rule of thumb

Phil Marshall emailed me, asking about the original citation / derivation of the rule of thumb that a source detected in an image at some signal-to-noise ratio [s/n] can be centroided to an accuracy of about the FWHM divided by [s/n]. It was funny he asked, because we had discussed the very same issue only days earlier in responding to the referee for the faint-motion paper. Rix found King (1983), which probably is the first paper to discuss this (interested if anyone out there knows a more recent reference). Nowadays, the standard answer is the Cramer-Rao bound (Robert Lupton said this in response to a query from me), but that isn't quite the answer most people are looking for.

1 comment:

  1. Here are some other/earlier references that I think are relevant. First here is very comprehensive reference for generic elliptical gaussians (Condon 1997, see Eq. 21):


    And a much earlier comprehensive treatment of 1D gaussians (Kaper 1966, see Eq. 5.8):


    Both of the above show the derivations that yield an error in the centroid of ~ FWHM/SNR.