .
N f 2 β cos h 1 ( 1 / χ ) / [ D H ( u 2 , α ) ] .
N max N min = [ P ( u 2 , α ) π H ( u 2 , α ) ] 1 ξ cos h 1 ( 1 / χ ) .
π H ( u 2 , α ) / P ( u 2 , α ) ( 1 / ξ ) cos h 1 ( 1 / χ ) × 10 3 .
π H ( u 2 , α ) / P ( u 2 , α ) ( 1 / ξ ) cos h 1 ( 1 / χ ) × 10 3 = 10 2 .
N min f 2 π β ξ / D P ( u 2 , α ) ,
N min f 4 π ξ ( λ 0 λ 2 ) / D r 0 λ 0 2 ,
N max N min 4 π ( π ) 1 2 c ( λ 0 λ 2 ) cos h 1 ( 1 / χ ) γ λ 0 2 ξ .
n 1 = 2 π N f e 2 m e ω 0 2 ω 2 ( ω 0 2 ω 2 ) 2 + ω 2 γ 2 N f r 0 λ 0 2 ω 0 4 π ω 0 ω ( ω 0 ω ) 2 + γ 2 / 4 ,
N ( υ ) d υ = N ( M / 2 π k T ) 1 2 exp ( M υ 2 / 2 k T ) d υ .
n 1 = N f ( M 2 π k T ) 1 2 r 0 λ 0 2 ω 0 4 π [ ( ω 0 * ω ) ( ω 0 * ω ) 2 + ( γ 2 / 4 ) × exp ( M υ 2 2 k T ) ] d υ .
y = ( ω 0 * ω 0 / β ) , β = ( ω 0 / c ) ( 2 k T / M ) 1 2 , α = γ / 2 β , u = ( ω ω 0 / β ) .
n 1 = 1 2 N f r 0 λ 0 2 c ( π ) 1 2 β ( y u ) e y 2 d y ( y u ) 2 + α 2 .

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