Abstract

Nonlinear regression techniques, when applied to sky exposures obtained using a Fabry–Perot interferometer (FPI), are able to recover atmospheric neutral wind and temperature through inversion of the resulting fringe pattern. Current inversion methods often account for temporal fluctuation of the etalon’s optical path length (caused by temperature variation in the instrument housing, for example) by characterizing the system function using isolated exposures of a frequency-stabilized laser. Because these path length changes correspond directly to shifts in the fringe pattern, they can significantly increase the total wind velocity uncertainty between laser exposures. We propose an extension to current regression techniques allowing for characterization of the optical path length and measurement of neutral wind and temperature simultaneously, thus reducing the need for frequent isolated laser exposures. This is achieved by using the laser as a pilot signal that enters the aperture of the instrument during sky exposures. We show that the extension can lead to a lower variance estimator for velocity when the optical path length has a significant time-varying component. Additionally, several pragmatic physical configurations that would allow for construction of a piloted signal in a real system are tested and compared using an FPI installation at the Urbana Atmospheric Observatory.

© 2019 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), special issue on Upper Atmosphere Tutorials from the 2001 Joint CEDAR SCOSTEP Meeting.
    [Crossref]
  2. D. Rees, “Observations and modelling of ionospheric and thermospheric disturbances during major geomagnetic storms: a review,” J. Atmos. Terr. Phys. 57, 1433–1457 (1995), special issue on Observations and Modelling of Solar-Terrestrial Relationships.
    [Crossref]
  3. T. L. Killeen and P. B. Hays, “Doppler line profile analysis for a multichannel Fabry-Perot interferometer,” Appl. Opt. 23, 612–620 (1984).
    [Crossref]
  4. 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]
  5. Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
    [Crossref]
  6. M. A. 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]
  7. B. C. G. Marques, C. A. Tepley, J. T. Fentzke, R. Eva, 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. Space Phys. 117, 16458 (2012).
    [Crossref]
  8. 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]
  9. M. Conde, “Deriving wavelength spectra from fringe images from a fixed-gap single-etalon Fabry-Perot spectrometer,” Appl. Opt. 41, 2672–2678 (2002).
    [Crossref]
  10. B. J. Harding, T. W. Gehrels, and J. J. Makela, “Nonlinear regression method for estimating neutral wind and temperature from Fabry-Perot interferometer data,” Appl. Opt. 53, 666–673 (2014).
    [Crossref]
  11. R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
    [Crossref]
  12. M. Newville, “Non-linear least-squares minimization and curve-fitting for python,” 2018, https://Lmfit.github.io/lmfit-py .
  13. J. J. Makela, J. W. Meriwether, J. P. Lima, E. S. Miller, and S. J. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
    [Crossref]

2017 (2)

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
[Crossref]

2014 (1)

2012 (1)

B. C. G. Marques, C. A. Tepley, J. T. Fentzke, R. Eva, 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. Space Phys. 117, 16458 (2012).
[Crossref]

2011 (1)

2009 (1)

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

2004 (1)

R. Heelis, “Electrodynamics in the low and middle latitude ionosphere: a tutorial,” J. Atmos. Sol. Terr. Phys. 66, 825–838 (2004), special issue on Upper Atmosphere Tutorials from the 2001 Joint CEDAR SCOSTEP Meeting.
[Crossref]

2002 (1)

2001 (1)

1995 (2)

D. Rees, “Observations and modelling of ionospheric and thermospheric disturbances during major geomagnetic storms: a review,” J. Atmos. Terr. Phys. 57, 1433–1457 (1995), special issue on Observations and Modelling of Solar-Terrestrial Relationships.
[Crossref]

M. A. 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]

1984 (1)

Armstrong, S. J.

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

Artamonov, M.

R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
[Crossref]

Baumgardner, J. L.

Beletsky, A.

R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
[Crossref]

Biondi, M. A.

Conde, M.

dos Santos, P. T.

B. C. G. Marques, C. A. Tepley, J. T. Fentzke, R. Eva, 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. Space Phys. 117, 16458 (2012).
[Crossref]

Ejiri, M. K.

Eva, R.

B. C. G. Marques, C. A. Tepley, J. T. Fentzke, R. Eva, 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. Space Phys. 117, 16458 (2012).
[Crossref]

Fentzke, J. T.

B. C. G. Marques, C. A. Tepley, J. T. Fentzke, R. Eva, 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. Space Phys. 117, 16458 (2012).
[Crossref]

Gehrels, T. W.

Gonzalez, S. A.

B. C. G. Marques, C. A. Tepley, J. T. Fentzke, R. Eva, 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. Space Phys. 117, 16458 (2012).
[Crossref]

Harding, B. J.

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), special issue on Upper Atmosphere Tutorials from the 2001 Joint CEDAR SCOSTEP Meeting.
[Crossref]

Huang, Y.

Jin, H.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

Kadota, T.

Katoh, Y.

Killeen, T. L.

Komolmis, T.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

Komonjida, S.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

Lima, J. P.

J. J. Makela, J. W. Meriwether, J. P. Lima, E. S. Miller, and S. J. 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.

Marques, B. C. G.

B. C. G. Marques, C. A. Tepley, J. T. Fentzke, R. Eva, 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. Space Phys. 117, 16458 (2012).
[Crossref]

Medvedeva, I.

R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
[Crossref]

Meriwether, J.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[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. P. Lima, E. S. Miller, and S. J. Armstrong, “The remote equatorial nighttime observatory of ionospheric regions project and the international heliospherical year,” Earth Moon Planets 104, 211–226 (2009).
[Crossref]

Mikhalev, A.

R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
[Crossref]

Miller, E. S.

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

Nakamura, Y.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

Neudegg, D.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

Nozawa, S.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

Ogawa, T.

Otsuka, Y.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[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.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

Rees, D.

D. Rees, “Observations and modelling of ionospheric and thermospheric disturbances during major geomagnetic storms: a review,” J. Atmos. Terr. Phys. 57, 1433–1457 (1995), special issue on Observations and Modelling of Solar-Terrestrial Relationships.
[Crossref]

Satoh, M.

Sherwood, P. J.

Shinagawa, H.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

Shiokawa, K.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[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.

Syrenova, T.

R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
[Crossref]

Tepley, C. A.

B. C. G. Marques, C. A. Tepley, J. T. Fentzke, R. Eva, 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. Space Phys. 117, 16458 (2012).
[Crossref]

Vasilyev, R.

R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
[Crossref]

Yuile, C.

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

Zherebtsov, G.

R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
[Crossref]

Zipf, M. E.

Appl. Opt. (6)

Earth Moon Planets (1)

J. J. Makela, J. W. Meriwether, J. P. Lima, E. S. Miller, and S. J. 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)

Y. Nakamura, K. Shiokawa, Y. Otsuka, S. Oyama, S. Nozawa, T. Komolmis, S. Komonjida, D. Neudegg, C. Yuile, J. Meriwether, H. Shinagawa, and H. Jin, “Measurement of thermospheric temperatures using OMTI Fabry-Perot interferometers with 70-mm etalon,” Earth, Planets Space 69, 57 (2017).
[Crossref]

J. Atmos. Sol. Terr. Phys. (1)

R. Heelis, “Electrodynamics in the low and middle latitude ionosphere: a tutorial,” J. Atmos. Sol. Terr. Phys. 66, 825–838 (2004), special issue on Upper Atmosphere Tutorials from the 2001 Joint CEDAR SCOSTEP Meeting.
[Crossref]

J. Atmos. Terr. Phys. (1)

D. Rees, “Observations and modelling of ionospheric and thermospheric disturbances during major geomagnetic storms: a review,” J. Atmos. Terr. Phys. 57, 1433–1457 (1995), special issue on Observations and Modelling of Solar-Terrestrial Relationships.
[Crossref]

J. Geophys. Res. Space Phys. (1)

B. C. G. Marques, C. A. Tepley, J. T. Fentzke, R. Eva, 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. Space Phys. 117, 16458 (2012).
[Crossref]

Solar-Terrestrial Phys. (1)

R. Vasilyev, M. Artamonov, A. Beletsky, G. Zherebtsov, I. Medvedeva, A. Mikhalev, and T. Syrenova, “Registering upper atmosphere parameters in east Siberia with Fabry-Perot interferometer Keo scientific ‘Arinae’,” Solar-Terrestrial Phys. 3, 61–75 (2017).
[Crossref]

Other (1)

M. Newville, “Non-linear least-squares minimization and curve-fitting for python,” 2018, https://Lmfit.github.io/lmfit-py .

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Figures (11)

Fig. 1.
Fig. 1. Monte Carlo simulations testing the ability of both standard and piloted deconvolution to retrieve a 100 m/s wind having a temperature of 800 K. Retrieval using standard deconvolution (top row). Retrieval using piloted deconvolution (bottom row). Each column is for a different SNR. In general, standard deconvolution exhibits better inversion performance; at a given SNR, velocity and temperature uncertainties (and also biases) are smaller for standard deconvolution.
Fig. 2.
Fig. 2. Monte Carlo simulation results demonstrating biases over velocity and temperature. Notice the presence of a velocity bias when the true velocity is negative. The magnitude of the bias increases at higher negative true velocities, reaching around 20 m/s at 300 m / s (panel a). Both the inverted velocity and temperature variance increase with true temperature (panels b and d). A velocity bias appears with increasing true temperature (panel b), reaching around 15 m / s at a true temperature of 1200 K. The temperature error did not appear to appreciably change with true velocity (panel c).
Fig. 3.
Fig. 3. Monte Carlo simulation results demonstrating biases over SNR. There appears to be a velocity bias of around 10 m / s that appears at high SNR. No temperature biases over SNR were apparent.
Fig. 4.
Fig. 4. Sample and estimated uncertainties as a function of SNR. Velocity uncertainties tend to be underestimated by a factor of around 3 at higher SNRs. Temperature uncertainties are slightly underestimated but more closely reflect the sample uncertainties.
Fig. 5.
Fig. 5. Velocity and temperature error as a function of single-step optical path length fluctuation in the presence of changes to wind, temperature, laser intensity, and sky brightness. Velocity error appears to slightly depend on Δ d , most visible for extreme single-step fluctuations (notice the structure near Δ d = ± 2 nm at higher SNR); however, the source of the dependence is currently unclear. The velocity uncertainties do not tend to decrease between SNR = 5 and SNR = 25 . Temperature errors are well-behaved, exhibiting no biases as a function of Δ d and exhibiting a decrease in uncertainty at higher SNRs.
Fig. 6.
Fig. 6. Standard deconvolution interpolation error assuming a 5 nm amplitude, 20 min period sinusoidal gap variation. Panel a shows Δ d ( t ) , and panels b, c, and d show the interpolation error e v d for sky exposure times of 3, 6, and 9 min, respectively.
Fig. 7.
Fig. 7. Reference uncertainties calculated across a realistic range of variation amplitudes and sky exposure times for three characteristic gap variation periods. In general, longer exposure times, larger amplitude variations, and shorter characteristic periods lead to an increased inability to describe the true variation with linear interpolation and are associated with increased reference uncertainties.
Fig. 8.
Fig. 8. Typical FPI hardware configuration.
Fig. 9.
Fig. 9. Proposed modified configurations for piloted deconvolution.
Fig. 10.
Fig. 10. Images obtained for each of the three modified data collection methods. Overlaid in white is a plot of the θ -integrated fringes.
Fig. 11.
Fig. 11. Example inversion on integrated data collected at the Urbana Atmospheric Observatory using the specular method. The associated fringe is shown in Fig. 10(c). The data are shown in black. The reconstructed signal is shown in green.

Tables (3)

Tables Icon

Table 1. Model Parameters

Tables Icon

Table 2. Inversion Performance

Tables Icon

Table 3. Total Velocity Uncertainty

Equations (16)

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

S ( r , t ) = A ( r , λ , t ) Y ( λ , t ) d λ
S ˜ ( r , t ) = λ 1 λ 2 A ( r , λ , t ) [ Y ( λ , t ) + δ ( λ λ p ) ] d λ + B ( t ) = λ 1 λ 2 A ( r , λ , t ) Y ( λ , t ) d λ + A ( r , λ p , t ) + B ( t ) .
A ( r , λ , t ) = I 0 ( t ) 0 r m 1 + I 1 ( t ) ( s r m ) + I 2 ( t ) ( s r m ) 2 1 + 4 R ( t ) ( 1 R ( t ) ) 2 sin 2 ( 2 π λ n d ( t ) ( α ( t ) r ) 2 + 1 ) e ( s r ) 2 σ ( r , t ) 2 2 π σ ( r , t ) d s ,
σ ( r , t ) = σ 0 ( t ) + σ 1 ( t ) sin ( π r r m ) + σ 2 ( t ) cos ( π r r m ) ,
Y ( λ , t ) = Y bg ( t ) + Y line ( t ) Δ λ ( t ) exp [ 1 2 ( λ λ c ( t ) Δ λ ( t ) ) 2 ] ,
λ c ( t ) = λ 0 ( 1 + v ( t ) c ) ,
Δ λ ( t ) = λ 0 c k T ( t ) m .
S ˜ ( r , t ) = λ 0 δ / 2 λ 0 + δ / 2 A ( r , λ , t ) Y ( λ , t ) d λ + A ( r , λ p , t ) + B ( t ) = lim Δ λ 0 [ j = 1 δ Δ λ A ( r , λ j * , t ) Y ( λ j * , t ) Δ λ ] + A ( r , λ p , t ) + B ( t ) ,
S ˜ ( r i , t ) j = 1 N A ( r i , λ j , t ) Y ( λ j , t ) Δ λ + A ( r i , λ p , t ) + B ( t ) ,
m ( t ) = A ( t ) y ( t ) + A p ( t ) + B 1 + e ( t ) ,
= s ( t ) + e ( t ) ,
E [ m ( t ) m ( t ) T ] = E { [ s ( t ) + e ( t ) ] [ s ( t ) + e ( t ) ] T } ,
= Σ s ( t ) + Σ e ( t ) + Σ e s ( t ) ,
q ^ ( t ) = argmin q Σ m 1 / 2 ( t ) e ( t ) 2 2 = argmin q { [ m ( t ) s ( t ) ] T Σ m 1 ( t ) [ m ( t ) s ( t ) ] } = argmin q i = 1 M [ m i ( t ) s i ( t ) ] 2 σ m i 2 ( t ) ,
Δ d U ( 2.5 , 2.5 ) ( nm ) Δ v U ( 100 , 100 ) ( m / s ) Δ T U ( 100 , 100 ) ( K ) Δ I 0 U ( 100 , 100 ) ( counts ) Δ Y line U ( 100 , 100 ) ( counts ) ,
e v d ( t ) = c d [ Δ d ( t ) Δ d S ( t ) ] .

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