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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 60, Iss. 5 — May. 1, 1970
  • pp: 659–666

Resolvability of Objects from the Standpoint of Statistical Parameter Estimation

CARL W. HELSTROM  »View Author Affiliations


JOSA, Vol. 60, Issue 5, pp. 659-666 (1970)
http://dx.doi.org/10.1364/JOSA.60.000659


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Abstract

The values of the radiance at points of an incoherently radiating object are considered as parameters of the statistical description of the field at the aperture of an observing optical instrument. By means of the Cramér-Rao inequality, a lower bound is set to the mean-square errors of unbiased estimates of the radiance values. The errors are shown to increase rapidly when the object is sampled at points separated by less than a conventional resolution interval.

Citation
CARL W. HELSTROM, "Resolvability of Objects from the Standpoint of Statistical Parameter Estimation," J. Opt. Soc. Am. 60, 659-666 (1970)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-60-5-659


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References

  1. H. Wolter, in Progress in Optics. I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), p. 157.
  2. Y. T. Lo, J. Appl. Phys. 32, 2052 (1961).
  3. C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).
  4. L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
  5. C. W. Helstrom, J. Opt. Soc. Am. 59, 164 (1969).
  6. C. W. Helstrom, J. Opt. Soc. Am. 60, 521 (1970).
  7. D. Gabor, in Progress in Optics I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), p. 109.
  8. C. W. Helstrom, Statistical Theory of Signal Detection, 2nd ed. (Pergamon Press, Ltd., Oxford, 1968), pp. 69–72.
  9. Reference 5, Eqs. (1.8) and (1.9).
  10. H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, New Jersey, 1946), pp. 473 ff.
  11. C. R. Rao, Bull. Calcutta Math. Soc. 37, 81 (1945).
  12. L. Schmetterer, Mathematische Statistik (Springer-Verlag, New York, 1966), p. 63.
  13. Reference 5, Appendix B.
  14. C. W. Helstrom, J. Opt. Soc. Am. 60, 233 (1970).
  15. Reference 1, Eq. (A4).
  16. C. W. Helstrom, J. Opt. Soc. Am. 59, 924 (1969), Eq. (5.10).
  17. Reference 5, Eq. (6.3), in which F=M.
  18. Reference 6, Sec. I, especially Eqs. (1.15) and (1.21).

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