Abstract

The self-emission from the splitting layer of a Fourier-transform infrared interferometer is modeled with basic properties of optical thin films. The resulting equation gives explicitly the self-emission contribution in terms of the temperature, the complex refractive index, the reflection coefficient, and the thickness of the beam splitter layer.

© 1998 Optical Society of America

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References

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  1. H. E. Revercomb, H. Buijs, H. B. Howell, D. D. Laporte, W. L. Smith, L. A. Sromovsky, “Calibration of IR Fourier transform spectrometers: solution to a problem with the high-resolution interferometer sounder,” Appl. Opt. 27, 3210–3218 (1988).
  2. C. Weddigen, C. E. Blom, M. Höpfner, “Phase corrections for the emission sounder MIPAS-FT,” Appl. Opt. 32, 4586–4589 (1993).
    [CrossRef] [PubMed]
  3. J.-M. Thériault, C. Bradette, A. Villemaire, M. Chamberland, J. Giroux, “Differential detection with a double-beam interferometer,” in Electro-Optical Technology for Remote Chemical Detection and Identification II, M. Fallahi, E. Howden, eds., Proc. SPIE3082, 65–75 (1997).
    [CrossRef]
  4. J.-M. Thériault, “Modeling responsivity and self-emission of a double-beam Fourier transform infrared interferometer,” Appl. Opt.37, 0000–0000 (1998), to be published.
  5. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

1993 (1)

1988 (1)

Blom, C. E.

Bradette, C.

J.-M. Thériault, C. Bradette, A. Villemaire, M. Chamberland, J. Giroux, “Differential detection with a double-beam interferometer,” in Electro-Optical Technology for Remote Chemical Detection and Identification II, M. Fallahi, E. Howden, eds., Proc. SPIE3082, 65–75 (1997).
[CrossRef]

Buijs, H.

Chamberland, M.

J.-M. Thériault, C. Bradette, A. Villemaire, M. Chamberland, J. Giroux, “Differential detection with a double-beam interferometer,” in Electro-Optical Technology for Remote Chemical Detection and Identification II, M. Fallahi, E. Howden, eds., Proc. SPIE3082, 65–75 (1997).
[CrossRef]

Giroux, J.

J.-M. Thériault, C. Bradette, A. Villemaire, M. Chamberland, J. Giroux, “Differential detection with a double-beam interferometer,” in Electro-Optical Technology for Remote Chemical Detection and Identification II, M. Fallahi, E. Howden, eds., Proc. SPIE3082, 65–75 (1997).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

Höpfner, M.

Howell, H. B.

Laporte, D. D.

Revercomb, H. E.

Smith, W. L.

Sromovsky, L. A.

Thériault, J.-M.

J.-M. Thériault, “Modeling responsivity and self-emission of a double-beam Fourier transform infrared interferometer,” Appl. Opt.37, 0000–0000 (1998), to be published.

J.-M. Thériault, C. Bradette, A. Villemaire, M. Chamberland, J. Giroux, “Differential detection with a double-beam interferometer,” in Electro-Optical Technology for Remote Chemical Detection and Identification II, M. Fallahi, E. Howden, eds., Proc. SPIE3082, 65–75 (1997).
[CrossRef]

Villemaire, A.

J.-M. Thériault, C. Bradette, A. Villemaire, M. Chamberland, J. Giroux, “Differential detection with a double-beam interferometer,” in Electro-Optical Technology for Remote Chemical Detection and Identification II, M. Fallahi, E. Howden, eds., Proc. SPIE3082, 65–75 (1997).
[CrossRef]

Weddigen, C.

Appl. Opt. (2)

Other (3)

J.-M. Thériault, C. Bradette, A. Villemaire, M. Chamberland, J. Giroux, “Differential detection with a double-beam interferometer,” in Electro-Optical Technology for Remote Chemical Detection and Identification II, M. Fallahi, E. Howden, eds., Proc. SPIE3082, 65–75 (1997).
[CrossRef]

J.-M. Thériault, “Modeling responsivity and self-emission of a double-beam Fourier transform infrared interferometer,” Appl. Opt.37, 0000–0000 (1998), to be published.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

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Figures (2)

Fig. 1
Fig. 1

Ray tracings showing the output amplitudes (A1 and A2) for beams of unit amplitude incident on (a) input 1, (b) input 2, (c) the amplitude reflection and transmission coefficients of a thin layer beam splitter.

Fig. 2
Fig. 2

Ray tracings for the modelization of the self-emission from the splitting layer. Graybody radiation and stray light can emanate from the layer and interfere with itself to create a significant contribution to the raw spectrum (see text).

Equations (33)

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A 1 = rt + tr   exp i ϕ ,
A 2 = rr + tt   exp i ϕ ,
ϕ = 2 π ν x
r = r 1 1 - exp - 2 i δ 1 - r 1 2   exp - 2 i δ ,
t = 1 - r 1 2 exp - i δ 1 - r 1 2   exp - 2 i δ ,
δ = 2 π ν nd   cos θ ,
r 1 = - r 1 ,
t 1 t 1 = 1 - r 1 2 .
t = r H   exp - i   π 2 ,
H = 1 - r 1 2 2 r 1   sin δ .
I 1 = A 1 A 1 * = rt + tr   exp i ϕ r * t * + t * r *   exp - i ϕ ,
I 2 = A 2 A 2 * = r 2 + t 2   exp i ϕ r * 2 + t * 2   exp - i ϕ .
I 1 = 2 R 2 H 2 + 2 R 2 H 2   cos ϕ ,
I 2 = R 2 + R 2 H 2 + 2 R 2 H 2   cos ϕ - π .
e 1 = ε in t 1 + r 1 2 t 1   exp - 2 α exp - 2 i Δ + r 1 4 t 1   exp - 4 α exp - 4 i Δ +   ,
Δ = 2 π ν n 1 eff d   cos θ 1 ,
α = 2 π ν k 1 eff d   cos θ 1 ,
e 1 = ε in t 1   exp - α exp - i Δ 1 - r 1 2   exp - 2 α exp - 2 i Δ ,
e 1 = ε in t t 1 exp α exp i Δ .
e 2 = ε in - r 1 t 1 t .
A 1 = e 1 t = ε in t 2 t 1 exp α exp i Δ ,
A 2 = e 2 r   exp i ϕ = ε in - r 1 t 1 tr   exp i ϕ ,
A 1 + A 2 = ε in t t 1 t   exp α exp i Δ - r 1 r   exp i ϕ .
I a = ε in T T 1 ( T   exp 2 α + RR 1 - r 1   exp α × rt *   exp i ϕ - Δ + r * t   exp - i ϕ - Δ ) ,
e 1 = ε in - r 1 t 1 t ,
e 2 = ε in t t 1 exp α exp i Δ ,
I b = ε in T T 1 ( R   exp 2 α + TR 1 - r 1   exp α × rt *   exp i ϕ + Δ + r * t   exp - i ϕ + Δ ) .
E lay = ε in T T 1 - r 1   exp α 2   cos   Δ rt *   exp i ϕ + r * t   exp - i ϕ .
t = rH   exp i π / 2 ,
H H   exp i θ H = 1 - r 1 2 r 1 1 exp α - i Δ - exp - α + i Δ .
E lay = ε in T T 1 - r 1   exp α 2   cos   Δ rr * H   exp i ϕ - π 2 - θ H + r * r H   exp - i ϕ - π 2 - θ H ,
E lay = ε in T T 1 r 1   exp α 2   cos   Δ 2 RH cos ϕ + π 2 - θ H ,
ε in = 1 - exp - 2 α B T BS ,

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