Interpretation of data in multidimensional spaces and its application to Coulomb-explosion imaging

A solution is presented for the problem of interpreting measurements of data from many degrees of freedom where binning is prohibitive. A binninglike procedure is introduced in which data and theory are represented by a set of independent expectation values. A comparison between theory and experiment is then performed by a conventional procedure together with an additional test of the independence of the expectation values. Associated uncorrelated errors are derived as well. The application of this method to Coulomb-explosion imaging is discussed. The method is illustrated by the analysis of the bending angle distribution of the CH2+ molecule from Coulomb-explosion imaging measurements.