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.

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  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).

Cramér, H.

H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, New Jersey, 1946), pp. 473 ff.

Gabor, D.

D. Gabor, in Progress in Optics I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), p. 109.

Harris, R. W.

C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).

Helstrom, C. W.

C. W. Helstrom, Statistical Theory of Signal Detection, 2nd ed. (Pergamon Press, Ltd., Oxford, 1968), pp. 69–72.

C. W. Helstrom, J. Opt. Soc. Am. 59, 164 (1969).

C. W. Helstrom, J. Opt. Soc. Am. 60, 521 (1970).

C. W. Helstrom, J. Opt. Soc. Am. 60, 233 (1970).

C. W. Helstrom, J. Opt. Soc. Am. 59, 924 (1969), Eq. (5.10).

Lo, Y. T.

Y. T. Lo, J. Appl. Phys. 32, 2052 (1961).

Mandel, L.

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

Rao, C. R.

C. R. Rao, Bull. Calcutta Math. Soc. 37, 81 (1945).

Rushforth, C. K.

C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).

Schmetterer, L.

L. Schmetterer, Mathematische Statistik (Springer-Verlag, New York, 1966), p. 63.

Wolf, E.

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

Wolter, H.

H. Wolter, in Progress in Optics. I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), p. 157.

Other (18)

H. Wolter, in Progress in Optics. I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), p. 157.

Y. T. Lo, J. Appl. Phys. 32, 2052 (1961).

C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

C. W. Helstrom, J. Opt. Soc. Am. 59, 164 (1969).

C. W. Helstrom, J. Opt. Soc. Am. 60, 521 (1970).

D. Gabor, in Progress in Optics I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), p. 109.

C. W. Helstrom, Statistical Theory of Signal Detection, 2nd ed. (Pergamon Press, Ltd., Oxford, 1968), pp. 69–72.

Reference 5, Eqs. (1.8) and (1.9).

H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, New Jersey, 1946), pp. 473 ff.

C. R. Rao, Bull. Calcutta Math. Soc. 37, 81 (1945).

L. Schmetterer, Mathematische Statistik (Springer-Verlag, New York, 1966), p. 63.

Reference 5, Appendix B.

C. W. Helstrom, J. Opt. Soc. Am. 60, 233 (1970).

Reference 1, Eq. (A4).

C. W. Helstrom, J. Opt. Soc. Am. 59, 924 (1969), Eq. (5.10).

Reference 5, Eq. (6.3), in which F=M.

Reference 6, Sec. I, especially Eqs. (1.15) and (1.21).

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