EP2507069B1 - Security element, value document comprising such a security element, and method for producing such a security element - Google Patents

Description

The present invention relates to a security element for a security paper, value document or the like, a value document with such a security element and a method for producing such a security element.

Items to be protected are often provided with a security element that allows verification of the authenticity of the item and at the same time serves as protection against unauthorized reproduction.

Items to be protected include, for example, security papers, identity and value documents (such as banknotes, chip cards, passports, identification cards, identity cards, stocks, investments, certificates, vouchers, checks, tickets, credit cards, health cards, etc.) as well as product security elements such as security items. Labels, seals, packaging, etc.

A technique widely used in the field of security elements, which gives a practically flat film a three-dimensional appearance, are various forms of holography. For the application of a security feature, in particular on banknotes, however, these techniques have some disadvantages. On the one hand, the quality of the three-dimensional representation of a hologram depends strongly on the lighting conditions. Especially with diffuse lighting, the representations of holograms are often barely visible. Furthermore, holograms have the disadvantage that they are present in everyday life in many places and therefore their special position as a security feature disappears.

Based on this, the object of the invention is to avoid the disadvantages of the prior art and in particular to provide a security element for a security paper, document of value or the like, in which a good three-dimensional appearance is achieved with an extremely flat design of the security element.

According to the invention the object is achieved by a security element for a security paper, value document or the like according to claim 1. Thus, an extremely flat security element, in which, for example, the maximum height of the facets is not greater than 10 microns, can be provided, which nevertheless produces a very good three-dimensional impression when viewed. It is therefore possible, by means of a (macroscopically) flat area, to reproduce a surface which appears to be very curved, for the observer. In principle, arbitrarily shaped three-dimensional configurations of the perceptible surface can be produced in this manner. Thus, portraits, objects, motifs or other three-dimensional appearing objects can be recreated. The three-dimensional impression is always related to the actual spatial form of the surface area. Thus, the surface area may be flat or even curved. However, it is always related to this base shape achieved three-dimensional appearance, so that for a viewer, the surface area then does not appear even or curved in the same manner as the surface area itself.

The surface area that can be perceived as a protruding and / or recessed surface is understood here in particular to mean that the surface area can be perceived as a continuously curved surface. So the area z. B. be perceived as a surface with an apparent curvature, which differs from the curvature or actual spatial shape of the surface area. With the security element according to the invention can according to z. B. a curved surface can be imitated by adjusting the corresponding reflection behavior.

The surface area is in particular a continuous surface area. However, the surface area can also have gaps or even comprise non-contiguous subareas. In this way, the area may be interleaved with other security features. In the other security features, it may, for. B. can be a true color hologram, so that a viewer can perceive the true color hologram and the front and / or recessed surface, which are provided by the surface area according to the invention together.

The orientation of the facets is chosen in particular such that the surface area is perceptible to a viewer as a non-planar surface.

The plurality of pixels each having a plurality of the optically effective facets having the same orientation per pixel may be 51% of the number of pixels be. However, it is also possible that the majority is greater than 60%, 70%, 80% or in particular greater than 90% of the number of pixels.

Furthermore, it is also possible for all the pixels of the surface area to each have a plurality of the optically active facets with the same orientation.

The optically active facets can be designed as reflective and / or transmissive facets.

The facets may be formed in a surface of the carrier. Further, it is possible that the facets are formed both in the top and in the bottom of the carrier and facing each other. In this case, the facets are preferably designed as transmissive facets having a refractive effect, wherein, of course, the carrier itself is also transparent or at least translucent. The dimensions and orientations of the facets are then selected, in particular, such that for a viewer, a surface is perceivable so that it projects forward and / or backward in relation to the actual spatial form of the top and / or underside of the carrier.

The carrier may be formed as a layer composite. In this case, the facets may lie at an interface within the laminar structure. So the facets z. B. embossed in an embossing lacquer on a carrier film, then metallized and embedded in a further lacquer layer (eg protective lacquer or adhesive lacquer).

In particular, in the case of the security element according to the invention, the facets can be embodied as embedded facets.

In particular, the optically active facets are designed such that the pixels have no optically diffractive effect.

The dimensions of the optically active facets can be between 1 μm and 300 μm, preferably between 3 μm and 100 μm, and particularly preferably between 5 μm and 30 μm. In particular, there is preferably a substantially beam-optical reflection behavior or a substantially beam-optical refraction effect.

The dimensions of the pixels are chosen such that the area of the pixels is smaller by at least one order of magnitude and preferably by at least two orders of magnitude than the area of the area. In this case, the area of the surface area as well as the area of the pixels is to be understood as meaning in particular the area when projected in the direction of the macroscopic surface normal of the surface area onto a plane.

In particular, the dimensions of the pixels can be chosen such that the dimensions of the pixels are at least in one direction at least an order of magnitude and preferably at least two orders of magnitude smaller than the dimensions of the surface of the surface region.

The maximum extent of a pixel is preferably between 5 μm and 5 mm, preferably between 10 μm and 300 μm, particularly preferably between 20 μm and 100 μm. The pixel shape and / or the pixel size may, but need not, vary within the security element.

The grating period of the facets per pixel (the facets may form a periodic or aperiodic grating, eg a sawtooth grating) is preferably between 1 μm and 300 μm or between 3 μm and 300 μm, preferably between 3 .mu.m and 100 .mu.m, or between 5 .mu.m and 100 .mu.m, more preferably between 5 .mu.m and 30 .mu.m, or between 10 .mu.m and 30 .mu.m. In particular, the grating period is selected such that at least two facets of the same orientation are contained per pixel and that diffraction effects virtually no longer play a role for incident light (eg from the wavelength range from 380 nm to 750 nm). Since no or no practically relevant diffraction effects occur, the facets can be referred to as achromatic facets and the pixels as achromatic pixels, which cause a directed achromatic reflection. The security element thus has an achromatic reflectivity with respect to the lattice structure present through the facets of the pixels.

The facets are preferably formed as substantially planar surface pieces. The chosen formulation, according to which the facets are formed as essentially flat surface pieces, takes account of the fact that in practice production-related generally never perfectly flat surface pieces can be produced.

The orientation of the facets is determined in particular by their inclination and / or their azimuth angle. Of course, the orientation of the facets can also be determined by other parameters. In particular, these are two mutually orthogonal parameters, such. B. the two components of the normal vector of each facet.

On the facets, a reflective or reflection-increasing coating (in particular a metallic or high-refractive coating) may be formed at least in regions. The reflective or reflection-enhancing coating may be a metallic coating, for example vapor-deposited. As a coating material, in particular Aluminum, gold, silver, copper, palladium, chromium, nickel and / or tungsten and their alloys. Alternatively, the reflective or reflection-enhancing coating may be formed by a coating with a high refractive index material.

The reflective or reflection-enhancing coating may in particular be formed as a partially permeable coating.

In a further embodiment, a color-shifting coating may be formed on the facets at least in regions. The color-shifting coating can be designed in particular as a thin-layer system or thin-film interference coating. In this case, for example, a layer sequence of metal layer - dielectric layer - metal layer or a layer sequence of three dielectric layers, wherein the refractive index of the middle layer is less than the refractive index of the other two layers, are realized. As the dielectric material, for example, ZnS, SiO ₂ , TiO ₂ , MgF ₂ can be used.

The color-shifting coating can also be designed as an interference filter, thin semitransparent metal layer with selective transmission by plasma resonance effects, nanoparticles, etc. The color-shifting layer can in particular also be realized as a liquid-crystal layer, diffractive relief structure or sub-wavelength grating. A thin-film system with a reflector, dielectric, absorber structure (formed on the facets in this order) is also possible.

As already described, the thin-film system plus facet can not only be designed as a facet / reflector / dielectric / absorber, but also as a facet / absorber / dielectric / reflector. The order depends in particular depending on which side the security element should be viewed from. Furthermore, color shift effects visible on both sides are also possible if the thin-film system plus facet is embodied, for example, as absorber / dielectric / absorber / facet or absorber / dielectric / reflector / dielectric / absorber / facet.

The color-shifting coating can be designed not only as a thin-film system but also as a liquid-crystal layer (in particular of cholesteric liquid-crystalline material).

If a diffusely scattering object is to be readjusted, a scattering coating or surface treatment of the facets can be provided. Such a coating or treatment may be scattered according to Lambert's cosine law or there may be a scattered reflection with a directional distribution different from Lambert's cosine law. In particular, scattering with pronounced preferential direction is interesting here.

In the production of the facets via an embossing process, the embossing surface of the embossing tool, with which the shape of the facets can be embossed into the carrier or into a layer of the carrier, can additionally be provided with a microstructure in order to produce specific effects. For example, the embossing surface of the embossing tool can be provided with a rough surface, so that facets with scattered reflection arise in the end product.

In the case of the security element according to the invention, preferably at least two facets can be provided per pixel. It can also be three, four, five or more facets.

In the case of the security element according to the invention, the number of facets per pixel can in particular be selected so that a maximum predetermined facet height is not exceeded. The maximum facet height can be, for example, 20 μm or even 10 μm.

Furthermore, in the case of the security element according to the invention, the grating period of the facets can be chosen to be the same for all pixels. However, it is also possible for one or more of the pixels to have different grating periods. Furthermore, it is possible that the grating period varies within a pixel and is thus not constant. Furthermore, in the grating period, a phase information can be imprinted, which is used to encode further information. In particular, a verification mask having grating structures can be provided which have the same periods and azimuth angles as the facets in the security element according to the invention. In one subregion of the verification mask, the grids can have the same phase parameter as the security element to be verified and, in other regions, a specific phase difference. If the verification mask is placed over the security element, the different areas will appear differently bright or dark due to the moiré effect. In particular, the verification mask can be provided on the same object to be protected as the security element according to the invention.

In the case of the security element according to the invention, the surface area can be designed in such a way that it can be perceived by an observer as an imaginary surface. By this is meant in particular that the security element according to the invention shows a reflection behavior that is not produced with a real macroscopically curved surface can. In particular, the imaginary surface can be perceived as a rotating mirror, the z. B. rotates 90 °.

Such an imaginary surface and in particular such a rotating mirror is very easily detectable and verifiable for a viewer.

In principle, any real arched reflecting or transmitting surface can be modified into an imaginary surface by means of the surface area of the security element according to the invention. This can be z. B. be realized in that the azimuth angle of all facets are changed, for example, be rotated by a certain angle. This can be interesting effects. If, for example, all azimuth angles are rotated by 45 ° to the right, the surface area for a viewer, when illuminated directly from above, is a curved surface that is apparently illuminated from the top right. Twisting all the azimuth angles by 90 °, the light reflections move when tilted in a direction that is perpendicular to the direction that a viewer would expect. This unnatural reflection behavior then makes it no longer possible for a viewer, for example, to decide whether the curved perceptible surface is present in front of or behind (in relation to the surface area).

Furthermore, by means of an aperiodic grating or the introduction of random phase parameters, selective diffraction effects can be suppressed.

It is also possible to "murmur" the orientations of the facets (ie to change slightly from the optimum shape for the surface to be re-set), for example to readjust matte surfaces. Thus the surface area does not only seem to jump forward and / or back compared to its actual spatial form, but it can also be given a register-accurate positioned texture.

Furthermore, in addition to the area area, the carrier may have a further surface area, which is preferably interleaved with the one area area and, in particular, is designed as a further security feature. Such training can z. B. as nesting or as a multi-channel image. The further surface region can be divided into a multiplicity of pixels, each comprising at least one optically active facet, in the same way as the one surface region, wherein preferably the plurality of pixels each have a plurality of the optically effective facets with the same orientation per pixel and the facets are so oriented that for a viewer of the other surface area as compared to its actual spatial shape curved or protruding and / or receding surface is perceptible. As a result, z. B. two different three-dimensional representations can be realized.

By means of the nesting of a surface area z. B. with additional register-accurate color or gray level information (combination, for example, with true color hologram or halftone image, for example, based on sub-wavelength grids) are superimposed.

Furthermore, in the arrangement of the facets, a phase information can be hidden or stored as a further security feature.

In the case of the security element according to the invention, at least one facet can have a light-scattering microstructure on its surface. Of course, several or even all facets may have such a light-scattering microstructure on the facet surface.

For example, the light-scattering microstructure may be formed as a coating. In particular, it is possible to embed the facets and to use as embedding material one with which the desired light-scattering microstructure can be realized.
With such a configuration can be scattering objects with the security element according to the invention, such. B. a marble figure, a plaster model, etc. be readjusted.

Of course, the facets can also be embedded in a colored material in order to additionally realize a color effect or to recreate a colored object.
In the case of the security element according to the invention, the orientations of a plurality of facets with respect to the orientations for producing the protruding and / or recessed surface may be changed such that the protruding and / or recessed surface is still perceptible, but with a surface which appears to be matt. Thus, the protruding and / or recessed surface can also be presented with a matte surface appearance.
The invention also includes a method for producing a security element for security papers, value documents or the like, according to claim 17. The production method according to the invention can in particular be developed so that the security element according to the invention and the developments of the security element according to the invention can be produced.
The manufacturing method may further include the step of calculating the pixels from a surface to be tracked. In this calculation step, the facets (their dimensions and their orientations) are calculated for all pixels. On the basis of this data, the height modulation of the surface area can then be carried out.

In the manufacturing method according to the invention, the step of coating the facets may be further provided. The facets can be provided with a reflective or reflection-enhancing coating. The reflective or reflection-enhancing coating can be a complete silvering or even a semi-transparent coating.
To generate the height-modulated surface of the carrier, known microstructuring methods can be used, such as embossing methods. For example, suitable structures in resist materials can also be exposed, possibly refined, molded and used for the production of embossing tools, using methods known from semiconductor production (photolithography, electron beam lithography, laser beam lithography, etc.). There may be known methods for embossing in thermoplastic Foils or in films coated with radiation-curing paints are used. The carrier may have a plurality of layers, which are successively applied and possibly structured and / or may be composed of several parts.

The security element can be designed, in particular, as a security thread, tear-open thread, security strip, security strip, patch or as a label for application to a security paper, value document or the like. In particular, the security element can span transparent or at least translucent areas or recesses.

The term security paper is understood here in particular as the precursor that can not be processed to a value document which, in addition to the security element according to the invention, may also have further authenticity features (such as, for example, luminescent substances provided in the volume). Value documents are here understood, on the one hand, documents produced from security papers. On the other hand, value documents can also be other documents and objects which can be provided with the security element according to the invention, so that the value documents have non-copyable authenticity features, whereby an authenticity check is possible and at the same time unwanted copying is prevented.

It is further provided an embossing tool with an embossing surface, with which the shape of the facets of a security element according to the invention (including its developments) can be embossed in the carrier or in a layer of the carrier.

The embossing surface preferably has the inverted shape of the surface contour to be embossed, wherein this inverted shape is advantageously produced by the formation of corresponding depressions.

Furthermore, the security element according to the invention can be used as a master for the exposure of volume holograms or for purely decorative purposes.

To expose the volume hologram, a photosensitive layer in which the volume hologram is to be formed may be brought into contact with the front of the master, and thus with the front of the security element, directly or with the interposition of a transparent optical medium.

Then, the photosensitive layer and the master are exposed with a coherent light beam, whereby the volume hologram is written in the photosensitive layer. The procedure can be the same or similar to that in the DE 101006 016139 A1 be described procedure for generating a volume hologram. The basic procedure is described, for example, in Sections Nos. 70 to 79 on pages 7 and 8 of the cited document in conjunction with US Pat Figures 1a, 1b, 2a and 2b described. This is the entire content of DE 10 2006 016 139 A1 with respect to the production of volume holograms incorporated in the present application.

It is understood that the features mentioned above and those yet to be explained below can be used not only in the specified combinations but also in other combinations or alone, without departing from the scope of the present invention.

Figur 1

eine Draufsicht einer Banknote mit einem erfindungsgemäßen Sicherheitselement 1;

Figur 2

eine vergrößerte Draufsicht eines Teils der Fläche 3 des Sicherheitselementes 1;

Figur 3

eine Querschnittsansicht entlang der Linie 6 in Figur 2;

Figur 4

eine schematische perspektivische Darstellung des Pixels 4₇ von Figur 2;

Figur 5

eine Schnittansicht einer weiteren Ausführungsform einiger Facetten des Sicherheitselementes 1;

Figur 6

eine Schnittansicht einer weiteren Ausführungsform einiger Facetten des Sicherheitselementes 1;

Figur 7

eine Schnittansicht zur Erläuterung der Berechnung der Facetten;

Figur 8

eine Draufsicht zur Erläuterung eines Quadratrasters zur Berechnung der Pixel;

Figur 9

eine Draufsicht zur Erläuterung eines 60°-Rasters zur Berechnung der Pixel;

Figur 10

eine Draufsicht auf drei Pixel 4 der Fläche 3;

Figur 11

eine Querschnittsansicht der Darstellung von Figur 10;

Figur 12

eine Draufsicht auf drei Pixel 4 der Fläche 3;

Figur 13

eine Querschnittsansicht der Draufsicht von Figur 12;

Figur 14

eine Draufsicht auf drei Pixel 4 der Fläche 3;

Figur 15

eine Schnittansicht der Draufsicht von Figur 14;

Figur 16

eine Draufsicht zur Erläuterung der Berechnung der Pixel gemäß einer weiteren Ausführungsform;

Figur 17

eine Schnittansicht der Anordnung der Facetten der Pixel auf einer zylindrischen Grundfläche;

Figur 18

eine Schnittansicht zur Erläuterung der Herstellung der Pixel für die Anwendung gemäß Figur 17;

Figuren 19 - 21

Darstellungen zur Erläuterung der Winkel bei reflektiven und transmissiven Facetten;

Figur 22

eine Schnittansicht einer nachzustellenden reflektiven Oberfläche;

Figur 23

eine Schnittansicht einer die Oberfläche gemäß Figur 22 nachstellenden Linse 22;

Figur 24

eine Schnittansicht der transmissiven Facetten für die Nachbildung der Linse gemäß Figur 23;

Figur 25

eine Schnittansicht einer nachzustellenden reflektiven Oberfläche;

Figur 26

eine Schnittansicht einer die Oberfläche gemäß Figur 25 nachstellenden Linse 22;

Figur 27

eine Schnittansicht der entsprechenden transmissiven Facetten zur Nachbildung der Linse gemäß Figur 24;

Figur 28

eine Schnittansicht einer Ausführungsform, bei der auf beiden Seiten des Trägers 8 transmissive Facetten ausgebildet sind;

Figur 29

eine Schnittansicht gemäß einer weiteren Ausführungsform, bei der auf beiden Seiten des Trägers 8 transmissive Facetten ausgebildet sind;

Figur 30

eine Darstellung zur Erläuterung der Winkel bei der Ausführungsform, bei der auf beiden Seiten des Trägers 8 transmissive Facetten ausgebildet sind;

Figur 31

eine schematische Schnittansicht eines Prägewerkzeuges zur Herstellung des erfindungsgemäßen Sicherheitselementes gemäß Figur 5.

Fig. 32a -32 c

Darstellungen zur Erläuterung eingebetteter Facetten, wobei die Facetten als reflektive Facetten ausgebildet sind;

Fig. 33a + 33b

Darstellungen zur Erläuterung eingebetteter Facetten, wobei die Facetten als transmissive Facetten ausgebildet sind;

Figur 34

eine Darstellung zur Erläuterung eingebetteter streuender Facetten, und

Figur 35

eine Darstellung zur Erläuterung eingebetteter matt glänzender Facetten.

The invention will be explained in more detail by way of example with reference to the accompanying drawings, which also disclose features essential to the invention. For better clarity, a scale and proportioned representation is omitted in the figures. Show it:

FIG. 1

a plan view of a banknote with a security element 1 according to the invention;

FIG. 2

an enlarged plan view of a portion of the surface 3 of the security element 1;

FIG. 3

a cross-sectional view taken along the line 6 in FIG FIG. 2 ;

FIG. 4

a schematic perspective view of the pixel 4 ₇ of FIG. 2 ;

FIG. 5

a sectional view of another embodiment of some facets of the security element 1;

FIG. 6

a sectional view of another embodiment of some facets of the security element 1;

FIG. 7

a sectional view for explaining the calculation of the facets;

FIG. 8

a plan view for explaining a square grid for calculating the pixels;

FIG. 9

a plan view for explaining a 60 ° grid for calculating the pixels;

FIG. 10

a plan view of three pixels 4 of the surface 3;

FIG. 11

a cross-sectional view of the representation of FIG. 10 ;

FIG. 12

a plan view of three pixels 4 of the surface 3;

FIG. 13

a cross-sectional view of the top view of FIG. 12 ;

FIG. 14

a plan view of three pixels 4 of the surface 3;

FIG. 15

a sectional view of the top view of FIG. 14 ;

FIG. 16

a plan view for explaining the calculation of the pixels according to another embodiment;

FIG. 17

a sectional view of the arrangement of the facets of the pixels on a cylindrical base surface;

FIG. 18

a sectional view for explaining the preparation of the pixels for the application according to FIG. 17 ;

FIGS. 19-21

Representations explaining the angles in reflective and transmissive facets;

FIG. 22

a sectional view of a nachzustellenden reflective surface;

FIG. 23

a sectional view of the surface according to FIG. 22 adjusting lens 22;

FIG. 24

a sectional view of the transmissive facets for the replica of the lens according to FIG. 23 ;

FIG. 25

a sectional view of a nachzustellenden reflective surface;

FIG. 26

a sectional view of the surface according to FIG. 25 adjusting lens 22;

FIG. 27

a sectional view of the corresponding transmissive facets for simulating the lens according to FIG. 24 ;

FIG. 28

a sectional view of an embodiment in which on both sides of the carrier 8 transmissive facets are formed;

FIG. 29

a sectional view according to another embodiment, in which on both sides of the carrier 8 transmissive facets are formed;

FIG. 30

an illustration for explaining the angle in the embodiment in which on both sides of the carrier 8 transmissive facets are formed;

FIG. 31

a schematic sectional view of a stamping tool for producing the security element according to the invention according to FIG. 5 ,

Fig. 32a -32c

Representations for explaining embedded facets, wherein the facets are formed as reflective facets;

Fig. 33a + 33b

Representations for explaining embedded facets, wherein the facets are formed as transmissive facets;

FIG. 34

a representation for explaining embedded scattering facets, and

FIG. 35

a representation explaining embedded matt shiny facets.

At the in FIG. 1 In the embodiment shown, the security element 1 according to the invention is integrated in a banknote 2 in such a way that the security element 1 differs from the security element 1 shown in FIG FIG. 1 shown front side of the banknote 2 is visible.

The security element 1 is formed as a reflective security element 1 with a rectangular outer contour, wherein the limited by the rectangular outer contour surface 3 is divided into a plurality of reflective pixels 4, of which a small part increases in FIG. 2 are shown as a plan view.

The pixels 4 are square here and have an edge length in the range of 10 to several 100 microns. Preferably, the edge length is not larger as 300 μm. In particular, it may be in the range between 20 and 100 microns.

The edge length of the pixels 4 is chosen in particular such that the area of each pixel 4 is smaller than the area 3 by at least one order of magnitude, preferably by two orders of magnitude.

The plurality of pixels 4 each have a plurality of reflective facets 5 of the same orientation, wherein the facets 5 are the optically effective surfaces of a reflective sawtooth grid.

In FIG. 3 the sectional view along the line 6 for six adjacent pixels 4 ₁ , 4 ₂ , 4 ₃ , 4 ₄ , 4 ₅ and 4 _{6 is} shown, the illustration in FIG. 3 as well as in the other figures is not to scale for better representation is not true to scale. Furthermore, to simplify the illustration in FIGS. 1 to 3 as well as in FIG FIG. 4 the reflective coating on the facets 5 not shown.

The sawtooth grid of the pixels 4 is formed here in a surface 7 of a carrier 8, wherein the thus structured surface 7 preferably with a reflective coating (in FIG. 3 not shown). The carrier 8 may be, for example, a radiation-curing plastic (UV resin) which is applied to a carrier foil, not shown, (for example, a PET foil).

As FIG. 3 can be seen, the pixels 4 ₁ , 4 ₂ , 4 ₄ , 4 ₅ and 4 ₆ each have three facets 5, the orientation per pixel 4 ₁ , 4 ₂ , 4 ₄ , 4 ₅ and 4 ₆ is the same. The sawtooth gratings and thus also the facets 5 of these pixels are the same except for their different inclination σ ₁ , σ ₄ (for simplification of the FIGS Representation are only the inclination angle σ ₁ and σ ₄ of each facet 5 of the pixels 4 ₁ and 4 ₄ drawn). The pixel 4 ₃ here has only a single facet 5.

Seen in plan view ( FIG. 2 ) are the facets 5 of the pixels 4 ₁ - 4 ₆ strip-shaped mirror surfaces which are aligned parallel to each other. The orientation of the facets 5 is chosen so that for a viewer, the surface 3 as compared to their actual (macroscopic) spatial form, which here is the shape of a flat surface, forward and / or recessed surface is perceptible. Here a viewer takes in the FIG. 3 shown in section surface 9 true when he looks at the facets 5. This is achieved by choosing the orientations of the facets 5 which reflect the incident light L1 as if it were incident on a surface according to the line 9 in FIG FIG. 3 indicated spatial form falls, as shown schematically by the incident light L2. The reflection generated by the facets 5 of a pixel 4 corresponds to the average reflection of the area of the surface 9 that has been converted or readjusted by the corresponding pixel 4.

In the case of the security element 1 according to the invention, a three-dimensional elevation profile is thus readjusted by a grid-structured arrangement of reflective sawtooth structures (facets 5 per pixel 4) which mimic the reflection behavior of the height profile. With the surface 3 can thus be generated any three-dimensionally perceptible motifs, such. a person, parts of a person, a number or other objects.

In addition to the slope σ of the individual facets 5, the azimuth angle α of the trailing surface must also be adapted. For the pixels 4 ₁ - 4 ₆ the azimuth angle α is relative to the direction according to arrow P1 ( FIG. 2 ) 0 °. For the pixel 4 ₇ , the azimuth angle α is approximately 170 °, for example. The sawtooth grid of pixel 4 ₇ is in FIG. 4 shown schematically in three-dimensional representation.

To produce the security element 1, the reflective sawtooth structures can be written, for example, by means of gray scale lithography in a photoresist, then developed, galvanically molded, embossed in UV paint (carrier) and mirrored. The mirror coating can be realized, for example, by means of an applied metal layer (vapor-deposited, for example). Typically, an aluminum layer with a thickness of eg 50 nm is applied. Of course, other metals such as silver, copper, chromium, iron, etc., or alloys thereof may also be used. Also, as an alternative to metals, high-index coatings can be applied, for example ZnS or TiO ₂ . The evaporation can be full surface. However, it is also possible to carry out a coating only in regions or in a grid-shaped manner, so that the security element 1 is partially transparent or translucent.

The period Λ of the facets 5 is the same for all pixels 4 in the simplest case. However, it is also possible to vary the period Λ of the facets 5 per pixel 4. For example, the pixel 4 _{7 has} a smaller period Λ than the pixels 4 ₁ - 4 ₆ (FIG. 2). In particular, the period Λ of the facets 5 can be chosen randomly for each pixel. By varying the choice of the period Λ of the sawtooth gratings for the facets 5, any visibility of a diffraction pattern due to the sawtooth gratings can be minimized.

Within a pixel 4, a fixed period Λ is provided. In principle, however, it is also possible to vary the period Λ within a pixel 4, so that aperiodic sawtooth gratings per pixel 4 are present.

The period Λ of the facets 5 is on the other hand preferably between 3 microns and 300 microns to avoid unwanted diffraction effects on the one hand and to minimize the necessary film thickness (thickness of the support 8). In particular, the distance is between 5 .mu.m and 100 .mu.m, wherein a distance between 10 .mu.m and 30 .mu.m is particularly preferred.

In the embodiment described here, the pixels 4 are square. However, it is also possible to form the pixels 4 rectangular. Also, other pixel shapes may be used, such as a parallelogram or hexagonal pixel shape. The pixels 4 preferably have dimensions which on the one hand are greater than the spacing of the facets 5 and on the other hand are so small that the individual pixels 4 do not disturb the unaided eye. The size range resulting from these requirements is between about 10 and a few 100 μm.

Gradients σ and azimuth angles α of the facets 5 within a pixel 4 then result from the slope of the adjusted height profile 9.

In addition to the slope σ and the azimuth angle α, a phase parameter p _i can optionally also be introduced for each pixel 4. The surface relief of the security element 1 can then be described in the i-th pixel 4 _i by the following height function h _i (x, y): $$H_i\left(x.y\right)=A_i\left[\left(-x\cdot sin{\alpha }_i+y\cdot cOs{\alpha }_i+p_i\right)mOd\mathrm{}{\mathrm{\Lambda }}_i\right]$$

Here, A _{i are} the amplitude of the sawtooth grid, α _i the azimuth angle and Λ _i the grating period. "mod" stands for the modulo operation and delivers the positive rest in division. The amplitude factor Ai results from the slope of the trailing surface profile 9.

By changing the phase parameter p _i , the sawtooth gratings or the facets 5 of different pixels 4 can be displaced relative to one another. For the parameters p _i , random values or other values varying per pixel 4 can be used. As a result, a possibly still visible diffraction pattern of the sawtooth grating (the facets 5 per pixel 4) or the raster grating of the pixels 4 can be eliminated, which can otherwise cause undesirable color effects. Furthermore, due to the varied phase parameters p _{i, there are} also no excellent directions in which the sawtooth gratings of adjacent pixels 4 fit together particularly well or particularly poorly, which prevents visible anisotropy.

In the case of the security element 1 according to the invention, the azimuth angle α and the gradients σ of the facets 5 per pixel 4 can be selected such that they do not correspond as well as possible to the trailing surface 9, but deviate somewhat therefrom. For this purpose, a (preferably random) component can be added thereto for each pixel 4 to the optimum value for adjusting the surface 9 in accordance with a suitable distribution. Depending on the size of the pixel 4 and the strength of the noise (standard deviation of the distribution) so different interesting effects can be achieved. For very fine pixels 4 (around 20 μm), the otherwise shiny surface appears increasingly dull with increasing noise. For larger pixels (around 50 μm) you get a look comparable to a metallic finish. For very large pixels (several 100 μm), the individual pixels 4 are resolved by the unaided eye. They then appear like rough but smooth sections that light up brightly from different angles.

The strength of the noise can be chosen differently for different pixels 4, as a result of which the domed surface can appear differently smooth or dull at different points. Thus, for example, the effect can be created that the viewer perceives the surface 3 as a smooth protruding and / or receding surface, which has a matte lettering or texture.

Furthermore, it is possible to apply a color-shifting coating, in particular a thin-film system, to the facets 5. For example, the thin film system may include first, second, and third dielectric layers formed on each other, wherein the first and third layers have a higher refractive index than the second layer. Due to the different inclinations of the facets 5 different colors are perceptible to a viewer without having to rotate the security element 1. The perceivable surface thus has a certain color spectrum.

The security element 1 can in particular be designed as a multi-channel image, which has different, nested part surfaces, wherein at least one of the partial surfaces is formed in accordance with the invention, so that this partial surface is perceived by the viewer as a spatial partial surface. Of course, the other partial surfaces may also be formed in the manner described by means of pixels 4 with at least one facet 5. The other partial surfaces may, but need not, be perceptible as an area that protrudes and / or rebounds relative to the actual spatial form. The nesting may for example be checkerboard-like or strip-like. By interleaving several faces, interesting effects can be achieved. If eg the adjustment of a spherical surface is interlaced with the representation of a number, this can be carried out in such a way that gives the viewer the impression that the number is inside a glass sphere with a half-mirrored surface.

In addition to the already described use of color-shifting coatings, it is also possible to provide the security element 1 according to the invention additionally with color information. Thus, e.g. Color be printed on the facets 5 (either transparent or thin) or provided below an at least partially transparent or translucent sawtooth structure. For example, a coloring of a motif represented by the pixels 4 can thereby be carried out. If e.g. If a portrait is readjusted, the color layer can provide the face color.

A combination with a true color hologram or kinegram, in particular the interlacing with a true color hologram, which shows a colored representation of the surface 9 which is traced with the pixels 4, is also possible. Thus, the achromatic three-dimensional image of an object appears colored at certain angles.

Furthermore, a combination with a sub-wavelength grating is possible. In particular, the interlaced representation of the same motif by both techniques is advantageous, in which the three-dimensional effect of the sawtooth structures is combined with the color information of the subwavelength gratings.

The surface 9 which is traced with the pixels 4 may, in particular, be a so-called imaginary surface. Below is the here Training a reflection or transmission behavior understood that can not be generated with a real domed reflective or transmitting surface.

To further explain the concept of the imaginary surface, a mathematical criterion for delimiting real surfaces is introduced below and explained using the example of a rotating mirror.

In the adjustment of a real curved surface, this can be described by a height function h (x, y). Here one can assume that the function h (x, y) is differentiable (non-differentiable functions could be approximated by differentiable functions, which would ultimately produce the same effect on the observer). If we now integrate the gradient of h (x, y) along an arbitrarily closed curve C, the integral vanishes: $${\displaystyle {\oint }_C\nabla H\left(x.y.\right)d\overrightarrow{s}}=0$$

Figuratively speaking, this means that along a closed path, the same height differences run high as down and finally arrive at the same height again. The sum of the height differences overcome in this way must therefore be zero.

In the inventive security element 1, the slope and the azimuth of the facets 5 correspond to the gradient of the height function. In this case, it is now possible to construct cases in which the slope and the azimuth of the facets 5 merge into one another virtually continuously, but no height function can be found with which the above integral disappears. In this case we should talk about the reenactment of an imaginary surface.

A special version is eg a rotating mirror. For this, one first considers the adjustment of a real convex mirror with a parabolic profile. The height function is given by $$H\left(x.y\right)=-\mathrm{<figure-callout\; id="2"\; label="c\; x"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c\; </figure-callout>}\left(x^{}\right)\left({}^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}^2\right)$$

und $$A\left(x,y\right)=2c\sqrt{\left(x^2+y^2\right)}$$

Where c> 0 is a constant and determines the curvature of the mirror. In such a mirror, the viewer can see an upright miniature mirror image of himself. The parameters of the sawtooth structures are then given by $$\alpha \left(x.y\right)=\arctan \left(x.y\right)$$

and $$A\left(x.y\right)=2c\sqrt{\left(x^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}^2\right)}$$

If one then adds a constant angle δ to the azimuth angle α, the mirror image is rotated by precisely this angle. Unless δ is an integer multiple of 180 °, it creates an imaginary surface. For example, if you choose δ = 90 °, the mirror image is rotated by 90 ° and you get a mirror image that can not be achieved with a smooth curved real surface. If one sets the gradient of h equal to the slope of the sawtooth structures, then one can now find closed curves in which the above integral does not disappear. For example, a curve K results along a circle around the center point with radius R> 0 $${\displaystyle {\oint }_K\nabla H\left(x.y\right)}d\overrightarrow{s}={\displaystyle {\oint }_{K}2c\cdot ds=4\pi cR\ne 0}$$

Figuratively speaking, this rotating mirror thus provides a surface, in which one runs continuously uphill along a circle, but at the end arrives again at the same altitude at which one started. Obviously, there is no such real surface.

In the previously described security elements 1 it was assumed that the surface is designed as a reflective surface. However, the same effects of the three-dimensional effect can essentially also be achieved in transmission if the sawtooth structures or the pixels 4 with the facets 5 (including the carrier 8) are at least partially transparent. The sawtooth structures preferably lie between two layers having different refractive indices. In this case, the security element 1 then appears to the viewer like a glass body with a curved surface.

The described advantageous embodiments can also be used for the transmissive design of the security element 1. For example, the rotating mirror of an imaginary surface can see through the image.

The transmissive design of the security element will be described in more detail below in connection with the FIGS. 19 to 29 described.

The security against forgery of the security element 1 according to the invention can be increased by further features visible only with aids, which can also be referred to as hidden features.

Thus, e.g. in the phase parameters of each pixel 4 additional information is encoded. In particular, a verification mask can be produced with lattice structures which have the same periods and azimuth angles as the security element 1 according to the invention. In a partial area of the area, the lattices of the verification mask can have the same phase parameter as the security element to be verified, in other areas a certain phase difference , These different areas will appear differently bright or dark due to moiré effects if the security element 1 and the verification mask are overlaid.

In particular, the verification mask can also be provided in the banknote 2 or the other element provided with the security element 1.

The pixels 4 may have other outlines in addition to the outline shapes described. With a magnifying glass or a microscope, these outlines can then be recognized.

Furthermore, in a small proportion of the pixels 4, instead of the corresponding saw teeth or facets 5, any other structure can also be embossed or inscribed without the unaided eye noticing this. In this case, these pixels are not part of the surface 3, so that there is an interleaving of the surface 3 with the differently formed pixels. These other formed pixels may be, for example, every 100th pixel compared to the pixels 4 of the face 3. It is possible to introduce into these pixels a micro font or a logo, for example 10 μm letters in a 40 μm pixel.

In the exemplary embodiments described so far, the facets in the surface 7 of the carrier 8 are formed in such a way that the lowest points or the minimum height values of all the facets 5 (FIG. FIG. 3 ) lie in one plane. However, it is also possible to form the facets 5 such that the mean values of the heights of all facets 5 are at the same level as in FIG. 5 is shown schematically. Furthermore, it is possible to design the facets 5 in such a way that the peak values or the maximum height values of all the facets 5 of the pixels 4 are at the same level as in FIG FIG. 6 is indicated schematically.

In FIG. 7 is a sectional view in the same way as in FIG. 3 shown, but for the pixel 4 ₄ a mirror surface 10 is located, which adjusts the surface 9 in the region of the pixel 4 ₄ . With a pixel size of, for example, 20 μm to 100 μm, such a mirror surface 10 would lead to undesirably large heights d being present. At a mirror inclination of 45 °, the corresponding mirror surface 10 would project from the xy plane by 20 μm to 100 μm. However, it is preferred that maximum heights d of 10 μm are desired. Therefore, the mirror surface 10 is subjected to a modulo d operation, so that the in FIG. 7 5, wherein the normal vectors n of the facets 5 correspond to the normal vector n of the mirror surface 10.

The surface 9 to be readjusted can be present, for example, as a set of x, y values, each with assigned height h in the z direction (3D bitmap). Such a 3D bitmap may have a defined square or 60 ° grid in the xy plane ( FIGS. 8, 9 ) being constructed. The halftone dots are connected in such a way that a surface coverage in the xy plane with triangular tiles results, as in FIGS. 8 and 9 is shown schematically.

At the three vertices of each tile one takes the h-values from the 3D-Bitmap. The smallest of these h-values is subtracted from the h-values of the three vertices of the tiles. With these new h-values at the corner points, a sawtooth surface is constructed from inclined triangles (triangular plane pieces). The plane pieces projecting too far out of the x-y plane are replaced by the facets 5. This gives the area description for the facets 5 and can produce the security element 1 according to the invention.

The surface 9 to be readjusted can be given by a mathematical formula f (x, y, z) = h (x, y) -z = 0. The facets 5 or their orientations are obtained from tangent planes of the surface 9 to be adjusted. These can be determined from the mathematical derivation of the function f (x, y, z). The facet 5 attached at a point xo, yo is described by the normal vector: $$\stackrel{\rightharpoonup }{n}=\left(\begin{array}{c}{\mathrm{n}}_{\mathrm{x}}\\ {\mathrm{n}}_{\mathrm{y}}\\ {\mathrm{n}}_{\mathrm{z}}\end{array}\right)=\left(\begin{array}{c}\frac{\partial f}{\partial y}\left(x_0.y_0.z_0\right)\\ \frac{\partial f}{\partial y}\left(x_0.y_0.z_0\right)\\ \frac{\partial f}{\partial z}\left(x_0.y_0.z_0\right)\end{array}\right)/\sqrt{{\left(\frac{\partial f}{\partial x}\left(x_0.y_0.z_0\right)\right)}^2+{\left(\frac{\partial f}{\partial y}\left(x_0.y_0.z_0\right)\right)}^2+{\left(\frac{\partial f}{\partial z}\left(x_0.y_0.z_0\right)\right)}^2}$$

The azimuth angle α of the tangential plane is arctan (n _y / n _x ) and the slope angle σ of the tangential plane is arccos n _z . The area f (x, y, z) = can be arbitrarily curved and (x ₀ , y ₀ , z ₀ ) is the point on the area for which the calculation is being performed. The calculation is performed successively for all points selected for the sawtooth structure.

From the oblique planes with the normal vectors thus calculated, which are to be attached to the selected points in the xy plane, areas are cut out so that adjacent xy points Overlaps of the associated elements are avoided. The sloping plane pieces, which protrude too far out of the xy plane, are subdivided into smaller facets 5, as in connection with FIG. 7 has been described.

dabei sind x_i, y_i, z_i die Dreiecks-Eckpunkte.The surface to be replicated may be described by triangular patches wherein the planar triangular pieces are stretched between selected points which lie within and at the edge of the surface to be replicated. The triangles can be described as plane pieces by the following mathematical function f (x, y, z) $$\mathrm{f}\left(\mathrm{x}.\mathrm{y}.\mathrm{z}\right)=\left|\begin{array}{ccc}\mathrm{x}-{\mathrm{x}}_1& \mathrm{y}-{\mathrm{y}}_1& \mathrm{z}-{\mathrm{z}}_1\\ {\mathrm{x}}_2-{\mathrm{x}}_1& {\mathrm{y}}_2-{\mathrm{y}}_1& {\mathrm{z}}_2-{\mathrm{z}}_1\\ {\mathrm{x}}_3-{\mathrm{x}}_1& {\mathrm{y}}_3-{\mathrm{y}}_1& {\mathrm{z}}_3-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\end{array}\right|=0$$

where x _i , y _i , z _{i are} the triangle vertices.

In this case, the surface can be projected into the xy plane and the individual triangles can be tilted according to their normal vector. The sloping plane pieces form the facets and, if they protrude too far out of the xy plane, as in conjunction with FIG. 7 has been described, divided into smaller facets 5.

If the nachzustellende surface is given by triangular patches, you can also proceed as follows. The entire surface to be replicated is subjected at once (or portions of each surface) to a Fresnel construction modulo d (or modulo di). Since the nachzustellende surface consists of layer pieces, created automatically on the xy plane triangles that are filled with the facets 5.

The construction of the facets can also be carried out as follows. In the x-y plane, over which the surface 9 to be tracked is defined, one chooses suitable x-y points and connects them so that an area coverage of the x-y plane with polygon tiles results. Over a randomly chosen point (e.g., a vertex) in each tile, one determines the normal vector from the overlying surface 9 to be tracked in. A fresnel mirror corresponding to the normal vector (multi-faceted pixel 4) is now placed in each tile.

Preferably, square tiles or pixels 4 are used. However, any (irregular) tiling is possible in principle. The tiles can connect to each other (which is preferred because of the greater efficiency) or it can be joints between the tiles (for example, in the case of circular tiles).

The pitch angle σ of the plane can be represented as follows $$\mathrm{\sigma }={\mathrm{arccos\; n}}_{\mathrm{z}}=\arccos \raisebox{1ex}{$\frac{\partial f}{\partial z}$}\!\left/ \!\raisebox{-1ex}{$\sqrt{{\left(\frac{\partial f}{\partial x}\right)}^2+{\left(\frac{\partial f}{\partial \mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}\right)}^2+{\left(\frac{\partial f}{\partial \mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}\right)}^2}$}\right.$$

wobei α = 0° bis 180° für n_y > 0 und α = 180° bis 360° für n_y < 0.The azimuth angle α of the slope can be represented as follows $$\mathrm{\alpha }=\arctan \left({\mathrm{n}}_{\mathrm{y}}/{\mathrm{n}}_{\mathrm{x}}\right)=\arctan \raisebox{1ex}{$\frac{\partial \mathrm{f}}{\partial \mathrm{y}}$}\!\left/ \!\raisebox{-1ex}{$\frac{\partial \mathrm{f}}{\partial \mathrm{x}}$}\right..$$

where α = 0 ° to 180 ° for n _y > 0 and α = 180 ° to 360 ° for n _y <0.

The determination of the facets 5 according to the invention, including their orientations, can be carried out in two fundamentally different ways. Thus, the x-y plane can be divided into pixels 4 (or tiles) and for each pixel 4 the normal vector for the reflective planar surface is determined, which is then converted into several facets 5 of the same orientation. Alternatively, it is possible to approximate the surface 9 to be adjusted by plane pieces, if it is not already given by plane pieces, and then to divide the plane pieces into the individual facets 5.

In the first approach, therefore, a tiling in the x-y plane is first determined. The tiling can be created completely arbitrarily. However, it is also possible that the tiling consists of all the same squares with the side length a, where a is preferably in the range of 10 to 100 microns. However, the tiling can also consist of different shaped tiles that fit together exactly or where joints occur. The tiles can be shaped differently and contain coding or hidden information. In particular, the tiles can be adapted to the projection of the surface to be adjusted in the x-y plane.

You then define in any way a reference point in each tile. The normal vectors in the points of the surface to be adjusted, which lie vertically above the reference points in the tiles, are assigned to the corresponding tiles. If, in the surface to be followed above the reference point, a plurality of normal vectors are assigned to the reference point (eg at an edge or corner where a plurality of surface pieces one another), one can determine an average normal vector from these normal vectors.

You define a subdivision in each tile in the x-y plane. This subdivision can be arbitrary. The azimuth angle α and the pitch angle σ are then calculated from the normal vector. Optionally, one can also define an offset system which assigns an offset (height value) to each facet 5. The offset may be arbitrary in any area of the subdivision. However, it is also possible to apply the offset in such a way that the mean values of the facets 5 are all at the same level or that the maximum values of all facets 5 are at the same level.

In the subdivisions in the associated tiles, inclined planes are then computationally attached as facets with the normal vector associated with the tile, taking into account the offset system. The thus calculated surface shape is then formed in the surface 7 of the carrier 8.

However, you can not just define any subdivision in each tile in the xy plane. For example, you can also define grid lines that are approximately or exactly perpendicular to the projection of the normal vector in the xy plane. The grid lines can have any distances to each other. However, it is also possible that the distances of the grid lines follow a certain scheme. Thus, for example, grid lines can not be provided exactly parallel to each other, for example to avoid interference. However, it is also possible that the grid lines are parallel to each other, but have different distances. The different distances of the grid lines may include a coding. Furthermore, it is possible that the grid lines of all facets 5 in each pixel 4 have the same distances. The distance can be in the range of 1 .mu.m to 20 .mu.m.

The grid lines may also have equal distances within each tile or within each pixel 4, but vary per pixel 4. The grating line spacing Λ _i and the pitch angle σ _{i of} the associated facet 5 determine the structure thickness d _i = Λ _i · tan σ _i , where di is preferably 1 to 10 μm.

The facets 5 can also all have the same height d. Then, the lattice constant is determined in regions by the slope angle σ _{i of} the associated facet i: Λ _i = d / tan σ _i .

The azimuth angle α and the pitch angle σ are then determined from the normal vector. The sawtooth grid defined by grid lines, azimuth angle and pitch angle is computationally mounted in the associated tile taking into account the offset system.

It is also possible to start from a surface to be adjusted 9, which is made up of layer pieces i (or which is processed so that it builds up of layer pieces i), wherein the texture depth of the surface to be adjusted and the dimensions of the layer pieces are much larger than the di ,

For example, the plane pieces i are each given by three corner points x _1i , y _1i , z _1i ; x _2i , y _2i , z _2i ; x _3i , y _3i , z _3i .

$$\left(\mathrm{z}-{\mathrm{z}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{x}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{y}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{y}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{x}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{y}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{y}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|=0$$

The relief of plane pieces is represented by z = f (x, y), where $$\left(\mathrm{x}-{\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="imgf0001.png"\; state="\{\{state\}\}">x</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{3,}\mathrm{i}}{\mathrm{-<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|-\left(\mathrm{y}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{x}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{x}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|+$$

$$\left(\mathrm{z}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{x}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{x}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|=0$$

This results in resolved to z $$\mathrm{z}={\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}+\frac{\left(\mathrm{y}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{x}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{x}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|-\left(\mathrm{x}-{\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="imgf0001.png"\; state="\{\{state\}\}">x</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|}{\left|\begin{array}{cc}{\mathrm{x}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{x}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|}$$

The sought sawtooth surface, whose structure thickness in the regions i is smaller than di, results from z modulo di, where z is calculated from the above formula and where the x and y values in the calculation are each within the range defined by x _1i , y _1i ; x _2i , y _2i ; x _3i , y _3i given triangle lie in the xy plane.

The sawtooth surface thus calculated is automatically composed of the facets 5. In the process, the lattice constants Λ _i in the regions i $${\mathrm{\Lambda }}_{\mathrm{i}}={\mathrm{d}}_{\mathrm{i}}/\tan {\mathrm{\sigma }}_{\mathrm{i}}$$

wobei σ_i der Steigungswinkel des durch x_1i, y_1i, z_1i; x_2i, y_2i, z_2i; x_3i, y_3i, z_3i gegebenen Dreiecks ist.If a uniform lattice constant Λ is desired, the following di are to be used $${\mathrm{d}}_{\mathrm{i}}=\mathrm{\Lambda \; tan}{\mathrm{\sigma }}_{\mathrm{i}}$$

where σ _{i is} the _{helix angle of the helix} through x _1i , y _1i , z _1i ; x _2i , y _2i , z _2i ; x _3i , y _3i , z _3i given triangle.

The following alternative procedure is possible. In the following formula A, a surface 9 to be readjusted above the xy plane is described by triangular plane pieces $$\mathrm{z}={\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}+\frac{\left(\mathrm{y}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{x}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{x}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|-\left(\mathrm{x}-{\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="imgf0001.png"\; state="\{\{state\}\}">x</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|}{\left|\begin{array}{cc}{\mathrm{x}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{x}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|}$$

The _{plane pieces} i are each given by three vertices x _1i , y _1i , z _1i ; x _2i , y _2i , z _2i ; x _3i , y _3i , z _3i .

The vertices are numbered such that z _{1i is} the smallest value among the three values z _1i , z _2i , z _3i (z _1i = min (z _1i , z _2i , z _3i )).

The following formula B represents a sawtooth surface, which adjusts the three-dimensional impression of the given by the formula A, nachzustellenden surface 9 $$\mathrm{z}=\frac{\left(\mathrm{y}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{x}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{x}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|-\left(\mathrm{x}-{\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="imgf0001.png"\; state="\{\{state\}\}">x</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\right)\cdot \left|\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|}{\left|\begin{array}{cc}{\mathrm{x}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{2,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\\ {\mathrm{x}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{x}}_{\mathrm{1,}\mathrm{i}}& {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{3,}\mathrm{i}}-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="imgf0001.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,}\mathrm{i}}\end{array}\right|}$$

As can be seen, the sawtooth surface according to formula B differs from the surface to be _adjusted according to formula A in that the value z is subtracted from the minimum value z _1i in the region i. The sawtooth surface according to formula B consists of inclined triangles attached to the xy plane.

If a maximum thickness di for the structure depth is specified, it may be that the maximum thickness is exceeded at the sawtooth surface according to formula B. In contrast, the formation of the individual facets with the same normal vector according to z modulo di, where z is calculated from the above formula B and the x and y values in the calculation in each case within x _1i , y _1i ; x _2i , y _2i ; x _3i , y _3i given triangle lie in the xy plane.

The sawtooth surface thus calculated is composed of the triangular regions which are filled with the facets 5, the lattice constants A in the regions i resulting in Λ _i = d _i / tan σ _i . The angle σ _i is the pitch angle of the angle through x _1i , y _1i , z _1i ; x _2i , y _2i , z _2i ; x _3i , y _3i , z _3i given triangle.

By way of example, the procedures shown here for surfaces to be followed, which are described by triangles and which are converted into multi-faceted pixels 4 in accordance with the invention, are to be understood by way of example. In general, in nachzustellenden surfaces that are described by plane pieces, according to the invention proceed as follows. The layer pieces are divided into sections. For the subdivisions, a value (for example, the minimum value of z in the section) is subtracted. Thus, according to the invention, a sawtooth lattice is obtained which is flatter than the surface 9 to be replicated and which in each case has the same normal vectors in the sections.

This sawtooth lattice mimics the original surface 9 to be followed, including its three-dimensional impression. This sawtooth grid is flatter than a sawtooth grid created with the same procedure without subdividing the pixels 4 into a plurality of facets 5 according to the invention.

In FIG. 10 3, a plan view of three pixels 4 of the surface 3 according to a further embodiment is shown, wherein the pixels 4 are irregular (solid lines) with irregular subdivisions or facets 5 (dashed lines). The pixel borders and subdivisions are here straight lines, but they can also be curved.

In FIG. 11 the corresponding cross-sectional view is shown, wherein the normal vectors of the facets 5 are shown schematically. Per pixel 4, the normal vectors of all facets 5 are the same while being different from pixel 4 to pixel 4. The normal vectors lie obliquely in space and generally not in the plane of the drawing, as in FIG. 11 for simplicity.

In FIG. 12 FIG. 11 is a plan view with the same pitch of pixels 4 as shown in FIG. 11, but with the division (facets 5) per pixel 4 being different. In the illustrated embodiment, the grating period A of the facets 5 in each pixel 4 is constant, but different from pixel 4 to pixel 4.

FIG. 13 shows the corresponding cross-sectional view.

In FIG. 14 a further modification is shown wherein the pixel shape is the same as in FIG FIG. 10 , However, the subdivision per pixel 4 is coded. Every second grid line spacing is twice the previous grid line spacing. In FIG. 15 the corresponding cross-sectional view is shown.

If the surface to be tracked is given as a contour line image, one can determine the normal vectors as follows. You choose discrete points on the contour lines 15 (in FIG. 16 is a schematic plan view shown) and connects these points so that a triangular tiling arises. The calculation of the normal vector for the triangles is done as already described.

$${\mathrm{x}}_{\mathrm{trans}}=2\mathrm{\pi r\Phi }/\mathrm{360,}\Phi =360x_{\mathrm{trans}}/2\mathrm{\pi r}$$

In the previous embodiments, the normal vector was always calculated relative to the xy plane. However, it is also possible to calculate the normal vector with respect to a curved base, such as a cylindrical surface. In this case, the security element on a bottle label (for example, at the bottleneck) can be provided so that then the trailing surface can be perceived undisturbed by a viewer spatially. For this purpose, only the normal vector n relative to the cylindrical surface has to be converted into the normal vector n _{trans in} relation to a plane, so that the production methods described above can be used. If the security element according to the invention is then applied as a bottle label to the bottleneck (with the cylindrical curvature), the trailing surface 9 can then be perceived undistorted in a three-dimensional manner. The conversion to be performed results from the following formulas $$\mathrm{x}=\mathrm{r\; sin\Phi }.\Phi =\mathrm{arsin\; x}/\mathrm{r}$$

$${\mathrm{x}}_{\mathrm{trans}}=2\mathrm{\pi r\Phi }/\mathrm{360,}\Phi =360x_{\mathrm{trans}}/2\mathrm{\pi r}$$

wobei n = Normalenvektor über (x,y).The normal vector n _trans at the position (x _trans , y) can be calculated as follows. $${\overrightarrow{\mathrm{n}}}_{\mathrm{trans}}=\left(\begin{array}{ccc}\cos \phi & 0& \sin \phi \\ 0& 1& 0\\ -\sin \phi & 0& \cos \phi \end{array}\right)\cdot \overrightarrow{\mathrm{n}}$$

in which n = Normal vector over (x, y).

The security element 1 according to the invention can be designed not only as a reflective security element 1, but also as a transmissive security element 1, as already mentioned. In this case, the facets 5 are not mirrored and the carrier 8 is made of a transparent or at least translucent material, the viewing being done in a transparent manner. When illuminated from behind, a user should perceive the trailing surface 9 as if there is a front-illuminated inventive reflective security element 1.

The facets 5 calculated for a reflective security element 1 are replaced by data for microprisms 16, the corresponding angles in reflection (FIG. FIG. 19 ) and for transmissive prisms 16 in FIGS. 20 and 21 are shown. FIG. 20 shows the incidence on the inclined facets 5, whereas FIG. 21 shows the incidence on the smooth side, which is preferred because of the possible larger incidence angles.

The azimuth angle of the reflective facet 5 is referred to as α _s and the pitch angle of the facet 5 is referred to as σ _s . The refractive index of the microprism 16 is n, the azimuth angle of the microprism 16 is α _p = 180 ° + α _s . The pitch angle of the micro prism 16 according to FIG. 20 is sin (σ _p + 2 σ _s ) = n sin σ _p , where for small angles 2 σ _s = (n - 1) σ _p and 4 σ _s = σ _p (for n = 1.5).

The pitch angle of the micro prism 16 after FIG. 21 is sin (2 σ _s ) = n sin β; sin (σ _p ) = n sin (σ _p - β), where for small angles 4 σ _s = σ _p (for n = 1.5).

$${\mathrm{n}}_{\mathrm{x}}=\cos \alpha \cdot \sqrt{1-{\cos }^2\sigma },n_{\mathrm{y}}=\sin \alpha \cdot \sqrt{1-{\cos }^2\sigma }$$

The components of the normal vector are known for α and σ: $${\mathrm{n}}_{\mathrm{z}}=\mathrm{cos\sigma }.n_{\mathrm{y}}/{\mathrm{n}}_{\mathrm{x}}=\mathrm{sin\; .alpha}/\cos .n_{\mathrm{x}}{}^2+{\mathrm{n}}_{\mathrm{y}}{}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">n\; </figure-callout>}}_{\mathrm{z}}{}^2=1$$

$${\mathrm{n}}_{\mathrm{x}}=\cos \alpha \cdot \sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\sigma }.n_{\mathrm{y}}=\sin \alpha \cdot \sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\sigma }$$

In FIG. 22 schematically a nachzustellende reflective surface 9 with a mound 20 and a trough 21 is shown. The negative focal length -f of the specular hill 20 is r / 2, and the positive focal length f of the specular trough 21 is r / 2.

In FIG. 23 schematically a lens 22 is shown, which has a transparent concave portion 23 and a transparent convex portion 24. The concave portion 23 simulates the specular mound 20, wherein the negative focal length -f of the concave portion 23 is 2r. The transparent convex portion 24 simulates the specular well 21 and has a positive focal length f = 2r.

The lens 22 according to FIG. 23 can be replaced by the Sägezahnordnung according to Figure 24.

The arrows in FIGS. 20 to 23 schematically show the beam path for incident light L. From these ray curves it can be seen that the lens 22 in transmission adjusts the surface 9 as desired.

In the FIGS. 25 to 27 an example is shown in which the sawtooth side is on the light incident side. Otherwise, the representation of Figure 25 corresponds to the representation of FIG. 22 , corresponds to the representation of FIG. 26 the representation in FIG. 23 and corresponds to the representation of FIG. 27 the representation in FIG. 24 ,

To calculate the transmissive sawtooth structures, the methods described above can be used.

In the FIG. 27 shown transparent sawtooth structure substantially corresponds to a cast of a corresponding reflective sawtooth structure for adjusting the surface 9 according to FIG. 25 , However, the trailing surface in transparency (at a refractive index of 1.5) appears much flatter than in reflection. Therefore, the height of the sawtooth structure is preferably increased or the number of facets 5 per pixel 4 is increased.

Of course it is also possible to provide the sawtooth structures described with a semi-transparent mirroring. In this case, the trailing surface 9 usually appears deeper structured in reflection than in transparency.

Furthermore, it is possible to provide both sides of a transparent or at least translucent support 8 with a sawtooth structure having the plurality of microprisms 16, as shown in FIG FIGS. 28 and 29 is indicated. at FIG. 28 the sawtooth structures 25, 26 are mirror-symmetrical on both sides. at FIG. 29 the two sawtooth structures 25, 27 are not mirror-symmetrical.

For calculating a sawtooth structure 25 and 27 according to FIGS. 28 and 29 it can be assumed that the sawtooth structure 25, 27 is composed of a prismatic surface 28 with a pitch angle σ _p and an auxiliary prism 29 attached thereto with a pitch angle σ _h , as in FIG FIG. 30 is shown schematically. Thus, σ _p + σ _{h is} the effective total prism angle.

$${\mathrm{\sigma }}_{\mathrm{p}}+{\mathrm{\sigma }}_{\mathrm{h}}=\mathrm{\beta }1+\mathrm{\beta }\mathrm{2,}$$

If the relief slope angle to be mimicked is denoted by σ _s , then the following applies since the angle sum in the triangle is 180 °: $$90°-\mathrm{<figure-callout\; id="1"\; label="\beta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\beta </figure-callout>}1+90°-\mathrm{<figure-callout\; id="2"\; label="\beta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\beta </figure-callout>}2+{\mathrm{\sigma }}_{\mathrm{p}}+{\mathrm{\sigma }}_{\mathrm{H}}=180°$$

$${\mathrm{\sigma }}_{\mathrm{p}}+{\mathrm{\sigma }}_{\mathrm{H}}=\mathrm{<figure-callout\; id="1"\; label="\beta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\beta </figure-callout>}1+\mathrm{<figure-callout\; id="2"\; label="\beta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\beta </figure-callout>}\mathrm{2,}$$

ergibt sich für: $${\mathrm{\sigma }}_{\mathrm{p}}-\arcsin \left(\left(\sin {\mathrm{\sigma }}_{\mathrm{p}}\right)/\mathrm{n}\right)=\arcsin \left(\left(\sin \left(2{\mathrm{\sigma }}_{\mathrm{s}}+{\mathrm{\sigma }}_{\mathrm{h}}\right)\right)/\mathrm{n}\right)-{\mathrm{\sigma }}_{\mathrm{h}}$$

Due to the law of refraction $$\sin {\mathrm{\sigma }}_{\mathrm{p}}=\mathrm{<figure-callout\; id="1"\; label="n\; sin\; \beta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">n\; sin\; \beta </figure-callout>}\mathrm{1,}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0001.png"\; state="\{\{state\}\}">sin</figure-callout>}\left(2{\mathrm{\sigma }}_{\mathrm{s}}+{\mathrm{\sigma }}_{\mathrm{H}}\right)=\mathrm{<figure-callout\; id="2"\; label="n\; sin\; \beta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">n\; sin\; \beta </figure-callout>}2$$

results for: $${\mathrm{\sigma }}_{\mathrm{p}}-\arcsin \left(\left(\sin {\mathrm{\sigma }}_{\mathrm{p}}\right)/\mathrm{n}\right)=\mathrm{<figure-callout\; id="2"\; label="arcsin\; sin"\; filenames="imgf0001.png"\; state="\{\{state\}\}">arcsin\; </figure-callout>}\left(\left(\sin \right)\right)\left(\left(\left(2{\mathrm{\sigma }}_{\mathrm{s}}+{\mathrm{\sigma }}_{\mathrm{H}}\right)\right)/\mathrm{n}\right)-{\mathrm{\sigma }}_{\mathrm{H}}$$

Thus, starting from the imaged relief slope angle σ _s at z. B. predefined auxiliary prism slope angle σ _h the desired slope angle σ _{p of} the prismatic surface 28 are easily calculated.

It should be noted that in the calculations given above, the imitation of a mirror relief by prisms was assumed to be perpendicular. When tilted, distortions may result and when viewed in white light, colored edges may appear shown motive, since the incoming refractive index n is dependent on wavelength.

The in the FIGS. 1 to 30 Reflective or refractive security elements shown can also be embedded in transparent material or provided with a protective layer.

An embedding is done in particular to protect the micro-optical elements from dirt and abrasion and to prevent unauthorized readjustment by embossing the surface structure.

Example: Embedded mirrors

When embedding a protective layer, the properties of the micro-optical layer with the facets 5 change Figures 32a-c this behavior is illustrated for embedded mirrors (the facets 5 are formed as mirrors), where FIG. 32a shows the arrangement before embedding.

When the mirrors are embedded in a transparent layer 40, the direction in which a mirror image appears, such as FIG. 32b shows. If the original reflection effect is to be achieved in the case of a relief adjusted by embedded micromirror 5, this must be taken into account in the case of the inclination angle of the micromirrors, see FIG. 32c ,

Example: Embedded prisms

For embedded prisms 16, a refractive index difference between prism material and potting material 40 is required and must be taken into account when calculating the light beam deflection.

FIG. 33b schematically shows the adjustment of the reflective array of FIG. 32a by a transmitting prism arrangement with exposed prisms 16, as already z. B. in the Figures 19-27 discussed.

FIG. 33b schematically shows a possible adjustment of the reflective array of FIG. 32a by embedded prisms 16, wherein the refractive indices of prism material and potting material 40 must differ.

Example: Embedded scattering facets

In the two previous examples the reproduction of reflecting objects was demonstrated. For the adjustment of scattering objects (eg marble figure, plaster model) scattering facets can be used, an example (see FIG. 34 ):
The following structure is realized on a film 41 as a carrier material: The embossed facets 5, which adjust the object surface, are located on the back of the film. The facets 5 have dimensions of, for example, 10 microns to 20 microns. At the facets 5, a lacquer 42 pigmented with titanium oxide (particle size about 1 μm) is applied, so that the facets 5 are filled with this scattering material. The viewing side is indicated by the arrow P2.

Example: embedded matt shiny facets

In the following way, a dull mirrored object can be readjusted (see FIG. 35 ):
The following structure is realized on a film 41 as a carrier material: The embossed facets 5, which adjust the object surface, are located on the back of the film. The facets 5 have dimensions of, for example, 10 microns to 20 microns. The embossed layer is provided with a semitransparent mirror coating 43 and applied to it with a titanium oxide (particle size about 1 micron) pigmented paint 42, so that the facets are filled with this scattering material. When viewed from the viewing side, the trailing object appears dull-glossy. The viewing side is indicated by the arrow P2.

Colored facets:

For the reproduction of colored objects, the embedding of the facets in the FIGS. 32b, 32c, 33b . 34 or 35 with colored material (also regionally differently colored material) take place.

The security element 1 according to the invention can be used as a security thread 19 (FIG. FIG. 1 ) be formed. Furthermore, the security element 1 can not only, as described, be formed on a carrier foil, from which it can be transferred in a known manner to the value document. It is also possible to design the security element 1 directly on the value document. Thus, a direct printing with subsequent embossing of the security element can be carried out on a polymer substrate, for example, to form a security element according to the invention in plastic banknotes. The security element according to the invention can be formed in a wide variety of substrates. In particular, it may be in or on a paper substrate, a paper with synthetic fibers, ie paper with a proportion x polymeric material in the range of 0 <x <100 wt .-%, a plastic film, for. As a film of polyethylene (PE), polyethylene terephthalate (PET), polybutylene terephthalate (PBT), polyethylene naphthalate (PEN), polypropylene (PP) or polyamide (PA), or a multilayer composite, in particular a composite of several different films (composite composite) or a paper-film composite (foil / paper / foil or paper / foil / Paper), wherein the security element may be provided in or on or between each of the layers of such a multilayer composite.

In FIG. 31 schematically an embossing tool 30 is shown with which the facets 5 in the carrier 8 according to FIG. 5 can be shaped. For this purpose, the embossing tool 30 has an embossing surface 31, in which the inverted shape of the surface structure to be embossed is formed.

Of course, not only for the embodiment according to FIG. 5 a corresponding embossing tool can be provided. Also for the other described embodiments, an embossing tool can be provided in the same way.

LIST OF REFERENCE NUMBERS

1

security element

2

bill

3

area

4

pixel

5

facets

6

line

7

surface

8th

carrier

9

trailing surface

10

mirror surface

15

contour

16

Microprismatic

19

security thread

20

hill

21

trough

22

lens

23

concave section

24

convex section

25

sawtooth

26

sawtooth

27

sawtooth

28

prismatic surface

29

auxiliary prism

30

embossing tool

31

embossing surface

40

transparent layer

41

foil

42

pigmented paint

43

semitransparent mirroring

L

incident light

L1

incident light

L2

incident light

P1

arrow

P2

arrow

Claims (19)

1. A security element for a security paper, value document or the like, having a carrier which has an areal region which is divided into a multiplicity of pixels which respectively comprise at least one optically active facet (5),
   whereby the majority of the pixels respectively have several of the optically active facets of identical orientation per pixel, and the facets are so oriented that the areal region is perceptible to a viewer as an area that protrudes and/or recedes relative to its actual spatial form, whereby the oriented facets reflect incident light in such a way, as if it falls on an configured or simulated surface, whereby the reflection generated by the facets of the pixel corresponds to the average reflection of the surface region configured or simulated by the corresponding pixel.
2. The security element according to claim 1, wherein the orientation of the facets is so chosen that the areal region is perceptible to a viewer as a non-planar area.
3. The security element according to claim 1 or 2, wherein the optically active facets are configured as reflective facets.
4. The security element according to any of the above claims, wherein the optically active facets are configured as transmissive facets with a refractive effect.
5. The security element according to any of the above claims, wherein the optically active facets are so configured that the pixels have no optically diffractive effect.
6. The security element according to any of the above claims, wherein the area of each pixel is smaller than the area of the areal region by at least one order of magnitude.
7. The security element according to any of the above claims, wherein the facets are formed in a surface of the carrier or wherein the facets are formed as embedded facets.
8. The security element according to any of the above claims, wherein the facets are configured as substantially planar area elements.
9. The security element according to any of the above claims, wherein the orientation of the facets is determined by their inclination and/or their azimuth angle.
10. The security element according to any of the above claims, wherein the facets form a periodic or aperiodic grating, and the grating period of the facets is between 1 µm and 300 µm, preferably between 3 µm and 100 µm, particularly preferably between 5 µm and 30 µm.
11. The security element according to any of the above claims, wherein there is formed on the facets at least in certain regions a reflective or reflection-enhancing coating and/or wherein there is formed on the facets at least in certain regions a color-shifting coating.
12. The security element according to any of the above claims, wherein the maximum extension of a pixel is between 5 µm and 5 mm, preferably between 10 µm and 300 µm, particularly preferably between 20 µm and 100 µm.
13. The security element according to any of the above claims, wherein the areal region is perceptible to a viewer as an imaginary area whose reflection behavior or transmission behavior cannot be produced with a real bulged reflective or transmissive surface, whereby the areal region is perceptible in particular as a rotating mirror.
14. The security element according to any of the above claims, wherein at least one facet has a light-scattering microstructure on its surface, whereby the light-scattering microstructure is preferably configured so as to effect a scattering with a preferential direction for producing a matt structure.
15. The security element according to any of the above claims, wherein the orientations of several facets are so changed relative to the orientations for producing the protruding and/or receding area that the protruding and/or receding area is still perceptible but with a surface of matt appearance.
16. A value document having a security element according to any of the above claims.
17. A manufacturing method for a security element for security papers, value documents or the like, wherein the surface of a carrier is so height-modulated in an areal region that the areal region is divided into a multiplicity of pixels respectively having at least one optically active facet,
    whereby the majority of the pixels respectively have several optically active facets of identical orientation per pixel, and the facets are so oriented that the areal region is perceptible to a viewer of the manufactured security element as an area that protrudes and/or recedes relative to its actual spatial form, whereby the oriented facets reflect incident light in such a way, as if it falls on a configured or simulated surface, whereby the reflection generated by the facets of the pixel corresponds to the average reflection of the region configured or simulated by the corresponding pixel of the surface configured or simulated.
18. An embossing tool having an embossing area with which the form of the facets of a security element according to any of claims 1 to 15 can be embossed into the carrier.
19. Use of a security element according to any of claims 1 to 15 as a master for exposing a volume hologram.

Images