In the following we give expressions for the covariance matrix (for details see 1), assuming that the (dominant) photon noise follows a Poisson distribution. Display Formula
(17)where and denote the indices of the matrix elements running from 1 to . The quantities on the right side represent data derived from measured DTOFs, and are the third and fourth centralized moments, respectively. The expressions for those submatrices of given in Eqs. (12)–(14) and (17) indicate that the respective moments are statistically dependent in case they are derived from the same DTOF, i.e., from the same distance . The covariances between and as well as between and turn out to be zero even for [Eqs. (15) and (16)]. However, they do not vanish in general as a property of the moments, but rather because of the specific property of the Poisson distribution (see 1).