Consistency and Symmetry Conditions for Plane Projections

Interdependences between plane projections of densities ρ(p) for various crystallographical structures are derived from the conditions of both the consistency and symmetry of projections. Some additional relations are obtained by treating plane projections as line projections of ρ̃$\text{}_{L}$(p) (ρ̃$\text{}_{L}$ is a line projection of ρ(p)) and using the consistency and symmetry conditions for the line projections. The relations found can be utilized for both an improvement of experimental spectra and a verification of various techniques used for e.g. correcting Compton profiles.