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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 11 — Nov. 1, 2007
  • pp: 3530–3546

Relativistic effects in earth-orbiting Doppler lidar return signals

Neil Ashby  »View Author Affiliations


JOSA A, Vol. 24, Issue 11, pp. 3530-3546 (2007)
http://dx.doi.org/10.1364/JOSAA.24.003530


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Abstract

Frequency shifts of side-ranging lidar signals are calculated to high order in the small quantities ( v c ) , where v is the velocity of a spacecraft carrying a lidar laser or of an aerosol particle that scatters the radiation back into a detector (c is the speed of light). Frequency shift measurements determine horizontal components of ground velocity of the scattering particle, but measured fractional frequency shifts are large because of the large velocities of the spacecraft and of the rotating earth. Subtractions of large terms cause a loss of significant digits and magnify the effect of relativistic corrections in determination of wind velocity. Spacecraft acceleration is also considered. Calculations are performed in an earth-centered inertial frame, and appropriate transformations are applied giving the velocities of scatterers relative to the ground.

© 2007 Optical Society of America

OCIS Codes
(010.1100) Atmospheric and oceanic optics : Aerosol detection
(010.3640) Atmospheric and oceanic optics : Lidar
(350.5720) Other areas of optics : Relativity

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: February 2, 2007
Revised Manuscript: June 27, 2007
Manuscript Accepted: July 11, 2007
Published: October 18, 2007

Citation
Neil Ashby, "Relativistic effects in earth-orbiting Doppler lidar return signals," J. Opt. Soc. Am. A 24, 3530-3546 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-11-3530


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References

  1. C. Møller, The Theory of Relativity, 2nd ed. (Clarendon Press, 1972) pp. 39-42.
  2. H. P. Robertson and T. W. Noonan, Relativity and Cosmology (Saunders, 1968) pp. 45 ff.
  3. R. D'Inverno, Introducing Einstein's Relativity (Clarendon Press, 1992) p. 40.
  4. V. S. R. Gudimetla and M. Kavaya, Special Relativity Corrections for Space-Based Lidar, Appl. Opt.38, 6374-6382 (1999).
  5. B. W. Parkinson and J. J. Spilker, Jr., Global Positioning System: Theory and Applications (American Institute of Aeronautics and Astronautics, 1996) Vol. I, pp. 161-165.

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