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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 36 — Dec. 20, 2009
  • pp: 6913–6922

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background

Serge Minin and Farzad Kamalabadi  »View Author Affiliations


Applied Optics, Vol. 48, Issue 36, pp. 6913-6922 (2009)
http://dx.doi.org/10.1364/AO.48.006913


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Abstract

We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, χ 2 , in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer–Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry–Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

© 2009 Optical Society of America

OCIS Codes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(300.2140) Spectroscopy : Emission
(300.3700) Spectroscopy : Linewidth
(300.6320) Spectroscopy : Spectroscopy, high-resolution
(010.0280) Atmospheric and oceanic optics : Remote sensing and sensors

ToC Category:
Spectroscopy

History
Original Manuscript: August 5, 2009
Revised Manuscript: November 12, 2009
Manuscript Accepted: November 15, 2009
Published: December 10, 2009

Citation
Serge Minin and Farzad Kamalabadi, "Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background," Appl. Opt. 48, 6913-6922 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-36-6913


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References

  1. S. C. Solomon, “Optical aeronomy,” Rev. Geophys. 29, 1089-1109 (1991).
  2. D. Pallamraju, J. Baumgardner, and S. Chakrabarti, “HIRISE a ground-based high-resolution imaging spectrograph using echelle grating for measuring daytime air glow/auroral emissions,” J. Atmos. Sol. Terr. Phys. 64, 1581-1587 (2002). [CrossRef]
  3. D. Pallamraju and S. Chakrabarti, “First ground-based measurements of OI 6300 angstrom daytime aurora over Boston in response to the 30 October 2003 geomagnetic storm,” Geophys. Res. Lett. 32, L03S10 (2005). [CrossRef]
  4. E. J. Mierkiewicz, F. L. Roesler, S. M. Nossal, and R. J. Reynolds, “Geocoronal hydrogen studies using Fabry-Perot interferometers, part 1: instrumentation, observations, and analysis,” J. Atmos. Sol. Terr. Phys. 68, 1520-1552 (2006). [CrossRef]
  5. D. Rees and A. H. Greenaway, “Doppler imaging -system--an optical device for measuring vector winds: 1. general-principles,” Appl. Opt. 22, 1078-1083 (1983). [CrossRef] [PubMed]
  6. G. G. Sivjee, T. J. Hallinan, and G. R. Swenson, “Fabry-Perot interferometer imaging system for thermospheric temperature and wind measurements,” Appl. Opt. 19, 2206-2209 (1980). [CrossRef] [PubMed]
  7. F. E. Barmore, “High-resolution observations of 6300-a oxygen line in day air glow,” Planet. Space Sci. 25, 185-191 (1977). [CrossRef]
  8. 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] [PubMed]
  9. M. Conde, J. D. Craven, T. Immel, E. Hoch, H. Stenbaek-Nielsen, T. Hallinan, R. W. Smith, J. Olson, W. Sun, L. A. Frank, and J. Sigwarth, “Assimilated observations of thermospheric winds, the aurora, and ionospheric currents over Alaska,” J. Geophys. Res. Space Phys. 106, 10493-10508 (2001). [CrossRef]
  10. P. B. Hays and R. G. Roble, “Technique for recovering doppler line profiles from Fabry-Perot interferometer fringes of very low intensity,” Appl. Opt. 10, 193-200 (1971). [CrossRef] [PubMed]
  11. J. Meriwether, M. Faivre, C. Fesen, P. Sherwood, and O. Veliz, “New results on equatorial thermospheric winds and the midnight temperature maximum,” Ann. Geophys. 26, 447-466 (2008). [CrossRef]
  12. D. Rees, A. H. Greenaway, R. Gordon, I. McWhirter, P. J. Charleton, and A. Steen, “The Doppler imaging-system--initial observations of the auroral thermosphere,” Planet. Space Sci. 32, 273 (1984). [CrossRef]
  13. C. A. Tepley, R. G. Burnside, J. W. Meriwether, P. B. Hays, and L. L. Cogger, “Spatial-mapping of the thermospheric neutral wind-field,” Planet. Space Sci. 32, 493-501 (1984). [CrossRef]
  14. L. S. Waldrop, R. B. Kerr, S. A. Gonzalez, M. P. Sulzer, J. Noto, and F. Kamalabadi, “Generation of metastable helium and the 1083 nm emission in the upper thermosphere,” J. Geophys. Res. Space Phys. 110, A08304 (2005). [CrossRef]
  15. R. B. Kerr, R. Garcia, X. He, J. Noto, R. S. Lancaster, C. A. Tepley, S. A. Gonzalez, J. Friedman, R. A. Doe, M. Lappen, and B. McCormack, “Periodic variations of geocoronal balmer-alpha brightness due to solar-driven exospheric abundance variations,” J. Geophys. Res. Space Phys. 106, 28797-28817 (2001). [CrossRef]
  16. R. B. Kerr, R. Garcia, X. He, J. Noto, R. S. Lancaster, C. A. Tepley, S. A. Gonzalez, J. Friedman, R. A. Doe, M. Lappen, and B. McCormack, “Secular variability of the geocoronal balmer-alpha brightness: magnetic activity and possible human influences,” J. Geophys. Res. Space Phys. 106, 28819-28829 (2001). [CrossRef]
  17. S. Nossal, F. L. Roesler, M. M. Coakley, and R. J. Reynolds, “Geocoronal hydrogen balmer-alpha line profiles obtained using Fabry-Perot annular summing spectroscopy: effective temperature results,” J. Geophys. Res. Space Phys. 102, 14541-14553 (1997). [CrossRef]
  18. S. Nossal, F. L. Roesler, J. Bishop, R. J. Reynolds, M. Haffner, S. Tufte, J. Percival, and E. J. Mierkiewicz, “Geocoronal h alpha intensity measurements using the wisconsin h alpha mapper Fabry-Perot facility,” J. Geophys. Res. Space Physics 106, 5605-5615 (2001). [CrossRef]
  19. J. Noto, R. B. Kerr, E. M. Shea, L. S. Waldrop, G. Fisher, J. Rudy, J. H. Hecht, S. A. Gonzalez, M. P. Sulzer, and R. Garcia, “Evidence for recombination as a significant source of metastable helium,” J. Geophys. Res. Space Phys. 103, 11595-11603 (1998). [CrossRef]
  20. G. R. Swenson, S. B. Mende, and S. P. Geller, “Fabry-Perot imaging observations of OH(8-3)--rotational temperatures and gravity-waves,” J. Geophys. Res. Space Phys. 95, 12251-12263 (1990). [CrossRef]
  21. T. L. Killeen and P. B. Hays, “Doppler line-profile analysis for a multichannel fabry-perot interferometer,” Appl. Opt. 23, 612-620 (1984). [CrossRef] [PubMed]
  22. M. M. Coakley, F. L. Roesler, R. J. Reynolds, and S. Nossal, “Fabry-Perot CCD annular-summing spectroscopy: study and implementation for aeronomy applications,” Appl. Opt. 35, 6479-6493 (1996). [CrossRef] [PubMed]
  23. M. Conde, “Deriving wavelength spectra from fringe images from a fixed-gap single-etalon Fabry-Perot spectrometer,” Appl. Opt. 41, 2672-2678 (2002). [CrossRef] [PubMed]
  24. S. Chakrabarti, “Ground based spectroscopic studies of sunlit air glow and aurora,” J. Atmos. Sol. Terr. Phys. 60, 1403-1423(1998). [CrossRef]
  25. G. Hernandez, “Analytical description of a Fabry-Perot spectrometer. 4. Signal noise limitations in data-retrieval--winds, temperature, and emission rate,” Appl. Opt. 17, 2967-2972(1978). [CrossRef] [PubMed]
  26. W. H. Press, S. A. Teukolsky, W. T. Vitterling, and B. P. Flannery, Numerical Recipes in Fortran 77: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1996), Chap. 15.
  27. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 3rd ed. (McGraw-Hill, 2003).
  28. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).
  29. N. Hagen, M. Kupinski, and E. L. Dereniak, “Gaussian profile estimation in one dimension,” Appl. Opt. 46, 5374-5383 (2007). [CrossRef] [PubMed]
  30. L. Lading and A. S. Jensen, “Estimating the spectral width of a narrowband optical signal,” Appl. Opt. 19, 2750-2756 (1980). [CrossRef] [PubMed]
  31. J. Ireland, “Precision limits to emission-line profile measuring experiments,” Astrophys. J. 620, 1132-1139 (2005). [CrossRef]
  32. D. A. Landman, R. Rousseldupre, and G. Tanigawa, “On the statistical uncertainties associated with line profile fitting,” Astrophys. J. 261, 732-735 (1982). [CrossRef]
  33. D. D. Lenz and T. R. Ayres, “Errors associated with fitting Gaussian profiles to noisy emission-line spectra,” Publ. Astron. Soc. Pac. 104, 1104-1106 (1992). [CrossRef]

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