EP2164705B1 - A method for manufacturing a seamless continuous material for security elements, a seamless continuous material for security elements and methods for manufacturing impression or embossing cylinders - Google Patents

Description

The invention relates to a continuous material for security elements with micro-optical moiré magnification arrangements and to a method for producing such continuous material.

Data carriers, such as valuables or identity documents, but also other valuables, such as branded goods, are often provided with security elements for the purpose of security, which permit verification of the authenticity of the data carrier and at the same time serve as protection against unauthorized reproduction. The security elements can be embodied, for example, in the form of a security thread embedded in a banknote, a covering film for a banknote with a hole, an applied security strip or a self-supporting transfer element which is applied to a value document after its manufacture.

Security elements with optically variable elements, which give the viewer a different image impression under different viewing angles, play a special role, since they can not be reproduced even with high-quality color copying machines. For this purpose, the security elements can be equipped with security features in the form of diffraction-optically effective microstructures or nanostructures, such as with conventional embossed holograms or other hologram-like diffraction structures, as described, for example, in the publications EP 0 330 33 A1 or EP 0 064 067 A1 are described.

It is also known to use lens systems as security features. For example, in the document EP 0 238 043 A2 a security thread of a transparent material described on the surface of a grid of several parallel cylindrical lenses is imprinted. The Thickness of the security thread is chosen so that it corresponds approximately to the focal length of the cylindrical lenses. On the opposite surface of a printed image is applied register accurate, the print image is designed taking into account the optical properties of the cylindrical lenses. Due to the focusing effect of the cylindrical lenses and the position of the printed image in the focal plane different subregions of the printed image are visible depending on the viewing angle. By appropriate design of the printed image so that information can be introduced, which are visible only at certain angles. By appropriate design of the printed image while "moving" images can be generated. However, as the document rotates about an axis parallel to the cylindrical lenses, the subject moves only approximately continuously from one location on the security thread to another location.

For some time, so-called Moire magnification arrangements are used as security features. The principal operation of such Moire magnification arrangements is in the article "The Moire Magnifier", MC Hutley, R. Hunt, RF Stevens and P. Savander, Pure Appl. Opt. 3 (1994), pp. 133-142 , described. In short, moiré magnification thereafter refers to a phenomenon that occurs when viewing a raster of identical image objects through a lenticular of approximately the same pitch. As with each pair of similar rasters, this results in a moire pattern, in which case each of the moire fringes appears in the form of an enlarged and / or rotated image of the repeated element of the image raster.

In the production of such moiré magnification arrangements, an endless security element film is usually first produced as roll material, with the use of conventional production methods always being used Breakage, especially gaps or misalignment in the appearance of the security elements occur. These fractures are due to the fact that the precursors for the stamping tools used in the manufacture are generally manufactured as flat sheets which are mounted on a printing or embossing cylinder. At the seams, the mutually adjacent image patterns usually do not match and lead after printing or embossing in the appearance of the finished security elements to motive disorders of the type mentioned.

The publication DE 10 2005 028162 A1 relates to a security element and a method for its production. The publication DE 199 47 397 A1 discloses a method for seamless engraving of patterns.

Based on this, the object of the invention is to avoid the disadvantages of the prior art and, in particular, to provide a method for producing security elements with micro-optical moiré magnification arrangements with trouble-free motif images, as well as a corresponding continuous material.

This object is achieved by the method for producing continuous material for security elements with the features of claim 1. An endless material for security elements, a manufacturing method for security elements and method for the production of printing or embossing cylinders are given in the independent claims. Further developments of the invention are the subject of the dependent claims.

The invention relates to a method for producing continuous material for security elements with micro-optical moiré magnification arrangements according to claim 1.

The distortion according to the invention can relate only to the motif grid, only the focusing element grid or both screens. Depending on the given grids, the motif grid and the focusing element grid may also require different distortions, as explained in more detail below.

In this method, a repeat q is set in step c) along the endless longitudinal direction of the endless material. In particular, the longitudinal direction repeat q is given by the circumference of a stamping or printing cylinder for the generation of the motif grid and / or the focusing element grid.

liegt, und es wird eine lineare Transformation V ermittelt, die P auf Q abbildet. Als in der Nähe des Endpunkts Q liegender Gitterpunkt wird mit Vorteil ein Gitterpunkt P gewählt, dessen Abstand von Q entlang des Gittervektors oder der beiden Gittervektoren jeweils weniger als 10 Gitterperioden, bevorzugt weniger als 5, besonders bevorzugt weniger als 2 und insbesondere weniger als eine Gitterperiode beträgt. Insbesondere kann der dem Endpunkt Q nächstliegende Gitterpunkt als Gitterpunkt P gewählt werden.In step d), a grid point P of the first and / or the second grid is selected, which is close to the end point Q of the vector given by the longitudinal direction repeat $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

and a linear transformation V is detected which maps P to Q. Advantageously, a grid point P whose distance from Q along the grid vector or the two grid vectors is less than 10 grid periods, preferably less than 5, more preferably less than 2 and in particular less than one grid period, is chosen as the grid point lying near the end point Q is. In particular, the grid point closest to the end point Q can be selected as the grid point P.

berechnet, wobei $\left(\begin{array}{c}{\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{p}}_{\mathrm{y}}\end{array}\right)$

und $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

die Koordinatenvektoren des Gitterpunkts P bzw. des Endpunkts Q und $\overrightarrow{b}=\left(\begin{array}{c}{\mathrm{b}}_{\mathrm{x}}\\ {\mathrm{b}}_{\mathrm{y}}\end{array}\right)$

und $\overrightarrow{a}=\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

beliebige Vektoren darstellen. Um gering verzerrte Gitter zu erhalten, unterscheiden sich die Vektoren a und b dabei mit Vorteil nach Betrag und Richtung nur wenig oder sind sogar gleich. Nach einem einfachen Spezialfall wird die lineare Transformation V unter Verwendung der Beziehung $$\mathrm{V}=\left(\begin{array}{cc}1& 0\\ 0& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}1& {\mathrm{p}}_{\mathrm{x}}\\ 0& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}=\left(\begin{array}{cc}1& -{\mathrm{p}}_{\mathrm{x}}/{\mathrm{p}}_{\mathrm{y}}\\ 0& \mathrm{q}/{\mathrm{p}}_{\mathrm{y}}\end{array}\right)$$

berechnet.The linear transformation V will be useful using the relationship $$\mathrm{V}=\left(\begin{array}{cc}{\mathrm{b}}_{\mathrm{x}}& 0\\ {\mathrm{b}}_{\mathrm{y}}& \dot{\mathrm{q}}\end{array}\right)\cdot {\left(\begin{array}{cc}{\mathrm{a}}_{\mathrm{x}}& {\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}$$

calculated, where $\left(\begin{array}{c}{\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{p}}_{\mathrm{y}}\end{array}\right)$

and $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

the coordinate vectors of the grid point P and the end point Q and $\overrightarrow{b}=\left(\begin{array}{c}{\mathrm{b}}_{\mathrm{x}}\\ {\mathrm{b}}_{\mathrm{y}}\end{array}\right)$

and $\overrightarrow{a}=\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

represent any vectors. To obtain slightly distorted lattices, the vectors differ a and b with advantage for amount and direction only a little or are even the same. After a simple special case, the linear transformation V is calculated using the relationship $$\mathrm{V}=\left(\begin{array}{cc}1& 0\\ 0& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}1& {\mathrm{p}}_{\mathrm{x}}\\ 0& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}=\left(\begin{array}{cc}1& -{\mathrm{p}}_{\mathrm{x}}/{\mathrm{p}}_{\mathrm{y}}\\ 0& \mathrm{q}/{\mathrm{p}}_{\mathrm{y}}\end{array}\right)$$

calculated.

• ein Gitterpunkt P des ersten und/oder des zweiten Gitters ausgewählt, der in der Nähe des Endpunkts Q des durch den Längsrichtungs-Rapport gegebenen Vektors $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$
  
  liegt,
• ein Gitterpunkt A des ersten und/ oder des zweiten Gitters ausgewählt, der in der Nähe des Endpunkts B des durch den Querrichtungs-Rapport gegebenen Vektors $\left(\begin{array}{c}\mathrm{b}\\ 0\end{array}\right)$
  
  liegt, und
• eine lineare Transformation V ermittelt, die P auf Q und A auf B abbildet.

In addition to specifying a longitudinal direction repeat, in step c) a repeat b along the transverse direction of the endless material can be specified. In particular, it can be provided that the continuous material is cut into parallel longitudinal strips in a later method step, wherein the transverse direction repeat b is given by the width of these longitudinal strips. Appropriately, in step d)

• a grid point P of the first and / or the second grid selected near the end point Q of the vector given by the longitudinal direction repeat $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$
  
  lies,
• a grid point A of the first and / or the second grid selected near the end point B of the vector given by the cross-direction repeat $\left(\begin{array}{c}\mathrm{b}\\ 0\end{array}\right)$
  
  lies, and
• determines a linear transformation V that maps P to Q and A to B.

Preferably, the grid points located near the end points Q and B are those grid points P and A whose distances of Q or B along the grid vector or the two grid vectors are each less than 10 grid periods, preferably less than 5, particularly preferably less than 2 and in particular less than one grating period. In particular, the grid point closest to the end point Q can be selected as grid point P and the grid point closest to the end point B can be selected as grid point A.

berechnet, wobei $\left(\begin{array}{c}{\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{p}}_{\mathrm{y}}\end{array}\right)$

und $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

die Koordinatenvektoren des Gitterpunkts P bzw. des Endpunkts Q darstellen, und $\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

und $\left(\begin{array}{c}\mathrm{b}\\ 0\end{array}\right)$

die Koordinatenvektoren des Gitterpunkts A bzw. des Endpunkts B darstellen.The linear transformation V becomes advantageous using the relationship $$\mathrm{V}=\left(\begin{array}{cc}\mathrm{b}& 0\\ 0& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}{\mathrm{a}}_{\mathrm{x}}& {\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}$$

calculated, where $\left(\begin{array}{c}{\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{p}}_{\mathrm{y}}\end{array}\right)$

and $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

represent the coordinate vectors of the grid point P and the end point Q, and $\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

and $\left(\begin{array}{c}\mathrm{b}\\ 0\end{array}\right)$

represent the coordinate vectors of the grid point A and the end point B, respectively.

In addition to the longitudinal direction repeat, the cross direction repeat b can be specified.

• ein gewünschtes, bei Betrachtung zu sehendes Bild mit einem oder mehreren Moire-Bildelementen festgelegt wird, wobei die Anordnung von vergrößerten Moire-Bildelementen in Form eines zweidimensionalen Bravais-Gitters, dessen Gitterzellen durch Vektoren t ₁ und t ₂ gegeben sind, gewählt werden,
• das Fokussierelementeraster in Schritt b) als eine Anordnung von Mikrofokussierelementen in Form eines zweidimensionalen Bravais-Gitters, dessen Gitterzellen durch Vektoren w ₁ und w ₂ gegeben sind, bereitgestellt wird, und
• in Schritt a) das Motivraster mit den Mikromotivelementen unter Verwendung der Beziehungen

$$\overleftrightarrow{U}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overleftrightarrow{T}$$

$$\overrightarrow{r}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overrightarrow{R}+{\overrightarrow{r}}_0$$

berechnet wird, wobei $\overrightarrow{R}=\left(\begin{array}{c}X\\ Y\end{array}\right)$

einen Bildpunkt des gewünschten Bilds, $\overrightarrow{r}=\left(\begin{array}{c}x\\ y\end{array}\right)$

einen Bildpunkt des Motivrasters, ${\overrightarrow{r}}_0=\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)$

eine Verschiebung zwischen der Anordnung von Mikrofokussierelementen und der Anordnung von Mikromotivelementen darstellt, und die Matrizen T, W und U durch $\overleftrightarrow{T}=\left(\begin{array}{cc}{t}_{11}& t_{12}\\ t_{21}& {\mathrm{<figure-callout\; id="22"\; label="t"\; filenames="imgf0001.png"\; state="\{\{state\}\}">t</figure-callout>}}_{22}\end{array}\right),\mathrm{}\overleftrightarrow{W}=\left(\begin{array}{cc}{w}_{11}& w_{12}\\ w_{21}& w_{22}\end{array}\right)$

bzw. $\overleftrightarrow{U}=\left(\begin{array}{cc}{u}_{11}& u_{12}\\ u_{21}& u_{22}\end{array}\right)$

gegeben sind, wobei t_1i, t_2i, u_1i, u_2i bzw. w_1i, w_2i die Komponenten der Gitterzellenvektoren t _i, u _i und w _i , mit i =1, 2 darstellen.In a preferred embodiment of the manufacturing method is provided that

• a desired image to be viewed with one or more Moire pixels is determined, the arrangement of enlarged moire pixels in the form of a two-dimensional Bravais lattice, the lattice cells thereof by vectors t ₁ and t _{2 are} given to be chosen
• the focussing element raster in step b) as an array of microfocusing elements in the form of a two-dimensional Bravais lattice, whose lattice cells are represented by vectors w ₁ and w ₂ are provided, and
• in step a) the motif grid with the micromotif elements using the relationships

$$\overleftrightarrow{U}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overleftrightarrow{T}$$

$$\overrightarrow{r}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overrightarrow{R}+{\overrightarrow{r}}_0$$

is calculated, where $\overrightarrow{R}=\left(\begin{array}{c}X\\ Y\end{array}\right)$

a pixel of the desired image, $\overrightarrow{r}=\left(\begin{array}{c}x\\ y\end{array}\right)$

a pixel of the motif grid, ${\overrightarrow{r}}_0=\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)$

represents a displacement between the array of microfocusing elements and the array of micromotif elements, and the matrices T . W and U by $\overleftrightarrow{T}=\left(\begin{array}{cc}{t}_{11}& t_{12}\\ t_{21}& {\mathrm{<figure-callout\; id="22"\; label="t"\; filenames="imgf0001.png"\; state="\{\{state\}\}">t</figure-callout>}}_{22}\end{array}\right).\mathrm{}\overleftrightarrow{W}=\left(\begin{array}{cc}{w}_{11}& w_{12}\\ w_{21}& w_{22}\end{array}\right)$

respectively. $\overleftrightarrow{U}=\left(\begin{array}{cc}{u}_{11}& u_{12}\\ u_{21}& {\mathrm{<figure-callout\; id="22"\; label="u"\; filenames="imgf0001.png"\; state="\{\{state\}\}">u</figure-callout>}}_{22}\end{array}\right)$

where t _1i , t _2i , u _1i , u _2i and w _1i , w _{2i are} the components of the lattice cell _vectors t _i , u _i and w _i , with i = 1, 2 represent.

• ein gewünschtes, bei Betrachtung zu sehendes Bild mit einem oder mehreren Moire-Bildelementen festgelegt wird,
• das Fokussierelementeraster in Schritt b) als eine Anordnung von Mikrofokussierelementen in Form eines zweidimensionalen Bravais-Gitters, dessen Gitterzellen durch Vektoren w ₁ und w ₂ gegeben sind, bereitgestellt wird,
• eine gewünschte Bewegung des zu sehenden Bildes beim seitlichen Kippen und beim vor-rückwärtigen Kippen der Moiré-Vergrößerungsanordnung festgelegt wird, wobei die gewünschte Bewegung in Form der Matrixelemente einer Transformationsmatrix A vorgegeben wird, und
• in Schritt a) das Motivraster mit den Mikromotivelementen unter Verwendung der Beziehungen $$\overleftrightarrow{U}=\left(\overleftrightarrow{I}-{\overleftrightarrow{A}}^{-1}\right)\cdot \overleftrightarrow{W}$$
  
  und $$\overrightarrow{r}={\overleftrightarrow{A}}^{-1}\cdot \overrightarrow{R}+{\overrightarrow{r}}_0$$
  
  berechnet wird, wobei $\overrightarrow{R}=\left(\begin{array}{c}X\\ Y\end{array}\right)$
  
  einen Bildpunkt des gewünschten Bilds, $\overrightarrow{r}=\left(\begin{array}{c}x\\ y\end{array}\right)$
  
  einen Bildpunkt des Motivbilds, ${\overrightarrow{r}}_0=\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)$
  
  eine Verschiebung zwischen der Anordnung von Mikrofokussierelementen und der Anordnung von Mikromotivelementen darstellt, und die Matrizen A, W und U durch $\overleftrightarrow{A}=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right),$
  
  $\overleftrightarrow{W}=\left(\begin{array}{cc}{w}_{11}& w_{12}\\ w_{21}& {\mathrm{<figure-callout\; id="22"\; label="w"\; filenames="imgf0001.png"\; state="\{\{state\}\}">w</figure-callout>}}_{22}\end{array}\right)$
  
  bzw. $\overleftrightarrow{U}=\left(\begin{array}{cc}{u}_{11}& u_{12}\\ u_{21}& {\mathrm{<figure-callout\; id="22"\; label="u"\; filenames="imgf0001.png"\; state="\{\{state\}\}">u</figure-callout>}}_{22}\end{array}\right)$
  
  gegeben sind, wobei u_1i, u_2i bzw. w_1i, w_2i die Komponenten der Gitterzellenvektoren u _i und w _i, mit i =1, 2 darstellen.

In another likewise preferred embodiment of the production method, it is provided that

• determining a desired image to be viewed with one or more moire pixels,
• the focussing element raster in step b) as an array of microfocusing elements in the form of a two-dimensional Bravais lattice, whose lattice cells are represented by vectors w ₁ and w ₂ are provided,
• determining a desired movement of the image to be seen in the case of lateral tilting and tilting of the moiré magnification arrangement back and forth, the desired movement being in the form of the matrix elements of a transformation matrix A is given, and
• in step a) the motif grid with the micromotif elements using the relationships $$\overleftrightarrow{U}=\left(\overleftrightarrow{I}-{\overleftrightarrow{A}}^{-1}\right)\cdot \overleftrightarrow{W}$$
  
  and $$\overrightarrow{r}={\overleftrightarrow{A}}^{-1}\cdot \overrightarrow{R}+{\overrightarrow{r}}_0$$
  
  is calculated, where $\overrightarrow{R}=\left(\begin{array}{c}X\\ Y\end{array}\right)$
  
  a pixel of the desired image, $\overrightarrow{r}=\left(\begin{array}{c}x\\ y\end{array}\right)$
  
  a pixel of the motif image, ${\overrightarrow{r}}_0=\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)$
  
  represents a displacement between the array of microfocusing elements and the array of micromotif elements, and the matrices A . W and U by $\overleftrightarrow{A}=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right).$
  
  $\overleftrightarrow{W}=\left(\begin{array}{cc}{w}_{11}& w_{12}\\ w_{21}& {\mathrm{<figure-callout\; id="22"\; label="w"\; filenames="imgf0001.png"\; state="\{\{state\}\}">w</figure-callout>}}_{22}\end{array}\right)$
  
  respectively. $\overleftrightarrow{U}=\left(\begin{array}{cc}{u}_{11}& u_{12}\\ u_{21}& {\mathrm{<figure-callout\; id="22"\; label="u"\; filenames="imgf0001.png"\; state="\{\{state\}\}">u</figure-callout>}}_{22}\end{array}\right)$
  
  where u _1i , u _2i and w _1i , w _{2i are} the components of the lattice cell _vectors u _i and w _i , with i = 1, 2 represent.

In both variants mentioned, the vectors u ₁ and u ₂ , or w ₁ and w _{2 are} spatially dependent, with the local period parameters | u ₁ |, | u ₂ |, ∠ ( u ₁ , u ₂ ) or | w ₁ |, | w ₂ |, ∠ ( w ₁ , w ₂ ) change only slowly in relation to the periodicity length.

The motif grid and the focusing element grid are expediently arranged on opposite surfaces of an optical spacer layer. The spacer layer may comprise, for example, a plastic film and / or a lacquer layer.

In an advantageous embodiment of the method, step e) comprises providing a printing or embossing cylinder with the distorted focusing element grid. In step e), a flat plate may be provided with the distorted focusing element grid, and the flat plate or a flat impression of the plate may be mounted on a printing or embossing cylinder to form a cylinder with sutures having a cylinder circumference q. Alternatively, in step e), a coated cylinder with cylinder circumference q can be provided with the distorted focusing element grid by a material-removing method, in particular by laser ablation.

Method step e) may comprise impressing the distorted focusing element grid in an embossable lacquer layer, in particular in a thermoplastic lacquer or UV lacquer, which is arranged on the front side of an optical spacer layer.

In a further advantageous embodiment of the method, the step e) comprises providing a printing or embossing cylinder with the distorted motif grid. In step e), a flat plate may be provided with the distorted motif grid, and the flat plate or a flat impression of the plate may be mounted on a printing or embossing cylinder so that a cylinder with seams with a cylinder circumference q is formed. Alternatively, in step e), a coated cylinder with cylinder circumference q can be provided with the distorted motif grid by a material-removing method, in particular by laser ablation.

Method step e) may also include impressing the distorted motif grid in an embossable lacquer layer, in particular in a thermoplastic lacquer or UV lacquer, which is arranged on the back of an optical spacer layer. In another variant of the method, step e) comprises printing the distorted motif grid on a carrier layer, in particular on the back side of an optical spacer layer.

The invention further relates to a continuous material for security elements for security papers, documents of value and the like according to claim 12.

The motif grid and the focusing element grid of the continuous material are arranged with a repeat q along the endless longitudinal direction of the endless material and with a repeat b along the transverse direction of the endless material.

The invention further comprises a method for producing a security element for security papers, value documents and the like, in which an endless material of the described type is produced and cut in the desired form of the security element. In particular, the endless material is thereby cut into longitudinal strips of the same width and with an identical arrangement of the micro-optical moire magnification arrangements. A security element for security papers, value documents and the like can be made from a continuous material of the type described are produced, in particular with the method just mentioned.

In a further aspect, the invention comprises a method for producing a printing or embossing cylinder according to claim 14 for the production of the focusing element grid in a production method for continuous material of the type described.

A flat plate can be provided with the distorted focusing element grid, and the flat plate or a flat impression of the plate is mounted on a printing or embossing cylinder, so that a cylinder with seams with a cylinder circumference q is formed. According to an alternative, a coated cylinder with cylinder circumference q is provided with the distorted focusing element grid by a material-removing method, in particular by laser ablation. The first and second grids are two-dimensional Bravais grids.

In a further aspect, the invention comprises a method for producing a printing or embossing cylinder according to claim 15 for the production of the motif grid in a production method for continuous material of the type described.

In this case, a flat plate with the distorted motif grid can be provided, and the flat plate or a flat impression of the plate is mounted on a printing or embossing cylinder, so that a cylinder with seams with a cylinder circumference q is formed. As an alternative, a coated cylinder with cylinder circumference q provided with the distorted motif grid by a material-removing process, in particular by laser ablation. The first and second grids are two-dimensional Bravais grids.

In all variants, the moiré magnification arrangements as Fokussierelementraster, in particular lenticular, but also other types of grid, such as hole grids or grid of concave mirrors, have. In all these cases, the inventive method can be used with advantage when cylindrical tools are used for embossing or printing.

Further embodiments and advantages of the invention are explained below with reference to the figures. For better clarity, a scale and proportioned representation is omitted in the figures.

Fig. 1

eine schematische Darstellung einer Banknote mit einem eingebetteten Sicherheitsfaden und einem aufgeklebten Transferelement,

Fig. 2

schematisch den Schichtaufbau eines Sicherheitsfadens im Querschnitt,

Fig. 3

in (a) und (b) eine Illustration der bei Herstellungsverfahren nach dem Stand der Technik auftretenden Bruchstellen im Erscheinungsbild von Sicherheitselementen mit Moire-Vergrößerungsanordnungen,

Fig. 4

ein Motivraster, dessen Mikromotivelemente durch auf den Gitterplätzen eines niedrigsymmetrischen Bravais-Gitters liegende Buchstaben "F" gebildet sind,

Fig. 5

schematisch die Verhältnisse bei der Betrachtung einer MoireVergrößerungsanordnung zur Definition der auftretenden Größen,

Fig. 6

ein Motivraster in Form eines zweidimensionalen BravaisGitters mit den Einheitszellen-Seitenvektoren u ₁ und u ₂ und dem eingezeichneten Umfang q des für die Erzeugung des Motivrasters vorgesehenen Druckzylinders,

Fig. 7

ein Motivraster wie in Fig. 6 mit dem eingezeichneten Umfang q und der Breite b der Streifen, in die das geprägte Endlosmaterial geschnitten werden soll,

Fig. 8

ein Motivraster in Form eines eindimensionalen Translationsgitters mit einem Translationsvektor u und dem vorgegebenen Längsrapport q, und

Fig. 9

ein Motivraster wie in Fig. 8 mit eingezeichnetem Längsrapport q und Querrapport b.

Show it:

Fig. 1

a schematic representation of a banknote with an embedded security thread and a glued transfer element,

Fig. 2

schematically the layer structure of a security thread in cross section,

Fig. 3

in (a) and (b) an illustration of the breakages in the appearance of security elements with moiré magnification arrangements occurring in prior art production methods,

Fig. 4

a motif grid whose micromotif elements are formed by letters "F" lying on the lattice sites of a low-symmetry Bravais lattice,

Fig. 5

schematically the conditions when considering a MoireVergrößerungsanordnung to define the occurring sizes,

Fig. 6

a motif grid in the form of a two-dimensional Bravais grid with the unit cell side vectors u ₁ and u ₂ and the marked circumference q of the printing cylinder provided for the generation of the motif grid,

Fig. 7

a motif grid like in Fig. 6 with the drawn circumference q and the width b of the strips into which the embossed continuous material is to be cut,

Fig. 8

a motif grid in the form of a one-dimensional translation grid with a translation vector u and the predetermined longitudinal repeat q, and

Fig. 9

a motif grid like in Fig. 8 with drawn longitudinal repeat q and transverse repeat b.

The method according to the invention will now be explained using the example of the production of a security element for a banknote. Fig. 1 shows a schematic representation of a banknote 10, which is provided with two security elements 12 and 16. The first security element represents a security thread 12 that emerges at certain window areas 14 on the surface of the banknote 10, while it is embedded in the intervening areas inside the banknote 10. The second security element is formed by a glued transfer element 16 of any shape. The security element 16 can also be designed in the form of a cover film, which is arranged over a window area or a through opening of the banknote.

Both the security thread 12 and the transfer element 16 may include a moire magnification arrangement. The mode of operation and the production method according to the invention for such arrangements will be described in more detail below with reference to the security thread 12.

Fig. 2 schematically shows the layer structure of the security thread 12 in cross section, wherein only the parts of the layer structure required for the explanation of the functional principle are shown. The security thread 12 includes a carrier 20 in the form of a transparent plastic film, in the embodiment an approximately 20 micron thick polyethylene terephthalate (PET) film. The upper side of the carrier film 20 is provided with a grid-like arrangement of microlenses 22 which form on the surface of the carrier film a two-dimensional Bravais grid with a preselected symmetry. The Bravais lattice has a hexagonal lattice symmetry or the symmetry of a parallelogram lattice.

The spacing of adjacent microlenses 22 is preferably chosen as small as possible in order to ensure the highest possible area coverage and thus a high-contrast representation. The spherically or aspherically configured microlenses 22 preferably have a diameter between 5 μm and 50 μm and in particular a diameter between only 10 μm and 35 μm and are therefore not visible to the naked eye. It is understood that in other designs, larger or smaller dimensions come into question. For example, in the case of Moire Magnifier structures, the microlenses can have a diameter of between 50 μm and 5 mm for decorative purposes, while in the case of Moire Magnifier structures, which are to be decipherable only with a magnifying glass or a microscope, dimensions below 5 μm are also used can come.

On the underside of the carrier film 20, a motif layer 26 is arranged, which also contains a grid-like arrangement of identical micromotif elements 28. The arrangement of the micromotif elements 28 forms a two-dimensional Bravais lattice with a preselected symmetry, again assuming a parallelogram lattice for illustration. As in Fig. 2 indicated by the offset of the micromotif elements 28 relative to the microlenses 22, the Bravais lattice of the micromotif elements differs 28 in its symmetry and / or in the size of its lattice parameters according to the invention slightly from the Bravais lattice of the microlenses 22 to produce the desired moire magnification effect. The grating period and the diameter of the micromotif elements 28 are of the same order of magnitude as those of the microlenses 22, ie preferably in the range of 5 .mu.m to 50 .mu.m and in particular in the range of 10 .mu.m to 35 .mu.m, so that the micromotif elements 28 themselves are visible to the naked eye are not recognizable. In designs with the above-mentioned larger or smaller microlenses, of course, the micromotif elements are correspondingly larger or smaller.

The optical thickness of the carrier film 20 and the focal length of the microlenses 22 are coordinated so that the micromotif elements 28 are located approximately at the distance of the lens focal length. The carrier foil 20 thus forms an optical spacer layer which ensures a desired constant spacing of the microlenses 22 and the micromotif elements 28.

Due to the slightly different lattice parameters, the observer sees a slightly different subregion of the micromotif elements 28 when viewed from above through the microlenses 22, so that the multiplicity of microlenses 22 as a whole produces an enlarged image of the micromotif elements 28. The resulting moiré magnification depends on the relative difference of the lattice parameters of the Bravais gratings used. If, for example, the grating periods of two hexagonal gratings differ by 1%, the result is a 100-fold moire magnification.

In the production of security elements with such Moire magnification arrangements, an endless security element film is usually first produced as a roll material, with known production methods always breaking points 30 occur in appearance 32, as in Fig. 3 (a) illustrated. These breakages in appearance are due to the fact that the precursors for the stamping tools used in the manufacture are generally made as flat sheets which are mounted on a printing or embossing cylinder 34, as shown schematically in FIG Fig. 3 (b) shown. At the seams 36, the adjacent motif grids 38, 38 'and / or the associated lenticular grid generally do not coincide and, after printing or embossing, lead to motif disturbances in the form of gaps or an offset in the appearance of the finished security elements.

Even if the designs required for moiré magnification arrangements are generated directly in cylindrical form without going over flat plates, the complicated patterns of the lenticular grid and the motif grid usually do not fit seamlessly, ie completely and without offset, onto a given cylinder surface.

For the explanation of the procedure according to the invention, first with reference to FIGS FIGS. 4 and 5 the required sizes are defined and briefly described.

According to the invention, the micromotif elements 28 and the microlenses 22 are each in the form of a raster, wherein in the context of this description raster is understood to mean a two-dimensional periodic or at least locally periodic arrangement of the lenses or the motif elements. A periodic raster can always be described here by a two-dimensional Bravais lattice with constant lattice parameters. In the case of a locally periodic arrangement, the period parameters may change from place to place, but only slowly in relation to the periodicity length, so that the microasters can always be described locally with sufficient accuracy by means of Bravais gratings with constant grid parameters. For the sake of simplicity of illustration, a periodic arrangement of the microelements is therefore always assumed below.

The FIGS. 4 and 5 schematically show a non-scale illustrated moire magnification arrangement 50 with a motif plane 52 in which a in Fig. 4 more precisely arranged motif grid 40 is arranged and with a lens plane 54 in which the microlens grid is located. The moiré magnification arrangement 50 produces a moiré image plane 56 in which the magnified image perceived by the viewer 58 is described.

The motif grid 40 includes a plurality of micromotif elements 42 in the form of the letter "F" arranged at the lattice sites of a low-symmetry Bravais lattice 44. The unit cell of in Fig. 4 shown parallelogram grating can by vectors u ₁ and u ₂ (with the components u ₁₁ , u ₂₁ and u ₁₂ , u ₂₂ ) are shown. In compact notation, the unit cell can also be represented in matrix form by a motif grid matrix u be specified: $$\overleftrightarrow{U}=\left({\overleftrightarrow{u}}_1.{\overleftrightarrow{u}}_2\right)=\left(\begin{array}{cc}{u}_{11}& u_{12}\\ u_{21}& {\mathrm{<figure-callout\; id="22"\; label="u"\; filenames="imgf0001.png"\; state="\{\{state\}\}">u</figure-callout>}}_{22}\end{array}\right)$$

In the same way, the arrangement of microlenses in the lens plane 54 is described by a two-dimensional Bravais lattice whose lattice cell is represented by the vectors w ₁ and w ₂ (with the components w ₁₁ , w ₂₁ and w ₁₂ , w ₂₂ ) is given. With the vectors t ₁ and t ₂ (with the components t ₁₁ , t ₂₁ and t ₁₂ , t ₂₂ ), the grid cell in the moire image plane 56 is described.

ist ein allgemeiner Punkt der Motivebene 52 bezeichnet, mit $\overrightarrow{R}=\left(\begin{array}{c}X\\ Y\end{array}\right)$

ein allgemeiner Punkt der Moire-Bildebene 56. Diese Größen genügen bereits, um eine senkrechte Betrachtung (Betrachtungsrichtung 60) der Moire-Vergrößerungsanordnung zu beschreiben. Um auch nicht-senkrechte Betrachtungsrichtungen wie etwa die Richtung 62 berücksichtigen zu können, wird zusätzlich eine Verschiebung zwischen Linsenebene 54 und Motivebene 52 zugelassen, die durch einen Verschiebungsvektor ${\overrightarrow{r}}_0=\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)$

in der Motivebene 52 angegeben wird. Analog zur Motivrastermatrix werden zur kompakten Beschreibung des Linsenrasters und des Bildrasters die Matrizen $\overleftrightarrow{W}=\left(\begin{array}{cc}{w}_{11}& w_{12}\\ w_{21}& w_{22}\end{array}\right)$

und $\overleftrightarrow{T}=\left(\begin{array}{cc}{t}_{11}& t_{12}\\ t_{21}& t_{22}\end{array}\right)$

verwendet.With $\overrightarrow{r}=\left(\begin{array}{c}x\\ y\end{array}\right)$

is a general point of the motif level 52, with $\overrightarrow{R}=\left(\begin{array}{c}X\\ Y\end{array}\right)$

a general point of moire image plane 56. These quantities are already sufficient to describe a perpendicular viewing (viewing direction 60) of the moiré magnification arrangement. In order to be able to take into account non-perpendicular viewing directions, such as the direction 62, a shift between the lens plane 54 and the motive plane 52 is additionally permitted by a displacement vector ${\overrightarrow{r}}_0=\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)$

is indicated in the motif level 52. Analogous to the motif grid matrix, the matrices are used to compactly describe the lens raster and the image raster $\overleftrightarrow{W}=\left(\begin{array}{cc}{w}_{11}& w_{12}\\ w_{21}& {\mathrm{<figure-callout\; id="22"\; label="w"\; filenames="imgf0001.png"\; state="\{\{state\}\}">w</figure-callout>}}_{22}\end{array}\right)$

and $\overleftrightarrow{T}=\left(\begin{array}{cc}{t}_{11}& t_{12}\\ t_{21}& {\mathrm{<figure-callout\; id="22"\; label="t"\; filenames="imgf0001.png"\; state="\{\{state\}\}">t</figure-callout>}}_{22}\end{array}\right)$

used.

und die Bildpunkte der Moiré-Bildebene 56 können mithilfe der Beziehung $$\overleftrightarrow{R}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{W}-\overleftrightarrow{U}\right)}^{-1}\cdot \left(\overrightarrow{r}-{\overrightarrow{r}}_0\right)$$

aus den Bildpunkten der Motivebene 52 bestimmt werden. Umgekehrt ergeben sich die Gittervektoren der Mikromotivelement-Anordnung aus dem Linsenraster und dem gewünschten Moiré-Bild-Gitter durch $$\overleftrightarrow{U}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overleftrightarrow{T}$$

und $$\overrightarrow{r}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overrightarrow{R}+{\overrightarrow{r}}_0.$$

The moiré image grating results from the grating vectors of the micromotif element array and the microlens array $$\overleftrightarrow{T}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{W}-\overleftrightarrow{U}\right)}^{-1}\cdot \overleftrightarrow{U}$$

and the pixels of the moiré image plane 56 can be determined using the relationship $$\overleftrightarrow{R}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{W}-\overleftrightarrow{U}\right)}^{-1}\cdot \left(\overrightarrow{r}-{\overrightarrow{r}}_0\right)$$

be determined from the pixels of the motif level 52. Conversely, the grating vectors of the micromotif element array result from the lenticular grid and the desired moiré image grating $$\overleftrightarrow{U}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overleftrightarrow{T}$$

and $$\overrightarrow{r}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overrightarrow{R}+{\overrightarrow{r}}_0,$$

die die Koordinaten der Punkte der Motivebene 52 und der Punkte der Moire-Bildebene 56 ineinander überführt, $$\overrightarrow{R}=\overleftrightarrow{A}\cdot \left(\overrightarrow{r}-{\overrightarrow{r}}_0\right),\mathrm{bzw}.\mathrm{}\overrightarrow{r}={\overleftrightarrow{A}}^{-1}\cdot \overleftrightarrow{R}+{\overrightarrow{r}}_0,$$

so können aus jeweils zwei der vier Matrizen U, W, T, A die beiden anderen berechnet werden. Insbesondere gilt: $$\overleftrightarrow{T}=\overleftrightarrow{A}\cdot \overleftrightarrow{U}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{W}-\overleftrightarrow{U}\right)}^{-1}\cdot \overleftrightarrow{U}=\left(\overrightarrow{A}-\overleftrightarrow{I}\right)\cdot \overleftrightarrow{W}$$

$$\overleftrightarrow{U}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overleftrightarrow{T}={\overleftrightarrow{A}}^{-1}\cdot \overleftrightarrow{T}=\left(\overleftrightarrow{I}-{\overleftrightarrow{A}}^{-1}\right)\cdot \overleftrightarrow{W}$$

$$\overleftrightarrow{W}=\overleftrightarrow{U}\cdot {\left(\overleftrightarrow{T}-\overleftrightarrow{U}\right)}^{-1}\cdot \overleftrightarrow{T}={\left(\overleftrightarrow{A}-\overleftrightarrow{I}\right)}^{-1}\cdot \overleftrightarrow{T}={\left(\overleftrightarrow{A}-\overleftrightarrow{I}\right)}^{-1}\cdot \overleftrightarrow{A}\cdot \overleftrightarrow{U}$$

$$\overleftrightarrow{A}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{W}-\overleftrightarrow{U}\right)}^{-1}=\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)\cdot {\overleftrightarrow{W}}^{-1}=\overleftrightarrow{T}\cdot {\overleftrightarrow{U})}^{-1}$$

Define the transformation matrix $\overleftrightarrow{A}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{W}-\overleftrightarrow{U}\right)}^{-1}.$

which converts the coordinates of the points of the motif plane 52 and the points of the moire image plane 56 into each other, $$\overrightarrow{R}=\overleftrightarrow{A}\cdot \left(\overrightarrow{r}-{\overrightarrow{r}}_0\right).\mathrm{respectively},\mathrm{}\overrightarrow{r}={\overleftrightarrow{A}}^{-1}\cdot \overleftrightarrow{R}+{\overrightarrow{r}}_0.$$

so can each have two of the four matrices U . W . T . A the other two are calculated. In particular: $$\overleftrightarrow{T}=\overleftrightarrow{A}\cdot \overleftrightarrow{U}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{W}-\overleftrightarrow{U}\right)}^{-1}\cdot \overleftrightarrow{U}=\left(\overrightarrow{A}-\overleftrightarrow{I}\right)\cdot \overleftrightarrow{W}$$

$$\overleftrightarrow{U}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overleftrightarrow{T}={\overleftrightarrow{A}}^{-1}\cdot \overleftrightarrow{T}=\left(\overleftrightarrow{I}-{\overleftrightarrow{A}}^{-1}\right)\cdot \overleftrightarrow{W}$$

$$\overleftrightarrow{W}=\overleftrightarrow{U}\cdot {\left(\overleftrightarrow{T}-\overleftrightarrow{U}\right)}^{-1}\cdot \overleftrightarrow{T}={\left(\overleftrightarrow{A}-\overleftrightarrow{I}\right)}^{-1}\cdot \overleftrightarrow{T}={\left(\overleftrightarrow{A}-\overleftrightarrow{I}\right)}^{-1}\cdot \overleftrightarrow{A}\cdot \overleftrightarrow{U}$$

$$\overleftrightarrow{A}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{W}-\overleftrightarrow{U}\right)}^{-1}=\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)\cdot {\overleftrightarrow{W}}^{-1}=\overleftrightarrow{T}\cdot {\overleftrightarrow{U})}^{-1}$$

The transformation matrix A also describes the movement of a moire image as the moire-forming assembly 50 moves, resulting from the movement of the motif plane 52 against the lens plane 54. The columns of the transformation matrix A can be interpreted as vectors, where $$\overleftrightarrow{A}=\left(\begin{array}{cc}{\mathrm{a}}_{11}& {\mathrm{a}}_{12}\\ {\mathrm{a}}_{21}& {\mathrm{a}}_{22}\end{array}\right).\mathrm{}{\overrightarrow{a}}_1=\left(\begin{array}{c}{\mathrm{a}}_{11}\\ {\mathrm{a}}_{21}\end{array}\right).\mathrm{}{\overrightarrow{a}}_2=\left(\begin{array}{c}{\mathrm{a}}_{12}\\ {\mathrm{a}}_{22}\end{array}\right),$$

You can see now that the vector a ₁ indicates in which direction the moiré image moves when tilting the arrangement of motif and lenticular raster laterally, and that the vector a ₂ indicates in which direction the Moirebild moves, if one tilts the arrangement of subject and lenticular grid forward.

The direction of movement results at a given A as follows: With lateral tilting of the motif plane, the moire moves at an angle γ ₁ to the horizontal, given by $$\mathrm{<figure-callout\; id="1"\; label="tan\; \gamma "\; filenames="imgf0004.png,imgf0005.png"\; state="\{\{state\}\}">tan\; </figure-callout>}{\gamma }_{}{}_1=\frac{{\mathrm{a}}_{21}}{{\mathrm{a}}_{11}},$$

Analogously, the moire moves in front-rearward tilting at an angle γ ₂ to the horizontal, given by $$\tan {\gamma }_2=\frac{{\mathrm{a}}_{22}}{{\mathrm{a}}_{12}},$$

According to the invention, the images given in particular by (M1) to (M4) are now supplemented by further linear transformations which describe a distortion of the Bravais grid of the motif grid or of the lens grid, and which are selected so that the motif grid and / or the Lenticular grid periodically repeated in a predetermined repeat. The procedure according to the invention will now be explained in more detail with reference to a few concrete examples.

Example 1:

Regarding Fig. 6 is a motif image 70 with a motif grid in the form of a two-dimensional Bravais grid with the unit cell side vectors u ₁ and u ₂ and the circumference q of the intended for the generation of the motif grid printing or embossing cylinder. In order to accommodate the given motif image, on the one hand, without breakage on the cylinder, but to change the given motif raster as little as possible, the procedure according to the invention is as follows:

mit ganzen Zahlen m und n erfasst. Das Motivbild 70 kann unterbrechungsfrei genau dann auf einem Zylinder mit dem Umfang q angebracht werden, wenn es ganze Zahlen M und N gibt, für die gilt: $$\mathrm{M}\cdot {\bar{u}}_1+\mathrm{N}\cdot {\bar{u}}_2=\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$$

wobei die Umfangsrichtung im Folgenden ohne Beschränkung der Allgemeinheit als γ-Richtung in einem kartesischen Koordinatensystem gewählt wird. Der Endpunkt Q dieses durch den Umfang des Zylinders definierten Vektors $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

ist in Fig. 6 ebenfalls eingezeichnet. Ein nach Gesichtspunkten wie Motivgröße, Vergrößerung, Bewegung berechnetes Motivgitter oder auch ein entsprechend berechnetes Linsenraster genügen in der Regel der Bedingung (1) nicht.All grid points of the given motif grid are through $\left\{\mathrm{m}\cdot {\overrightarrow{u}}_1+\mathrm{n}\cdot {\overrightarrow{u}}_2\right\}$

recorded with integers m and n. The motif image 70 can be applied without interruption to a cylinder with the circumference q if and only if there are integers M and N for which: $$\mathrm{M}\cdot {\tilde{u}}_1+\mathrm{N}\cdot {\tilde{u}}_2=\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$$

wherein the circumferential direction is chosen in the following without restriction of the generality as γ-direction in a Cartesian coordinate system. The end point Q of this vector defined by the circumference of the cylinder $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

is in Fig. 6 also marked. A motif grid calculated according to aspects such as motif size, magnification, movement or a correspondingly calculated lenticular grid usually do not satisfy condition (1).

Therefore, according to the invention, the Bravais lattice of the motif grid 70 is slightly distorted by a linear transformation so that the condition (1) for the distorted Bravais lattice is satisfied. The distorted grid then repeats periodically with a longitudinal direction repeat q and therefore fits without gaps and without offset on an associated printing or embossing cylinder with circumference q.

des unverzerrten Bravais-Gitters ausgewählt, der in der Nähe des Endpunkts Q liegt. Für eine möglichst geringe Verzerrung kann dazu, wie etwa in Fig. 6, der dem Endpunkt Q nächstliegende Gitterpunkt P ausgewählt werden. Die konkrete Auswahl des Gitterpunkts P kann beispielsweise dadurch erfolgen, dass per Computer die Koordinaten aller Gitterpunkte in einer Fläche ermittelt werden, die etwas größer ist als eine Abrollung des Zylinders (mindestens einige Gitterzellen größer im Umfang und in der Breite) und dass aus diesen Gitterpunkten dann derjenige mit dem kleinsten Abstand zu Q bestimmt wird.To determine a suitable transformation, a grid point P = $\left(\begin{array}{c}{\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{p}}_{\mathrm{y}}\end{array}\right)$

of the undistorted Bravais lattice located near the endpoint Q. For as little distortion as possible, such as in Fig. 6 , the grid point P closest to the end point Q is selected. The concrete selection of the grid point P can be effected, for example, by the coordinates of all grid points in the computer be determined a surface which is slightly larger than a roll of the cylinder (at least some grid cells larger in size and in width) and that from these grid points then the one with the smallest distance to Q is determined.

den Gitterpunkt P auf den Endpunkt Q ab, und bewirkt daher die gewünschte Verzerrung. Als neues, geringfügig verzerrtes Bravais-Gitter für das Motivbild wird das durch $$\overleftrightarrow{U}\prime =\overleftrightarrow{V}\cdot \overleftrightarrow{U}$$

gegebene Motivraster-Gitter verwendet. Entsprechend können die neuen Koordinaten $\overrightarrow{r}\prime =\left(\begin{array}{c}x\prime \\ y\prime \end{array}\right)$

eines allgemeinen Punktes $\overrightarrow{r}=\left(\begin{array}{c}x\\ y\end{array}\right)$

der Motivebene 52 mittels $$\left(\begin{array}{c}\mathrm{x}\text{'}\\ \mathrm{y}\text{'}\end{array}\right)=\overleftrightarrow{\mathrm{V}}\cdot \left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)=\left(\begin{array}{c}\mathrm{x}-\mathrm{y}\cdot {\mathrm{p}}_{\mathrm{x}}/{\mathrm{p}}_{\mathrm{y}}\\ \mathrm{y}\cdot \mathrm{q}/{\mathrm{p}}_{\mathrm{y}}\end{array}\right)$$

berechnet werden.
Auf diese Weise erhält man ein Motivbild mit einem Motivraster in Form eines Bravais-Gitters mit Einheitszellen-Seitenvektoren u '₁ und u '₂ und Bildpunkten r ', gegeben durch die Beziehungen (2a), (3) und (4), das lückenlos und ohne Versatz auf den vorgegebenen Druck- oder Prägezylinder passt.How easy to see forms the linear transformation $$\overleftrightarrow{\mathrm{V}}=\left(\begin{array}{cc}1& 0\\ 0& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}1& {\mathrm{p}}_{\mathrm{x}}\\ 0& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}=\left(\begin{array}{cc}1& -{\mathrm{p}}_{\mathrm{x}}/{\mathrm{p}}_{\mathrm{y}}\\ 0& \mathrm{q}/{\mathrm{p}}_{\mathrm{y}}\end{array}\right)$$

the grid point P on the end point Q, and therefore causes the desired distortion. As a new, slightly distorted Bravais grid for the motif image is through $$\overleftrightarrow{U}\text{'}=\overleftrightarrow{V}\cdot \overleftrightarrow{U}$$

given motif grid grid used. Accordingly, the new coordinates $\overrightarrow{r}\text{'}=\left(\begin{array}{c}x\text{'}\\ y\text{'}\end{array}\right)$

a general point $\overrightarrow{r}=\left(\begin{array}{c}x\\ y\end{array}\right)$

the motif level 52 means $$\left(\begin{array}{c}\mathrm{x}\text{'}\\ \mathrm{y}\text{'}\end{array}\right)=\overleftrightarrow{\mathrm{V}}\cdot \left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)=\left(\begin{array}{c}\mathrm{x}-\mathrm{y}\cdot {\mathrm{p}}_{\mathrm{x}}/{\mathrm{p}}_{\mathrm{y}}\\ \mathrm{y}\cdot \mathrm{q}/{\mathrm{p}}_{\mathrm{y}}\end{array}\right)$$

be calculated.
In this way one obtains a motif image with a motif grid in the form of a Bravais lattice with unit cell side vectors u ' ₁ and u ' ₂ and pixels r 'given by the relationships (2a), (3) and (4), which fits seamlessly and without offset on the given printing or embossing cylinder.

The effect of lattice distortion can be estimated from the typical dimensions of the embossing cylinders and grid cells. Usually, the grid cell dimensions are on the order of 20 microns, the circumference of a suitable embossing cylinder at about 20 cm or more. For a distortion on the order of a grid cell dimension Thus, based on the cylinder circumference, a relative change of the grating of only 1: 10000 results. Thus, the properties of the generated moiré image, such as magnification and movement angle, change only in the per thousand range and are therefore not recognizable to a viewer. Also, the above-mentioned larger distances between grid point P and end point Q still provide very good to acceptable results with relative changes in the grid in the range of up to several percent.

Example 2:

Like Example 1, Example 2 proceeds from a given motif image from a motif grid in the form of a two-dimensional Bravais grid with the unit cell side vectors u ₁ , and u ₂ and the circumference q of the intended for the generation of the motif grid printing cylinder.

mit beliebigen Vektoren $\overrightarrow{b}=\left(\begin{array}{c}{\mathrm{b}}_{\mathrm{x}}\\ {\mathrm{b}}_{\mathrm{y}}\end{array}\right)$

und $\overrightarrow{a}=\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

verwendet, die ebenfalls den Punkt P auf den Endpunkt Q abbildet.However, for the lattice transformation, instead of the linear transformation defined by equation (2a), the more general linear transformation becomes $$\overleftrightarrow{\mathrm{V}}=\left(\begin{array}{cc}{\mathrm{b}}_{\mathrm{x}}& 0\\ {\mathrm{b}}_{\mathrm{y}}& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}{\mathrm{a}}_{\mathrm{x}}& {\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}$$

with any vectors $\overrightarrow{b}=\left(\begin{array}{c}{\mathrm{b}}_{\mathrm{x}}\\ {\mathrm{b}}_{\mathrm{y}}\end{array}\right)$

and $\overrightarrow{a}=\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

which also maps the point P to the end point Q.

The untransformed grating and the transformed grating differ as little as possible when the vectors b and a differ as little as possible or even equal.

• 2.1 Wählt man b und a gleich groß und beide gleichgerichtet senkrecht zur Umfangsrichtung des Zylinders, also $\overrightarrow{a}=\overrightarrow{b}=\left(\begin{array}{c}\mathrm{b}\\ 0\end{array}\right),$
  
  so vereinfacht sich die Transformation (2b) zur oben angegebene Transformation (2a).
• 2.2 Wählt man $\overrightarrow{b}=\overrightarrow{a}={\overrightarrow{u}}_1,$
  
  so bleibt bei der Transformation der Gittervektor u ₁ erhalten, lediglich der Gittervektor u ₂ wird geringfügig so geändert, dass das verzerrte Gitter auf den Zylinder passt.
• 2.3 Wählt man $\overrightarrow{b}=\overrightarrow{a}={\overrightarrow{u}}_2,$
  
  so bleibt bei der Transformation der Gittervektor u ₂ erhalten und der Gittervektor u ₁ wird geringfügig so geändert, dass das verzerrte Gitter auf den Zylinder passt.

For illustration, some special cases are picked out:

• 2.1 Choosing one b and a the same size and both rectified perpendicular to the circumferential direction of the cylinder, ie $\overrightarrow{a}=\overrightarrow{b}=\left(\begin{array}{c}\mathrm{b}\\ 0\end{array}\right).$
  
  thus, the transformation (2b) simplifies the transformation (2a) given above.
• 2.2 Choosing one $\overrightarrow{b}=\overrightarrow{a}={\overrightarrow{u}}_1.$
  
  so the grid vector remains in the transformation u ₁ , only the grid vector u ₂ is slightly changed so that the distorted grid fits the cylinder.
• 2.3 Choosing one $\overrightarrow{b}=\overrightarrow{a}={\overrightarrow{u}}_2.$
  
  so the grid vector remains in the transformation u ₂ and the grid vector u ₁ is slightly changed so that the distorted grid fits the cylinder.

Example 3:

Regarding Fig. 7 In Example 3, as in Example 1, a motif image 80 having a motif grid in the form of a two-dimensional Bravais lattice with the unit cell side vectors is shown u ₁ and u ₂ and the circumference q of the intended for the generation of the motif grid printing or embossing cylinder specified. In addition, the embossed endless material is to be cut in a subsequent process step in strips of width b, the moire pattern on all strips should be the same side.

des unverzerrten Bravais-Gitters ausgewählt, der in der Nähe des Endpunkts Q liegt. Zusätzlich wird ein Gitterpunkt A = $\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

ausgewählt, der in der Nähe des Endpunkts B des durch den gewünschten Querrichtungs-Rapport gegebenen Vektors $\left(\begin{array}{c}b\\ 0\end{array}\right)$

liegt.The distorted Bravais grid of the motif image 80 in this example should therefore be repeated periodically in the γ direction with the longitudinal direction repeat q and periodically in the x direction with the transverse direction repeat b. To determine a suitable transformation, according to the invention a lattice point $\mathrm{P}=\left(\begin{array}{c}{\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{p}}_{\mathrm{y}}\end{array}\right)$

of the undistorted Bravais lattice located near the endpoint Q. In addition, a grid point A = $\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

selected near the endpoint B of the vector given by the desired cross-direction repeat $\left(\begin{array}{c}b\\ 0\end{array}\right)$

lies.

verwendet, die, wie man unmittelbar sieht, einen Spezialfall der allgemeinen Transformation (2b) mit $\overrightarrow{b}=\left(\begin{array}{c}b\\ 0\end{array}\right)$

darstellt. Diese Transformation V bildet den Gitterpunkt P auf den Endpunkt Q und den Gitterpunkt A auf den Endpunkt B ab. Da P und A jeweils in der Nähe der Endpunkte Q bzw. B gewählt wurden, ist die resultierende Verzerrung des Gitters klein.The transformation then becomes a linear transformation $$\overleftrightarrow{\mathrm{V}}=\left(\begin{array}{cc}\mathrm{b}& 0\\ \mathrm{0}& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}{\mathrm{a}}_{\mathrm{x}}& {\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}$$

which, as one immediately sees, involves a special case of the general transformation (2b) $\overrightarrow{b}=\left(\begin{array}{c}b\\ 0\end{array}\right)$

represents. This transformation V maps the grid point P to the end point Q and the grid point A to the end point B. Since P and A are respectively selected near the endpoints Q and B, the resulting distortion of the grating is small.

The motive image transformed via the relationships (2c) and (3) and the motive image transformed via the relations (2c) and (4) are structurally repeated in the x-direction with period b and in the γ-direction with period q. The motif image therefore fits seamlessly and without offset on the given printing or embossing cylinder and can be cut after production in identical strips of width b.

Example 4:

• Zunächst wird eine Gitteranordnung $\overleftrightarrow{\mathrm{W}}=\left({\overrightarrow{w}}_1,{\overrightarrow{w}}_2\right)=\left(\begin{array}{cc}{\mathrm{w}}_{11}& {\mathrm{w}}_{12}\\ {\mathrm{w}}_{21}& {\mathrm{<figure-callout\; id="22"\; label="w"\; filenames="imgf0001.png"\; state="\{\{state\}\}">w</figure-callout>}}_{22}\end{array}\right)$
  
  für ein Linsenraster beliebig vorgegeben. Falls diese Gitteranordnung nicht zu dem für die Herstellung des Linsenrasters vorgesehenen Zylinderumfang passt, wird sie, wie bei Beispiel 1 oder 2 mit Bezug beschrieben, in eine passende Anordnung umgerechnet.

Example 4 describes a preferred approach in making an overall moiré magnification arrangement:

• First, a grid arrangement $\overleftrightarrow{\mathrm{W}}=\left({\overrightarrow{w}}_1.{\overrightarrow{w}}_2\right)=\left(\begin{array}{cc}{\mathrm{w}}_{11}& {\mathrm{w}}_{12}\\ {\mathrm{w}}_{21}& {\mathrm{<figure-callout\; id="22"\; label="w"\; filenames="imgf0001.png"\; state="\{\{state\}\}">w</figure-callout>}}_{22}\end{array}\right)$
  
  arbitrarily specified for a lenticular grid. If this grid arrangement does not match the cylinder circumference provided for the production of the lenticular grid, it is converted into a suitable arrangement as described in example 1 or 2 with reference to FIG.

Furthermore, an enlargement and movement behavior is specified for the moire pattern, which, as explained above, is determined by a motion matrix A can express. From the lenticular grid W and the motion matrix A you can use the relationship (M2) to create the motif grid grid U determine: $$\overleftrightarrow{U}=\overleftrightarrow{W}-{\overleftrightarrow{A}}^{-1}\cdot \overleftrightarrow{W}$$

gegeben ist.The resulting moiré pattern appears in the image plane with a grid array T , by $$\overleftrightarrow{T}=\overleftrightarrow{A}\cdot \overleftrightarrow{U}$$

given is.

A motif image arranged in a motif grid grid calculated according to the relationship (5) will generally not fit without interruption to an independently given cylinder diameter, so that one with This cylinder-embossed film material in the rhythm of the cylinder circumference disturbances in the motif image and thus also in the moiré image shows.

ersetzt. Damit erhält man auch eine neue Bewegungsmatrix A', wobei das durch diese Bewegungsmatrix A ' beschriebene neue Vergrößerungs- und Bewegungs-Verhalten bei erfindungsgemäßem Vorgehen lediglich unwesentlich von dem durch die ursprüngliche Bewegungsmatrix A beschriebenen, gewünschten Vergrößerungs- und Bewegungs-Verhalten abweicht.According to the invention, the motif grid grid U therefore, as described in Example 1 or 2, by a transformed motif grid $\overleftrightarrow{U}\text{'}=\overleftrightarrow{V}\cdot \overleftrightarrow{U}$

replaced. This also gives you a new motion matrix A ', by the motion matrix A 'described new magnification and movement behavior in accordance with inventive method only insignificantly from that by the original motion matrix A described, desired magnification and movement behavior deviates.

und das sich ergebende transformierte Moirémuster erscheint in der Bildebene mit einer Gitter-Anordnung T ', die durch $$\overleftrightarrow{T}\prime =\overleftrightarrow{A}\prime \cdot \overleftrightarrow{U}\prime =\overleftrightarrow{V}\cdot \overleftrightarrow{T}$$

gegeben ist.Concrete is the new movement matrix A ', which describes the magnification and motion behavior of the transformed grid, given by $$\overleftrightarrow{A}\text{'}=\overleftrightarrow{V}\cdot \overleftrightarrow{A}\cdot {\overleftrightarrow{V}}^{-1}$$

and the resulting transformed moiré pattern appears in the image plane with a grid array T ', by $$\overleftrightarrow{T}\text{'}=\overleftrightarrow{A}\text{'}\cdot \overleftrightarrow{U}\text{'}=\overleftrightarrow{V}\cdot \overleftrightarrow{T}$$

given is.

Example 5:

Example 5 gives a calculation example for moiré-forming gratings for the procedures explained in Examples 1 to 4. The simpler For the sake of illustration, a hexagonal lattice symmetry is assumed for each raster.

The lenticular grid is a hexagonal lattice with 20 μm side length. The motif grid should have the same side length, but be rotated by an angle of 0.573 ° relative to the lenticular grid. The moire pattern should have an approximately 100-fold magnification and approximately orthoparallactic motion in the image plane.

The lenticular grid W is chosen so that it already fits on a cylinder with 200 mm circumference: $$\overleftrightarrow{\mathrm{W}}=\left(\begin{array}{cc}{\mathrm{w}}_{11}& {\mathrm{w}}_{12}\\ {\mathrm{w}}_{21}& {\mathrm{<figure-callout\; id="22"\; label="w"\; filenames="imgf0001.png"\; state="\{\{state\}\}">w</figure-callout>}}_{22}\end{array}\right)=0.02\cdot \left(\begin{array}{cc}\mathrm{<figure-callout\; id="30"\; label="cos"\; filenames="imgf0002.png"\; state="\{\{state\}\}">cos</figure-callout>}30°& \cos \left(-30°\right)\\ \mathrm{<figure-callout\; id="30"\; label="sin"\; filenames="imgf0002.png"\; state="\{\{state\}\}">sin</figure-callout>}30°& \sin \left(-30°\right)\end{array}\right)=0.02\cdot \left(\begin{array}{cc}0.866025...& 0.866025...\\ 0.5& -0.5\end{array}\right)$$

For the motif grid grid rotated by 0.573 °, the desired magnification of 100 times and approximately orthoparallactic motion results: $$\overleftrightarrow{\mathrm{U}}=\left(\begin{array}{cc}0.01741965& 0.01721964\\ 0.00982628& -0.01017271\end{array}\right)$$

ersetzt, wobei $$\mathrm{V}=\left(\begin{array}{cc}1& 0\\ 0& 200\end{array}\right)·{\left(\begin{array}{cc}1& p_x\\ 0& p_y\end{array}\right)}^{-1}$$

mit (p_x ; p_y) = (0,00811617; 199,99992) gewählt wird, so dass sich $$\overleftrightarrow{\mathrm{U}}\prime =\left(\begin{array}{cc}\mathrm{0,01741924}& \mathrm{0,01722006}\\ \mathrm{0,00982630}& -\mathrm{0,01017271}\end{array}\right)$$

ergibt.However, this motif grid grid does not fit without interruption on a cylinder with a 200 mm circumference and is therefore according to the invention by a transformed motif grid grid $\overleftrightarrow{U}\text{'}=\overleftrightarrow{V}\cdot \overleftrightarrow{U}$

replaced, where $$\mathrm{V}=\left(\begin{array}{cc}1& 0\\ 0& 200\end{array}\right)·{\left(\begin{array}{cc}1& p_x\\ 0& p_y\end{array}\right)}^{-1}$$

with (p _x ; p _y ) = (0.00811617; 199.99992) is chosen so that $$\overleftrightarrow{\mathrm{U}}\text{'}=\left(\begin{array}{cc}0.01741924& 0.01722006\\ 0.00982630& -0.01017271\end{array}\right)$$

results.

gegeben.The original and the transformed motion matrix are through $$\overleftrightarrow{\mathrm{A}}=\left(\begin{array}{cc}0.50000& 99.99875\\ -99.99875& 0.50000\end{array}\right)\mathrm{respectively},\mathrm{}\overleftrightarrow{\mathrm{A}}\text{'}=\left(\begin{array}{cc}0.49796& 99.99874\\ -100.40622& 0.49796\end{array}\right)$$

given.

The moire magnification of the original motif grid is by design 100.0 times, the magnification with the transformed motif grid is horizontally 100.4-fold and vertically 100.0-fold, so has changed only insignificantly. The transformed motif grid grid results in a trouble-free motif image on a printing or embossing cylinder with a circumference of 200 mm, whereas the original motif grid lattice creates motif distortions in the motif Fig. 3 (a) shown type leads.

Example 6:

Example 6 is based on Example 5, in addition to the endless material produced in this example is cut into identical strips with a width of 40 mm.

First, as in Example 5, the undistorted motif grid is calculated from the lenticular grid and the desired magnification and motion behaviors: $$\overleftrightarrow{\mathrm{U}}=\left(\begin{array}{cc}0.01741965& 0.01721964\\ 0.00982628& -0.01017271\end{array}\right)$$

ersetzt, wobei $$\overleftrightarrow{\mathrm{V}}=\left(\begin{array}{cc}40& 0\\ 0& 200\end{array}\right)\cdot {\left(\begin{array}{cc}{\mathrm{a}}_{\mathrm{x}}& {\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}$$

gewählt wird mit (p_x; p_y) = (0,00811617; 199,99992) und (a_x ; a_y) = (39,99495; -0,00994503), so dass sich $$\mathrm{U}\prime =\left(\begin{array}{cc}\mathrm{0,01742912}& \mathrm{0,01722982}\\ \mathrm{0,0098363}& -\mathrm{0,01015558}\end{array}\right)$$

ergibt.However, this motif grid does not fit nondisruptively on a cylinder with a circumference of 200 mm, nor does it repeat periodically at a distance of 40 mm. It is therefore according to the invention by a transformed motif grid grid $\overleftrightarrow{U}\text{'}=\overleftrightarrow{V}\cdot \overleftrightarrow{U}$

replaced, where $$\overleftrightarrow{\mathrm{V}}=\left(\begin{array}{cc}40& 0\\ 0& 200\end{array}\right)\cdot {\left(\begin{array}{cc}{\mathrm{a}}_{\mathrm{x}}& {\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}$$

is chosen with (p _x ; p _y ) = (0.00811617; 199.99992) and (a _x ; a _y ) = (39.99495; -0.00994503), so that $$\mathrm{U}\text{'}=\left(\begin{array}{cc}0.01742912& 0.01722982\\ 0.0098363& -0.01015558\end{array}\right)$$

results.

For the transformed motion matrix results in this case: $$\overleftrightarrow{\mathrm{A}}\text{'}=\left(\begin{array}{cc}0.485129& 102.55493\\ 100.39976& -0.788365\end{array}\right)$$

The moiré magnification of the original motif grid lattice is 100.0-fold by design, the magnification with the transformed motif grid is horizontally 100.4-fold and perpendicular 102.6-fold, so has changed only slightly. In addition, results with the transformed motif grid grid on a printing or embossing cylinder with 200 mm circumference a trouble-free motif image, which has adjacent strips of a width of 40 mm adjacent to each other for further processing.

Example 7:

As explained above, moiré magnifiers can be realized not only with two-dimensional gratings but also with linear translation structures, for example with cylindrical lenses as microfocusing elements and with motifs that are arbitrarily extended in one direction as micromotif elements. Even with such linear translation structures, the Moire Magnifier data can be adapted to a given rapport with advantage, as now with reference to the motif images 90 and 95 of FIGS. 8 and 9 explained.

A linear translation structure can be defined by a translation vector u describe, so by a displacement width d and a shift direction ψ , as in Fig. 8 shown. The parallel lines 92 in FIG Fig. 8 stand schematically for a with the translation vector u moved repeatedly arranged motif. In addition, a vector of length q is drawn with the end point Q, which stands for the given longitudinal repeat.

gilt. Wenn dies, wie im in Fig. 8 dargestellten Ausführungsbeispiel, nicht der Fall ist, kann diese Bedingung in der folgenden Weise durch eine geringfügige Änderung der Größen d, ψ oder q erfüllt werden.Such a translation structure can then be accommodated in the repeat without impact position if ψ = 0, or if there is an integer n such that $$\mathrm{nd}/\sin \psi =\mathrm{q}$$

applies. If this, as in in Fig. 8 is not the case, this condition can be met in the following manner by a slight change of the quantities d, ψ or q.

As already described in example 1, a transformation matrix V can be found with the aid of which the motif structure and the movement behavior can be adapted to the repeat with a minimum change. In Fig. 8 is a point P located on the translation structure near the point Q.

bildet dann den Punkt P auf den Punkt Q ab.The transformation V described by the above equation (2a) $$\mathrm{V}=\left(\begin{array}{cc}1& 0\\ 0& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}1& {\mathrm{p}}_{\mathrm{x}}\\ 0& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}=\left(\begin{array}{cc}1& -{\mathrm{p}}_{\mathrm{x}}/{\mathrm{p}}_{\mathrm{y}}\\ 0& \mathrm{q}/{\mathrm{p}}_{\mathrm{y}}\end{array}\right)$$

then maps the point P to the point Q.

verwendet. Die neuen Koordinaten eines Punktes (x',y') in der zum vorgegebenen Rapport passenden Motivebene, die gegenüber den alten Koordinaten (x,y) in der nicht zum vorgegebenen Rapport passenden alten Motivebene geringfügig geändert sind, sind dann wie bei Gleichung (4) gegeben durch $$\left(\begin{array}{c}\mathrm{x}\text{'}\\ \mathrm{y}\text{'}\end{array}\right)=\mathrm{V}\cdot \left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)=\left(\begin{array}{c}\mathrm{x}-\mathrm{y}\cdot {\mathrm{p}}_{\mathrm{x}}/{\mathrm{p}}_{\mathrm{y}}\\ \mathrm{y}\cdot \mathrm{q}/{\mathrm{p}}_{\mathrm{y}}\end{array}\right)$$

As a new, slightly distorted and the given rapport matching motif translation grid then becomes a grid with the translation vector $$\overrightarrow{\mathrm{u}}\text{'}=\mathrm{V}\cdot \overrightarrow{\mathrm{u}}$$

used. The new coordinates of a point (x ', y') in the motif plane matching the given rapport, which are slightly changed compared to the old coordinates (x, y) in the old motive plane not matching the given repeat, are then as in equation (4 given by $$\left(\begin{array}{c}\mathrm{x}\text{'}\\ \mathrm{y}\text{'}\end{array}\right)=\mathrm{V}\cdot \left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)=\left(\begin{array}{c}\mathrm{x}-\mathrm{y}\cdot {\mathrm{p}}_{\mathrm{x}}/{\mathrm{p}}_{\mathrm{y}}\\ \mathrm{y}\cdot \mathrm{q}/{\mathrm{p}}_{\mathrm{y}}\end{array}\right)$$

The new motion matrix A 'in the translation grid matching the given repeat, which only slightly compared to the old motion matrix A. as described in equation (7) is given by: $$\mathrm{A}\text{'}={\mathrm{VAV}}^{-1}$$

Analogous to the adaptation in the case of a two-dimensional Bravais grid according to example 3, an adaptation to a transverse repeat can also be effected in the case of a linear translation structure in addition to adaptation to the longitudinal repeat, as can be seen from the motif image 95 of FIG Fig. 9 explained.

The longitudinal repeat is in Fig. 9 represented by a vector (0, q) with end point Q, the transverse repeat by a vector (b, 0) with end point B. Furthermore, points P and A are selected with the coordinates (p _x , p _y ) and (a _x , a _y ) in the translation structure, which are close to Q and B, respectively.

As described in example 3, this information provides a transformation matrix V, with the help of which the motif structure and the movement behavior can be adapted with minimal change to both repetitions, namely with equation (2c): $$\mathrm{V}=\left(\begin{array}{cc}\mathrm{b}& 0\\ 0& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}{\mathrm{a}}_{\mathrm{x}}& {\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}$$

It will be appreciated that the methods described herein of seamlessly placing a motif grid in a repeat are also applicable for seamlessly placing a lenticular grid in a repeat (eg, on an embossing cylinder).

Example 8 Embossing or impression cylinder with seams

An example of the fabrication and seamless imaging of lenticular cylinders and motif grid cylinders having seams will now be described in greater detail.

In this example, the printing or embossing cylinders themselves have seams, the design of moire magnification arrangements is inventively designed so that it fits together before and after a seam.

8. 1 lenticular cylinder:

By means of different techniques, plates can be produced with latticed, free-standing, generally cylindrical resist structures, which are referred to as lacquer points. These paint spots are produced in a lattice-like arrangement which results for the lenticular grid using the above-described relationships (1) to (8).

Such plates can be produced for example by means of classical photolithography, by means of lithographic direct-write methods, such as laser-writing or e-beam lithography, or by suitable combinations of both approaches.

In a thermal reflow process, the plate is then heated with the paint dots, so that the resist structures flow away and generally form lattice-shaped arranged small hills, preferably small spherical caps. Shaped in transparent materials These hill lens properties, lens diameter, lens curvature, focal length on the geometric structure of the paint dots, especially their diameter and the thickness of the paint layer, can be determined.

Another possibility is the direct structuring of the plates with latticed, free-standing hills, for example by means of laser ablation. In particular, plastic, ceramic or metal surfaces are processed with high-energy laser radiation, for example with excimer laser radiation.

On a plate produced in this way, the so-called resist master, a nickel layer, for example 0.05 to 0.2 mm thick, is deposited and this is lifted off the plate. This gives a nickel foil, the so-called shim, with depressions that correspond to the above hills in the Resistmaster. This nickel foil is suitable as an embossing stamp for embossing a lenticular grid.

The nickel foil is precisely cut to size and welded with the embossing recesses outwards to a cylindrical tube, the sleeve. The sleeve can be attached to an embossing cylinder. In the exposure control for the emboss pattern, since the cylinder circumference including the sleeve has been taken into account by using the relationships (1) to (8) according to the present invention, the grating period also fits in the area of the weld.

With the aid of this embossing cylinder, the calculated lens grid is then embossed into an embossable lacquer layer, for example a thermoplastic lacquer or UV lacquer, on the front side of a foil.

8. 2 motif grid cylinders:

The production takes place analogously to the lenticular cylinder, wherein plates are prepared with lattice-shaped, free-standing, freely designed motifs.

According to the invention, lens raster, motif raster and cylinder circumference are in the relationships given by equations (1) to (8), so that the grating period also fits in the area of the weld seam.

Using this embossing cylinder, the motif grid is embossed into an embossable lacquer layer, for example a thermoplastic lacquer or UV lacquer, on the back side of the foil, which contains the associated lenticular grid on the front side. To increase the contrast, the motif grid can be colored.

Overall, a moiré magnification arrangement is obtained, which shows an enlarged and moved motif and, compared to the prior art, shows a substantially improved behavior in the case of the embossing seams occurring in roll material.

The further processing of the double-sided with lenticular grid and motif grid embossed film can be done in different ways. For example, the motif grid can be metallized over the entire area, or the motif grid can be obliquely vapor-deposited, and then a two-dimensional application of a color layer to the partially metallized areas can take place, or the embossed motif grid can be applied by full-surface application of Colored layers and subsequent wiping be colored.

Example 9 Embossing or impression cylinder without seams

Seamless cylinders for use in embossing or printing machines as such are state of the art and, for example, from the documents WO 2005/036216 A2 or DE 10126264 A1 known. However, there is no teaching how to design such cylinders to meet the special requirements of moire magnification arrangements.

In a preferred moiré magnification arrangement, a lenticular grid is mounted on one side of a film and a matching motif grid on the other side of the film. In this case, embossing or impression cylinders are imaged, for example, according to the methods described in the prior art, wherein the design is carried out according to the above-described inventive calculation using the relationships (1) to (8).

Such cylinders can be made, for example, as follows.

9.1 Lens grid cylinder:

In a metal, ceramic or plastic-coated cylinder by laser ablation, in particular by material removal using a computer-controlled laser, trough-shaped lattice-like recesses created which serve as embossing or printing forms for a lenticular grid. In this case, the programming of the laser feed control according to the invention is carried out using the relationships (1) to (8), so that a seamless pattern without interruption arises on the cylinder.

9. 2 motif grid cylinders:

In a metal, ceramic or plastic-coated cylinder lattice-like arranged recessed motifs or relief-like raised motifs are introduced in recessed environment by laser ablation, in particular by material removal using a computer-controlled laser, which serve as embossing or printing forms for a motif grid. In this case, the programming of the laser feed control according to the invention is carried out using the relationships (1) to (8), so that a seamless pattern without interruption arises on the cylinder.

With the aid of these embossing cylinders, embossable layers of lacquer, for example thermoplastic lacquer or UV lacquer, on the front and back side of a foil imprint lenticular and motif grid. To increase the contrast, the motif grid can be colored, as described in Example 7.

According to the present invention, lenticular, motif and cylinder circumferences are in the relationships given by equations (1) to (8) so as to obtain moiré magnification arrangements having an enlarged and moved motive, and moreover exhibit no discontinuities in roll material in periodicity ,

It should be noted that the cylinder circumferences of lens and motif cylinders may be the same or different, and the calculation by the relationships (1) to (8) provides the desired results in magnification and motion performance of the moiré magnification arrangement in the latter case in the latter case as well.

The further processing of the double-sided impressed with lenticular grid and motif grid film can be done in the manner described in Example 7 types. Likewise, the mentioned lenticular and motif grid cylinders can be used as printing forms. This is particularly suitable for the motif grid cylinder.

A particularly preferred production method is obtained when a lenticular grid is introduced by means of embossing in an embossable lacquer layer, for example a thermoplastic lacquer or UV lacquer, of a foil, and the associated motif grid is applied to the opposite side of the foil by means of classical printing processes.

Claims (15)

1. A method for manufacturing endless material for security elements (12; 16) having micro-optical moiré magnification arrangements that exhibit a motif grid composed of a plurality of micromotif elements (28) and a focusing element grid composed of a plurality of microfocusing elements (22) for moiré-magnified viewing of the micromotif elements (28), in which

   a) a motif grid composed of an at least locally periodic arrangement of micromotif elements (28) in the form of a first two-dimensional lattice is provided,

   b) a focusing element grid composed of an at least locally periodic arrangement of a plurality of microfocusing elements (22) in the form of a second two-dimensional lattice is provided,

   - wherein the first and/or second lattice exhibits a hexagonal lattice symmetry or the symmetry of a parallelogram lattice, and is, in addition to the orientation of the lattice vectors with respect to each other, determined by a fixed orientation of the lattice to the endless material, especially to the longitudinal axis thereof, and wherein each lattice from the class of two-dimensional Bravais lattices with hexagonal lattice symmetry or the symmetry of a parallelogram lattice having a fixed orientation from 0-360° is selectable as the first and/ or second lattice,

   c) a pattern repeat of the motif grid and/or of the focusing element grid on the endless material is specified,

   d) it is checked whether the lattice of the motif grid and/or the lattice of the focusing element grid repeats periodically in the specified pattern repeat, and if this is not the case, a linear transformation is determined that distorts the first and/or the second lattice such that it repeats periodically in the specified pattern repeat, and

   e) for the further manufacture of the endless material, the motif grid or the focusing element grid is replaced by the motif grid that is distorted by the determined linear transformation, or the focusing element grid that is distorted by the determined linear transformation,
   wherein in step c), a pattern repeat q along the endless longitudinal direction of the endless material is specified, and
   wherein in step d), a lattice point P of the first and/or the second lattice is selected that lies near the endpoint Q of the vector $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

   

   given by the longitudinal pattern repeat, and a linear transformation V is determined that maps P to Q.
2. The method according to claim 1, characterized in that, as the lattice point lying near the endpoint Q, a lattice point P is chosen whose distance from Q along the lattice vector or both lattice vectors is in each case less than 10 lattice periods, preferably less than 5, particularly preferably less than 2 and especially less than one lattice period, or that the lattice point closest to the endpoint Q is chosen as the lattice point P.
3. The method according to claims 1 or 2, characterized in that the linear transformation V is calculated using the relationship $$\mathrm{V}=\left(\begin{array}{cc}{\mathrm{b}}_{\mathrm{x}}& 0\\ {\mathrm{b}}_{\mathrm{y}}& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}{\mathrm{a}}_{\mathrm{x}}& {\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1},$$

   

   wherein $\left(\begin{array}{c}{\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{p}}_{\mathrm{y}}\end{array}\right)$

   

   and $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

   

   represent the coordinate vectors of the lattice point P and the endpoint Q, and $\overrightarrow{b}=\left(\begin{array}{c}{\mathrm{b}}_{\mathrm{x}}\\ {\mathrm{b}}_{\mathrm{y}}\end{array}\right)$

   

   and $\overrightarrow{a}=\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

   

   arbitrary vectors.
4. The method according to at least one of claims 1 to 3, characterized in that the linear transformation V is calculated using the relationship $$\mathrm{V}=\left(\begin{array}{cc}1& 0\\ 0& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}1& {\mathrm{p}}_{\mathrm{x}}\\ 0& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1}=\left(\begin{array}{cc}1& -{\mathrm{p}}_{\mathrm{x}}/{\mathrm{p}}_{\mathrm{y}}\\ 0& \mathrm{q}/{\mathrm{p}}_{\mathrm{y}}\end{array}\right),$$

   

   wherein $\left(\begin{array}{c}{\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{p}}_{\mathrm{y}}\end{array}\right)$

   

   and $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

   

   represent the coordinate vectors of the lattice point P and the endpoint Q.
5. The method according to claim 1, wherein
   in step c), a pattern repeat q along the endless longitudinal direction of the endless material is specified and a pattern repeat b along the transverse direction of the endless material is specified, and
   in step d)

   - a lattice point P of the first and/or the second lattice is selected that lies near the endpoint Q of the vector $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

   

   given by the longitudinal pattern repeat,

   - a lattice point A of the first and/or the second lattice is selected that lies near the endpoint B of the vector $\left(\begin{array}{c}\mathrm{b}\\ 0\end{array}\right)$

   

   given by the transverse pattern repeat, and

   - a linear transformation V is determined that maps P to Q and A to B.
6. The method according to claim 5, characterized in that, in a later method step, the endless material is cut into parallel longitudinal strips, and the transverse pattern repeat b is given by the width of these longitudinal strips.
7. The method according to claim 5 or 6, characterized in that, as the lattice points lying near the endpoints Q and B, such lattice points P and A are chosen whose distances from Q and B along the lattice vector or both lattice vectors is in each case less than 10 lattice periods, preferably less than 5, particularly preferably less than 2 and especially less than one lattice period.
8. The method according to claim 7, characterized in that the lattice point closest to the endpoint Q is chosen as the lattice point P, and the lattice point closest to the endpoint B as the lattice point A, wherein preferably the linear transformation V is calculated using the relationship $$\mathrm{V}=\left(\begin{array}{cc}\mathrm{b}& 0\\ \mathrm{b}& \mathrm{q}\end{array}\right)\cdot {\left(\begin{array}{cc}{\mathrm{a}}_{\mathrm{x}}& {\mathrm{p}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}& {\mathrm{p}}_{\mathrm{y}}\end{array}\right)}^{-1},$$

   

   wherein $\left(\begin{array}{c}{\mathrm{p}}_{\mathrm{x}}\\ \mathrm{p}{}_{\mathrm{y}}\end{array}\right)$

   

   and $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

   

   represent the coordinate vectors of the lattice point P and the endpoint Q, and $\left(\begin{array}{c}{\mathrm{a}}_{\mathrm{x}}\\ {\mathrm{a}}_{\mathrm{y}}\end{array}\right)$

   

   and $\left(\begin{array}{c}\mathrm{b}\\ 0\end{array}\right)$

   

   the coordinate vectors of the lattice point A and the endpoint B.
9. The method according to a least one of claims 1 to 8, characterized in that the first and second lattice are two-dimensional Bravais lattices, wherein preferably

   - a desired image that is visible when viewed and has one or more moire image elements is defined, the arrangement of magnified moiré image elements being chosen in the form of a two-dimensional Bravais lattice whose lattice cells are given by vectors t ₁ and t ₂,

   - the focusing element grid in step b) is provided as an arrangement of microfocusing elements in the form of a two-dimensional Bravais lattice whose lattice cells are given by vectors w ₁ and w ₂, and

   - in step a), the motif grid having the micromotif elements is calculated using the relationships $$\overleftrightarrow{U}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overleftrightarrow{T}$$

   

   and $$\overrightarrow{r}=\overleftrightarrow{W}\cdot {\left(\overleftrightarrow{T}+\overleftrightarrow{W}\right)}^{-1}\cdot \overrightarrow{R}+{\overrightarrow{r}}_0,$$

   

   wherein $\overrightarrow{R}=\left(\begin{array}{c}X\\ Y\end{array}\right)$

   

   represents an image point of the desired image, $\overrightarrow{r}=\left(\begin{array}{c}x\\ y\end{array}\right)$

   

   an image point of the motif grid, ${\overrightarrow{r}}_0=\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)$

   

   a displacement between the arrangement of microfocusing elements and the arrangement of micromotif elements, and the matrices T, W and U are given by $\overleftrightarrow{T}=\left(\begin{array}{cc}{t}_{11}& t_{12}\\ t_{21}& t_{22}\end{array}\right),$

   

   $\overleftrightarrow{W}=\left(\begin{array}{cc}{w}_{11}& w_{12}\\ w_{21}& w_{22}\end{array}\right)$

   

   and $\overleftrightarrow{U}=\left(\begin{array}{cc}{u}_{11}& u_{12}\\ u_{21}& u_{22}\end{array}\right),$

   

   with t_1i, t_2i, u_1i, u_2i and w_1i, w_2i representing the components of the lattice cell vectors t _i , u _i and w _i , where i=1, 2.
10. The method according to claim 9, characterized in that

    - a desired image that is visible when viewed and has one or more moiré image elements is defined,

    - the focusing element grid in step b) is provided as an arrangement of microfocusing elements in the form of a two-dimensional Bravais lattice whose lattice cells are given by vectors w ₁ and w ₂,

    - a desired movement of the visible image when the moiré magnification arrangement is tilted laterally and when tilted forward and back is defined, the desired movement being specified in the form of the matrix elements of a transformation matrix A , and

    - in step a), the motif grid having the micromotif elements is calculated using the relationships $$\overleftrightarrow{U}={\left(\overleftrightarrow{I}+{\overleftrightarrow{A}}^{-1}\right)}^{-1}\cdot \overleftrightarrow{W}$$

    

    and $$\overrightarrow{r}={\overleftrightarrow{A}}^{-1}\cdot \overrightarrow{R}+{\overrightarrow{r}}_0,$$

    

    wherein $\overrightarrow{R}=\left(\begin{array}{c}X\\ Y\end{array}\right)$

    

    represents an image point of the desired image, $\overrightarrow{r}=\left(\begin{array}{c}x\\ y\end{array}\right)$

    

    an image point of the motif image, ${\overrightarrow{r}}_0=\left(\begin{array}{c}{x}_0\\ y_0\end{array}\right)$

    

    a displacement between the arrangement of microfocusing elements and the arrangement of micromotif elements, and the matrices A, W and U are given by $\overleftrightarrow{A}=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right),$

    

    $\overleftrightarrow{W}=\left(\begin{array}{cc}{w}_{11}& w_{12}\\ w_{21}& w_{22}\end{array}\right)$

    

    and $\overleftrightarrow{U}=\left(\begin{array}{cc}{u}_{11}& u_{12}\\ u_{21}& u_{22}\end{array}\right),$

    

    with u_1i, u_2i and w_1i, w_2i representing the components of the lattice cell vectors u _i and w _i , where i=1,2.
11. The method according to at least one of claims 1 to 10, characterized in that the motif grid and the focusing element grid are arranged at opposing surfaces of an optical spacing layer, and/or that step e) comprises providing an impression or embossing cylinder (34) with the distorted focusing element grid, and/or that step e) comprises providing an impression or embossing cylinder (34) with the distorted motif grid.
12. An endless material for security elements for security papers, value documents and the like, manufacturable according to one of claims 1 to 11, having micro-optical moiré magnification arrangements that

    - exhibit a motif grid composed of an at least locally periodic arrangement of micromotif elements (28) in the form of a first two-dimensional Bravais lattice,

    - exhibit a focusing element grid composed of an at least locally periodic arrangement of a plurality of microfocusing elements (22) in the form of a second two-dimensional Bravais lattice for moiré-magnified viewing of the micromotif elements,

    - wherein the first and/or second Bravais lattice exhibits a hexagonal lattice symmetry or the symmetry of a parallelogram lattice, and is, in addition to the orientation of the lattice vectors with respect to each other also determined by a fixed orientation of the lattice to the endless material, especially to the longitudinal axis thereof, and wherein in the fixed orientation none of the two lattice vectors of the two-dimensional Bravais lattice is parallel to the longitudinal axis of the endless material,

    - the motif grid and the focusing element grid being arranged on the endless material, gaplessly and free of misalignment, with a specified pattern repeat, and

    - wherein the motif grid and the focusing element grid are arranged on the endless material, gaplessly and free of misalignment, with the specified pattern repeat, on a length of 10 meters or more, preferably on a length of 100 meters or more, and particularly preferably on a length of 1,000 meters or more.
13. A method for manufacturing a security element (12; 16) for security papers, value documents and the like, in which an endless material according to one of claims 1 to 11 is manufactured and cut in the desired shape of the security element (12; 16), wherein the endless material is preferably cut into longitudinal strips of equal width and having an identical arrangement of the micro-optical moiré magnification arrangements.
14. A method for manufacturing an impression or embossing cylinder (34) for producing the focusing element grid in the manufacturing method of claims 1 to 11, in which

    - a focusing element grid composed of an at least locally periodic arrangement of a plurality of microfocusing elements (22) in the form of a two-dimensional lattice, as well as the circumference q of the finished impression or embossing cylinder (34), is specified,

    - wherein the lattice exhibits a hexagonal lattice symmetry or the symmetry of a parallelogram lattice, and is, in addition to the orientation of the lattice vector with respect to each other, determined by a fixed orientation of the lattice to a cylinder surface of the impression or embossing cylinder, especially to the circumferential direction thereof, and wherein each lattice from the class of two-dimensional Bravais lattices with hexagonal lattice symmetry or the symmetry of a parallelogram lattice having a fixed orientation from 0-360° is selectable as said lattice,

    - the lattice of the focusing element grid is distorted by means of a linear transformation such that it repeats periodically in the pattern repeat of the specified circumference q, wherefore a lattice point P of the lattice of the focusing element grid is selected that lies near the endpoint Q of the vector $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

    

    given by the circumference of the finished impression or embossing cylinder (34), and a linear transformation V is determined that maps P to Q, and

    - an impression or embossing cylinder is provided with the distorted focusing element grid.
15. A method for manufacturing an impression or embossing cylinder (34) for producing the motif grid in the manufacturing method of claims 1 to 11, in which

    - a motif grid composed of an at least locally periodic arrangement of a plurality of micromotif elements (28) in the form of a two-dimensional lattice, as well as the circumference q of the finished impression or embossing cylinder (34), is specified,

    - wherein the lattice exhibits a hexagonal lattice symmetry or the symmetry of a parallelogram lattice, and is, in addition to the orientation of the lattice vectors with respect to each other, determined by a fixed orientation of the lattice to a cylinder surface of the impression or embossing cylinder, especially to the circumferential direction thereof, and wherein each lattice from the class of two-dimensional Bravais lattices with hexagonal lattice symmetry or the symmetry of a parallelogram lattice having a fixed orientation from 0-360° is selectable as said lattice,

    - the motif grid is distorted by means of a linear transformation such that it repeats periodically in the pattern repeat of the specified circumference q, wherefore a lattice point P of the motif grid is selected that lies near the endpoint Q of the vector $\left(\begin{array}{c}0\\ \mathrm{q}\end{array}\right)$

    

    given by the circumference of the finished impression or embossing cylinder (34), and a linear transformation V is determined that maps P to Q, and

    - an impression or embossing cylinder is provided with the distorted motif grid.

Images