Abstract

Ghosts in Fourier-transform spectrometry are important for three reasons: they can give rise to spurious coincidences of frequency differences in spectral analysis, distort the phase correction, and set a limit to the attainable signal-to-noise ratio. The various types of ghost, originating from amplitude modulation, phase modulation, and intermodulation, are described and discussed, together with some hardware and software artifacts. Recipes are given for identifying these features and, where possible, avoiding harmful effects from them.

© 1996 Optical Society of America

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References

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  1. M. C. Hutley, Diffraction Gratings (Academic, London, 1982), pp. 49–51, 78, 142–151.
  2. G. Guelachvili, “Distortions in Fourier spectra and diagnosis,” in Spectrometric Techniques II, G. A. Vanasse, ed. (Academic, London, 1981), pp. 1–62.
  3. 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]
  4. J. W. Brault, “Solar Fourier transform spectroscopy,” Oss. e Mem. dell Oss. Astrofis. di Arcetri 106, 33–50 (1978).
  5. A. P. Thorne, C. J. Harris, I. Wynne-Jones, R. C. M. Learner, G. Cox, “A Fourier transform spectrometer for the vacuum ultraviolet: design and performance,” J. Phys. E 20, 54–60 (1987).
    [CrossRef]
  6. J. W. Brault, “Fourier transform spectrometry,” in Proceedings of the Fifteenth Advanced Course of the Swiss Society of Astronomy and Astrophysics, A. O. Benz, M. C. E. Huber, M. Mayor, eds, Saas Fee, 1985 (Souverny, Observatoire de Genève, 1985), pp. 1–61.

1995 (1)

1987 (1)

A. P. Thorne, C. J. Harris, I. Wynne-Jones, R. C. M. Learner, G. Cox, “A Fourier transform spectrometer for the vacuum ultraviolet: design and performance,” J. Phys. E 20, 54–60 (1987).
[CrossRef]

1978 (1)

J. W. Brault, “Solar Fourier transform spectroscopy,” Oss. e Mem. dell Oss. Astrofis. di Arcetri 106, 33–50 (1978).

Abrams, M. C.

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, “Solar Fourier transform spectroscopy,” Oss. e Mem. dell Oss. Astrofis. di Arcetri 106, 33–50 (1978).

J. W. Brault, “Fourier transform spectrometry,” in Proceedings of the Fifteenth Advanced Course of the Swiss Society of Astronomy and Astrophysics, A. O. Benz, M. C. E. Huber, M. Mayor, eds, Saas Fee, 1985 (Souverny, Observatoire de Genève, 1985), pp. 1–61.

Cox, G.

A. P. Thorne, C. J. Harris, I. Wynne-Jones, R. C. M. Learner, G. Cox, “A Fourier transform spectrometer for the vacuum ultraviolet: design and performance,” J. Phys. E 20, 54–60 (1987).
[CrossRef]

Guelachvili, G.

G. Guelachvili, “Distortions in Fourier spectra and diagnosis,” in Spectrometric Techniques II, G. A. Vanasse, ed. (Academic, London, 1981), pp. 1–62.

Harris, C. J.

A. P. Thorne, C. J. Harris, I. Wynne-Jones, R. C. M. Learner, G. Cox, “A Fourier transform spectrometer for the vacuum ultraviolet: design and performance,” J. Phys. E 20, 54–60 (1987).
[CrossRef]

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, London, 1982), pp. 49–51, 78, 142–151.

Learner, R. C. M.

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]

A. P. Thorne, C. J. Harris, I. Wynne-Jones, R. C. M. Learner, G. Cox, “A Fourier transform spectrometer for the vacuum ultraviolet: design and performance,” J. Phys. E 20, 54–60 (1987).
[CrossRef]

Thorne, A. P.

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]

A. P. Thorne, C. J. Harris, I. Wynne-Jones, R. C. M. Learner, G. Cox, “A Fourier transform spectrometer for the vacuum ultraviolet: design and performance,” J. Phys. E 20, 54–60 (1987).
[CrossRef]

Wynne-Jones, I.

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]

A. P. Thorne, C. J. Harris, I. Wynne-Jones, R. C. M. Learner, G. Cox, “A Fourier transform spectrometer for the vacuum ultraviolet: design and performance,” J. Phys. E 20, 54–60 (1987).
[CrossRef]

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

J. Phys. E (1)

A. P. Thorne, C. J. Harris, I. Wynne-Jones, R. C. M. Learner, G. Cox, “A Fourier transform spectrometer for the vacuum ultraviolet: design and performance,” J. Phys. E 20, 54–60 (1987).
[CrossRef]

Oss. e Mem. dell Oss. Astrofis. di Arcetri (1)

J. W. Brault, “Solar Fourier transform spectroscopy,” Oss. e Mem. dell Oss. Astrofis. di Arcetri 106, 33–50 (1978).

Other (3)

J. W. Brault, “Fourier transform spectrometry,” in Proceedings of the Fifteenth Advanced Course of the Swiss Society of Astronomy and Astrophysics, A. O. Benz, M. C. E. Huber, M. Mayor, eds, Saas Fee, 1985 (Souverny, Observatoire de Genève, 1985), pp. 1–61.

M. C. Hutley, Diffraction Gratings (Academic, London, 1982), pp. 49–51, 78, 142–151.

G. Guelachvili, “Distortions in Fourier spectra and diagnosis,” in Spectrometric Techniques II, G. A. Vanasse, ed. (Academic, London, 1981), pp. 1–62.

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Figures (7)

Fig. 1
Fig. 1

Spectrum of an inadequately smoothed sodium lamp, taken with the IC FT spectrometer at two different scanning speeds: (a) 0.747 mm/s, (b) 0.424 mm/s. The separation of the 100-Hz modulation ghosts and their widths is inversely proportional to the scan speed, whereas the amplitudes are proportional to the speed.

Fig. 2
Fig. 2

Phase ghosts in a spectrum taken with the NSO FT spectrometer. The positions of the various ghosts are shown schematically in (a); the actual ghosts either side of the 10,351-cm−1 Ar I line are shown in (b), and the same set on either side of the 10,837-cm−1 Ar I line in (c). The light source was a high-current argon-iron hollow-cathode lamp, and the two Ar I lines have intensities of 125,000 and 100,000 on a scale for which the rms noise in regions well away from strong lines is unity. The height of each box is ±50 on this scale, and its width is 400 mHz, or 3.7 cm−1.

Fig. 3
Fig. 3

Low-frequency phase noise from the same spectrum as Fig. 2 at the bases of the two strong Ar I lines (a) 10,351 cm−1, (b) 10,837 cm−1. The intensity scale is linear over the range ±10 and logarithmic thereafter. The +190-mHz ghost of the 10,351-cm−1 line is overlaid by an emission line.

Fig. 4
Fig. 4

Schematic diagram of third-order intermodulation ghosts from three strong lines, A, B, and C.

Fig. 5
Fig. 5

Intermodulation ghosts from the same spectrum as Figs. 2 and 3. (a) and (b) show third-order ghosts from four strong lines A, B, C, and D, mixed three at a time in (a) and two at a time in (b); (c) shows some examples of fifth-order ghosts from four lines. The four lines generating the ghosts are (on the same intensity scale as Fig. 2) A = 10,958 cm−1, intensity 120,000 (self-absorbed); B = 10,838 cm−1, intensity 100,000; C = 10,351 cm−1, intensity 125,000; D = 10,217 cm−1, intensity 54,000. Note the flat tops of all ghosts involving the self-absorbed line A, except where it enters twice to produce a triangle.

Fig. 6
Fig. 6

Illustration of three problems in phase correction. (a) shows a phase spectrum in the UV region (42,600 to 56,900 cm−1, taken in fourth alias on the IC FT spectrometer in which a dot shows the phase of each spectral point above the discriminator, and the length of the line above it is proportional to the logarithm of the modulus of the intensity of that point. The plot shows (i) a 2π phase flip between the real lines at top left and those at center bottom, (ii) lines folded back from the third alias at the left of the bottom half, and (iii) laser ghosts of strong lines at longer wavelength toward the right of the top half. The parents of most of these ghosts have been suppressed by the antialiasing filter and are therefore not folded back, but the point marked G is the laser ghost of a strong line P outside the alias that is folded back at F. The lines F and G are plotted in (b) to show that they are faithful reproductions of the parent line P, which is shown plotted from a different spectrum in (c).

Fig. 7
Fig. 7

Example of the malign influence of one strong bad point on phase correction, plotted in the same way as Fig. 6. (a) shows the raw phase from lines above the discriminator in a third alias spectrum from 35,500 to 53,300 cm−1, with one point from the second alias very close to the left-hand side. Plot (b) shows the fitted phase polynomial when this bad point is removed: the phase curve is almost a straight line, and the corrected phase points all lie very close to zero. In (c) the phase has been fitted without removing the bad point: the phase polynomial has been forced into a cubic, and most of the lines have corrected phases significantly different from zero.

Tables (1)

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Table 1 Nine Ghosts from Mixing of Three Frequencies: Δ1 = σ A − σ B , Δ2 = σ B − σ C , Δ3 = σ A − σ C

Equations (13)

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f = v σ ,
Ghost amplitude Parent amplitude = π σ 0 α Δ ~ α .
δ ( Δ x ) = Δ t ( δ v ) .
I out = α I in + β I in 2 + γ I in 3 + .
δ ϕ 1 / ( SNR ) .
I ( x ) [ 1 + ( x ) ] = I ( x ) + I ( x ) ( x ) S ( σ ) + S ( σ ) * E ( σ ) ,
( x ) = e ( x ) + o ( x ) E ( σ ) = E e ( σ ) + i E o ( σ ) ,
S obs ( σ ) = S ( σ ) + [ S ( σ ) * E e ( σ ) ] .
I [ x + ( x ) ] I ( x ) + I ( x ) ( x ) .
I ( x ) S ( σ ) ,
I ( x ) 2 π i σ S ( σ ) .
I ( x + ) S ( σ ) + [ 2 π i σ S ( σ ) ] * E ( σ ) .
S obs ( σ ) = S ( σ ) - 2 π [ σ S ( σ ) ] * E o ( σ ) S ( σ ) - 2 π σ [ S ( σ ) * E o ( σ ) ] .

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