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 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
Full Article | PDF ArticleMore Like This
Nicolas Roux, François Goudail, and Philippe Réfrégier
J. Opt. Soc. Am. A 22(11) 2532-2541 (2005)
Charles L. Matson and Alim Haji
J. Opt. Soc. Am. A 23(11) 2702-2713 (2006)
Siavash Yazdanfar, Changhuei Yang, Marinko V. Sarunic, and Joseph A. Izatt
Opt. Express 13(2) 410-416 (2005)