Velocity map imaging (VMI) is used in mass spectrometry and in angle resolved photo-electron spectroscopy to determine the lateral momentum distributions of charged particles accelerated towards a detector. VM-images are composed of projected Newton spheres with a common centre. The 2D images are usually evaluated by a decomposition into base vectors each representing the 2D projection of a set of particles starting from a centre with a specific velocity distribution. We propose to evaluate 1D projections of VM-images in terms of 1D projections of spherical functions, instead. The proposed evaluation algorithm shows that all distribution information can be retrieved from an adequately chosen set of 1D projections, alleviating the numerical effort for the interpretation of VM-images considerably. The obtained results produce directly the coefficients of the involved spherical functions, making the reconstruction of sliced Newton spheres obsolete.