Abstract

An assessment is made of the spectral noise in Fourier-transform spectroscopy caused by sampling errors in the interferogram acquisition. Numerical evaluations are performed in the case of the REFIR (radiation explorer in the far infrared) instrument developed for the measurement of the long-wavelength Earth emissions from satellite platforms. In this case the slow response of a room-temperature pyroelectric detector, the relatively short acquisition time, the broadband operation, and the wish for a relaxed requirement of the mirror drive accuracy make sampling error an important issue. Different sampling methods can be considered for reduction of the spectral noise induced by sampling errors. The effects of different sampling methods are quantified and discussed for the selection of the most-suitable option for this instrument. We find that only sampling methods that introduce some compensation (either analog or digital) of the frequency dependence of amplitude and phase components of the acquisition-system responsivity provide satisfactory results. In particular, the equal time sampling followed by a digital filter and numerical resampling has been examined minutely with a simulation model used to perform sensitivity tests of the main parameters that characterize the procedure.

© 2001 Optical Society of America

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References

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    [CrossRef]
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1999 (3)

L. Palchetti, A. Barbis, J. E. Harries, D. Lastrucci, “Design and mathematical modelling of the space-borne far-infrared Fourier transform spectrometer for REFIR experiment,” Infrared Phys. Technol. 40, 367–377 (1999).
[CrossRef]

D. L. Cohen, “Performance degradation of a Michelson interferometer due to random sampling errors,” Appl. Opt. 38, 139–151 (1999).
[CrossRef]

B. Carli, A. Barbis, J. E. Harries, L. Palchetti, “Design of an efficient broadband far-infrared Fourier-transform spectrometer,” Appl. Opt. 38, 3945–3950 (1999).
[CrossRef]

1998 (1)

A. Barbis, B. Carli, U. Cortesi, A. Gignoli, “Optical path difference measurement for high-resolution Fourier spectrometer,” J. Opt. 29, 141–145 (1998).
[CrossRef]

1996 (2)

1979 (1)

1977 (1)

1975 (1)

1972 (1)

Aaronson, S. M.

Barbis, A.

L. Palchetti, A. Barbis, J. E. Harries, D. Lastrucci, “Design and mathematical modelling of the space-borne far-infrared Fourier transform spectrometer for REFIR experiment,” Infrared Phys. Technol. 40, 367–377 (1999).
[CrossRef]

B. Carli, A. Barbis, J. E. Harries, L. Palchetti, “Design of an efficient broadband far-infrared Fourier-transform spectrometer,” Appl. Opt. 38, 3945–3950 (1999).
[CrossRef]

A. Barbis, B. Carli, U. Cortesi, A. Gignoli, “Optical path difference measurement for high-resolution Fourier spectrometer,” J. Opt. 29, 141–145 (1998).
[CrossRef]

Bell, E. E.

Brault, J. W.

Carli, B.

B. Carli, A. Barbis, J. E. Harries, L. Palchetti, “Design of an efficient broadband far-infrared Fourier-transform spectrometer,” Appl. Opt. 38, 3945–3950 (1999).
[CrossRef]

A. Barbis, B. Carli, U. Cortesi, A. Gignoli, “Optical path difference measurement for high-resolution Fourier spectrometer,” J. Opt. 29, 141–145 (1998).
[CrossRef]

Cohen, D. L.

Connes, P.

Cortesi, U.

A. Barbis, B. Carli, U. Cortesi, A. Gignoli, “Optical path difference measurement for high-resolution Fourier spectrometer,” J. Opt. 29, 141–145 (1998).
[CrossRef]

Endemann, M.

M. Endemann, G. Lange, B. Fladt, “MIPAS for Envisat-1,” in Space Optics 1994: Earth Observation and Astronomy, G. Cerrutti-Maori, P. Roussel, eds., Proc. SPIE2209, 36–47 (1994).

Fladt, B.

M. Endemann, G. Lange, B. Fladt, “MIPAS for Envisat-1,” in Space Optics 1994: Earth Observation and Astronomy, G. Cerrutti-Maori, P. Roussel, eds., Proc. SPIE2209, 36–47 (1994).

Gignoli, A.

A. Barbis, B. Carli, U. Cortesi, A. Gignoli, “Optical path difference measurement for high-resolution Fourier spectrometer,” J. Opt. 29, 141–145 (1998).
[CrossRef]

Harries, J. E.

L. Palchetti, A. Barbis, J. E. Harries, D. Lastrucci, “Design and mathematical modelling of the space-borne far-infrared Fourier transform spectrometer for REFIR experiment,” Infrared Phys. Technol. 40, 367–377 (1999).
[CrossRef]

B. Carli, A. Barbis, J. E. Harries, L. Palchetti, “Design of an efficient broadband far-infrared Fourier-transform spectrometer,” Appl. Opt. 38, 3945–3950 (1999).
[CrossRef]

Lange, G.

M. Endemann, G. Lange, B. Fladt, “MIPAS for Envisat-1,” in Space Optics 1994: Earth Observation and Astronomy, G. Cerrutti-Maori, P. Roussel, eds., Proc. SPIE2209, 36–47 (1994).

Lastrucci, D.

L. Palchetti, A. Barbis, J. E. Harries, D. Lastrucci, “Design and mathematical modelling of the space-borne far-infrared Fourier transform spectrometer for REFIR experiment,” Infrared Phys. Technol. 40, 367–377 (1999).
[CrossRef]

Learner, R. C. M.

Michel, G.

Palchetti, L.

L. Palchetti, A. Barbis, J. E. Harries, D. Lastrucci, “Design and mathematical modelling of the space-borne far-infrared Fourier transform spectrometer for REFIR experiment,” Infrared Phys. Technol. 40, 367–377 (1999).
[CrossRef]

B. Carli, A. Barbis, J. E. Harries, L. Palchetti, “Design of an efficient broadband far-infrared Fourier-transform spectrometer,” Appl. Opt. 38, 3945–3950 (1999).
[CrossRef]

Sanderson, R. B.

Thorne, A. P.

Zachor, A. S.

Appl. Opt. (8)

Infrared Phys. Technol. (1)

L. Palchetti, A. Barbis, J. E. Harries, D. Lastrucci, “Design and mathematical modelling of the space-borne far-infrared Fourier transform spectrometer for REFIR experiment,” Infrared Phys. Technol. 40, 367–377 (1999).
[CrossRef]

J. Opt. (1)

A. Barbis, B. Carli, U. Cortesi, A. Gignoli, “Optical path difference measurement for high-resolution Fourier spectrometer,” J. Opt. 29, 141–145 (1998).
[CrossRef]

Other (1)

M. Endemann, G. Lange, B. Fladt, “MIPAS for Envisat-1,” in Space Optics 1994: Earth Observation and Astronomy, G. Cerrutti-Maori, P. Roussel, eds., Proc. SPIE2209, 36–47 (1994).

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Figures (12)

Fig. 1
Fig. 1

Earth’s spectral radiance expected at TOA.

Fig. 2
Fig. 2

NESR requirement (solid curve) and NESR value corresponding to SNR = 100 (dashed curve) for the REFIR instrument.

Fig. 3
Fig. 3

n s due to position error in the case of ETS (solid curve) compared with NESR requirement for the REFIR experiment (dashed curve).

Fig. 4
Fig. 4

n s due to speed error (solid curve) and to phase contribution of the speed error only (dotted curve) in the case of ESS with delay compensation (time delay t c = 2.2 µs) compared with NESR requirement (dashed cuve).

Fig. 5
Fig. 5

n s due to speed error in the case of ESS (solid curve) with electronic frequency compensation of the detector response (high-pass circuit and fifth-order Butterworth-type filter, both at 4 kHz) compared with NESR requirement (dashed curve).

Fig. 6
Fig. 6

Diagram of data acquisition in the ETS with digital filter and numerical resampling.

Fig. 7
Fig. 7

n s in the case of ETS with digital filter and numerical resampling (solid curve) compared with NESR requirement (dashed curve).

Fig. 8
Fig. 8

Average spectral noise as a function of the oversampling factor.

Fig. 9
Fig. 9

Average spectral noise as a function of the number of zeros in the sinc function used for resampling the interferogram (scanning prolongation).

Fig. 10
Fig. 10

Average spectral noise as a function of the error on the detector cut-off frequency.

Fig. 11
Fig. 11

Average spectral noise as a function of the clock frequency.

Fig. 12
Fig. 12

Average spectral noise as a function of the bit resolution.

Equations (8)

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

I ξ=-+ σuSσexp2πiσξdσ,
xax=x+Δxx, vax=v+Δvx.
Imx=-+ σvSσexp2πiσxdσ+i2πΔxx-+ σvSσσ exp2πiσxdσ+Δvx-+ σvSσσ exp2πiσxdσ,
Smσ=S0σ+Speσ+Sseσ,
S0σ=σvSσ*IBσσv, Speσ=i2π σvSσσ*xσ*IBσ|σv, Sseσ=σvSσσ*vσ*IBσ|σv.
nsσ=|Smσ-Sσ|.
(f)=Afexpiϕf-2πitcf,
Aσvexpiϕσv-2πitcfSσσ+iϕσv-2πtcσvSσσσv*vσ*IBσ.

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