Patent ID: 8786521

Claim:
A security element for security papers, value documents, or other non-transitory data carriers, the security element comprising: (A) a motif layer including a motif image that is subdivided into a plurality of cells, in each of which are arranged imaged regions of a planar target image defined by an image function f(x,y), (B) a viewing grid composed of a plurality of viewing elements for reconstructing the target image when the motif image is viewed with the aid of the viewing grid, the motif image of the motif layer having an image function m(x,y) that is given by m ⁡ ( x , y ) = f ⁡ ( ( x y ) + ( A ⁡ ( x , y ) - I ) · ( ( ( ( x y ) + w d ⁡ ( x , y ) ) ⁢ mod ⁢ ⁢ W ) - w d ⁡ ( x , y ) - w c ⁡ ( x , y ) ) ) · g ⁡ ( x , y ) ⁢ ⁢ ⁢ where ⁢ ⁢ w d ⁡ ( x , y ) = W · ( d 1 ⁡ ( x , y ) d 2 ⁡ ( x , y ) ) ⁢ ⁢ and ⁢ ⁢ w c ⁡ ( x , y ) = W · ( c 1 ⁡ ( x , y ) c 2 ⁡ ( x , y ) ) , such that the planar target image is reconstructed when the motif image of the motif layer is viewed through the viewing grid; wherein a unit cell of the viewing grid being described by lattice cell vectors w 1 = ( w 11 w 21 ) ⁢ ⁢ and ⁢ ⁢ w 2 = ( w 12 w 22 ) and combined in the matrix W = ( w 11 w 12 w 21 w 22 ) , the matrix A ⁡ ( x , y ) = ( a 11 ⁡ ( x , y ) a 12 ⁡ ( x , y ) a 21 ⁡ ( x , y ) a 22 ⁡ ( x , y ) ) describes a desired magnification and movement behavior of the reconstructed planar target image, the vector (c 1 (x,y), c 2 (x,y)), where 0≦c 1 (x,y),c 2 (x,y)<1, indicates position of the center of the viewing elements relative to the cells of the motif image of the motif layer, the vector (d 1 (x,y), d 2 (x,y)), where 0≦d 1 (x,y), d 2 (x, y)<1, represents a location-dependent displacement of cell boundaries of the plurality of cells in the motif image of the motif layer, g(x,y) is a mask function for adjusting visibility of the reconstructed planar target image, and wherein the reconstructed planar target image either exhibits no periodicity, or exhibits a periodicity that is described by a 2×2 matrix P, wherein the periodicity unit cell is not equal to (A−I) W.