Abstract

A new method for measuring atmospheric refraction angles is presented, with in-orbit measurements demonstrating a precision of ±0.02  arcsec (±0.1μrad). Key advantages of the method are the following: (1) Simultaneous observation of two celestial points during occultation (i.e., top and bottom edges of the solar image) eliminates error from instrument attitude uncertainty. (2) The refraction angle is primarily a normalized difference measurement, causing only scale error, not absolute error. (3) A large number of detector pixels are used in the edge location by fitting to a known edge shape. The resulting refraction angle measurements allow temperature sounding up to the lower mesosphere.

© 2009 Optical Society of America

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  1. L. M. Jones, F. F. Fischbach, and J. W. Peterson, “Satellite measurements of atmospheric structure by refraction,” Planet. Space Sci. 9, 351-352 (1962).
    [CrossRef]
  2. G. M. Grechko, A. S. Gurvich, V. A. Lyakhov, S. A. Savchenko, and S. V. Sokolovskiy, “Results of an investigation of refraction during the third expedition on the Salyut-6 Orbiter,” Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., Engl. Transl. 17, 835-841(1981).
  3. R. L. White, W. E. Tanner, and R. S. Polidan, “Star line-of-sight refraction observations from the orbiting astronomical observatory Copernicus and deduction of stratospheric structure in the tropical region,” J. Geophys. Res. 88, 8535-8542 (1983).
    [CrossRef]
  4. R. J. Vervack, Jr., J. H. Yee, J. F. Carbary, and F. Morgan, “Atmospheric remote sensing using a combined extinctive and stellar occultation technique. 3. Inversion methods for refraction measurements,” J. Geophys. Res. 107, doi:10.1029/2001JD000796 (2002).
    [CrossRef]
  5. D. M. Ward and B. M. Herman, “Refractive sounding by use of satellite solar occultation measurements including an assessment of its usefulness to the Stratospheric Aerosol and Gas Experiment Program,” Appl. Opt. 37, 8306-8317(1998).
    [CrossRef]
  6. E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
    [CrossRef]
  7. R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
    [CrossRef]
  8. K. Hocke, “Inversion of GPS meteorology data,” Ann. Geophys. 15, 443-450 (1997).
    [CrossRef]
  9. A. K. Steiner, G. Kirchengast, and H. P. Ladreiter, “Inversion, error analysis and validation of GPS/MET occultation data,” Ann. Geophys. 17, 122-138 (1999).
    [CrossRef]
  10. G. Fjeldbo, A. J. Kliore, and V. R. Eshleman, “The neutral atmosphere of Venus as studied with the Mariner V Radio Occultation Experiments,” Astron. J. 76, 123-140(1971).
    [CrossRef]
  11. R. A. Phinney and D. C. Anderson, “On the radio occultation method for studying planetary atmospheres,” J. Geophys. Res. 73, 1819-1827 (1968).
    [CrossRef]
  12. B. Edlen, “The refractive index of air,” Metrologia 2, 71-80(1966).
    [CrossRef]
  13. P. E. Ciddor and R. J. Hill, “Refractive index of air. 2. Group index,” Appl. Opt. 38, 1663-1667 (1999).
    [CrossRef]
  14. L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
    [CrossRef]
  15. M. A. Whiteley, “Design of a space-borne Sun tracking system.,” M.S. thesis, (Utah State University, 2006).
  16. J. C. Burton, K. W. Miller, and S. K. Park, “Rectangularly and hexagonally sampled imaging system fidelity analysis,” Proc. SPIE 1961, 81-92 (1993).
    [CrossRef]
  17. S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170-177 (1991).
    [CrossRef]
  18. L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).
  19. A. E. Hedin, “Extension of the MSIS Thermosphere Model into the middle and lower atmosphere,” J. Geophys. Res. 96, 1159-1172 (1991).
    [CrossRef]

2009 (1)

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

2005 (1)

L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).

2002 (1)

R. J. Vervack, Jr., J. H. Yee, J. F. Carbary, and F. Morgan, “Atmospheric remote sensing using a combined extinctive and stellar occultation technique. 3. Inversion methods for refraction measurements,” J. Geophys. Res. 107, doi:10.1029/2001JD000796 (2002).
[CrossRef]

1999 (2)

A. K. Steiner, G. Kirchengast, and H. P. Ladreiter, “Inversion, error analysis and validation of GPS/MET occultation data,” Ann. Geophys. 17, 122-138 (1999).
[CrossRef]

P. E. Ciddor and R. J. Hill, “Refractive index of air. 2. Group index,” Appl. Opt. 38, 1663-1667 (1999).
[CrossRef]

1998 (1)

1997 (1)

K. Hocke, “Inversion of GPS meteorology data,” Ann. Geophys. 15, 443-450 (1997).
[CrossRef]

1996 (2)

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

1993 (1)

J. C. Burton, K. W. Miller, and S. K. Park, “Rectangularly and hexagonally sampled imaging system fidelity analysis,” Proc. SPIE 1961, 81-92 (1993).
[CrossRef]

1991 (2)

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170-177 (1991).
[CrossRef]

A. E. Hedin, “Extension of the MSIS Thermosphere Model into the middle and lower atmosphere,” J. Geophys. Res. 96, 1159-1172 (1991).
[CrossRef]

1983 (1)

R. L. White, W. E. Tanner, and R. S. Polidan, “Star line-of-sight refraction observations from the orbiting astronomical observatory Copernicus and deduction of stratospheric structure in the tropical region,” J. Geophys. Res. 88, 8535-8542 (1983).
[CrossRef]

1981 (1)

G. M. Grechko, A. S. Gurvich, V. A. Lyakhov, S. A. Savchenko, and S. V. Sokolovskiy, “Results of an investigation of refraction during the third expedition on the Salyut-6 Orbiter,” Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., Engl. Transl. 17, 835-841(1981).

1971 (1)

G. Fjeldbo, A. J. Kliore, and V. R. Eshleman, “The neutral atmosphere of Venus as studied with the Mariner V Radio Occultation Experiments,” Astron. J. 76, 123-140(1971).
[CrossRef]

1968 (1)

R. A. Phinney and D. C. Anderson, “On the radio occultation method for studying planetary atmospheres,” J. Geophys. Res. 73, 1819-1827 (1968).
[CrossRef]

1966 (1)

B. Edlen, “The refractive index of air,” Metrologia 2, 71-80(1966).
[CrossRef]

1962 (1)

L. M. Jones, F. F. Fischbach, and J. W. Peterson, “Satellite measurements of atmospheric structure by refraction,” Planet. Space Sci. 9, 351-352 (1962).
[CrossRef]

Anderson, D. C.

R. A. Phinney and D. C. Anderson, “On the radio occultation method for studying planetary atmospheres,” J. Geophys. Res. 73, 1819-1827 (1968).
[CrossRef]

Anthes, R.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Bailey, S.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Bertiger, W. I.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Brown, C.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Burton, J.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Burton, J. C.

L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).

J. C. Burton, K. W. Miller, and S. K. Park, “Rectangularly and hexagonally sampled imaging system fidelity analysis,” Proc. SPIE 1961, 81-92 (1993).
[CrossRef]

Businger, S.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Carbary, J. F.

R. J. Vervack, Jr., J. H. Yee, J. F. Carbary, and F. Morgan, “Atmospheric remote sensing using a combined extinctive and stellar occultation technique. 3. Inversion methods for refraction measurements,” J. Geophys. Res. 107, doi:10.1029/2001JD000796 (2002).
[CrossRef]

Ciddor, P. E.

Cook, J.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Deaver, L.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Edlen, B.

B. Edlen, “The refractive index of air,” Metrologia 2, 71-80(1966).
[CrossRef]

Eshleman, V. R.

G. Fjeldbo, A. J. Kliore, and V. R. Eshleman, “The neutral atmosphere of Venus as studied with the Mariner V Radio Occultation Experiments,” Astron. J. 76, 123-140(1971).
[CrossRef]

Exner, M.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Eyre, J. R.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Feng, D.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Fischbach, F. F.

L. M. Jones, F. F. Fischbach, and J. W. Peterson, “Satellite measurements of atmospheric structure by refraction,” Planet. Space Sci. 9, 351-352 (1962).
[CrossRef]

Fish, C.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Fjeldbo, G.

G. Fjeldbo, A. J. Kliore, and V. R. Eshleman, “The neutral atmosphere of Venus as studied with the Mariner V Radio Occultation Experiments,” Astron. J. 76, 123-140(1971).
[CrossRef]

Gorbunov, M.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Gordley, L. L.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).

Grechko, G. M.

G. M. Grechko, A. S. Gurvich, V. A. Lyakhov, S. A. Savchenko, and S. V. Sokolovskiy, “Results of an investigation of refraction during the third expedition on the Salyut-6 Orbiter,” Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., Engl. Transl. 17, 835-841(1981).

Gurvich, A. S.

G. M. Grechko, A. S. Gurvich, V. A. Lyakhov, S. A. Savchenko, and S. V. Sokolovskiy, “Results of an investigation of refraction during the third expedition on the Salyut-6 Orbiter,” Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., Engl. Transl. 17, 835-841(1981).

Hajj, G. A.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Hansen, S.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Hardy, K.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Hedin, A. E.

A. E. Hedin, “Extension of the MSIS Thermosphere Model into the middle and lower atmosphere,” J. Geophys. Res. 96, 1159-1172 (1991).
[CrossRef]

Herman, B.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Herman, B. M.

Hervig, M.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Hervig, M. E.

L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).

Hill, R. J.

Hocke, K.

K. Hocke, “Inversion of GPS meteorology data,” Ann. Geophys. 15, 443-450 (1997).
[CrossRef]

Jones, L. M.

L. M. Jones, F. F. Fischbach, and J. W. Peterson, “Satellite measurements of atmospheric structure by refraction,” Planet. Space Sci. 9, 351-352 (1962).
[CrossRef]

Kemp, J.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Kirchengast, G.

A. K. Steiner, G. Kirchengast, and H. P. Ladreiter, “Inversion, error analysis and validation of GPS/MET occultation data,” Ann. Geophys. 17, 122-138 (1999).
[CrossRef]

Kliore, A. J.

G. Fjeldbo, A. J. Kliore, and V. R. Eshleman, “The neutral atmosphere of Venus as studied with the Mariner V Radio Occultation Experiments,” Astron. J. 76, 123-140(1971).
[CrossRef]

Kuo, Y.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Kursinski, E. R.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Ladreiter, H. P.

A. K. Steiner, G. Kirchengast, and H. P. Ladreiter, “Inversion, error analysis and validation of GPS/MET occultation data,” Ann. Geophys. 17, 122-138 (1999).
[CrossRef]

Leroy, S. S.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Liu, L.

L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).

Lyakhov, V. A.

G. M. Grechko, A. S. Gurvich, V. A. Lyakhov, S. A. Savchenko, and S. V. Sokolovskiy, “Results of an investigation of refraction during the third expedition on the Salyut-6 Orbiter,” Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., Engl. Transl. 17, 835-841(1981).

Magill, B.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Magill, B. E.

L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).

Marshall, T.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

McCleese, D. J.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

McHugh, M. J.

L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).

Meehan, T.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Meehan, T. K.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Melbourne, W.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Melbourne, W. G.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Miller, K. W.

J. C. Burton, K. W. Miller, and S. K. Park, “Rectangularly and hexagonally sampled imaging system fidelity analysis,” Proc. SPIE 1961, 81-92 (1993).
[CrossRef]

Morgan, F.

R. J. Vervack, Jr., J. H. Yee, J. F. Carbary, and F. Morgan, “Atmospheric remote sensing using a combined extinctive and stellar occultation technique. 3. Inversion methods for refraction measurements,” J. Geophys. Res. 107, doi:10.1029/2001JD000796 (2002).
[CrossRef]

Nagatani, R. N.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Narayanswamy, R.

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170-177 (1991).
[CrossRef]

Park, S. K.

J. C. Burton, K. W. Miller, and S. K. Park, “Rectangularly and hexagonally sampled imaging system fidelity analysis,” Proc. SPIE 1961, 81-92 (1993).
[CrossRef]

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170-177 (1991).
[CrossRef]

Paxton, G.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Peterson, J. W.

L. M. Jones, F. F. Fischbach, and J. W. Peterson, “Satellite measurements of atmospheric structure by refraction,” Planet. Space Sci. 9, 351-352 (1962).
[CrossRef]

Phinney, R. A.

R. A. Phinney and D. C. Anderson, “On the radio occultation method for studying planetary atmospheres,” J. Geophys. Res. 73, 1819-1827 (1968).
[CrossRef]

Polidan, R. S.

R. L. White, W. E. Tanner, and R. S. Polidan, “Star line-of-sight refraction observations from the orbiting astronomical observatory Copernicus and deduction of stratospheric structure in the tropical region,” J. Geophys. Res. 88, 8535-8542 (1983).
[CrossRef]

Reichenbach, S. E.

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170-177 (1991).
[CrossRef]

Rocken, C.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Romans, L. J.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Russell, J. M.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).

Savchenko, S. A.

G. M. Grechko, A. S. Gurvich, V. A. Lyakhov, S. A. Savchenko, and S. V. Sokolovskiy, “Results of an investigation of refraction during the third expedition on the Salyut-6 Orbiter,” Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., Engl. Transl. 17, 835-841(1981).

Schofield, J. T.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Schreiner, W.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Shumway, A.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Sokolovskiy, S. V.

G. M. Grechko, A. S. Gurvich, V. A. Lyakhov, S. A. Savchenko, and S. V. Sokolovskiy, “Results of an investigation of refraction during the third expedition on the Salyut-6 Orbiter,” Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., Engl. Transl. 17, 835-841(1981).

Sokolovsky, S.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Solheim, F.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Steiner, A. K.

A. K. Steiner, G. Kirchengast, and H. P. Ladreiter, “Inversion, error analysis and validation of GPS/MET occultation data,” Ann. Geophys. 17, 122-138 (1999).
[CrossRef]

Tanner, W. E.

R. L. White, W. E. Tanner, and R. S. Polidan, “Star line-of-sight refraction observations from the orbiting astronomical observatory Copernicus and deduction of stratospheric structure in the tropical region,” J. Geophys. Res. 88, 8535-8542 (1983).
[CrossRef]

Thompson, E.

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

Thornton, C. L.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Trenberth, K.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Vervack, R. J.

R. J. Vervack, Jr., J. H. Yee, J. F. Carbary, and F. Morgan, “Atmospheric remote sensing using a combined extinctive and stellar occultation technique. 3. Inversion methods for refraction measurements,” J. Geophys. Res. 107, doi:10.1029/2001JD000796 (2002).
[CrossRef]

Ward, D. M.

Ware, R.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

White, R. L.

R. L. White, W. E. Tanner, and R. S. Polidan, “Star line-of-sight refraction observations from the orbiting astronomical observatory Copernicus and deduction of stratospheric structure in the tropical region,” J. Geophys. Res. 88, 8535-8542 (1983).
[CrossRef]

Whiteley, M. A.

M. A. Whiteley, “Design of a space-borne Sun tracking system.,” M.S. thesis, (Utah State University, 2006).

Yee, J. H.

R. J. Vervack, Jr., J. H. Yee, J. F. Carbary, and F. Morgan, “Atmospheric remote sensing using a combined extinctive and stellar occultation technique. 3. Inversion methods for refraction measurements,” J. Geophys. Res. 107, doi:10.1029/2001JD000796 (2002).
[CrossRef]

Yunck, T. P.

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Zou, X.

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Ann. Geophys. (2)

K. Hocke, “Inversion of GPS meteorology data,” Ann. Geophys. 15, 443-450 (1997).
[CrossRef]

A. K. Steiner, G. Kirchengast, and H. P. Ladreiter, “Inversion, error analysis and validation of GPS/MET occultation data,” Ann. Geophys. 17, 122-138 (1999).
[CrossRef]

Appl. Opt. (2)

Astron. J. (1)

G. Fjeldbo, A. J. Kliore, and V. R. Eshleman, “The neutral atmosphere of Venus as studied with the Mariner V Radio Occultation Experiments,” Astron. J. 76, 123-140(1971).
[CrossRef]

Bull. Am. Meteorol. Soc. (1)

R. Ware, M. Exner, D. Feng, M. Gorbunov, K. Hardy, B. Herman, Y. Kuo, T. Meehan, W. Melbourne, C. Rocken, W. Schreiner, S. Sokolovsky, F. Solheim, X. Zou, R. Anthes, S. Businger, and K. Trenberth, “GPS sounding of the atmosphere from low Earth orbit: preliminary results,” Bull. Am. Meteorol. Soc. 77, 19-40 (1996).
[CrossRef]

Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., Engl. Transl. (1)

G. M. Grechko, A. S. Gurvich, V. A. Lyakhov, S. A. Savchenko, and S. V. Sokolovskiy, “Results of an investigation of refraction during the third expedition on the Salyut-6 Orbiter,” Izv. Russ. Acad. Sci. Atmos. Oceanic Phys., Engl. Transl. 17, 835-841(1981).

J. Atmos. Solar-Terr. Phys. (1)

L. L. Gordley, M. Hervig, C. Fish, J. M. Russell III, S. Bailey, J. Cook, S. Hansen, A. Shumway, G. Paxton, L. Deaver, T. Marshall, J. Burton, B. Magill, C. Brown, E. Thompson, and J. Kemp, “The Solar Occultation For Ice Experiment (SOFIE),” J. Atmos. Solar-Terr. Phys. 71, 300-315, doi:10.1016/j.jastp.2008.07.012 (2009).
[CrossRef]

J. Geophys. Res. (4)

A. E. Hedin, “Extension of the MSIS Thermosphere Model into the middle and lower atmosphere,” J. Geophys. Res. 96, 1159-1172 (1991).
[CrossRef]

R. L. White, W. E. Tanner, and R. S. Polidan, “Star line-of-sight refraction observations from the orbiting astronomical observatory Copernicus and deduction of stratospheric structure in the tropical region,” J. Geophys. Res. 88, 8535-8542 (1983).
[CrossRef]

R. J. Vervack, Jr., J. H. Yee, J. F. Carbary, and F. Morgan, “Atmospheric remote sensing using a combined extinctive and stellar occultation technique. 3. Inversion methods for refraction measurements,” J. Geophys. Res. 107, doi:10.1029/2001JD000796 (2002).
[CrossRef]

R. A. Phinney and D. C. Anderson, “On the radio occultation method for studying planetary atmospheres,” J. Geophys. Res. 73, 1819-1827 (1968).
[CrossRef]

Metrologia (1)

B. Edlen, “The refractive index of air,” Metrologia 2, 71-80(1966).
[CrossRef]

Opt. Eng. (1)

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170-177 (1991).
[CrossRef]

Planet. Space Sci. (1)

L. M. Jones, F. F. Fischbach, and J. W. Peterson, “Satellite measurements of atmospheric structure by refraction,” Planet. Space Sci. 9, 351-352 (1962).
[CrossRef]

Proc. SPIE (2)

L. L. Gordley, M. J. McHugh, M. E. Hervig, J. C. Burton, L. Liu, B. E. Magill, and J. M. Russell, “Temperature, pressure and high-fidelity pointing knowledge for solar occultation using 2D focal plane arrays,” Proc. SPIE 5883, 588310 (2005).

J. C. Burton, K. W. Miller, and S. K. Park, “Rectangularly and hexagonally sampled imaging system fidelity analysis,” Proc. SPIE 1961, 81-92 (1993).
[CrossRef]

Science (1)

E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K. Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G. Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N. Nagatani, “Initial results of radio occultation observations of Earth's atmosphere using the Global Positioning System,” Science 271, 1107-1110 (1996).
[CrossRef]

Other (1)

M. A. Whiteley, “Design of a space-borne Sun tracking system.,” M.S. thesis, (Utah State University, 2006).

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Figures (13)

Fig. 1
Fig. 1

Refraction geometry. The red line depicts the path of light through the Earth’s limb to the sensor, shown as a large solid dot. The refraction angle, α, is the change in direction of the ray from when it enters the atmosphere to where it is received at the sensor. This is approximately the difference between the geometric angle and the observed impact angle at the satellite ( θ G minus θ O ). The radius at the impact tangent point, the point of closest approach for the observed ray at angle θ O , is called the impact radius, r O . The altitude above the surface for the same point is called the impact altitude. The true refracted point of minimum perigee is labeled r T .

Fig. 2
Fig. 2

Refracted and unrefracted images of the setting Sun at five different snapshot times as they would appear from a low-Earth orbit. The chosen elapsed time between image 2 and image 5 is the time, Δ t , required for the straight ray to the top edge of the Sun to move one unrefracted solar extent relative to the constant geopotential height horizon. Δ t = t 5 t 2 . Note that α T ( t 5 ) = α B ( t 5 Δ t ) . It can be shown that α B ( t ) = E o E ( t ) + α B ( t Δ t ) , where E o is the unrefracted vertical extent and E ( t ) is the refracted (observed) vertical extent (note E o = E ( t ) above the atmosphere).

Fig. 3
Fig. 3

Search State (grid is not to scale). Search mode uses a modulus of 16 to allow full grid search in less than 0.01 s .

Fig. 4
Fig. 4

Coarse State. Position of the image is further refined after the Search State to provide location accuracy necessary for initiating Fine Track State.

Fig. 5
Fig. 5

Fine Tracking State (illustrative—not to scale). The Sun image is kept within the FPA by the spacecraft. The science FOV is fixed relative to the Sun sensor FOV. Tracking the solar edges locates the science FOV relative to the solar image and provides the image extent used for refraction angle measurements. Center sums are used to measure atmospheric transmission, which is incorporated into the edge intensity model.

Fig. 6
Fig. 6

Removal of a unique readout noise produced by the Sun sensor electronics.

Fig. 7
Fig. 7

Empirical Top Edge Model. The black line is the Boltzmann function model for top edge. The red are the 560,000 individual data points from the top edge and the many events used to determine the parameters for the Boltzmann function.

Fig. 8
Fig. 8

Empirical Bottom Edge Model. The black line is the Boltzmann function model for bottom edge. The red are the 560,000 individual data points from the bottom edge and the many events used to determine the parameters for the Boltzmann function.

Fig. 9
Fig. 9

Solar Extent and 5-point running standard deviation for event 6104. The green line is standard deviation of measured extent and blue is the measured extent.

Fig. 10
Fig. 10

Measured “Solar Image Shrinkage” plotted with inferred refraction angle. “Shrinkage” is typically 4% (at high altitudes) less than the refraction angle at the bottom of the solar image.

Fig. 11
Fig. 11

Temperature profile, retrieved from refraction profile in Fig. 10, compared to the NCEP/MSIS combined profile and profile retrieved from the SOFIE 4.3 μm channel.

Fig. 12
Fig. 12

Comparison of temperature profiles for two events, late fall and summer of 2008. Black is the temperature retrieval from the SOFIE 4.3 μm radiometer channel. The red is from the refraction angle analysis. The green, added for comparison, is from the NCEP product, extended above 50 km with MSIS.

Fig. 13
Fig. 13

Statistical comparison of 31 temperature profiles retrieved from refraction angle versus those retrieved from CO 2 transmission. Temperature and pressure from CO 2 transmission is used to simulate a refraction angle upper boundary. The three comparisons are for three different upper boundary merge windows, which are roughly 15 km high with bottom starting at approximately 55, 60, and 65 km . Also plotted is the standard deviation about the mean difference. (The bias between 40 and 50 km is a known error in the SOFIE temperature retrieval using the 4.3 μm CO 2 transmission and will be corrected in a future data release.)

Equations (21)

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

d P = P g d z / ( R T ) = ρ g d z .
n ( r 0 O ) = exp [ 1 π r 0 O α ( r O ) [ ( r O ) 2 ( r 0 O ) 2 ] 1 / 2 d r O ] .
r O = r T n ( r T ) .
α B = θ B G θ B O
α T = θ T G θ T O .
α B α T = θ B G θ T G ( θ B O θ T O ) = E o E ,
α B ( t ) = E o E ( t ) + α T ( t ) .
θ B G ( t ) = θ T G ( t ) + E o = θ T G ( t + Δ t ( t ) ) .
θ B O ( t ) = θ T O ( t ) + E ( t ) ,
θ B O ( t ) = θ T O ( t ) + E ( t ) = θ T O ( t + Δ t ( t ) ) .
α B ( t ) = E o E ( t ) + α B ( t Δ t ) .
V [ j ] = i = M 1 M 2 FPA [ i , j ] H [ i ] = j = N 1 N 2 FPA [ i , j ]
v c = j N j × V [ j ] j N V [ j ] , h c = i M i × H [ i ] i M H [ i ] .
R [ i , j ] = FPA [ i , j ] ( i = 1 M j = 1 N FPA [ i , j ] M × N ) ,
H ( i ) = C j = n 1 n 2 I ( i , j ) R ( i , j ) = j = n 1 n 2 FPA ( i , j ) ,
H C ( i ) = C j = n 1 n 2 I ( i , j ) = K H ( i ) ,
K = j = n 1 n 2 I ( i , j ) / ( j = n 1 n 2 I ( i , j ) R ( i , j ) ) .
y = a 1 + ( a 0 a 1 ) ( 1 + e ( x a 2 a 3 ) ) ,
For the high elevation For the low elevation (top) edge: (bottom) edge: a 0 = 0.0500416 a 0 = 0.595815 a 1 = 0.464446 a 1 = 0.000650605 a 2 = 0.00534758 a 2 = 0.991427 a 3 = 0.00404353 a 3 = 0.00716971
E = ( 512 X ) × 7.10 60 ( elevation in arcmins ) ,
A = ( Y 511 ) × 7.18 60 ( azimuth in arcmins ) .

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