A new method for determining the transfer function of an Acousto optical tunable filter

A. Mahieux; V. Wilquet; R. Drummond; D. Belyaev; A. Federova; A.C. Vandaele

doi:10.1364/OE.17.002005

A new method for determining the transfer function of an Acousto optical tunable filter

A. Mahieux, V. Wilquet, R. Drummond, D. Belyaev, A. Federova, and A.C. Vandaele

Optics Express
Vol. 17,
Issue 3,
pp. 2005-2014
(2009)
•https://doi.org/10.1364/OE.17.002005

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A. Mahieux, V. Wilquet, R. Drummond, D. Belyaev, A. Federova, and A.C. Vandaele, "A new method for determining the transfer function of an Acousto optical tunable filter," Opt. Express 17, 2005-2014 (2009)

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Related Topics
Table of Contents Category
- Fourier optics and signal processing
Previously assigned OCIS codes
- Acousto-optical signal processing (070.1060)
- Absorption (300.1030)

About this Article
History
- Original Manuscript: November 13, 2008
- Revised Manuscript: December 22, 2008
- Manuscript Accepted: January 1, 2009
- Published: January 30, 2009

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Open Access

Abstract

The current study describes the determination of the transfer function of an Acousto Optical Tunable Filter from the in-flight solar observations of the SOIR instrument on board Venus Express. An approach is proposed in order to reconstruct the transfer function profile from the analysis of various solar lines. Moreover this technique allows the determination of the evolution of the transfer function as a function of the AOTF radio frequency.

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References

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Publication

D. Nevejans, E. Neefs, E. Van Ransbeeck, S. Berkenbosch, R. Clairquin, L. De Vos, W. Moelans, S. Glorieux, A. Baeke, O. Korablev, I. Vinogradov, Y. Kalinnikov, B. Bach, J.-P. Dubois, and E. Villard, “Compact high-resolution space-borne echelle grating spectrometer with AOTF based on order sorting for the infrared domain from 2.2 to 4.3 micrometer,” Appl. Opt. 45, 5191–5206 (2006).
[Crossref] [PubMed]
A. Mahieux, S. Berkenbosch, R. Clairquin, D. Fussen, N. Mateshvili, E. Neefs, D. Nevejans, B. Ristic, A. C. Vandaele, V. Wilquet, D. Belyaev, A. Fedorova, O. Korablev, E. Villard, F. Montmessin, and J.-L. Bertaux, “In-Flight performance and calibration of SPICAV SOIR on board Venus Express,” Appl. Opt. 47, 2252-65 (2008).
[Crossref] [PubMed]
J. L. Bertaux, D. Nevejans, O Korablev, E. Villard, E. Quemerais, E. Neefs, F. Montmessin, F. Leblanc, J. P. Dubois, and E. Dimarellis, “SPICAV on Venus Express: Three spectrometers to study the global structure and composition of the Venus atmosphere,” Planet. Space Sci. 55,1673–1700 (2007).
[Crossref]
D. V. Titov e. al., “Venus Express science planning,” Planetary and Space Science 54, 1279–1297 (2006).
[Crossref]
D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acousto-optic imaging spectropolarimetry for remote sensing,” Appl. Opt. 33, 7412–7424 (1994).
[Crossref] [PubMed]
J. Xu and R. Stroud, “Acousto-Optic devices,” John Wiley & Sons, Inc., New-York, 1992.
A. C. Vandaele, M. De Maziere, R. Drummond, A. Mahieux, E. Neefs, V. Wilquet, D. Belyaev, A. Fedorova, O. Korablev, F. Montmessin, and J.-L. Bertaux, “Composition of the Venus mesosphere measured by SOIR on board Venus Express,” J. Geophysic. Res., doi:10.1029/2008JE003140 (2008).
[Crossref]
M. S. Gottlieb, “Acousto-optical Tunable filter,” in Design and fabrication of acousto-optic devices, A. P. Goutzoulis, D. R. Pape, and S. V. Kulakov, eds., pp. 197–283, Marcel Dekker, New-York (1994).
F. Hase, P. Demoulin, A. J. Aauval, G C. Toon, P. F. Bernath, A. Goldman, J. W. Hannigan, and C. P. Rinsland, “An empirical line-by-line model for the infrared solar transmittance spectrum from 700 to 5000 cm4,” J. Quant. Spectrosc. Radiat. Transfer 102, 450–463 (2006).
[Crossref]

2008 (2)

A. Mahieux, S. Berkenbosch, R. Clairquin, D. Fussen, N. Mateshvili, E. Neefs, D. Nevejans, B. Ristic, A. C. Vandaele, V. Wilquet, D. Belyaev, A. Fedorova, O. Korablev, E. Villard, F. Montmessin, and J.-L. Bertaux, “In-Flight performance and calibration of SPICAV SOIR on board Venus Express,” Appl. Opt. 47, 2252-65 (2008).
[Crossref] [PubMed]

A. C. Vandaele, M. De Maziere, R. Drummond, A. Mahieux, E. Neefs, V. Wilquet, D. Belyaev, A. Fedorova, O. Korablev, F. Montmessin, and J.-L. Bertaux, “Composition of the Venus mesosphere measured by SOIR on board Venus Express,” J. Geophysic. Res., doi:10.1029/2008JE003140 (2008).
[Crossref]

2007 (1)

J. L. Bertaux, D. Nevejans, O Korablev, E. Villard, E. Quemerais, E. Neefs, F. Montmessin, F. Leblanc, J. P. Dubois, and E. Dimarellis, “SPICAV on Venus Express: Three spectrometers to study the global structure and composition of the Venus atmosphere,” Planet. Space Sci. 55,1673–1700 (2007).
[Crossref]

2006 (3)

D. V. Titov e. al., “Venus Express science planning,” Planetary and Space Science 54, 1279–1297 (2006).
[Crossref]

F. Hase, P. Demoulin, A. J. Aauval, G C. Toon, P. F. Bernath, A. Goldman, J. W. Hannigan, and C. P. Rinsland, “An empirical line-by-line model for the infrared solar transmittance spectrum from 700 to 5000 cm4,” J. Quant. Spectrosc. Radiat. Transfer 102, 450–463 (2006).
[Crossref]

D. Nevejans, E. Neefs, E. Van Ransbeeck, S. Berkenbosch, R. Clairquin, L. De Vos, W. Moelans, S. Glorieux, A. Baeke, O. Korablev, I. Vinogradov, Y. Kalinnikov, B. Bach, J.-P. Dubois, and E. Villard, “Compact high-resolution space-borne echelle grating spectrometer with AOTF based on order sorting for the infrared domain from 2.2 to 4.3 micrometer,” Appl. Opt. 45, 5191–5206 (2006).
[Crossref] [PubMed]

1994 (1)

D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acousto-optic imaging spectropolarimetry for remote sensing,” Appl. Opt. 33, 7412–7424 (1994).
[Crossref] [PubMed]

Aauval, A. J.

Bach, B.

Baeke, A.

Belyaev, D.

Bergstralh, J.

D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acousto-optic imaging spectropolarimetry for remote sensing,” Appl. Opt. 33, 7412–7424 (1994).
[Crossref] [PubMed]

Berkenbosch, S.

Bernath, P. F.

Bertaux, J. L.

Bertaux, J.-L.

Clairquin, R.

De Maziere, M.

De Vos, L.

Demoulin, P.

Dimarellis, E.

Drummond, R.

Dubois, J. P.

Dubois, J.-P.

Fedorova, A.

Fussen, D.

Glenar, D. A.

D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acousto-optic imaging spectropolarimetry for remote sensing,” Appl. Opt. 33, 7412–7424 (1994).
[Crossref] [PubMed]

Glorieux, S.

Goldman, A.

Gottlieb, M. S.

M. S. Gottlieb, “Acousto-optical Tunable filter,” in Design and fabrication of acousto-optic devices, A. P. Goutzoulis, D. R. Pape, and S. V. Kulakov, eds., pp. 197–283, Marcel Dekker, New-York (1994).

Hannigan, J. W.

Hase, F.

Hillman, J. J.

D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acousto-optic imaging spectropolarimetry for remote sensing,” Appl. Opt. 33, 7412–7424 (1994).
[Crossref] [PubMed]

Kalinnikov, Y.

Korablev, O

Korablev, O.

Leblanc, F.

Mahieux, A.

Mateshvili, N.

Moelans, W.

Montmessin, F.

Neefs, E.

Nevejans, D.

Quemerais, E.

Rinsland, C. P.

Ristic, B.

Saif, B.

D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acousto-optic imaging spectropolarimetry for remote sensing,” Appl. Opt. 33, 7412–7424 (1994).
[Crossref] [PubMed]

Stroud, R.

J. Xu and R. Stroud, “Acousto-Optic devices,” John Wiley & Sons, Inc., New-York, 1992.

Titov, D. V.

D. V. Titov e. al., “Venus Express science planning,” Planetary and Space Science 54, 1279–1297 (2006).
[Crossref]

Toon, G C.

Van Ransbeeck, E.

Vandaele, A. C.

Villard, E.

Vinogradov, I.

Wilquet, V.

Xu, J.

J. Xu and R. Stroud, “Acousto-Optic devices,” John Wiley & Sons, Inc., New-York, 1992.

Appl. Opt. (3)

D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acousto-optic imaging spectropolarimetry for remote sensing,” Appl. Opt. 33, 7412–7424 (1994).
[Crossref] [PubMed]

J. Geophysic. Res. (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

Planet. Space Sci. (1)

Planetary and Space Science (1)

D. V. Titov e. al., “Venus Express science planning,” Planetary and Space Science 54, 1279–1297 (2006).
[Crossref]

Other (2)

J. Xu and R. Stroud, “Acousto-Optic devices,” John Wiley & Sons, Inc., New-York, 1992.

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Fig. 1. SOIR optics. The AOTF (3) is located after the entrance optics (1 and 2). The echelle grating (7) diffracts the incoming light, which is recorded by the detector (10).

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Fig. 2. SOIR spectrum construction process. Panel A depicts the CO₂ absorption lines at 2.99 μm (corresponding to diffraction order 149) at a very high resolution. Panel B shows the CO₂ absorption lines convolved by the instrument function. The dotted line is the AOTF transfer function for the diffraction order 149. The vertical dashed lines between the arrows show the limits of each diffraction order. Panel C depicts the spectrum after multiplication by the AOTF transfer function, i.e. what reaches the echelle grating in terms of transmittance. Panel D shows the contribution of each diffracted spectrum after the echelle grating. The orders 146, 147, 151 and 152 have small contributions, but may not be neglected. Finally, the simulated transmittance is represented in panel E, and is the sum of all diffracted orders contributions.

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Fig. 3. Definition of the interval variation of the wn_0i. This is a plot of one sinc² function (the one noted ‘0’) to show how the position of the wn_0i is constrained using the value of fwhm₀ . The width of the arrows equals to fwhm₀ .

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Fig. 4. Description of the interaction between the global model and the local model

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Fig. 5. Convergence of the global model for bin 1 of binning 2×12. The convergence occurred after 482 steps. Panel A shows the convergence of the function minimized by the Simplex algorithm. Panels B and C show the convergence of parameters a _{FWMH
₀} and b _{FWMH
₀}, and panels D and E concern the convergence of a _{I
₁} and b _{I
₁}.

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Fig. 6. Fit of the 2943.70 cm^-1 solar line. Panel A shows the fit of the solar line at 2943.70 cm^-1 solar line. This line has been scanned three times, during orbits 142.2 (20060910), 474.1 (20070808) and 490.1 (20070824). The measured AOTF transfer functions are plotted as solid lines; the fitted functions are plotted as dashed lines. They depict the models described in Eq. 2. Panel B shows the residuals of the fit of the three solar lines. Panel C shows the 5 sinc² functions, and panel D shows the final AOTF transfer function, obtained from the model described in Eq. (1).

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Fig. 7. AOTF final functions retrieved for bin 1 (binning 2×12) for several orders.

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Tables (1)

Table 1: Example of coefficients set of the AOTF transfer function fit for bin 2 of the binning cases 2x16.

View Table

Equations (3)

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

AOTF (wn) = \sum_{i = - 2}^{2} max (0, I_{i}) \cdot {sinc}^{2} [0.886 \cdot \frac{(wn - w n_{0 i})}{fwh m_{i}}]

{AOTF}_{j} (wn) = \underset{AOTF (wn)}{\underset{︸}{\sum_{i = - 2}^{2} max (0, I_{i}) {sinc}^{2} [0.886 \cdot \frac{(wn - w n_{0 i})}{fwh m_{i}}]}} + α_{j} \cdot wn + β_{j}

X = a_{x} \cdot wn + b_{x}

a_fwhm00	1.620E-3	a_wn0-1	-2.877E-3	a_I0-0	0
b_fwhm00	1.780E1	b_wn0-1	-7.281E0	b_I0-0	1
a_fwhm0-1	4.813E-3	a_wn01	2.574E-3	a_I0-1	-1.145E-5
b_fwhm0-1	8.476E0	b_wn01	1.348E1	b_I0-1	1.267E-1
a_fwhm01	-2.046E-3	a_wn0-2	-6.597E-3	a_I01	-3.440E-5
b_fwhm01	3.345E1	b_wn0-2	-3.358E1	b_I01	1.950E-1
a_fwhm0-2	5.314E-3	a_wn02	2.619E-4	a_I0-2	4.641E-5
b_fwhm0-2	2.214E0	b_wn02	4.811E1	b_I0-2	-6.093E-2
a_fwhm02	6.592E-3	a_I00	1.936E-5	a_I02	-8.524E-5
b_fwhm02	1.345E1	b_I00	9.246E-1	b_I02	3.360E-1

Abstract

References

2008 (2)

2007 (1)

2006 (3)

1994 (1)

Aauval, A. J.

Bach, B.

Baeke, A.

Belyaev, D.

Bergstralh, J.

Berkenbosch, S.

Bernath, P. F.

Bertaux, J. L.

Bertaux, J.-L.

Clairquin, R.

De Maziere, M.

De Vos, L.

Demoulin, P.

Dimarellis, E.

Drummond, R.

Dubois, J. P.

Dubois, J.-P.

Fedorova, A.

Fussen, D.

Glenar, D. A.

Glorieux, S.

Goldman, A.

Gottlieb, M. S.

Hannigan, J. W.

Hase, F.

Hillman, J. J.

Kalinnikov, Y.

Korablev, O

Korablev, O.

Leblanc, F.

Mahieux, A.

Mateshvili, N.

Moelans, W.

Montmessin, F.

Neefs, E.

Nevejans, D.

Quemerais, E.

Rinsland, C. P.

Ristic, B.

Saif, B.

Stroud, R.

Titov, D. V.

Toon, G C.

Van Ransbeeck, E.

Vandaele, A. C.

Villard, E.

Vinogradov, I.

Wilquet, V.

Xu, J.

Appl. Opt. (3)

J. Geophysic. Res. (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

Planet. Space Sci. (1)

Planetary and Space Science (1)

Other (2)

Cited By

Figures (7)

Tables (1)

Equations (3)

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