We present equations describing the basic grids that when superposed with themselves and then mutually translated create moiré patterns in the form of spherical, equilateral hyperbolic, and linear zone plates. The family of basic grids described forms a complete set of solutions. Moiré zone plates can serve as imaging elements with very long, variable focal lengths and have an application in alignment in the three-point technique. The derived solutions are then checked for cases of undesired residual translations and rotations. Evaluations of the focus based on paraxial ray tracing equations are also performed.