Abstract

The properties of the Fabry-Perot interferometer with an absorbing medium in the cavity have been investigated. When very large reflective finesse etalons are used, the interferometer behaves as a long-path absorption cell with a gain, defined as the ratio of the measured absorption over the sample absorption for the same path as the etalon spacer, equal to C1/2. (C is the etalon contrast.) Practical considerations make the plane Fabry-Perot unsuitable for this use because of the rather large area and surface finesse requirements. The spherical Fabry-Perot, on the other hand, is not constrained in the area requirement and thus appears to be the choice etalon for a long-path absorption cell. The results also show that interference filters, because of their high reflective finesse, have absorption effects which degrade their ultimate performance.

© 1985 Optical Society of America

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References

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  1. A. Perot, C. Fabry, “Méthode interférentielle pour la mesure des longeurs d’onde dans le spectre solaire,” C. R. Acad. Sci. 131, 700 (1900).
  2. K. W. Meissner, “Interference Spectroscopy. Part I,” J. Opt. Soc. Am. 31, 405 (1941); “Part II,” J. Opt. Soc. Am. 32, 185 (1942).
    [CrossRef]
  3. J. E. Mack, D. P. McNutt, F. L. Roesier, R. Chabbal, “The PEPSIOS Purely Inteferometric High-Resolutions Scanning Spectrometer. 1: The Pilot Model,” Appl. Opt. 2, 873 (1963).
  4. D. A. Jackson, “The Spherical Fabry-Perot Interferometer as an Instrument of High Resolving Power for use with External or with Internal Atomic Beams,” Proc. R. Soc. London Ser. A 263, 289 (1961).
    [CrossRef]
  5. A. Kastler, “Atomes à l’interieur d’un ipterféromètre Perot-Fabry,” Appl. Opt. 1, 17 (1962).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).
  7. P. Connes, “Augmentation du produit luminosité × résolution des interféromètres par l’emploi d’une différence de marche indépendante de l’incidence,” Rev. Opt. 35, 37 (1956).
  8. J. U. White, “Long Optical Paths of Large Aperture,” J. Opt. Soc. Am. 32, 285 (1942).
    [CrossRef]
  9. G. Hernandez, “Analytical Description of a Fabry-Perot Spectrometer. 3. Off-axis Behavior and Interference Filters,” Appl. Opt. 13, 2654 (1974).
    [CrossRef] [PubMed]
  10. K. L. Vander Sluis, J. R. McNally, “Fabry-Perot Interferometer with Finite Apertures,” J. Opt. Soc. Am. 46, 39 (1956).
    [CrossRef]
  11. R. Chabbal, “Recherche des meilleurs conditions d’utilization d’un spectromètre photoélectrique Fabry-Perot,” J. Rech. CRNS 24, 138 (1953).

1974

1963

1962

1961

D. A. Jackson, “The Spherical Fabry-Perot Interferometer as an Instrument of High Resolving Power for use with External or with Internal Atomic Beams,” Proc. R. Soc. London Ser. A 263, 289 (1961).
[CrossRef]

1956

P. Connes, “Augmentation du produit luminosité × résolution des interféromètres par l’emploi d’une différence de marche indépendante de l’incidence,” Rev. Opt. 35, 37 (1956).

K. L. Vander Sluis, J. R. McNally, “Fabry-Perot Interferometer with Finite Apertures,” J. Opt. Soc. Am. 46, 39 (1956).
[CrossRef]

1953

R. Chabbal, “Recherche des meilleurs conditions d’utilization d’un spectromètre photoélectrique Fabry-Perot,” J. Rech. CRNS 24, 138 (1953).

1942

1941

1900

A. Perot, C. Fabry, “Méthode interférentielle pour la mesure des longeurs d’onde dans le spectre solaire,” C. R. Acad. Sci. 131, 700 (1900).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

Chabbal, R.

J. E. Mack, D. P. McNutt, F. L. Roesier, R. Chabbal, “The PEPSIOS Purely Inteferometric High-Resolutions Scanning Spectrometer. 1: The Pilot Model,” Appl. Opt. 2, 873 (1963).

R. Chabbal, “Recherche des meilleurs conditions d’utilization d’un spectromètre photoélectrique Fabry-Perot,” J. Rech. CRNS 24, 138 (1953).

Connes, P.

P. Connes, “Augmentation du produit luminosité × résolution des interféromètres par l’emploi d’une différence de marche indépendante de l’incidence,” Rev. Opt. 35, 37 (1956).

Fabry, C.

A. Perot, C. Fabry, “Méthode interférentielle pour la mesure des longeurs d’onde dans le spectre solaire,” C. R. Acad. Sci. 131, 700 (1900).

Hernandez, G.

Jackson, D. A.

D. A. Jackson, “The Spherical Fabry-Perot Interferometer as an Instrument of High Resolving Power for use with External or with Internal Atomic Beams,” Proc. R. Soc. London Ser. A 263, 289 (1961).
[CrossRef]

Kastler, A.

Mack, J. E.

McNally, J. R.

McNutt, D. P.

Meissner, K. W.

Perot, A.

A. Perot, C. Fabry, “Méthode interférentielle pour la mesure des longeurs d’onde dans le spectre solaire,” C. R. Acad. Sci. 131, 700 (1900).

Roesier, F. L.

Vander Sluis, K. L.

White, J. U.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

Appl. Opt.

C. R. Acad. Sci.

A. Perot, C. Fabry, “Méthode interférentielle pour la mesure des longeurs d’onde dans le spectre solaire,” C. R. Acad. Sci. 131, 700 (1900).

J. Opt. Soc. Am.

J. Rech. CRNS

R. Chabbal, “Recherche des meilleurs conditions d’utilization d’un spectromètre photoélectrique Fabry-Perot,” J. Rech. CRNS 24, 138 (1953).

Proc. R. Soc. London Ser. A

D. A. Jackson, “The Spherical Fabry-Perot Interferometer as an Instrument of High Resolving Power for use with External or with Internal Atomic Beams,” Proc. R. Soc. London Ser. A 263, 289 (1961).
[CrossRef]

Rev. Opt.

P. Connes, “Augmentation du produit luminosité × résolution des interféromètres par l’emploi d’une différence de marche indépendante de l’incidence,” Rev. Opt. 35, 37 (1956).

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

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Figures (3)

Fig. 1
Fig. 1

Etalon measured absorption as a function of the sample absorption with the gain G as a parameter. Note the saturation effect as the sample absorption approaches large values.

Fig. 2
Fig. 2

Reflective finesse NR and gain G of an etalon cavity as a function of reflectivity values appropriate to this study.

Fig. 3
Fig. 3

Normalized etalon diameters for both the plane p and spherical s Fabry-Perot interferometers as a function of the reflective finesse NR. The calculations have been made for σ = 20,000 K.

Equations (45)

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A p ( b , ϕ p ) = b t 1 t 2 n = 0 n = [ b 2 r 2 2 exp ( i ϕ p ) ] n = b t 1 t 2 [ 1 b 2 r 2 2 exp ( i ϕ p ) ] 1 ,
ϕ p = 2 π 2 μ d σ cos θ .
I p ( b , ϕ p ) = A ( b , ϕ p ) × A * ( b , ϕ p ) = b 2 t 1 2 t 2 2 ( 1 + b 4 r 2 4 2 b 2 r 2 2 cos ϕ p ) 1 .
I p ( k , δ p ) = k τ 2 ( 1 + k 2 R 2 2 k R cos δ p ) 1 = k ( 1 R ) 2 τ A ( 1 + k 2 R 2 2 k R cos δ p ) 1 .
τ A = [ 1 A ( 1 R ) 1 ] 2 ,
I s ( k , δ s ) = k τ A ( 1 R ) 2 ( 1 + k 2 R 2 ) × ( 1 + k 4 R 4 2 k 2 R 2 cos δ s ) 1 ,
I p ( δ p ) = ( 1 R ) 2 r A ( 1 + R 2 2 R cos δ p ) 1 ,
τ 0 p = I p ( 0 ) = τ A ,
ω p , 1 / 2 = δ p , 1 / 2 π 1 = 2 π 1 sin 1 [ ( 1 R ) ( 2 R 1 / 2 ) 1 ] ( 1 R ) ( π R 1 / 2 ) 1 = N R 1 .
R ˆ = R k ,
I p ( k , δ p ) = [ k τ A ( 1 R ) 2 ( 1 R ˆ ) 2 ] ( 1 R ˆ ) 2 ( 1 + R ˆ 2 2 R ˆ cos δ p ) 1 = τ A k ( 1 R ˆ ) 2 ( 1 + R ˆ 2 2 R ˆ cos δ p ) 1 ,
τ A k = τ A k ( 1 R ) 2 ( 1 R ˆ ) 2 .
τ 0 p ( k ) = I p ( k , 0 ) = τ A k ( 1 R ) 2 ( 1 R ˆ ) 2 = τ A ( N R ˆ N R 1 ) 2 ,
ω p , 1 / 2 ( k ) = 2 π 1 sin 1 [ ( 1 R ˆ ) ( 2 R ˆ 1 / 2 ) 1 ] ( 1 R ˆ ) ( π R ˆ 1 / 2 ) 1 = N R ˆ 1 .
τ 0 p ( k ) [ ω p , 1 / 2 ( k ) ] 2 = ( N R ˆ ) 2 .
τ p ( k , δ p ) = I p ( k , δ p ) [ I p ( 1 , 0 ) ] 1 = [ k ( 1 R ) 2 ( 1 R ˆ ) 2 ] × ( 1 R ˆ ) 2 ( 1 + R ˆ 2 2 R ˆ cos δ p ) 1 ,
τ s ( k , δ p ) = I s ( k , δ s ) [ I s ( 1 , 0 ) ] 1 = [ k ( 1 R 2 ) 2 ( 1 + R ˆ 2 ) ( 1 + R 2 ) 1 ( 1 R ˆ 2 ) 2 ] × ( 1 R ˆ 2 ) 2 ( 1 + R ˆ 4 2 R ˆ 2 cos δ s ) 1 .
τ p ( k , 0 ) = I p ( k , 0 ) [ I p ( 1 , 0 ) ] 1 = k ( 1 R ) 2 ( 1 k R ) 2 ,
τ s ( k , 0 ) = I s ( k , 0 ) [ I s ( 1 , 0 ) ] 1 = k ( 1 R 2 ) 2 ( 1 + k 2 R 2 ) ( 1 k 2 R 2 ) 2 ( 1 + R 2 ) 1 .
= 1 k .
lim k 0 τ p ( k , 0 ) = lim 0 τ p ( k , 0 ) = lim k 0 k ( 1 R ) 2 ( 1 k R ) 2 = lim k 0 k [ 1 + R ( 1 k ) ( 1 R ) 1 ] 2 = k [ 1 + R ( 1 R ) 1 ] 2 ,
lim k 1 τ p ( k , 0 ) = lim 0 ( 1 ) [ 1 + R ( 1 R ) 1 ] 2 1 2 R ( 1 R ) 1 ; R ( 1 R ) 1 1 .
a ( k , 0 ) = 1 τ p ( k , 0 ) .
a ( k , 0 ) = { [ 1 + R ( 1 R ) 1 ] [ 1 + R ( 1 R ) 1 ] 2 × R ( 1 R ) 1 [ 1 + R ( 1 R ) 1 ] 1 } .
A ( k , 0 ) = a ( k , 0 ) ( 1 k ) 1 = 1 a ( k , 0 ) ,
lim 0 A ( k , 0 ) = 1 + 2 R ( 1 R ) 1 = 1 + 2 G = C 1 / 2 .
A 0 ( k , 0 ) = a ( k , 0 ) ( 1 k 0 ) 1 .
lim k 0 τ p ( k , 0 ) = k ( 1 + G ) 2 k G 2 ,
C k = I p ( k , 0 ) [ I p ( k , π ) ] 1 = τ p ( k , 0 ) [ τ p ( k , π ) ] 1 .
C = ( 1 + R ) 2 ( 1 R ) 2 ,
C k = 1 , R 1 = C ( 1 2 1 ) 2 ( 1 + G ) 2 .
lim G 1 C k = 1 = C ( 1 2 G ) .
T p ( k ) = τ 0 p ( k ) ( τ 0 p ) 1 = k ( 1 + G ) 2 ,
ω p , 1 / 2 ( k ) [ ω p , 1 / 2 ( 1 ) ] 1 = ( 1 + G ) k 1 / 2 = [ T p ( k ) ] 1 / 2 ,
lim 0 T p ( k ) = 1 2 G ,
lim 0 ω p , 1 / 2 ( k ) [ ω p , 1 / 2 ( I ) ] 1 = 1 + G .
D p = 100 R ( 2 + R ) ( 1 R 2 ) 1 ( σ Δ σ N R 2 1 ) 1 / 2 ,
D p n = D p d 1 / 2 = 200 R ( 2 + R ) ( 1 R 2 ) 1 ( σ N R ) 1 / 2 ,
D s = 2 [ ( 1 R 2 ) ( 2 π σ R ) 1 d 3 ] 1 / 4 ,
D s n = D s d 3 / 4 = 2 [ ( 1 R 2 ) ( 2 π σ R ) 1 ] 1 / 4 .
τ s ( k , 0 ) k [ 1 2 1 ( 1 k 2 ) ] [ 1 + 2 1 G ( 1 k 2 ) ] 2 .
lim k 0 τ s ( k , 0 ) = 2 1 k ( 1 + 2 1 G ) 2 ,
lim k 1 τ s ( k , 0 ) = lim 0 τ s ( k , 0 ) ( 1 + G ) 2
lim R 1 I p ( 1 , 0 ) = τ A ,
lim R 1 I s ( 1 , 0 ) = 2 1 τ A .

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