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The volumes of the islands are directly proportional to the relative probabilities of the ionisation processes.<ref name="LJF89"/> This useful quality of the map follows from a property of the [[Poisson distribution]], which governs the number of neon atoms in the focal volume and the number of electrons produced at a particular energy, <math>X_n(E_i)</math>. The property employed here is that the [[variance]] of a Poisson distribution is equal to its [[mean]] and this property is also inherited by covariance. Therefore the covariance plotted on the map is proportional to the number of neon atoms that produce pairs of electrons of particular energies. This makes covariance much more suitable for particle counting experiments than other bivariate estimators, such as [[Pearson's correlation coefficient]].
On the diagonal of the map there is an autocorrelation line. It is present there because the same spectra are used for the ''x'' and ''y'' axes. Thus, if an electron pulse is present at a particular energy on one axis, it is also present on the other axis giving the variance signal along the <math>E_x = E_y</math> line, which is usually stronger than the neighbouring covariance islands. The mirror symmetry of the map with respect to this line has the same origin. The autocorrelation line and the mirror symmetry are not present if two different detectors are used for the ''x'' and ''y'' signals, for example where one detector is used to detect ions and another to detect electrons.<ref name="LJF92">L J Frasinski, M Stankiewicz, P A Hatherly, G M Cross and K Codling “Molecular H<sub>2</sub> in intense laser fields probed by electron-electron electron-ion and ion-ion covariance techniques” ''Phys. Rev. A'' '''46''' R6789–R6792 (1992), [http://hdl.handle.net/10044/1/11612 open access]</ref>
[[Image:Parts of covariance map of neon.png|thumb|450px|'''Figure 4: Identification of neon ionization processes in the core-core (left) and core-valence (right) correlation regions.''' The top of the autocorrelation line is cut off to show the features behind. Symbols P, D, and A denote, respectively, ejection of a photoelectron, two photoelectrons (direct double photoionization by a single photon), and an Auger electron. The two detected electrons giving rise to the covariance signal are indicated by bold type.]]
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