A Geometrical Approach to Moiré Pattern Calculations

Moiré patterns can be calculated from the vector sums and differences of the spatial frequencies of the generating grids taken locally at various points in the field of overlap. Thus the spatial frequency at any point on a zone plate is given by the vector from that point to the zone-plate centre. Consequently two overlapping zone plates always give a difference moiré pattern represented by the distance between their centres. The analysis has been applied to a number of cases, involving line grids, zone plates, Girard grilles, and sets of equispaced concentric circles. In the latter case unequal sets give rise to a set of Cartesian ovals.