Abstract

When using a high-resolution Fourier transform spectrometer (FTS) in a cube-corner configuration, subharmonic ghosts are observed in the spectrum. These ghosts are attributable to parasitic diffuse reflections on the mirrors of the FTS arm. The reflected beams skip a part of the interferometer and travel a different path from the main beam thus experiencing a smaller optomechanical gain. These reflections are present in the reference laser channel as well as on the measurement channel, and each affect the estimated spectrum differently. The sampling grid generated by the reference laser has periodic errors that are synchronized with the fringe signal. The measured spectrum can therefore exhibit sampling jitter ghosts at submultiples of the reference laser wavenumber in addition to its own additive subharmonics. The diffuse reflection experiencing the nominal optomechanical gain, such as in a plane-mirror configuration, will impact directly on the instrument line shape and on the radiometric accuracy of the spectrometer since some radiation is not propagating at the expected angles in the instrument.

© 2007 Optical Society of America

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References

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  1. J. W. Brault, "New approach to high-precision Fourier transform spectrometer design," Appl. Opt. 35, 2891-2896 (1996).
    [CrossRef] [PubMed]
  2. B. van Ginneken, M. Stavridi, and J. J. Koenderink, "Diffuse and specular reflectance from rough surfaces," Appl. Opt. 37, 130-139 (1998).
    [CrossRef]
  3. J. Genest and P. Tremblay, "Instrument line shape of Fourier-transform spectrometers: analytic solutions for nonuniformly illuminated off-axis detectors," Appl. Opt. 38, 5438-5446 (1999).
    [CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic layout of the interferometer. The diaphragms are added to reduce parasitic reflections that result in subharmonic ghosts.

Fig. 2
Fig. 2

Spectrum of a DFB laser at 1552.6   nm ( σ I R = 6441 cm 1 ) obtained with Brault's sampling algorithm by using a 632.8   nm He–Ne reference laser. Subharmonic ghosts caused by parasitic diffuse reflections are identified.

Fig. 3
Fig. 3

Fourier transform of the reference laser fringes without resampling and without diaphragms.

Fig. 4
Fig. 4

Simulated DFB laser spectrum with subharmonic ghosts [from Eqs. (1) and (2)].

Fig. 5
Fig. 5

Fourier transform of the reference laser fringes, without resampling. With the diaphragms the ghosts disappear.

Fig. 6
Fig. 6

Comparison of the instrument line shape with the theoretical cardinal sine (sinc).

Fig. 7
Fig. 7

Difference between the theoretical cardinal sine and the observed line shapes, showing some small distortions in the side lobes.

Tables (1)

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Table 1 Wavenumbers of the Measured and Calculated Peaks Present in the Infrared Spectrum

Equations (2)

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I G M I R ( Δ X o ) = A cos [ 2 π ( σ I R / 4 ) Δ X o ] + B cos [ 2 π ( σ I R / 2 ) Δ X o ] + C cos [ 2 π ( 3 σ I R / 4 ) Δ X o ] + D cos [ 2 π ( σ I R ) Δ X o ] + E cos [ 2 π ( 3 σ I R / 2 ) Δ X o ] + F cos [ 2 π ( 2 σ I R ) Δ X o ] ,
I G M ref ( Δ X o ) = G cos [ 2 π ( σ ref / 2 ) Δ X o ] + H cos [ 2 π ( σ ref ) Δ X o ] + I cos [ 2 π ( 3 σ ref / 2 ) Δ X o ] ,

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