OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 8 — Mar. 10, 2011
  • pp: 1124–1135

Moment-matching method for extraction of asymmetric beam jitters and bore sight errors in simulations and experiments with actively illuminated satellites of small physical cross section

V. S. Rao Gudimetla and Jim F. Riker  »View Author Affiliations


Applied Optics, Vol. 50, Issue 8, pp. 1124-1135 (2011)
http://dx.doi.org/10.1364/AO.50.001124


View Full Text Article

Enhanced HTML    Acrobat PDF (425 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Optical returns from remote resident space-based objects such as satellites suffer from pointing and tracking errors. In a previously reported paper [ Appl. Opt. 46, 5608 (2007)], we developed a moment-matching technique that used the statistics of time series of these optical returns to extract information about bore sight and symmetric beam jitter errors (symmetric here implies that the standard deviations of the jitter measured along two orthogonal axes, perpendicular to the line of sight, are equal). In this paper, we extend that method to cover the case of asymmetric beam jitter and bore sight. The asymmetric beam jitter may be due to the combination of symmetric atmospheric turbulence beam jitter and optical beam train jitter. In addition, if a tracking control system is operating, even the residual atmospheric tracking jitter could be asymmetric because the power spectrum is different for the slewing direction compared to the cross-track direction. Analysis of the problem has produced a set of nonlinear equations that can be reduced to a single but much higher-order nonlinear equation in terms of one of the jitter variances. After solving for that jitter, all the equations can be solved to extract all jitter and bore sight errors. The method has been verified by using simulations and then tested on experimental data. In order to develop this method, we derived analytical expressions for the probability density function and the moments of the received total intensity. The results reported here are valid for satellites of small physical cross section, or else those with retroreflectors that dominate the signal return. The results are, in general, applicable to the theory of noncircular Gaussian speckle with a coherent background.

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors
(120.5630) Instrumentation, measurement, and metrology : Radiometry
(130.6750) Integrated optics : Systems
(010.1285) Atmospheric and oceanic optics : Atmospheric correction

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: September 20, 2010
Revised Manuscript: January 5, 2011
Manuscript Accepted: January 11, 2011
Published: March 7, 2011

Citation
V. S. Rao Gudimetla and Jim F. Riker, "Moment-matching method for extraction of asymmetric beam jitters and bore sight errors in simulations and experiments with actively illuminated satellites of small physical cross section," Appl. Opt. 50, 1124-1135 (2011)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-8-1124


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. V. S. R. Gudimetla and J. F. Riker, “Moment-matching method for extracting beam jitter and bore sight in experiments with satellites of small physical cross section,” Appl. Opt. 46, 5608–5616 (2007). [CrossRef]
  2. D. Voelz, “Flood Beam Experiments I,” PL-TR-96-1162, Air Force Research Laboratory, Kirtland Air Force Base, N.Mex. (1996).
  3. G. Lukesh, S. Chandler, and D. Voelz, “Estimation of laser system pointing performance by use of statistics of return photons,” Appl. Opt. 39, 1359–1371 (2000). [CrossRef]
  4. G. Lukesh, S. Chandler, and D. Voelz, “Estimation of laser system pointing performance via the statistics of return signal,” Proc. SPIE 3494, 111–121 (1998). [CrossRef]
  5. G. Lukesh, S. Chandler, and C. Barnard, “Estimation of satellite laser optical cross section: a comparison of simulation and field results,” Proc. SPIE 4167, 53–63 (2001). [CrossRef]
  6. G. Lukesh, S. Chandler, and D. Voelz, “Analysis of satellite laser optical cross sections from the Active Imaging Testbed,” Proc. SPIE 4538, 24–33 (2002). [CrossRef]
  7. S. Chandler and G. Lukesh, “The statistical analysis of received time-series signals from the laser illumination of remote objects through turbulence,” Proc. SPIE 6522, 65220D (2006). [CrossRef]
  8. D. K. Borah, D. Voelz, and S. Basu, “Maximum-likelihood estimation of a laser system pointing parameters by use of return photon counts,” Appl. Opt. 45, 2504–2509(2006). [CrossRef]
  9. D. K. Borah and D. G. Voelz, “Cramer–Rao lower bounds on estimation of laser beam pointing parameters by use of return photon signal,” Opt. Lett. 31, 1029–1031 (2006). [CrossRef]
  10. D. K. Borah, D. G. Voelz, G. Lukesh, and S. Chandler, “Maximum likelihood parameter estimation of a laser system using return photons,” Proc. SPIE 6522, 65220J (2006). [CrossRef]
  11. D. K. Borah and D. G. Voelz, “Estimation of laser beam pointing parameters in the presence of atmospheric turbulence,” Appl. Opt. 46, 6010–6018 (2007). [CrossRef]
  12. J. F. Riker, “Beam diameter at distant targets illuminated from Maui,” TEM 2004-07, Air Force Research Laboratory, Kirtland Air Force Base, N.Mex. (3 April 2004).
  13. A related summary and results of can be found in J. F. Riker, “Validation of active track Gaussian beam propagation and target signature prediction,” Proc. SPIE 4724, 45–56(2002). [CrossRef]
  14. J. F. Riker, “Exact tilt Strehl for degraded Gaussian beams,” TEM 2003-27, Air Force Research Laboratory, Kirtland Air Force Base, N. Mex., 30 September 2003.
  15. J. F. Riker, R.Q. Fugate, T. Holcomb, J. Kann, W. H. Lowrey, A. C. Slavin, J. M. Spinhirne, A. L. Tuffli, and J. Brown, “Active tracking with moderate power lasers,” Proc. SPIE 5552, 123–132 (2004) . [CrossRef]
  16. J. F. Riker, “Active track optical cross sections in the presence of local tilt,” presented at the SPIE International Symposium on Defense and Security, Orlando, Florida, April 2004.
  17. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (SPIE, 2007).
  18. R. K. Tyson and B. W. Frazier, Field Guide for Adaptive Optics (SPIE, 2004).
  19. B. E. Stribling, M. C. Roggemann, D. Archambeault, and R. B. Holmes, “Laser beam uplink jitter and bore sight estimation for a point source target,” presented at the SPIE International Symposium on Defense and Security, Orlando, Florida, April 2004. For information of readers, SPIE digital library does not provide a copy of this paper.
  20. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1978).
  21. V. S. R. Gudimetla, “Moments of the intensity of a non-circular Gaussian laser speckle in the diffraction field,” Opt. Commun. 130, 348–356 (1996). [CrossRef]
  22. J. W. Goodman, Statistical Optics (Wiley, 1985), Chaps. 2 and 3.
  23. G. Arfken, Mathematical Methods for Physicists (Academic, 1985), Chap. 11, p. 613.
  24. M. Nakagami, “The m-distribution-a general formula of intensity distribution of rapid fading,” in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, ed. (Pergamon, 1960), pp. 3–36.
  25. T. L. Saty and J. Braun, Nonlinear Mathematics (Dover, 1984), Chap. 1.
  26. Y. Bard, Nonlinear Parameter Estimation (Academic, 1974).
  27. G. R. Osche, “Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle,” Appl. Opt. 39, 4255–4262 (2000). [CrossRef]
  28. D. K. Borah and D. G. Voelz, “Pointing error effects on free space optical communication links in the presence of atmospheric turbulence,” J. Lightwave Technol. 27, 3965–3973(2009). [CrossRef]
  29. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill , 1984), Chap. 5, p. 156, Eq. 5-80.
  30. I. S. Gradshteyn and I. M. Rhyzhik, Tables of Integrals, Series and Products (Academic, 1980).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited