A description of the eigenvalue spectrum for the data set used in the 3d reconstruction for the map. A data set consisting of pure noise has a characteristic eigenvalue spectrum which depends on the number of images, the number of image elements and the noise statistics. Since the eigenvalues are only determined by the spacing and number of the sample points, the eigenvalue spectrum is not affected by the signal to noise in the data or the reliability of the orientations. This information is seen from the resolution dependence of the phase residual seen during refinement. For the eigenvectors to be significant, the associated eigenvalues should stand out from the noise eigenvalue spectrum.