Abstract

Thermal emission from beam splitters in Fourier transform infrared spectrometers causes spectral amplitudes that are in quadrature to those of radiation from the field of view or from the detector port. Beam-splitter emission is described as a superposition of radiation of electromagnetic dipoles with angular polarization correlation taken into account for the real refractive index. Surface emission shows characteristic differences compared with volume emission. Numerical data are given for experimental conditions adapted to those of the airborne limb sounder MIPAS-FT.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. E. Revercomb, H. Buijs, H. B. Howell, D. D. LaPorte, W. L. Smith, L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the High-Resolution Interferometer Sounder,” Appl. Opt. 27, 3210–3218 (1988).
    [CrossRef] [PubMed]
  2. Ch. Weddigen, C. E. Blom, M. Höpfner, “Phase corrections for the emission sounder MIPAS-FT,” Appl. Opt. 32, 4586–4589 (1993).
    [CrossRef] [PubMed]
  3. Th. Gulde, Ch. Piesch, C. E. Blom, H. Fischer, F. Fergg, G. Wildgruber, “The airborne MIPAS infrared emission experiment,” in Proceedings of the First International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1994), Vol. II, pp. 301–311.
  4. C. E. Blom, M. Höpfner, Ch. Weddigen, “Correction of phase anomalies of atmospheric emission spectra by the double-differencing method,” App. Opt. 35, 2649–2652 (1996).
    [CrossRef]
  5. J.-M. Thériault, “Beam splitter layer emission in Fourier-transform infrared interferometers,” Appl. Opt. 37, 8348–8351 (1998).
    [CrossRef]
  6. J.-M. Thériault, “Modeling the responsivity and self-emission of a double-beam Fourier-transform infrared interferometer,” Appl. Opt. 38, 505–515 (1999).
    [CrossRef]
  7. B. Carli, L. Palchetti, P. Raspollini, “Effect of beam splitter emission in Fourier transform spectroscopy,” Appl. Opt. 38, 7475–7480 (1999).
    [CrossRef]
  8. E. Hecht, “Radiation,” in Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), Chap. 3.4, pp. 47–56.
  9. G. Joos, “Die Polarisations- und Intensitätsverhältnisse bei Reflexion und Brechung,” in Lehrbuch der theoretischen Physik (Akademische Verlagsgesellschaft, Leipzig, 1950), Chap. 4, pp. 311–313.
  10. M. Born, E. Wolf, “Reflection and refraction of a plane wave,” in Principles of Optics, 6th ed. (Pergamon, Oxford1987), Chap. 1.5, pp. 36–47.
  11. R. S. Booth, J. W. Brault, A. Labeysie, “Basic theory of the ideal instrument,” in High Resolution in Astronomy: Fifteenth Advanced Course of the Swiss Society of Astronomy and Astrophysics, A. Bens, M. Huber, M. Mayor, eds. (Geneva Observatory, CH-1290 Sanverny, Switzerland, 1985), Chap. 2, pp. 4–6.
  12. Ref. 10, “The field of a linear electric dipole,” Chap. 2.2.3, pp. 81–84.

1999 (2)

1998 (1)

1996 (1)

C. E. Blom, M. Höpfner, Ch. Weddigen, “Correction of phase anomalies of atmospheric emission spectra by the double-differencing method,” App. Opt. 35, 2649–2652 (1996).
[CrossRef]

1993 (1)

1988 (1)

Blom, C. E.

C. E. Blom, M. Höpfner, Ch. Weddigen, “Correction of phase anomalies of atmospheric emission spectra by the double-differencing method,” App. Opt. 35, 2649–2652 (1996).
[CrossRef]

Ch. Weddigen, C. E. Blom, M. Höpfner, “Phase corrections for the emission sounder MIPAS-FT,” Appl. Opt. 32, 4586–4589 (1993).
[CrossRef] [PubMed]

Th. Gulde, Ch. Piesch, C. E. Blom, H. Fischer, F. Fergg, G. Wildgruber, “The airborne MIPAS infrared emission experiment,” in Proceedings of the First International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1994), Vol. II, pp. 301–311.

Booth, R. S.

R. S. Booth, J. W. Brault, A. Labeysie, “Basic theory of the ideal instrument,” in High Resolution in Astronomy: Fifteenth Advanced Course of the Swiss Society of Astronomy and Astrophysics, A. Bens, M. Huber, M. Mayor, eds. (Geneva Observatory, CH-1290 Sanverny, Switzerland, 1985), Chap. 2, pp. 4–6.

Born, M.

M. Born, E. Wolf, “Reflection and refraction of a plane wave,” in Principles of Optics, 6th ed. (Pergamon, Oxford1987), Chap. 1.5, pp. 36–47.

Brault, J. W.

R. S. Booth, J. W. Brault, A. Labeysie, “Basic theory of the ideal instrument,” in High Resolution in Astronomy: Fifteenth Advanced Course of the Swiss Society of Astronomy and Astrophysics, A. Bens, M. Huber, M. Mayor, eds. (Geneva Observatory, CH-1290 Sanverny, Switzerland, 1985), Chap. 2, pp. 4–6.

Buijs, H.

Carli, B.

Fergg, F.

Th. Gulde, Ch. Piesch, C. E. Blom, H. Fischer, F. Fergg, G. Wildgruber, “The airborne MIPAS infrared emission experiment,” in Proceedings of the First International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1994), Vol. II, pp. 301–311.

Fischer, H.

Th. Gulde, Ch. Piesch, C. E. Blom, H. Fischer, F. Fergg, G. Wildgruber, “The airborne MIPAS infrared emission experiment,” in Proceedings of the First International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1994), Vol. II, pp. 301–311.

Gulde, Th.

Th. Gulde, Ch. Piesch, C. E. Blom, H. Fischer, F. Fergg, G. Wildgruber, “The airborne MIPAS infrared emission experiment,” in Proceedings of the First International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1994), Vol. II, pp. 301–311.

Hecht, E.

E. Hecht, “Radiation,” in Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), Chap. 3.4, pp. 47–56.

Höpfner, M.

C. E. Blom, M. Höpfner, Ch. Weddigen, “Correction of phase anomalies of atmospheric emission spectra by the double-differencing method,” App. Opt. 35, 2649–2652 (1996).
[CrossRef]

Ch. Weddigen, C. E. Blom, M. Höpfner, “Phase corrections for the emission sounder MIPAS-FT,” Appl. Opt. 32, 4586–4589 (1993).
[CrossRef] [PubMed]

Howell, H. B.

Joos, G.

G. Joos, “Die Polarisations- und Intensitätsverhältnisse bei Reflexion und Brechung,” in Lehrbuch der theoretischen Physik (Akademische Verlagsgesellschaft, Leipzig, 1950), Chap. 4, pp. 311–313.

Labeysie, A.

R. S. Booth, J. W. Brault, A. Labeysie, “Basic theory of the ideal instrument,” in High Resolution in Astronomy: Fifteenth Advanced Course of the Swiss Society of Astronomy and Astrophysics, A. Bens, M. Huber, M. Mayor, eds. (Geneva Observatory, CH-1290 Sanverny, Switzerland, 1985), Chap. 2, pp. 4–6.

LaPorte, D. D.

Palchetti, L.

Piesch, Ch.

Th. Gulde, Ch. Piesch, C. E. Blom, H. Fischer, F. Fergg, G. Wildgruber, “The airborne MIPAS infrared emission experiment,” in Proceedings of the First International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1994), Vol. II, pp. 301–311.

Raspollini, P.

Revercomb, H. E.

Smith, W. L.

Sromovsky, L. A.

Thériault, J.-M.

Weddigen, Ch.

C. E. Blom, M. Höpfner, Ch. Weddigen, “Correction of phase anomalies of atmospheric emission spectra by the double-differencing method,” App. Opt. 35, 2649–2652 (1996).
[CrossRef]

Ch. Weddigen, C. E. Blom, M. Höpfner, “Phase corrections for the emission sounder MIPAS-FT,” Appl. Opt. 32, 4586–4589 (1993).
[CrossRef] [PubMed]

Wildgruber, G.

Th. Gulde, Ch. Piesch, C. E. Blom, H. Fischer, F. Fergg, G. Wildgruber, “The airborne MIPAS infrared emission experiment,” in Proceedings of the First International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1994), Vol. II, pp. 301–311.

Wolf, E.

M. Born, E. Wolf, “Reflection and refraction of a plane wave,” in Principles of Optics, 6th ed. (Pergamon, Oxford1987), Chap. 1.5, pp. 36–47.

App. Opt. (1)

C. E. Blom, M. Höpfner, Ch. Weddigen, “Correction of phase anomalies of atmospheric emission spectra by the double-differencing method,” App. Opt. 35, 2649–2652 (1996).
[CrossRef]

Appl. Opt. (5)

Other (6)

E. Hecht, “Radiation,” in Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), Chap. 3.4, pp. 47–56.

G. Joos, “Die Polarisations- und Intensitätsverhältnisse bei Reflexion und Brechung,” in Lehrbuch der theoretischen Physik (Akademische Verlagsgesellschaft, Leipzig, 1950), Chap. 4, pp. 311–313.

M. Born, E. Wolf, “Reflection and refraction of a plane wave,” in Principles of Optics, 6th ed. (Pergamon, Oxford1987), Chap. 1.5, pp. 36–47.

R. S. Booth, J. W. Brault, A. Labeysie, “Basic theory of the ideal instrument,” in High Resolution in Astronomy: Fifteenth Advanced Course of the Swiss Society of Astronomy and Astrophysics, A. Bens, M. Huber, M. Mayor, eds. (Geneva Observatory, CH-1290 Sanverny, Switzerland, 1985), Chap. 2, pp. 4–6.

Ref. 10, “The field of a linear electric dipole,” Chap. 2.2.3, pp. 81–84.

Th. Gulde, Ch. Piesch, C. E. Blom, H. Fischer, F. Fergg, G. Wildgruber, “The airborne MIPAS infrared emission experiment,” in Proceedings of the First International Airborne Remote Sensing Conference and Exhibition (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1994), Vol. II, pp. 301–311.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Schematic representation of a FTIR spectrometer with definitions and notation used in this paper. A balanced beam, incident from the upper left, is shown with partial beams 1 and 2 (see Subsection 3.A).

Fig. 2
Fig. 2

Illustration for the derivation of amplitude-related coefficients of reflection (R) and transmission (T) for sources (a) outside and (b) inside the BS. P1 and P2, points of reference; l, e or m for TE or TM waves, respectively.

Fig. 3
Fig. 3

Absolute values of amplitude-related coefficients of reflection (R) and transmission (T) for a radiation source (a) outside and (b) inside the BS under conditions adapted to MIPAS-FT (see text). The subscripts e and m signify TE and TM radiations, respectively, for the source outside or inside the BS (subscripts o or i). σ, wave number.

Fig. 4
Fig. 4

Schematic representation of the unbalanced beam incident from the detector port.

Fig. 5
Fig. 5

Modulated and unmodulated parts (subscripts cos and 0, respectively) for the balanced and the unbalanced beams (superscripts b and u, respectively) under MIPAS-FT experimental conditions [cf. Eqs. (30), (31), and (38)–(40)]. σ, wave number.

Fig. 6
Fig. 6

Schematic representation of the optical paths from the Hertzian dipole, P, to the IR lens for partial beams 1–6.

Fig. 7
Fig. 7

Definition of the polar angle, ϕ, of observation for the radiation of a Hertzian dipole, P. E and H, electric and magnetic fields, respectively; r, radial vector.

Fig. 8
Fig. 8

Orientations (arrow symbols) of the electric fields for the six partial beams shown in Fig. 6, which are due to the Cartesian components of an emitting dipole, P = (p x , p y , p z ).

Fig. 9
Fig. 9

Terms describing surface BSE as defined in Eqs. (53)–(56), under experimental conditions adapted to MIPAS-FT. σ, wave number.

Fig. 10
Fig. 10

Terms describing volume BSE as defined in Eqs. (57)–(59), under experimental conditions adapted to MIPAS-FT. σ, wave number.

Equations (59)

Equations on this page are rendered with MathJax. Learn more.

γ=4πn1-2σ=4πnσd cos θ2.
roe=-sinθ1-θ2/sinθ1+θ2,
toe=1+roe,
rie=-roe,
tie=1+rie,
rom=tanθ1-θ2/tanθ1+θ2,
tom=1+rom/n,
rim=-rom,
tim=1+rimn.
toltil=1+rolril=1-rol2.
Rol=rol+tolriltil expiγv=0 ril2ν expiνγ=rol1-expiγ/1-rol2 expiγ.
Tol=toltilv=0 ril2ν expivγ=1-rol2/1-rol2 expiγ.
|Rol|2+|Tol|2=1.
αl=arc tanrol2 sin γ/1-rol2 cos γ
Roe=|Roe| expiαe+γ+π/2,
Toe=|Toe|expiαe,
Rom=|Rom|expiαm+γ-π/2,
Tom=|Tom|expiαm.
Rie=rietiev=0 rie2ν expivγ=tierie/1-rie2 expiγ=|Rie|expiαe,
Tie=tiev=0 rie2ν expivγ=tie/1-rie2 expiγ=|Tie|expiαe,
Rim=rimtimv=0 rim2ν expivγ=timrim/1-rim2 expiγ=|Rim|expiαm+π,
Tim=timv=0 rim2ν expivγ=tim/1-rim2 expiγ=|Tim|expiαm.
OP1=2y1 sin θ1+ΔL+n1+Δ-y1 sin θ1-2=2ΔL+Δ+y1 sin θ1+γ/4πσ,
OP2=n1+2y1 sin θ1+ΔR-2+Δ-y1 sin θ1+2=2ΔR+Δ+y1 sin θ1+γ/4πσ.
A1e=1/2Roe-1Toe expi2πσOP1,
A2e=1/2Toe-1Roe expi2πσOP2,
A1m=1/2Rom+1Tom expi2πσOP1,
A2m=1/2Tom+1Rom expi2πσOP2.
Ib=|A1e+A2e|2+|A1m+A2m|2.
Ib=Iob+Icosb cos2πσX,
Iob=Icosb=|Roe|2|Toe|2+|Rom|2|Tom|2.
OP3=2y2 sin θ1+ΔL+γ/2πσ,
OP4=2y2 sin θ1+ΔR.
A3e=1/2Toe-1Toe expi2πσOP3,
A4e=1/2Roe-1Roe expi2πσOP4,
A3m=1/2Tom+1Tom expi2πσOP3,
A4m=1/2Rom+1Rom expi2πσOP4.
Iu=I0u+Icosu cos2πσX,
I0u=1-I0b,
Icosu=-Icosb.
OP1=Δ-yP sin θ1+γ1/2-δ/4πσ,
OP2=Δ-yP sin θ1+γ3/2+δ/4πσ,
OP3=2ΔL+Δ+yP sin θ1+γ3/2+δ/4πσ,
OP4=2ΔL+Δ+yP sin θ1+γ5/2-δ/4πσ,
OP5=2ΔR+Δ+yP sin θ1+γ1/2-δ/4πσ,
OP6=2ΔR+Δ+yP sin θ1+γ3/2+δ/4πσ.
Ax=sin θ2 sin ϑ cos φ-Tim expi2πσOP1-Rim expi2πσOP2+Tim+1Tom expi2πσOP3+Rim+1Tom expi2πσOP4+Tim+1Rom expi2πσOP5+Rim+1Rom expi2πσOP6.
Ay=cos θ2 sin ϑ sin φ+Tim expi2πσOP1-Rim expi2πσOP2-Tim+1Tom expi2πσOP3+Rim+1Tom expi2πσOP4+Tim+1Rom expi2πσOP5-Rim+1Rom expi2πσOP6.
Az=cos ϑ-Tie expi2πσOP1-Rie expi2πσOP2-Tie-1Toe expi2πσOP3-Rie-1Toe expi2πσOP4-Tie-1Roe expi2πσOP5-Rie-1Roe expi2πσOP6.
Iϑ, φ; xp, yp, zp; ΔL, ΔR, Δ=|Ax+Ay|2+|Az|2.
Ixp, yp, zp; ΔL, ΔR, Δ=|Ax|2¯+|Ay|2¯+|Az|2¯.
Ixp=δd; X=2ΔL-ΔR=|Rim|2+|Tim|2+|Rie|2+|Tie|2+2|Rim||Tim|cos 2θ2+|Rie||Tie|cosγ/2cos γδ-2|Rom|2|Rim||Tim|cos 2θ2+|Roe|2|Rie||Tie|sinγ/2sin γδ+Rom||Tom||Tim|2-|Rim|2cos 2θ2+|Roe||Toe||Tie|2-|Rie|2sin γδ cos 2πσX+|Rom||Tom||Tim|2+|Rim|2cos 2θ2+|Roe||Toe||Tie|2+|Rie|2cos γδ+2|Rom||Tom||Rim||Tim|+|Roe||Toe||Rie||Tie|cos(γ/2sin 2πσX.
IS±d/2; X=I±1/2S±IcosS cos2πσX+IsinS sin2πσX,
I±1/2S=|Rim|2+|Tim|2+|Rie|2+|Tie|2+2|Rim||Tim| cos 2θ2+|Rie||Tie|cosγ222|Rom|2|Rim||Tim|cos 2θ2+|Roe|2|Rie||Tie|sinγ22,
IcosS=|Rom||Tom||Tim|2-|Rim|2cos 2θ2+|Roe||Toe||Tie|2-|Rie|2sinγ2,
IsinS=|Rom||Tom||Tim|2+|Rim|2cos 2θ2+2|Rim||Tim|+|Roe||Toe||Tie|+|Rie|2cosγ2.
IVX=I0V+IsinV sin2πσX,
I0V=|Rim|2+|Tim|2+|Rie|2+|Tie|2+2|Rim||Tim|cos 2θ2+|Rie||Tie|sin γ/γ,
IsinV=|Rom||Tom||Tim|2+|Rim|2cos 2θ2+|Roe||Toe||Tie|2+|Rie|2sinγ/2γ/2+2|Rom||Tom||Rim||Tim|+|Roe||Toe||Rie||Tie|cosγ/2.

Metrics