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. In the case of a concentric band moiré image, base band grating layer and revealing line grating layer layouts may be produced according to geometric transformations, which yield, upon
relative displacement of the position sampled by the revealing layer on the base layer, a band moiré image whose patterns move either radially, circularly or according to a
spiral trajectory, depending on the orientation of the base band replication vector in the original non-transformed base layer space. In addition, it is possible to conceive a revealing line grating layer which when translated on top of the base band grating layer, generates a band moiré image which is subject to a periodic deformation. Furthermore, thanks also to the availability of a large number of geometric transformations and transformation variants (i.e. different values for the transformation constants), one may create documents having their own individualized document protection. The base band layer and the revealing layer may be separated by a small gap and form a fixed composed layer, where, thanks to the well-known
parallax effect, by tilting the composed layer in respect to an observer, different positions of the base layer are sampled and a dynamically moving moiré image is generated. A computing
system may automatically generate upon request an individualized protected security document having specific base band grating and revealing line grating layouts. The computing
system may then upon request generate and issue a security document incorporating the base band grating layer, a base band grating layer or a revealing line grating layer allowing to authenticate a previously issued security document. The presented methods may be used for creating an individualized protection for various categories of documents (banknotes, identity documents, checks, diploma,
travel documents, tickets) and valuable products (optical disks, CDs, DVDs, CD-ROMs, packages for medical drugs, products with affixed labels, watches).