Subpixel position measurement using 1D, 2D and 3D centroid algorithms with emphasis on applications in confocal microscopy

The accuracy with which centroid algorithms in 1D, 2D and 3D can estimate an object's position has been investigated. Three factors that can influence the method's accuracy have been investigated: systematic error of the algorithm, influence of photon noise and the influence of perturbations such as scanning nonlinearity. The variation of the accuracy with parameters that are relevant for confocal microscopy, such as object diameter and photon noise/pixel, has been considered. Theory and simulations presented show that the variation of the accuracy with respect to such parameters can differ drastically between the 1D, 2D and 3D cases. Experiments performed using microspheres show that the magnitudes of the three types of error can be approximately the same under normal operating conditions and that it is therefore necessary to take all three into account when assessing the total error.