Figure 4: Error in estimating the displacement of a particle location from the digitizing grid as a function of the size w of the mask used for centroid refinement. Heavy lines are quadrature sums of the error estimates in eqns. (12) and (13). Circles are Monte-Carlo calculations for Gaussian surfaces of revolution with additive noise and halfwidths s = 6 pixels (a) and s = 2 pixels (b). In both cases, the error estimate provides an adequate value for both the optimal kernel support, w, and for the accuracy of the position estimate at that value.