Abstract

Spatial heterodyne spectroscopy (SHS) is a Fourier-transform spectroscopic technique that simultaneously records all path differences using a detector array. Compared to conventional Fourier-transform spectroscopy that measures interferogram samples sequentially in the time domain, SHS is insensitive to a changing scene; however, the effects caused by differences in the detector elements and∕or the optics for each sample must be addressed with a flatfield correction. The flatfield correction is typically a characteristic of the instrument and does not change with the observed scene. We present three different flatfielding approaches. Each is based on different assumptions and is applicable depending on the instrumental effects dominating the flatfield.

© 2006 Optical Society of America

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  1. P. Cheben, I. Powell, S. Janz, and D. Xu, "Wavelength-dispersive device based on a Fourier-transform Michelson-type arrayed waveguide grating," Opt. Lett. 30, 1824-1826 (2005).
    [CrossRef] [PubMed]
  2. J. M. Harlander, R. J. Reynolds, and 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]
  3. J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, and 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 of Astronomy V, O. E. Siegmund and J.Vallerga, eds., Proc. SPIE 2280, 310-319 (1994).
  4. J. M. Harlander, F. L. Roesler, J. G. Cardon, C. R. Englert, and R. R. Conway, "SHIMMER: A spatial heterodyne spectrometer for remote sensing of Earth's middle Atmosphere," Appl. Opt. 41, 1343-1352 (2002).
    [CrossRef] [PubMed]
  5. J. M. Harlander, "Spatial heterodyne spectroscopy: interferometric performance at any wavelength without scanning," Ph.D. dissertation (University of Wisconsin-Madison, 1991).
  6. C. R. Englert, J. M. Harlander, J. G. Cardon, and F. L. Roesler, "Correction of phase distortion in spatial heterodyne spectroscopy," Appl. Opt. 43, 6680-6687 (2004).
    [CrossRef]
  7. J. M. Harlander, F. L. Roesler, C. R. Englert, J. G. Cardon, R. R. Conway, C. M. Brown, and J. Wimperis. "Robust monolithic ultraviolet interferometer for the SHIMMER instrument on STPSat-1," Appl. Opt. 42, 2829-2834 (2003).
    [CrossRef] [PubMed]
  8. C. R. Englert, J. T. Bays, J. C. Owrutsky, and J. M. Harlander, "SHIM-fire breadboard instrument design, integration and first measurements," NRL Memorandum Report NRL/MR/7640-05- 8926 (Naval Research Laboratory, 2005).

2005 (1)

2004 (1)

2003 (1)

2002 (1)

1992 (1)

J. M. Harlander, R. J. Reynolds, and 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]

Bays, J. T.

C. R. Englert, J. T. Bays, J. C. Owrutsky, and J. M. Harlander, "SHIM-fire breadboard instrument design, integration and first measurements," NRL Memorandum Report NRL/MR/7640-05- 8926 (Naval Research Laboratory, 2005).

Brown, C. M.

Cardon, J. G.

Cheben, P.

Conway, R. R.

Englert, C. R.

Harlander, J. M.

C. R. Englert, J. M. Harlander, J. G. Cardon, and F. L. Roesler, "Correction of phase distortion in spatial heterodyne spectroscopy," Appl. Opt. 43, 6680-6687 (2004).
[CrossRef]

J. M. Harlander, F. L. Roesler, C. R. Englert, J. G. Cardon, R. R. Conway, C. M. Brown, and 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, and 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, and 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, and 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 of Astronomy V, O. E. Siegmund and J.Vallerga, eds., Proc. SPIE 2280, 310-319 (1994).

C. R. Englert, J. T. Bays, J. C. Owrutsky, and J. M. Harlander, "SHIM-fire breadboard instrument design, integration and first measurements," NRL Memorandum Report NRL/MR/7640-05- 8926 (Naval Research Laboratory, 2005).

J. M. Harlander, "Spatial heterodyne spectroscopy: interferometric performance at any wavelength without scanning," Ph.D. dissertation (University of Wisconsin-Madison, 1991).

Jaehnig, K. P.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, and 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 of Astronomy V, O. E. Siegmund and J.Vallerga, eds., Proc. SPIE 2280, 310-319 (1994).

Janz, S.

Owrutsky, J. C.

C. R. Englert, J. T. Bays, J. C. Owrutsky, and J. M. Harlander, "SHIM-fire breadboard instrument design, integration and first measurements," NRL Memorandum Report NRL/MR/7640-05- 8926 (Naval Research Laboratory, 2005).

Powell, I.

Reynolds, R. J.

J. M. Harlander, R. J. Reynolds, and 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, and 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 of Astronomy V, O. E. Siegmund and J.Vallerga, eds., Proc. SPIE 2280, 310-319 (1994).

Roesler, F. L.

C. R. Englert, J. M. Harlander, J. G. Cardon, and F. L. Roesler, "Correction of phase distortion in spatial heterodyne spectroscopy," Appl. Opt. 43, 6680-6687 (2004).
[CrossRef]

J. M. Harlander, F. L. Roesler, C. R. Englert, J. G. Cardon, R. R. Conway, C. M. Brown, and 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, and 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, and 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, and 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 of Astronomy V, O. E. Siegmund and J.Vallerga, eds., Proc. SPIE 2280, 310-319 (1994).

Sanders, W. T.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, and 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 of Astronomy V, O. E. Siegmund and J.Vallerga, eds., Proc. SPIE 2280, 310-319 (1994).

Seo, S. M.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, and 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 of Astronomy V, O. E. Siegmund and J.Vallerga, eds., Proc. SPIE 2280, 310-319 (1994).

Tran, H. T.

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, and 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 of Astronomy V, O. E. Siegmund and J.Vallerga, eds., Proc. SPIE 2280, 310-319 (1994).

Wimperis, J.

Xu, D.

Appl. Opt. (3)

Astrophys. J. (1)

J. M. Harlander, R. J. Reynolds, and 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]

Opt. Lett. (1)

Other (3)

C. R. Englert, J. T. Bays, J. C. Owrutsky, and J. M. Harlander, "SHIM-fire breadboard instrument design, integration and first measurements," NRL Memorandum Report NRL/MR/7640-05- 8926 (Naval Research Laboratory, 2005).

J. M. Harlander, H. T. Tran, F. L. Roesler, K. P. Jaehnig, S. M. Seo, W. T. Sanders, and 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 of Astronomy V, O. E. Siegmund and J.Vallerga, eds., Proc. SPIE 2280, 310-319 (1994).

J. M. Harlander, "Spatial heterodyne spectroscopy: interferometric performance at any wavelength without scanning," Ph.D. dissertation (University of Wisconsin-Madison, 1991).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of basic non-field-widened SHS configuration. The dashed lines illustrate incoming wavefronts and the corresponding exiting wavefronts that are crossed with an angle of 2γ. The ray bundle for two interferogram samples is outlined showing that only a small section of the interferometer and optics is used for any individual interferogram sample.

Fig. 2
Fig. 2

Interferometer of the visible∕near-infrared breadboard instrument. The input is on the lower left-hand side of the cubic beam splitter. The gratings are mounted using commercial three-point mounts. The grating on the right is mounted on a translation stage and can be moved away or toward the beam splitter. All the components of this breadboard spectrometer are commercially available (see also Table 1).

Fig. 3
Fig. 3

Top panel: raw monochromatic interferogram (black) and the nonmodulated signal (gray) measured by blocking one interferometer arm at a time and adding the two measurements. Center panel: interferogram after application of the balanced arm flatfielding method. Bottom panel: real (black) and imaginary (gray) parts of the spectrum calculated from the corrected interferogram by phase correction, zero filling, and Fourier transformation. Since an unresolved line source was used for this measurement, the spectrum represents the instrumental line shape function.

Fig. 4
Fig. 4

Top panel: nonmodulated interferogram components measured with one arm blocked. Center panel: correction factor for the multiplicative term of the modulated interferometer part that is caused by the unbalanced arm contributions. Bottom panel: corrected interferogram.

Fig. 5
Fig. 5

Top panel: raw interferograms for three different grating locations resulting in a phase shift for each interferogram. Center panel: nonmodulated interferogram part (black) and the envelope of the modulated interferogram part (gray) as calculated from the raw interferograms. Bottom panel: corrected interferogram.

Fig. 6
Fig. 6

Top panel: nonmodulated interferogram part (black) and the envelope of the modulated interferogram part (gray) as in the center panel of Fig. 5 but for the entire interferogram. Center panel: corrected interferogram. Bottom panel: real part of the corrected spectrum and the difference between the corrected and uncorrected spectrum multiplied by 10.

Tables (1)

Tables Icon

Table 1 Key Design Parameters of the Visible∕Near-Infrared SHS Breadboard Instrument

Equations (16)

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I ( x ) = 1 2 0 B σ ( σ ) [ 1 + cos { 2 π [ 4 ( σ σ 0 ) tan θ L ] x } ] d σ ,
I ( x ) = 1 2 0 B ( κ ) [ 1 + cos { 2 π κ x } ] d κ ,
I ( x ) = 0 B ( κ ) { t A 2 ( x , κ ) + t B 2 ( x , κ ) + 2 ε ( x , κ ) t A ( x , κ ) t B ( x , κ ) × cos [ 2 π κ x + Θ ( x , κ ) ] } d κ ,
I ( x ) = 0 B ( κ ) R ( κ ) { t A       2 ( x ) + t B       2 ( x ) + 2 ε ( x , κ ) t A ( x ) t B ( x ) cos [ 2 π κ x + Θ ( x , κ ) ] } d κ ,
I ( x ) = 0 B ( κ ) R ( κ ) [ t A 2 ( x ) + t B 2 ( x ) ] d κ + 0 2 B ( κ ) R ( κ ) ε ( x , κ ) t A ( x ) t B ( x ) cos [ 2 π κ x + Θ ( x , κ ) ] d κ Nonmodulated term Modulated term
I U ( x ) = 0 B a ( κ ) R ( κ ) [ t A 2 ( x ) + t B 2 ( x ) ] d κ = [ t A 2 ( x ) + t B 2 ( x ) ] 0 B a ( κ ) R ( κ ) d κ = C 1 [ t A 2 ( x ) + t B 2 ( x ) ] ,
I ( x ) I U ( x ) = C 2 + 1 C 1 0 B ( κ ) R ( κ ) × { 2 ε ( x , κ ) t A ( x ) t B ( x ) t A 2 ( x ) + t B 2 ( x ) × cos [ 2 π κ x + Θ ( x , κ ) ] } d κ ,
I ( x ) I U ( x ) = C 2 + 1 C 1 0 { B ( κ ) R ( κ ) ε ( x , κ ) × cos [ 2 π κ x + Θ ( x , κ ) ] } d κ .
0 B ( κ ) R ( κ ) { 2 ε ( x , κ ) t A ( x ) t B ( x ) t A 2 ( x ) + t B 2 ( x ) × cos [ 2 π κ x + Θ ( x , κ ) ] } d κ x = 0.
I A ( x ) = 0 B a ( κ ) R ( κ ) t A 2 ( x ) d κ = t A 2 ( x ) 0 B a ( κ ) R ( κ ) d κ = C 1 t A 2 ( x ) ,
I B ( x ) = 0 B a ( κ ) R ( κ ) t B       2 ( x ) d κ = t B       2 ( x ) 0 B a ( κ ) R ( κ ) d κ = C 1 t B       2 ( x ) .
I ( x ) I A ( x ) + I B ( x ) = C 2 + 1 C 1 0 B ( κ ) R ( κ ) 2 ε ( x , κ ) t A ( x ) t B ( x ) t A 2 ( x ) + t B 2 ( x ) cos [ 2 πκ x + Θ ( x , κ ) ] . Modulated  term
I C ( x ) = 1 C 1 0 B ( κ ) R ( κ ) ε ( x , κ ) cos [ 2 π κ x + Θ ( x , κ ) ] d κ .
I i ( x ) = B ( κ 0 ) R ( κ 0 ) { t A 2 ( x ) + t B 2 ( x ) + 2 ε ( x , κ 0 ) t A ( x ) × t B ( x ) cos [ 2 π κ 0 x + Θ ( x , κ ) + φ i ] } = N ( x , κ 0 ) + M ( x , κ 0 ) cos [ 2 π κ 0 x + Θ ( x , κ ) + φ i ] , i = 1 , 2 , 3 φ 1 φ 2 φ 3 .
M ( x , κ 0 ) = I i ( x ) I j ( x ) cos Φ i ( x ) cos Φ j ( x ) , i j ,
N ( x , κ 0 ) = I 1 ( x ) M ( x , κ 0 ) cos Φ 1 ( x ) ,

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