Abstract

The detailed analysis of measured interferograms generally requires phase correction. Phase-shift correction methods are commonly used and well documented for conventional Fourier-transform spectroscopy. However, measured interferograms can show additional phase errors, depending on the optical path difference and signal frequency, which we call phase distortion. In spatial heterodyne spectroscopy they can be caused, for instance, by optical defects or image distortions, making them a characteristic of the individual spectrometer. They can generally be corrected without significant loss of the signal-to-noise ratio. We present a technique to measure phase distortion by using a measured example interferogram. We also describe a technique to correct for phase distortion and test its performance by using a simulation with a near-UV solar spectrum. We find that for our measured example interferogram the phase distortion is small and nearly frequency independent. Furthermore, we show that the presented phase-correction technique is especially effective for apodized interferograms.

© 2004 Optical Society of America

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References

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  1. J. M. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
    [CrossRef]
  2. J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, R. J. Reynolds, “Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, O. E. Siegmund, J. Vallerga, eds., Proc. SPIE2280, 310–319 (1994).
    [CrossRef]
  3. J. M. Harlander, F. L. Roesler, J. G. Cardon, C. R. Englert, R. R. Conway, “SHIMMER: a spatial heterodyne spectrometer for remote sensing of Earth’s middle atmosphere,” Appl. Opt. 41, 1343–1352 (2002).
    [CrossRef] [PubMed]
  4. B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
    [CrossRef]
  5. J. G. Cardon, C. R. Englert, J. M. Harlander, F. L. Roesler, M. H. Stevens, “SHIMMER on STS-112: development and proof-of-concept flight,” in AIAA Space 2003 Conference and Exposition (American Institute of Aeronautics and Astronautics, Reston, Va., 2003), AIAA paper 2003-6224.
  6. W. C. Martin, J. R. Fuhr, D. E. Kelleher, A. Musgrove, L. Podobedova, J. Reader, E. B. Saloman, C. J. Sansonetti, W. L. Wiese, P. J. Mohr, K. Olsen, “NIST Atomic Spectra Database (version 2.0, 1999),” http://physics.nist.gov/asd .
  7. M. L. Forman, W. H. Steel, G. V. Vanesse, “Correction of asymmetric interferograms obtained in Fourier spectroscopy,” J. Opt. Soc. Am. 56, 59–63 (1966).
    [CrossRef]
  8. J. W. Brault, “High precision Fourier transform spectroscopy: the critical role of phase correction,” Mikrochim. Acta 3, 215–227 (1987).
    [CrossRef]
  9. R. C. M. Learner, A. P. Thorne, I. Wynne-Jones, J. W. Brault, M. C. Abrams, “Phase correction of emission line Fourier transform spectra,” J. Opt. Soc. Am. A 12, 2165–2171 (1995).
    [CrossRef]
  10. D. B. Chase, “Phase correction in FT-IR,” Appl. Spectrosc. 36, 240–244 (1982).
    [CrossRef]
  11. R. L. Kurucz, I. Furenlid, J. Brault, L. Testerman, National Solar Observatory Atlas No. 1, (Harvard University, Cambridge, Mass., 1984).
  12. J. M. Harlander, F. L. Roesler, C. R. Englert, J. G. Cardon, R. R. Conway, C. M. Brown, J. Wimperis, “Robust monolithic ultraviolet interferometer for the SHIMMER instrument on STPSat-1,” Appl. Opt. 42, 2829–2834 (2003).
    [CrossRef] [PubMed]

2003 (1)

2002 (1)

1995 (1)

1992 (1)

J. M. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[CrossRef]

1987 (1)

J. W. Brault, “High precision Fourier transform spectroscopy: the critical role of phase correction,” Mikrochim. Acta 3, 215–227 (1987).
[CrossRef]

1982 (1)

1966 (1)

Abrams, M. C.

Berggren, R. R.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Brault, J.

R. L. Kurucz, I. Furenlid, J. Brault, L. Testerman, National Solar Observatory Atlas No. 1, (Harvard University, Cambridge, Mass., 1984).

Brault, J. W.

R. C. M. Learner, A. P. Thorne, I. Wynne-Jones, J. W. Brault, M. C. Abrams, “Phase correction of emission line Fourier transform spectra,” J. Opt. Soc. Am. A 12, 2165–2171 (1995).
[CrossRef]

J. W. Brault, “High precision Fourier transform spectroscopy: the critical role of phase correction,” Mikrochim. Acta 3, 215–227 (1987).
[CrossRef]

Brown, C. M.

Burgett, C. B.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Cardon, J. G.

Chase, D. B.

Conway, R. R.

Cooke, B. J.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Englert, C. R.

Forman, M. L.

Furenlid, I.

R. L. Kurucz, I. Furenlid, J. Brault, L. Testerman, National Solar Observatory Atlas No. 1, (Harvard University, Cambridge, Mass., 1984).

Goeller, R. M.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Harlander, J. M.

J. M. Harlander, F. L. Roesler, C. R. Englert, J. G. Cardon, R. R. Conway, C. M. Brown, J. Wimperis, “Robust monolithic ultraviolet interferometer for the SHIMMER instrument on STPSat-1,” Appl. Opt. 42, 2829–2834 (2003).
[CrossRef] [PubMed]

J. M. Harlander, F. L. Roesler, J. G. Cardon, C. R. Englert, R. R. Conway, “SHIMMER: a spatial heterodyne spectrometer for remote sensing of Earth’s middle atmosphere,” Appl. Opt. 41, 1343–1352 (2002).
[CrossRef] [PubMed]

J. M. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[CrossRef]

J. G. Cardon, C. R. Englert, J. M. Harlander, F. L. Roesler, M. H. Stevens, “SHIMMER on STS-112: development and proof-of-concept flight,” in AIAA Space 2003 Conference and Exposition (American Institute of Aeronautics and Astronautics, Reston, Va., 2003), AIAA paper 2003-6224.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, R. J. Reynolds, “Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, O. E. Siegmund, J. Vallerga, eds., Proc. SPIE2280, 310–319 (1994).
[CrossRef]

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Horton, R. F.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Howard, J. W.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Jaehnig, K. P.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, R. J. Reynolds, “Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, O. E. Siegmund, J. Vallerga, eds., Proc. SPIE2280, 310–319 (1994).
[CrossRef]

Kurucz, R. L.

R. L. Kurucz, I. Furenlid, J. Brault, L. Testerman, National Solar Observatory Atlas No. 1, (Harvard University, Cambridge, Mass., 1984).

LaDelfe, P. C.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Laubscher, B. E.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Learner, R. C. M.

Milligan, S.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Norton, P. R.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Obbink, G. M.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Reynolds, R. J.

J. M. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[CrossRef]

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, R. J. Reynolds, “Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, O. E. Siegmund, J. Vallerga, eds., Proc. SPIE2280, 310–319 (1994).
[CrossRef]

Roesler, F. L.

J. M. Harlander, F. L. Roesler, C. R. Englert, J. G. Cardon, R. R. Conway, C. M. Brown, J. Wimperis, “Robust monolithic ultraviolet interferometer for the SHIMMER instrument on STPSat-1,” Appl. Opt. 42, 2829–2834 (2003).
[CrossRef] [PubMed]

J. M. Harlander, F. L. Roesler, J. G. Cardon, C. R. Englert, R. R. Conway, “SHIMMER: a spatial heterodyne spectrometer for remote sensing of Earth’s middle atmosphere,” Appl. Opt. 41, 1343–1352 (2002).
[CrossRef] [PubMed]

J. M. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[CrossRef]

J. G. Cardon, C. R. Englert, J. M. Harlander, F. L. Roesler, M. H. Stevens, “SHIMMER on STS-112: development and proof-of-concept flight,” in AIAA Space 2003 Conference and Exposition (American Institute of Aeronautics and Astronautics, Reston, Va., 2003), AIAA paper 2003-6224.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, R. J. Reynolds, “Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, O. E. Siegmund, J. Vallerga, eds., Proc. SPIE2280, 310–319 (1994).
[CrossRef]

Sanders, W. T.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, R. J. Reynolds, “Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, O. E. Siegmund, J. Vallerga, eds., Proc. SPIE2280, 310–319 (1994).
[CrossRef]

Seo, S. M.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, R. J. Reynolds, “Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, O. E. Siegmund, J. Vallerga, eds., Proc. SPIE2280, 310–319 (1994).
[CrossRef]

Smith, B. W.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Steel, W. H.

Stegall, M.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Stevens, M. H.

J. G. Cardon, C. R. Englert, J. M. Harlander, F. L. Roesler, M. H. Stevens, “SHIMMER on STS-112: development and proof-of-concept flight,” in AIAA Space 2003 Conference and Exposition (American Institute of Aeronautics and Astronautics, Reston, Va., 2003), AIAA paper 2003-6224.

Testerman, L.

R. L. Kurucz, I. Furenlid, J. Brault, L. Testerman, National Solar Observatory Atlas No. 1, (Harvard University, Cambridge, Mass., 1984).

Thorne, A. P.

Tran, H. T.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, R. J. Reynolds, “Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, O. E. Siegmund, J. Vallerga, eds., Proc. SPIE2280, 310–319 (1994).
[CrossRef]

Vanesse, G. V.

Villeneuve, P. V.

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

Wimperis, J.

Wynne-Jones, I.

Appl. Opt. (2)

Appl. Spectrosc. (1)

Astrophys. J. (1)

J. M. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Mikrochim. Acta (1)

J. W. Brault, “High precision Fourier transform spectroscopy: the critical role of phase correction,” Mikrochim. Acta 3, 215–227 (1987).
[CrossRef]

Other (5)

R. L. Kurucz, I. Furenlid, J. Brault, L. Testerman, National Solar Observatory Atlas No. 1, (Harvard University, Cambridge, Mass., 1984).

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, R. J. Reynolds, “Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, O. E. Siegmund, J. Vallerga, eds., Proc. SPIE2280, 310–319 (1994).
[CrossRef]

B. E. Laubscher, B. W. Smith, B. J. Cooke, P. C. LaDelfe, R. R. Berggren, P. V. Villeneuve, R. M. Goeller, G. M. Obbink, S. Milligan, J. W. Howard, P. R. Norton, M. Stegall, C. B. Burgett, J. M. Harlander, R. F. Horton, “Infrared imaging spatial heterodyne spectrometer (IRISHS) experiment effort,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, X, G. C. Holst, ed., Proc. SPIE3701, 194–205 (1999).
[CrossRef]

J. G. Cardon, C. R. Englert, J. M. Harlander, F. L. Roesler, M. H. Stevens, “SHIMMER on STS-112: development and proof-of-concept flight,” in AIAA Space 2003 Conference and Exposition (American Institute of Aeronautics and Astronautics, Reston, Va., 2003), AIAA paper 2003-6224.

W. C. Martin, J. R. Fuhr, D. E. Kelleher, A. Musgrove, L. Podobedova, J. Reader, E. B. Saloman, C. J. Sansonetti, W. L. Wiese, P. J. Mohr, K. Olsen, “NIST Atomic Spectra Database (version 2.0, 1999),” http://physics.nist.gov/asd .

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the basic non-field-widened SHS configuration. The dashed lines illustrate an incoming wave front and the corresponding exiting wave fronts, which are crossed with an angle of 2γ. The ray bundle for one interferogram element is outlined, showing that only a small section of the interferometer and optics are used for any individual interferogram element. FTS, Fourier-transform spectrometer.

Fig. 2
Fig. 2

Black curve, power spectrum of a MnNe hollow-cathode lamp as measured by the SHIMMER-MIDDECK instrument versus spatial frequency of the recorded fringes. Gray curve, Gaussian functions (FWHM = 9.7 spectral elements) used to isolate individual emission lines in order to determine the frequency-dependent phase distortion.

Fig. 3
Fig. 3

Phase shift near the ZPD point for the four MnNe emission lines. The naming of the lines (A, B, C, D) follows from Fig. 2 and Table 2.

Fig. 4
Fig. 4

Bold, solid traces are the phase-shift-corrected total phase functions of the four MnNe emission lines listed in Table 2. The gray mesh is the phase plane that is fitted to the four phase functions. The two fit parameters are the Littrow wave number σ0, where the phase function is zero, and the parameter C, which is the linear slope increase of the phase functions with respect to the heterodyned wave number (σ0 - σ); see also Eq. (4).

Fig. 5
Fig. 5

Phase-shift-corrected phase distortion for the four emission lines listed in Table 2. All graphs are zero for pixel 0 owing to the phase-shift correction. The phase distortion does not show a significant frequency dependence (the curves basically fall on top of one another). The smoothness of the curves is caused by the narrow Gaussian isolation functions shown in Fig. 2. The phase distortion is small in the center of the detector array, and the maximum phase distortion is less than a fringe (2π), even for line D, which has the highest spatial frequency (∼467 fringes per detector width) of the four lines.

Fig. 6
Fig. 6

First simulation case: high spectral resolution and nonperiodic phase distortion. A: high-resolution solar spectrum multiplied with a typical interference filter transmittance. The leftmost, black mark indicates the Littrow frequency, and gray marks indicate the frequencies for which the phase-distortion functions are plotted in panel B. B: phase-distortion functions for the frequencies marked in panel A. C: black curve, real part of the uncorrected, phase-distorted spectrum. Gray, residuals between the uncorrected spectrum and the initial spectrum. D: black curve, phase-distortion-corrected spectrum. Gray, residuals between the phase-distortion-corrected spectrum and the initial spectrum multiplied by 10.

Fig. 7
Fig. 7

Second simulation case: high spectral resolution and periodic phase distortion. A: high-resolution solar spectrum multiplied with a typical interference filter transmittance. The leftmost, black mark indicates the Littrow frequency, and the gray marks indicate the frequencies for which the phase-distortion functions are plotted in panel B. B: phase-distortion functions for the frequencies marked in panel A. C: black curve, real part of the uncorrected, phase-distorted spectrum. Gray, residuals between the uncorrected spectrum and the initial spectrum. D: black curve, phase-distortion-corrected spectrum. Gray, residuals between the phase-distortion-corrected spectrum and the initial spectrum multiplied by 100. The residuals are more than an order of magnitude smaller than in the first simulation case (Fig. 6).

Fig. 8
Fig. 8

Third simulation case: lower spectral resolution and nonperiodic phase distortion. A: high-resolution solar spectrum convolved with the kernel ( 14, 12, 14), which is equivalent to an interferogram apodization with a Hanning function, multiplied with a typical interference filter transmittance. The leftmost, black mark indicates the Littrow frequency, and the gray marks indicate the frequencies for which the phase-distortion functions are plotted in panel B. B: phase-distortion functions for the frequencies marked in panel A. C: black curve, real part of the uncorrected, phase-distorted spectrum. Gray, residuals between the uncorrected spectrum and the initial spectrum multiplied by 10. D: black curve, phase-distortion-corrected spectrum. Gray, residuals between the phase-distortion-corrected spectrum and the initial spectrum multiplied by 100. The residuals are more than an order of magnitude smaller than in the first simulation case (Fig. 6) and well below the 1% level.

Tables (2)

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Table 1 Key Design Parameters of the SHIMMER-MIDDECK Instrument

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Table 2 Emission Lines Selected for This Study

Equations (9)

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Ix=- Aκ, xβκexpiκx+Φκ, x+exp-iκx+Φκ, xdκ.
Iκ0x=Aκ0, xβκ0expiκ0x+Φκ0, x+exp-iκ0x+Φκ0, x.
Iκ0x=Aκ0, xβκ0expiκ0x+Φκ0, x.
κ0x+Φκ0, x=arctanIκ0x/Iκ0x,
Ωσ, x=κσx=Cσ-σ0x.
Ix=- Aκ, xβκexpiκx+Aκ, xβκ×exp-iκx+2ϕxxdκ.
Gκκ=Fexp-iϕx, κ.
βCκ=- βUκGκκ-κdκ.
14, 12, 14

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