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Karl Wilh. Meissner, "Errata: Interference Spectroscopy. Part I," J. Opt. Soc. Am. 32, 211-211 (1942)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-32-4-211

References

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  1. H. M. Roeser, Sci. Pap. Bur. Stand. 16, 363 (1920).
    [Crossref]
  2. K. W. Meissner, Ann. d. Physik 31, 505 (1938).
    [Crossref]
  3. W. F. Meggers and C. G. Peters, Bull. Bur. Stand. 14, 728 (1919).

1938 (1)

K. W. Meissner, Ann. d. Physik 31, 505 (1938).
[Crossref]

1920 (1)

H. M. Roeser, Sci. Pap. Bur. Stand. 16, 363 (1920).
[Crossref]

1919 (1)

W. F. Meggers and C. G. Peters, Bull. Bur. Stand. 14, 728 (1919).

Meggers, W. F.

W. F. Meggers and C. G. Peters, Bull. Bur. Stand. 14, 728 (1919).

Meissner, K. W.

K. W. Meissner, Ann. d. Physik 31, 505 (1938).
[Crossref]

Peters, C. G.

W. F. Meggers and C. G. Peters, Bull. Bur. Stand. 14, 728 (1919).

Roeser, H. M.

H. M. Roeser, Sci. Pap. Bur. Stand. 16, 363 (1920).
[Crossref]

Ann. d. Physik (1)

K. W. Meissner, Ann. d. Physik 31, 505 (1938).
[Crossref]

Bull. Bur. Stand. (1)

W. F. Meggers and C. G. Peters, Bull. Bur. Stand. 14, 728 (1919).

Sci. Pap. Bur. Stand. (1)

H. M. Roeser, Sci. Pap. Bur. Stand. 16, 363 (1920).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1

Etalon spacer.

Fig. 2
Fig. 2

Path difference between two consecutive rays.

Fig. 3
Fig. 3

Formation of circular interference fringes in the focal plane of a lens.

Fig. 4
Fig. 4

Amplitudes of the transmitted waves due to multiple reflection.

Fig. 5
Fig. 5

Intensity distribution depending upon reflection power.

Fig. 6
Fig. 6

Interference system of two close lines.

Fig. 7
Fig. 7

Superposition of the intensity curves of two just resolved spectral lines.

Fig. 8(a)
Fig. 8(a)

Argon spectrum, 10 mm etalon (positive).

Fig. 8(b)
Fig. 8(b)

Helium spectrum, 3 mm etalon (negative).

Fig. 8(c)
Fig. 8(c)

Neon spectrum, 3 mm etalon (negative).

Fig. 8(d)
Fig. 8(d)

Neon spectrum, 10 mm etalon (negative).

Fig. 9
Fig. 9

(a) Magnesium λ8806A, 3.6 cm etalon. (b) λ5528A, 4.2 cm etalon. (c) λ5528A, 3.6 cm etalon.

Tables (1)

Tables Icon

Table II Magnesium line 5528A, etalon gap t=36.008 mm.

Equations (108)

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path difference = A B + B C - A F
phase difference = 2 π [ ( A B + B C ) / λ a - A F / λ g ] .
p = 2 t / λ a cos φ - 2 t tan φ sin ψ / λ g .
p = 2 t [ 1 / λ a cos φ - ( sin φ sin ψ / cos φ ) ( sin φ / λ a sin ψ ) ] ,
p = 2 t cos φ / λ a .
p = 2 t cos φ ν a .
cos φ i = f / ( f 2 + R i 2 ) 1 2 ( 1 - R i 2 / 2 f 2 ) ( 1 - D i 2 / 8 f 2 ) ,
p = ( 2 t / λ ) cos φ = ( 2 t / λ ) ( 1 - R 2 / 2 f 2 ) = ( 2 t / λ ) ( 1 - D 2 / 8 f 2 )
p = 2 t ν cos φ = 2 t ν ( 1 - R 2 / 2 f 2 ) = 2 t ν ( 1 - D 2 / 8 f 2 ) .
d p = - ( 2 t / λ ) sin φ d φ = - ( 2 t / λ ) ( R / f 2 ) d R .
Δ R = λ f 2 / 2 t R
p 0 = 2 t / λ - R 0 2 t / λ f 2 , p i = p 0 - i = 2 t / λ - R i 2 t / λ f 2 , p k = p 0 - k = 2 t / λ - R k 2 t / λ f 2 ,
( p i - p k ) = ( k - i ) = ( R k 2 - R i 2 ) t / λ f 2
( R k 2 - R i 2 ) / ( k - i ) = λ f 2 / t = Δ R 2 ,
( D k 2 - D i 2 ) / ( k - i ) = 4 λ f 2 / t = Δ D 2 .
P = 2 t / λ             or             P = 2 t ν .
P = 2 t / λ , p k = 2 t / λ - ( t / λ f 2 ) R k 2 .
= P - p k - k = ( t / λ f 2 ) R k 2 - k ,
= R k 2 ( R k 2 - R i 2 ) / ( k - i ) - k , = R i 2 ( R k 2 - R i 2 ) / ( k - i ) - i .
= D i 2 ( D k 2 - D i 2 ) / ( k - i ) - i .
= R i 2 / Δ R 2 - i = D i 2 / Δ D 2 - i .
= R 0 2 / Δ R 2 = D 0 2 / Δ D 2 .
D k 2 = D 0 2 + k Δ D 2
B = 6 ( n - 1 ) ( y n - y 1 ) + ( n - 3 ) ( y n - 1 - y 2 ) + n ( n 2 - 1 ) = n ( n 2 - 1 ) / 6
A = Y m - B X m
s · e i ω τ ,             s r e i ( ω τ - 2 π p ) ,             s r 2 e i ( ω t - 4 π p ) ,
A e i ω τ = s e i ω τ 1 k r ( k - 1 ) e - i 2 π p ( k - 1 ) = s e i ω τ ( 1 + r e - 2 π p i + r 2 e - 2 ( 2 π p ) i + ) = s e i ω τ / ( 1 - r e - 2 π p i ) .
I = s 2 / ( 1 - r e - 2 π p i ) ( 1 + r e + 2 π p i ) = s 2 / ( 1 + r 2 - 2 r cos 2 π p ) .
I = s 2 / ( ( 1 - r ) 2 + 4 r sin 2 ( π p ) ) . I = s 2 / ( 1 - r ) 2 1 + ( 4 r / ( 1 - r ) 2 ) sin 2 ( π p )
I max = s 2 / ( 1 - r ) 2 .
I min = s 2 / ( ( 1 - r ) 2 + 4 r ) = s 2 / ( 1 + r ) 2 .
I γ = I max ( 1 - r ) 2 / ( ( 1 - r ) 2 + 4 r sin 2 ( π γ ) ) . = I max / ( 1 + η 2 sin 2 ( π γ ) ) ,
η 2 = 4 r / ( 1 - r ) 2 .
I γ = I max / ( 1 + η 2 π 2 γ 2 ) .
I max / 2 = I max / ( 1 + η 2 π 2 γ 2 )
γ h = 1 / π η = ( 1 - r ) / 2 π r .
2 γ h = ( 1 - r ) / π r .
2 γ h = ( 1 - r ) π r + 1 24 ( ( 1 - r ) r ) 3 .
± p Δ λ = 2 t sin φ Δ φ = 2 t R d R / f 2 and Δ ν = ( p R Δ R ) / 2 t f 2 .
( p + 1 ) λ 1 = p λ 2
Δ λ = ( λ 2 - λ 1 ) = λ 1 / p = λ 1 2 / 2 t .
Spectral range :             Δ λ = λ / p = λ 2 / 2 t .
Δ ν = Δ λ λ 2 = 1 / 2 t .
D a = Δ φ / Δ λ = p / ( 2 t · sin φ ) = 1 / ( λ · tan φ )
D l = Δ R / Δ λ = p f 2 / 2 t R = f 2 / R λ .
A v = 2 γ h / 2 t = 2 γ h · Δ ν cm - 1 = 1 2 π t ( 1 - r ) r = Δ ν π ( 1 - r ) r cm - 1
A λ = λ 2 2 π t ( 1 - r ) r = Δ λ π ( 1 - r ) r A .
Resolving power             R = λ / Δ λ = p / Δ p .
I max : I min = 1 : 0.8 = 1.25.
I max = I ( p 0 ) + I ( p 0 ± Δ p )
I min = 2 I ( p 0 + Δ p / 2 )
( 1 + η sin 2 ( π p 0 + Δ p / 2 ) ) = 2.50 ( 1 + η sin 2 ( π p 0 + Δ p ) )
( 1 + η sin 2 ( π Δ p / 2 ) ) = 2.5 ( 1 + η sin 2 ( π Δ p ) .
1 + η sin 2 ( π p / 2 R ) = 2.5 ( 1 + η sin 2 ( π p / R ) .
π p / 2 R = ( ( 1 + 1.5 1 2 ) / 2 ) 1 2 / η 1 2 .
R = 2.98 p r 1 2 / ( 1 - r ) .
R = effective number of rays × order ,
N eff = 2.98 r 1 2 / ( 1 - r ) .
P a = P a + a = 2 t ν a             and             P b = p b + b = 2 t ν b .
ν a - ν b = ( p a - p b ) / 2 t + ( a - b ) / 2 t .
ν a - ν b = ( p a - p b ) / 2 t + ( D a k 2 / Δ D a 2 - D b k 2 / Δ D b 2 ) / 2 t .
ν a - ν b = ( p a - p b ) / 2 t + ( D a k 2 - D b k 2 ) / 2 t Δ D 2 .
Δ H Δ H Δ H Δ H Δ H D a 0 2 D a 1 2 D a 2 2 D a 3 2 D a 4 2 D a 5 2 D b 0 2 D b 1 2 D b 2 2 D b 3 2 D b 4 2 D b 5 2 D c 0 2 D c 1 2 D c 2 2 D c 3 2 D c 4 2 D c 5 2 Δ V 1 Δ V 2 .
( ν a - ν b ) = ( D a k 2 - D b k 2 ) / 2 t Δ D 2 = Δ V 1 / 2 t Δ H , ( ν b - ν c ) = ( D b k 2 - D c k 2 / 2 t Δ D 2 = Δ V 2 / 2 t Δ H ,
Δ H = 43.8 ,             Δ V 1 = 11.2 ,             Δ V 2 = 11.0.
Δ ν 1 = 11.2 / 7.2016 × 43.8 = 0.0355 cm - 1 , Δ ν 2 = 11.0 / 7.2016 × 43.8 = 0.0349 cm - 1 .
Δ λ = - ( Δ ν / ν 2 ) 10 8 A .
p = 2 t ( 1 - D 2 / 8 f 2 ) / λ ,
p 1 = 2 t ( 1 - D 2 / 8 f 2 ) / λ 1
p 2 = 2 t ( 1 - D 2 / 8 f 2 ) / λ 2 .
p 2 = p 1 · λ 1 / λ 2 · ( 1 - ( D 2 - D 2 ) / 8 f 2 ) .
f = ( 845.5 ± 0.5 ) mm ,             f 2 715 , 000 mm 2 .
p 1 = 43 , 280 ,             p 2 = 41 , 063 ,             p 3 = 43 , 342.
P = 2 t / λ = p + ,
= D k 2 : [ ( D k 2 - D i 2 ) / ( k - i ) ] - k
P 1 λ 1 = P 2 λ 2 = 2 t             or             P 2 = P 1 λ 1 / λ 2
( p 2 + 2 ) = ( p 1 + 1 ) λ 1 / λ 2 .
( p 1 + n + ) = ( p 2 + m + 2 ) λ 2 / λ 1
p 1 = p 1 + n             and             p 2 = p 2 + m .
( p 1 + 1 ) λ 1 = ( p 2 + 2 ) λ 2 = ( p 3 + 3 ) λ 3
( p 1 + 1 ) = ( p 1 - p 2 + 1 - 2 ) λ 2 / ( λ 2 - λ 1 )
( p 1 + 1 ) = ( p 1 - p 3 + 1 - 3 ) λ 3 / ( λ 3 - λ 1 ) .
p x = p s ( λ s / λ x ) ( 1 - ( D x 2 - D s 2 ) / 8 f 2 )
λ x = λ s ( p s / p x ) ( 1 - ( D x 2 - D s 2 ) / 8 f 2 ) .
λ x = λ s ( p s / p x ) ( 1 - d x 2 / k x 2 f 2 - d s 2 / k s 2 f 2 ) .
( p x + x ) = ( p s + s ) λ s / λ x
λ x = λ s ( p s + s ) / ( p x + x ) .
P s = 2 t 1 / λ s + 2 τ s / λ s , P s = 2 t 2 / λ s + 2 τ s / λ s , P x = 2 t 1 / λ x + 2 τ x / λ x , P x = 2 t 2 / λ x + 2 τ x / λ x .
λ x = λ s ( P s - P s ) / ( P x - P x ) .
P s / P x = ( λ x / λ s ) ( t 1 + τ s ) / ( t 1 + τ x ) = ( λ x / λ s ) ( 1 + ( τ s - τ x ) / t 1 )
λ x = ( λ s P s / P x ) ( 1 + ( τ x - τ s ) / t 1 ) = λ x + λ x ( τ x - τ s ) / t 1 = λ x + Δ λ x
λ x = ( λ s P s / P x ) ( 1 + ( τ x - τ s ) / t 2 ) = λ x + λ x ( τ x - τ s ) / t 2 = λ x + Δ λ x .
δ = 2 ( τ x - τ s ) λ x = λ x - λ x λ x 2 · 2 t 1 t 2 t 2 - t 1
Δ λ x = ( λ x - λ x ) t 2 / ( t 2 - t 1 )
Δ λ x = ( λ x - λ x ) t 1 / ( t 2 - t 1 ) .
λ x = λ s P s / P x ( 1 - ( τ x - τ s ) / t 1 ) = λ s P s / ( P x - 2 ( τ x - τ s ) / λ x ) = λ s P s / ( P x - δ ) .
Δ = λ ( n 0 - n 0 ) × ( ρ - ρ 0 ) / ρ 0 ,
Δ = λ ( n 0 - n 0 ) × ( ρ - ρ 0 ) / ρ 0 .
Δ = λ ( n 0 - n 0 ) × ( ρ - ρ 0 ) / ρ 0
Δ = λ ( n 0 - n 0 ) × ( ρ - ρ 0 ) / ρ 0 ,
Δ = Δ - Δ - ( ( λ - λ ) / λ ) × Δ .
λ = p λ / p .
λ = p λ 0 / p .
Δ = λ 0 - p λ 0 / p = λ 0 ( 1 - p λ 0 / p λ 0 ) = λ 0 ( 1 - λ λ 0 / λ λ 0 ) .
Δ = λ 0 ( 1 - n 0 n / n 0 n ) = λ 0 ( n 0 n - n 0 n ) / n 0 n = λ 0 ( n 0 n - n 0 n ) ,
( n - 1 ) / ρ = ( n 0 - 1 ) / ρ 0
( n - 1 ) / ρ = ( n 0 - 1 ) / ρ 0 .
Δ = λ 0 ( n 0 - n 0 ) ( ρ - ρ 0 ) / ρ 0 .