Model-based synthesis of band moire images for authenticating security documents and valuable products

The present invention relies on a band moiré image layout model capable of predicting the band moiré image layer layout produced when superposing a base band grating layer of a given layout and revealing line grating layer of a given layout. Both the base band grating layer and the revealing line grating layer may have a rectilinear or a curvilinear layout. The resulting band moiré image layout may also be rectilinear or curvilinear. Thanks to the band moiré image layout model, one can choose the layout of two layers selected from the set of base band grating layer, revealing line grating layer and band moiré image layer and obtain the layout of the third layer by computation, i.e. automatically. A computing system may automatically generate upon request an individualized protected security document having specific base band grating and revealing line grating layouts.