Abstract

The Earth’s thermosphere plays a critical role in driving electrodynamic processes in the ionosphere and in transferring solar energy to the atmosphere, yet measurements of thermospheric state parameters, such as wind and temperature, are sparse. One of the most popular techniques for measuring these parameters is to use a Fabry–Perot interferometer to monitor the Doppler width and breadth of naturally occurring airglow emissions in the thermosphere. In this work, we present a technique for estimating upper-atmospheric winds and temperatures from images of Fabry–Perot fringes captured by a CCD detector. We estimate instrument parameters from fringe patterns of a frequency-stabilized laser, and we use these parameters to estimate winds and temperatures from airglow fringe patterns. A unique feature of this technique is the model used for the laser and airglow fringe patterns, which fits all fringes simultaneously and attempts to model the effects of optical defects. This technique yields accurate estimates for winds, temperatures, and the associated uncertainties in these parameters, as we show with a Monte Carlo simulation.

© 2014 Optical Society of America

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References

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  1. R. Heelis, “Electrodynamics in the low and middle latitude ionosphere: a tutorial,” J. Atmos. Sol. Terr. Phys. 66, 825–838 (2004).
    [CrossRef]
  2. E. Kudeki, A. Akgiray, M. Milla, J. Chau, and D. L. Hysell, “Equatorial spread-F initiation: Post-sunset vortex, thermospheric winds, gravity waves,” J. Atmos. Sol. Terr. Phys. 69, 2416–2427 (2007).
    [CrossRef]
  3. T. J. Fuller-Rowell, M. V. Codrescu, R. J. Moffett, and S. Quegan, “Response of the thermosphere and ionosphere to geomagnetic storms,” J. Geophys. Res. 99, 3893 (1994).
    [CrossRef]
  4. M. Biondi, D. P. Sipler, M. E. Zipf, and J. L. Baumgardner, “All-sky Doppler interferometer for thermospheric dynamics studies,” Appl. Opt. 34, 1646–1654 (1995).
    [CrossRef]
  5. G. Hernandez, Fabry-Perot Interferometers, Cambridge Studies in Modern Optics (Cambridge University, 1988).
  6. C. G. M. Brum, C. A. Tepley, J. T. Fentzke, E. Robles, P. T. dos Santos, and S. A. Gonzalez, “Long-term changes in the thermospheric neutral winds over Arecibo: climatology based on over three decades of Fabry-Perot observations,” J. Geophys. Res. 117, A00H14 (2012).
    [CrossRef]
  7. T. Killeen and P. Hays, “Doppler line profile analysis for a multichannel Fabry-Perot interferometer,” Appl. Opt. 23, 612–620 (1984).
    [CrossRef]
  8. J. J. Makela, J. W. Meriwether, Y. Huang, and P. J. Sherwood, “Simulation and analysis of a multi-order imaging Fabry-Perot interferometer for the study of thermospheric winds and temperatures,” Appl. Opt. 50, 4403–4416 (2011).
    [CrossRef]
  9. K. Shiokawa, T. Kadota, M. K. Ejiri, Y. Otsuka, Y. Katoh, M. Satoh, and T. Ogawa, “Three-channel imaging fabry-perot interferometer for measurement of mid-latitude airglow,” Appl. Opt. 40, 4286–4296 (2001).
    [CrossRef]
  10. M. Conde, “Deriving wavelength spectra from fringe images from a fixed-gap single-etalon Fabry-Perot spectrometer,” Appl. Opt. 41, 2672–2678 (2002).
    [CrossRef]
  11. K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
    [CrossRef]
  12. J. J. Makela, J. W. Meriwether, J. Lima, E. S. Miller, and S. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
    [CrossRef]
  13. P. B. Hays and R. G. Roble, “A technique for recovering Doppler line profiles from Fabry-Perot interferometer fringes of very low intensity,” Appl. Opt. 10, 193–200 (1971).
    [CrossRef]
  14. S. Armstrong, “Fabry-Perot data analysis and simulation for the renoir observatories,” Master’s thesis, (University of Illinois, 2008).
  15. M. Newville, “Non-linear least-square minimization for python,” http://newville.github.io/lmfit-py/ (2013).

2012 (2)

C. G. M. Brum, C. A. Tepley, J. T. Fentzke, E. Robles, P. T. dos Santos, and S. A. Gonzalez, “Long-term changes in the thermospheric neutral winds over Arecibo: climatology based on over three decades of Fabry-Perot observations,” J. Geophys. Res. 117, A00H14 (2012).
[CrossRef]

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

2011 (1)

2009 (1)

J. J. Makela, J. W. Meriwether, J. Lima, E. S. Miller, and S. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
[CrossRef]

2007 (1)

E. Kudeki, A. Akgiray, M. Milla, J. Chau, and D. L. Hysell, “Equatorial spread-F initiation: Post-sunset vortex, thermospheric winds, gravity waves,” J. Atmos. Sol. Terr. Phys. 69, 2416–2427 (2007).
[CrossRef]

2004 (1)

R. Heelis, “Electrodynamics in the low and middle latitude ionosphere: a tutorial,” J. Atmos. Sol. Terr. Phys. 66, 825–838 (2004).
[CrossRef]

2002 (1)

2001 (1)

1995 (1)

1994 (1)

T. J. Fuller-Rowell, M. V. Codrescu, R. J. Moffett, and S. Quegan, “Response of the thermosphere and ionosphere to geomagnetic storms,” J. Geophys. Res. 99, 3893 (1994).
[CrossRef]

1984 (1)

1971 (1)

Akgiray, A.

E. Kudeki, A. Akgiray, M. Milla, J. Chau, and D. L. Hysell, “Equatorial spread-F initiation: Post-sunset vortex, thermospheric winds, gravity waves,” J. Atmos. Sol. Terr. Phys. 69, 2416–2427 (2007).
[CrossRef]

Armstrong, S.

J. J. Makela, J. W. Meriwether, J. Lima, E. S. Miller, and S. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
[CrossRef]

S. Armstrong, “Fabry-Perot data analysis and simulation for the renoir observatories,” Master’s thesis, (University of Illinois, 2008).

Baumgardner, J. L.

Biondi, M.

Brum, C. G. M.

C. G. M. Brum, C. A. Tepley, J. T. Fentzke, E. Robles, P. T. dos Santos, and S. A. Gonzalez, “Long-term changes in the thermospheric neutral winds over Arecibo: climatology based on over three decades of Fabry-Perot observations,” J. Geophys. Res. 117, A00H14 (2012).
[CrossRef]

Chau, J.

E. Kudeki, A. Akgiray, M. Milla, J. Chau, and D. L. Hysell, “Equatorial spread-F initiation: Post-sunset vortex, thermospheric winds, gravity waves,” J. Atmos. Sol. Terr. Phys. 69, 2416–2427 (2007).
[CrossRef]

Codrescu, M. V.

T. J. Fuller-Rowell, M. V. Codrescu, R. J. Moffett, and S. Quegan, “Response of the thermosphere and ionosphere to geomagnetic storms,” J. Geophys. Res. 99, 3893 (1994).
[CrossRef]

Conde, M.

dos Santos, P. T.

C. G. M. Brum, C. A. Tepley, J. T. Fentzke, E. Robles, P. T. dos Santos, and S. A. Gonzalez, “Long-term changes in the thermospheric neutral winds over Arecibo: climatology based on over three decades of Fabry-Perot observations,” J. Geophys. Res. 117, A00H14 (2012).
[CrossRef]

Ejiri, M. K.

Fentzke, J. T.

C. G. M. Brum, C. A. Tepley, J. T. Fentzke, E. Robles, P. T. dos Santos, and S. A. Gonzalez, “Long-term changes in the thermospheric neutral winds over Arecibo: climatology based on over three decades of Fabry-Perot observations,” J. Geophys. Res. 117, A00H14 (2012).
[CrossRef]

Fuller-Rowell, T. J.

T. J. Fuller-Rowell, M. V. Codrescu, R. J. Moffett, and S. Quegan, “Response of the thermosphere and ionosphere to geomagnetic storms,” J. Geophys. Res. 99, 3893 (1994).
[CrossRef]

Gonzalez, S. A.

C. G. M. Brum, C. A. Tepley, J. T. Fentzke, E. Robles, P. T. dos Santos, and S. A. Gonzalez, “Long-term changes in the thermospheric neutral winds over Arecibo: climatology based on over three decades of Fabry-Perot observations,” J. Geophys. Res. 117, A00H14 (2012).
[CrossRef]

Hamaguchi, Y.

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

Hays, P.

Hays, P. B.

Heelis, R.

R. Heelis, “Electrodynamics in the low and middle latitude ionosphere: a tutorial,” J. Atmos. Sol. Terr. Phys. 66, 825–838 (2004).
[CrossRef]

Hernandez, G.

G. Hernandez, Fabry-Perot Interferometers, Cambridge Studies in Modern Optics (Cambridge University, 1988).

Huang, Y.

Hysell, D. L.

E. Kudeki, A. Akgiray, M. Milla, J. Chau, and D. L. Hysell, “Equatorial spread-F initiation: Post-sunset vortex, thermospheric winds, gravity waves,” J. Atmos. Sol. Terr. Phys. 69, 2416–2427 (2007).
[CrossRef]

Kadota, T.

Katoh, Y.

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

K. Shiokawa, T. Kadota, M. K. Ejiri, Y. Otsuka, Y. Katoh, M. Satoh, and T. Ogawa, “Three-channel imaging fabry-perot interferometer for measurement of mid-latitude airglow,” Appl. Opt. 40, 4286–4296 (2001).
[CrossRef]

Killeen, T.

Kudeki, E.

E. Kudeki, A. Akgiray, M. Milla, J. Chau, and D. L. Hysell, “Equatorial spread-F initiation: Post-sunset vortex, thermospheric winds, gravity waves,” J. Atmos. Sol. Terr. Phys. 69, 2416–2427 (2007).
[CrossRef]

Lima, J.

J. J. Makela, J. W. Meriwether, J. Lima, E. S. Miller, and S. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
[CrossRef]

Makela, J. J.

J. J. Makela, J. W. Meriwether, Y. Huang, and P. J. Sherwood, “Simulation and analysis of a multi-order imaging Fabry-Perot interferometer for the study of thermospheric winds and temperatures,” Appl. Opt. 50, 4403–4416 (2011).
[CrossRef]

J. J. Makela, J. W. Meriwether, J. Lima, E. S. Miller, and S. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
[CrossRef]

Meriwether, J.

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

Meriwether, J. W.

J. J. Makela, J. W. Meriwether, Y. Huang, and P. J. Sherwood, “Simulation and analysis of a multi-order imaging Fabry-Perot interferometer for the study of thermospheric winds and temperatures,” Appl. Opt. 50, 4403–4416 (2011).
[CrossRef]

J. J. Makela, J. W. Meriwether, J. Lima, E. S. Miller, and S. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
[CrossRef]

Milla, M.

E. Kudeki, A. Akgiray, M. Milla, J. Chau, and D. L. Hysell, “Equatorial spread-F initiation: Post-sunset vortex, thermospheric winds, gravity waves,” J. Atmos. Sol. Terr. Phys. 69, 2416–2427 (2007).
[CrossRef]

Miller, E. S.

J. J. Makela, J. W. Meriwether, J. Lima, E. S. Miller, and S. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
[CrossRef]

Moffett, R. J.

T. J. Fuller-Rowell, M. V. Codrescu, R. J. Moffett, and S. Quegan, “Response of the thermosphere and ionosphere to geomagnetic storms,” J. Geophys. Res. 99, 3893 (1994).
[CrossRef]

Nozawa, S.

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

Ogawa, T.

Otsuka, Y.

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

K. Shiokawa, T. Kadota, M. K. Ejiri, Y. Otsuka, Y. Katoh, M. Satoh, and T. Ogawa, “Three-channel imaging fabry-perot interferometer for measurement of mid-latitude airglow,” Appl. Opt. 40, 4286–4296 (2001).
[CrossRef]

Oyama, S.

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

Quegan, S.

T. J. Fuller-Rowell, M. V. Codrescu, R. J. Moffett, and S. Quegan, “Response of the thermosphere and ionosphere to geomagnetic storms,” J. Geophys. Res. 99, 3893 (1994).
[CrossRef]

Roble, R. G.

Robles, E.

C. G. M. Brum, C. A. Tepley, J. T. Fentzke, E. Robles, P. T. dos Santos, and S. A. Gonzalez, “Long-term changes in the thermospheric neutral winds over Arecibo: climatology based on over three decades of Fabry-Perot observations,” J. Geophys. Res. 117, A00H14 (2012).
[CrossRef]

Satoh, M.

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

K. Shiokawa, T. Kadota, M. K. Ejiri, Y. Otsuka, Y. Katoh, M. Satoh, and T. Ogawa, “Three-channel imaging fabry-perot interferometer for measurement of mid-latitude airglow,” Appl. Opt. 40, 4286–4296 (2001).
[CrossRef]

Sherwood, P. J.

Shiokawa, K.

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

K. Shiokawa, T. Kadota, M. K. Ejiri, Y. Otsuka, Y. Katoh, M. Satoh, and T. Ogawa, “Three-channel imaging fabry-perot interferometer for measurement of mid-latitude airglow,” Appl. Opt. 40, 4286–4296 (2001).
[CrossRef]

Sipler, D. P.

Tepley, C. A.

C. G. M. Brum, C. A. Tepley, J. T. Fentzke, E. Robles, P. T. dos Santos, and S. A. Gonzalez, “Long-term changes in the thermospheric neutral winds over Arecibo: climatology based on over three decades of Fabry-Perot observations,” J. Geophys. Res. 117, A00H14 (2012).
[CrossRef]

Yamamoto, Y.

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

Zipf, M. E.

Appl. Opt. (6)

Earth Moon Planets (1)

J. J. Makela, J. W. Meriwether, J. Lima, E. S. Miller, and S. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
[CrossRef]

Earth Planets Space (1)

K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, M. Satoh, Y. Katoh, Y. Hamaguchi, Y. Yamamoto, and J. Meriwether, “Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies,” Earth Planets Space 64, 1033–1046 (2012).
[CrossRef]

J. Atmos. Sol. Terr. Phys. (2)

R. Heelis, “Electrodynamics in the low and middle latitude ionosphere: a tutorial,” J. Atmos. Sol. Terr. Phys. 66, 825–838 (2004).
[CrossRef]

E. Kudeki, A. Akgiray, M. Milla, J. Chau, and D. L. Hysell, “Equatorial spread-F initiation: Post-sunset vortex, thermospheric winds, gravity waves,” J. Atmos. Sol. Terr. Phys. 69, 2416–2427 (2007).
[CrossRef]

J. Geophys. Res. (2)

T. J. Fuller-Rowell, M. V. Codrescu, R. J. Moffett, and S. Quegan, “Response of the thermosphere and ionosphere to geomagnetic storms,” J. Geophys. Res. 99, 3893 (1994).
[CrossRef]

C. G. M. Brum, C. A. Tepley, J. T. Fentzke, E. Robles, P. T. dos Santos, and S. A. Gonzalez, “Long-term changes in the thermospheric neutral winds over Arecibo: climatology based on over three decades of Fabry-Perot observations,” J. Geophys. Res. 117, A00H14 (2012).
[CrossRef]

Other (3)

S. Armstrong, “Fabry-Perot data analysis and simulation for the renoir observatories,” Master’s thesis, (University of Illinois, 2008).

M. Newville, “Non-linear least-square minimization for python,” http://newville.github.io/lmfit-py/ (2013).

G. Hernandez, Fabry-Perot Interferometers, Cambridge Studies in Modern Optics (Cambridge University, 1988).

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Figures (8)

Fig. 1.
Fig. 1.

Example FPI airglow fringe image.

Fig. 2.
Fig. 2.

Example FPI laser calibration fringe image.

Fig. 3.
Fig. 3.

Example instrument function with best-fit ideal Airy function. The difference (residual) between data and model is also shown. Optical defects cause a large mismatch, which demands a more complex model.

Fig. 4.
Fig. 4.

Example instrument function with best-fit modified Airy function, and residual between data and modified Airy fit. Compare to Fig. 3.

Fig. 5.
Fig. 5.

Example airglow fringes with best-fit airglow model. Also shown is the residual, the difference between the data and the model.

Fig. 6.
Fig. 6.

Recovered wind and temperature for 104 simulated FPI measurements. Also shown are the sample and estimated uncertainty ellipses, which compare favorably, indicating accurate estimation of error bars.

Fig. 7.
Fig. 7.

Estimation errors in velocity and temperature as a function of true velocity and temperature for 103 simulated FPI measurements. A small, 0.4(m/s) velocity bias is present, but there is no bias in temperature. In 68% of the trials, the error bar contains zero (not shown), which matches the expectation from Gaussian statistics.

Fig. 8.
Fig. 8.

Estimation errors in velocity and temperature for 104 simulated FPI measurements, as a function of SNR. No biases are evident. In 68% of the trials, the error bar contains zero (not shown), which matches the expectation from Gaussian statistics.

Tables (2)

Tables Icon

Table 1. Parameters of the Forward Model for Laser Calibration Fringesa

Tables Icon

Table 2. Free Parameters of the Forward Model for Airglow Fringesa

Equations (17)

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

S(r)=A(r,λ)Y(λ)dλ,
A(r,λ)=I1+4R(1R)2sin2(2πntλcosθ(r)),
θ(r)=tan1(αr),
I=I0(1+I1(rrmax)+I2(rrmax)2),
A˜(r,λ)=0rmaxb(s,r)A(s,λ)ds,
b(s,r)=12πσ2e(sr)2σ2.
b(s,r)=12πσ(r)2e(sr)2σ(r)2,
σ(r)=σ0+σ1sin(πrrmax)+σ2cos(πrrmax).
S(r)=A˜(r,λ)Y(λ)dλ+B.
Y(λ)=Ybg+Ylineexp{12(λλcΔλ)2},
λc=λ0(1+vc),
Δλ=λ0ckTm,
χ2=i=0R1(Nlaser(ri)S(ri)σNlaser(ri))2,
A˜(r,λ)=i=0R1b(si,r)A(si,λ)Δsi,
S(ri)=j=0L1A˜(ri,λj)Y(λj)Δλ+B,
s=Ay+B1,
SNR=ΔSσN,

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