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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

  • Vol. 3, Iss. 11 — Nov. 1, 1986
  • pp: 1809–1815

Cramér–Rao lower bounds on the performance of charge-coupled-device optical position estimators

Kim A. Winick  »View Author Affiliations


JOSA A, Vol. 3, Issue 11, pp. 1809-1815 (1986)
http://dx.doi.org/10.1364/JOSAA.3.001809


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Abstract

The problem of optically estimating an object’s position by using a charge-coupled device (CCD) array composed of square pixels Δx on a side is analyzed. The object’s image spot at the CCD is assumed to have a Gaussian intensity profile with a 1/e point at a radial distance of 2 σ s from the peak, and the CCD noise is modeled as Poisson-distributed, dark-current shot noise. A two-dimensional Cramér–Rao bound is developed and used to determine a lower limit for the mean-squared error of any unbiased position estimator, and the maximum-likelihood estimator is also derived. For the one-dimensional position-estimation problem the lower bound is shown to be minimum for a pixel-to-image size ratio Δx/σs of between 1 and 2 over a wide range of signal-to-noise ratios. Similarly for the two-dimensional problem, the optimum ratio is shown to lie between 1.5 and 2.5. As is customary in direct detection systems, it is also observed that the lower bound is a function of both the signal power and noise power separately and not just of their ratio. Finally, the maximum-likelihood estimator is shown to be independent of the signal and noise powers at high signal-to-noise ratios.

© 1986 Optical Society of America

History
Original Manuscript: September 13, 1985
Manuscript Accepted: May 12, 1986
Published: November 1, 1986

Citation
Kim A. Winick, "Cramér–Rao lower bounds on the performance of charge-coupled-device optical position estimators," J. Opt. Soc. Am. A 3, 1809-1815 (1986)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-3-11-1809

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