The present invention relates to a security element for security papers, value documents and the like, having a microoptical moiré-type magnification arrangement for depicting a moiré image having one or more moiré image elements.
For protection, data carriers, such as value or identification documents, but also other valuable articles, such as branded articles, are often provided with security elements that permit the authenticity of the data carrier to be verified, and that simultaneously serve as protection against unauthorized reproduction. The security elements can be developed, for example, in the form of a security thread embedded in a banknote, a cover foil for a banknote having a hole, an applied security strip or a self-supporting transfer element that, after its manufacture, is applied to a value document.
Here, security elements having optically variable elements that, at different viewing angles, convey to the viewer a different image impression play a special role, since these cannot be reproduced even with top-quality color copiers. For this, the security elements can be furnished with security features in the form of diffraction-optically effective micro- or nanostructures, such as with conventional embossed holograms or other hologram-like diffraction patterns, as are described, for example, in publications EP 0 330 733 A1 and EP 0 064 067 A1.
It is also known to use lens systems as security features. For example, in publication EP 0 238 043 A2 is described a security thread composed of a transparent material on whose surface a grating composed of multiple parallel cylindrical lenses is embossed. Here, the thickness of the security thread is chosen such that it corresponds approximately to the focal length of the cylindrical lenses. On the opposing surface, a printed image is applied in perfect register, the printed image being designed taking into account the optical properties of the cylindrical lenses. Due to the focusing effect of the cylindrical lenses and the position of the printed image in the focal plane, depending on the viewing angle, different sub-areas of the printed image are visible. In this way, through appropriate design of the printed image, pieces of information can be introduced that are, however, visible only from certain viewing angles. Through the appropriate development of the printed image, also “moving” pictures can, indeed, be created. However, when the document is turned about an axis that runs parallel to the cylindrical lenses, the motif moves only approximately continuously from one location on the security thread to another location.
From publication U.S. Pat. No. 5,712,731 A is known the use of a moiré magnification arrangement as a security feature. The security device described there exhibits a regular arrangement of substantially identical printed microimages having a size up to 250 μm, and a regular two-dimensional arrangement of substantially identical spherical microlenses. Here, the microlens arrangement exhibits substantially the same division as the microimage arrangement. If the microimage arrangement is viewed through the microlens arrangement, then one or more magnified versions of the microimages are produced for the viewer in the regions in which the two arrangements are substantially in register.
The fundamental operating principle of such moiré magnification arrangements is described in the article “The moiré magnifier,” M. C. Hutley, R. Hunt, R. F. Stevens and P. Savander, Pure Appl. Opt. 3 (1994), pp. 133-142. In short, according to this article, moiré magnification refers to a phenomenon that occurs when a grid comprised of identical image objects is viewed through a lens grid having approximately the same grid dimension. As with every pair of similar grids, a moiré pattern results that, in this case, appears as a magnified and, if applicable, rotated image of the repeated elements of the image grid.
Based on that, it is the object of the present invention to avoid the disadvantages of the background art and especially to specify a security element having a microoptical moiré-type magnification arrangement that offers great freedom in the design of the motif images to be viewed.
This object is solved by the security element having the features of the main claim. A method for manufacturing such a security element, a security paper and a data carrier having such a security element are specified in the coordinated claims. Developments of the present invention are the subject of the dependent claims.
According to the present invention, a generic security element includes a microoptical moiré-type magnification arrangement having
In the context of this application, the term “moiré magnification arrangement” denotes embodiments in which the micromotif elements are identical to one another, are arranged regularly in the form of a lattice and, with their size, fit in a lattice cell. Here, the production of a moiré image from a plurality of regularly arranged, identical micromotif elements takes place according to the above-described principle of moiré magnification.
In the context of this application, the more general term “moiré-type magnification arrangement” denotes embodiments in which the micromotif element to be depicted can also be larger than one lattice cell of the motif image. The term “moiré-type magnification arrangement” thus encompasses the more particular moiré magnification arrangements. Here, the phrase that the dimension of the micromotif element is greater than one lattice cell of the motif image expresses the fact that, in its chosen or calculated orientation, the micromotif element does not fit within a lattice cell of the motif image, likewise viewed in the chosen or calculated orientation, such that, in general, in the event of a periodic repeat of the micromotif element, overlaps of adjacent micromotif elements can occur in the lattice cells. A micromotif element and a moiré image element correspond to each other if they transition into one another precisely through the imaging effected by the magnification arrangement, which can comprise the magnification, rotation, mirroring and shear mapping of the image element. This imaging can be specified, for example, by the transformation matrix A of the magnification arrangement described in greater detail below.
While conventional designs are limited to motif images having motif image elements that fit in a lattice cell of the motif grid, the measure according to the present invention permits, with moiré-type magnification arrangements, also motif image elements that are larger than one lattice cell to be depicted overlap-free in the moiré image. This gives the designer significantly greater design freedom in creating moiré motifs, since he is no longer strictly bound to the shape and size of the lattice cells of the motif grid. Furthermore, in this way, for a given total thickness of the magnification arrangement, particularly expansive moiré image elements are made possible in the first place.
On the other hand, with the aid of the distribution of a given motif element to multiple lattice cells, especially particularly thin magnification arrangements are manufactured. For technical reasons, the thickness of a moiré magnification arrangement corresponds namely to approximately the line screen of the motif grid used. Since, in conventional designs, the motif elements must each fit in one lattice cell, the thickness of the moiré magnification arrangement cannot be smaller than the smallest possible technically realizable motif size. This obstacle is overcome by the inventive distribution of a given motif element to multiple lattice cells.
For example, a motif element of the dimension a customarily requires a lattice cell of at least size a, and thus, due to general considerations, requires a thickness of the moiré magnification arrangement likewise on the order of a; in a concrete exemplary embodiment, the thickness be, for example, a minimum of 1.5*a. According to the present invention, with the half line screen a/2, the same motif element can be distributed to four lattice cells such that the thickness of the moiré-type magnification arrangement can be reduced to a value on the order of a/2, so in the cited exemplary embodiment, to a thickness of 1.5*a/2. In the case of a distribution to a larger number of lattice cells, the thickness can, of course be reduced even further.
Here, in a variant of the present invention, both the lattice cells of the motif image and the lattice cells of the focusing element grid are arranged periodically. Here, the periodicity length is especially between 3 μm and 50 μm, preferably between 5 μm and 30 μm, particularly preferably between about 10 μm and about 20 μm.
According to another variant of the present invention, locally, both the lattice cells of the motif image and the lattice cells of the focusing element grid are arranged periodically, the local period parameters changing only slowly in relation to the periodicity length. For example, the local period parameters can be periodically modulated across the expanse of the security element, the modulation period being especially at least 20 times, preferably at least 50 times, particularly preferably at least 100 times greater than the local periodicity length. In this variant, too, the local periodicity length is especially between 3 μm and 50 μm, preferably between 5 μm and 30 μm, particularly preferably between about 10 μm and about 20 μm.
The lattice cells of the motif image and the lattice cells of the focusing element grid advantageously each form, at least locally, a two-dimensional Bravais lattice, preferably a Bravais lattice having low symmetry, such as a parallelogram lattice. The use of Bravais lattices having low symmetry offers the advantage that moiré-type magnification arrangements having such Bravais lattices are very difficult to imitate since, for the creation of a correct image upon viewing, the very difficult-to-analyze low symmetry of the arrangement must be reproduced exactly. Furthermore, the low symmetry creates great freedom for differently chosen lattice parameters that can thus be used as a hidden identifier for protected products according to the present invention without this being, for a viewer, easily perceptible in the moiré-magnified image. On the other hand, all attractive effects that are realizable with higher-symmetry moiré magnification arrangements can also be realized with the preferred low-symmetry moiré-type magnification arrangements.
The lateral dimensions of the lattice cells of the motif image and the lattice cells of the focusing element grid are preferably below about 100 μm, preferably between about 5 μm and about 50 μm, particularly preferably between about 10 μm and about 35 μm.
The microfocusing elements are preferably formed by non-cylindrical microlenses, especially by microlenses having a circular or polygonally delimited base area. In other embodiments, the microfocusing elements can also be formed by elongated cylindrical lenses whose dimension in the longitudinal direction measures more than 250 μm, preferably more than 300 μm, particularly preferably more than 500 μm and especially more than 1 mm.
In further preferred designs, the microfocusing elements are formed by circular apertures, slit apertures, circular or slit apertures provided with reflectors, aspherical lenses, Fresnel lenses, GRIN (Gradient Refractive Index) lenses, zone plates, holographic lenses, concave reflectors, Fresnel reflectors, zone reflectors or other elements having a focusing or also masking effect.
The total thickness of the security element is advantageously below 50 μm, preferably below 30 μm and particularly preferably below 20 μm. Through the distribution according to the present invention, even still thinner designs having a total thickness of about 10 μm or less are possible, or even having a total thickness of about 5μm or less.
The micromotif image portions preferably form micromotif elements in the form of microcharacters or micropatterns and can especially be present in an embossed or printed layer.
In a second aspect, the present invention includes a generic security element having a microoptical moiré-type magnification arrangement for depicting a moiré image having multiple moiré image elements, having
According to an advantageous development of the present invention, the security element exhibits, in both aspects, an opaque cover layer to cover the moiré-type magnification arrangement in some regions. Thus, within the covered region, no moiré magnification effect occurs, such that the optically variable effect can be combined with conventional pieces of information or with other effects. This cover layer is advantageously present in the form of patterns, characters or codes and/or exhibits gaps in the form of patterns, characters or codes.
In all cited variants of the present invention, the motif image and the focusing element grid are preferably arranged at opposing surfaces of an optical spacing layer. The spacing layer can comprise, for example, a plastic foil and/or a lacquer layer.
Furthermore, the arrangement of microfocusing elements can be provided with a protective layer whose refractive index preferably differs from the refractive index of the microfocusing elements by at least 0.3, in the event that refractive lenses serve as microfocusing elements. In this case, due to the protective layer, the focal length of the lenses changes, which must be taken into account when dimensioning the radii of curvature of the lenses and/or the thickness of the spacing layer. In addition to the protection against environmental effects, such a protective layer also prevents the microfocusing element arrangement from being easily cast for counterfeiting purposes.
In all aspects of the present invention, the security element itself preferably constitutes a security thread, a tear strip, a security band, a security strip, a patch or a label for application to a security paper, value document or the like. In an advantageous embodiment, the security element can span a transparent or uncovered region of a data carrier. Here, different appearances can be realized on different sides of the data carrier.
The present invention also includes a method for manufacturing a security element having a microoptical moiré-type magnification arrangement for depicting a moiré image having one or more moiré image elements, in which
To determine such uniform motif subsets and the allocated focusing element subsets of the focusing element grid, in a preferred development of the method is provided that
Here, it is important that the motif subsets identified in step f) not only exhibit an overlap-free depiction of the micromotif elements, but that the identified motif subsets each also form, together with the corresponding focusing element subsets of the focusing element grid, moiré-type magnification arrangements that lead to the same target motif. This is expressed by the phrase that the motif subsets identified in step f) are all to be “uniform”.
In a further advantageous development of the method, it is provided that
A superlattice grid is understood here to be a grid whose unit cell includes multiple lattice cells of the underlying basic grid. For example, the unit cell of a simple superlattice grid can comprise 2×2, 2×3 or 3×2 lattice cells of the basic grid.
Preferably, in this method, after step g′), in a step
In step b), the focusing element grid is expediently defined in the form of a two-dimensional Bravais lattice whose lattice cells are given by vectors {right arrow over (w)}1 and {right arrow over (w)}2.In step c), the desired magnification and movement behavior is advantageously specified in the form of the matrix elements of a transformation matrix . Then, in step d), the micromotif element to be introduced into the motif plane and the motif grid are advantageously calculated using the relationships
=(−−1)·
and
{right arrow over (r)}=
−1
·{right arrow over (R)}+{right arrow over (r)}
0
representing an image point of the desired moiré image,
an image point of the motif image,
a displacement between the focusing element grid and the motif image, and the matrices , and the motif grating matrix being given by
with u1i, u2i and w1i, w2i representing the components of the lattice cell vectors {right arrow over (u)}i and {right arrow over (w)}i, where i=1,2.
In step f′), preferably a motif superlattice grid is selected that consists of n×m lattice cells of the motif grid, wherein, for n and m, preferably the smallest values are chosen that permit an overlap-free arrangement of the micromotif elements. In step g′), the focusing element grid is preferably broken down into n×m subgrids.
Advantageously, in step g″), the motif grid is broken down into n×m motif subgrids and, for each motif subgrid, the offset {right arrow over (v)}j of the motif subgrid with respect to the motif superlattice cell is determined, where j=1, . . . n*m.
Further, in step h′), advantageously, for each focusing element subgrid, the overlap-free arrangement of the micromotif elements identified in step f′) is displaced by the offset {right arrow over (v)}j of the associated motif subgrid, and the intersection of the focusing element subgrid with the displaced overlap-free arrangement of the micromotif elements is determined.
According to the second inventive aspect, the present invention also includes a method for manufacturing a security element having a microoptical moiré-type magnification arrangement for depicting a moiré image having multiple moiré image elements, in which
In both aspects of the present invention, the lattice parameters of the Bravais lattice can be location independent. However, it is likewise possible to modulate the lattice vectors of the motif grid and the focusing element grid, {right arrow over (u)}1 and {right arrow over (u)}2, or {right arrow over (w)}1 and {right arrow over (w)}2, location dependently, the local period parameters |{right arrow over (u)}1|, |{right arrow over (u)}2|, <({right arrow over (u)}1,{right arrow over (u)}2) and |{right arrow over (w)}1|,|{right arrow over (w)}2|, <({right arrow over (w)}1,{right arrow over (w)}2) changing, according to the present invention, only slowly in relation to the periodicity length. In this way it is ensured that, locally, the arrangements can always be reasonably described by Bravais lattices.
A security paper for manufacturing security or value documents, such as banknotes, checks, identification cards or the like, is preferably furnished with a security element of the kind described above. The security paper can especially comprise a carrier substrate composed of paper or plastic.
The present invention also includes a data carrier, especially a branded article, a value document, a decorative article, such as packaging, postcards or the like, having a security element of the kind described above. Here, the security element can especially be arranged in a window region, that is, a transparent or uncovered region of the data carrier.
Further exemplary embodiments and advantages of the present invention are described below with reference to the drawings. To improve clarity, a depiction to scale and proportion was dispensed with in the drawings.
Shown are:
The invention will now be explained using a security element for a banknote as an example. For this,
Both the security thread 12 and the transfer element 16 can include a moiré-type magnification arrangement according to an exemplary embodiment of the present invention. The operating principle and the inventive manufacturing method for such arrangements are described in greater detail in the following based on the transfer element 16.
The top of the substrate foil 20 is provided with a grid-shaped arrangement of microlenses 22 that form, on the surface of the substrate foil, a two-dimensional Bravais lattice having a prechosen symmetry. The Bravais lattice can exhibit, for example, a hexagonal lattice symmetry, but due to the higher counterfeit security, lower symmetries, and thus more general shapes, are preferred, especially the symmetry of a parallelogram lattice.
The spacing of adjacent microlenses 22 is preferably chosen to be as small as possible in order to ensure as high an areal coverage as possible and thus a high-contrast depiction. The spherically or aspherically designed microlenses 22 preferably exhibit a diameter between 5μm and 50 μm and especially a diameter between merely 10 μm and 35 μm and are thus not perceptible with the naked eye. It is understood that, in other designs, also larger or smaller dimensions may be used. For example, in the case of moiré magnifier patterns, the microlenses can exhibit, for decorative purposes, a diameter between 50 μm and 5 mm, while in moiré magnifier patterns that are to be decodable only with a magnifier or a microscope, also dimensions below 5 μm can be used.
On the bottom of the substrate foil 20, a motif layer 26 is arranged that includes a likewise grid-shaped arrangement of a plurality of lattice cells 24 having different micromotif image portions 28, 28′, 28″. As explained in greater detail below, taken together, the micromotif image portions of multiple spaced-apart lattice cells (24) of the motif layer (26) each form one micromotif element that corresponds to one of the moiré image elements of the magnified moiré image and whose dimension is larger than one lattice cell (24) of the motif image.
The arrangement of the lattice cells 24 likewise forms a two-dimensional Bravais lattice having a prechosen symmetry, a parallelogram lattice again being assumed for illustration. As indicated in
The optical thickness of the substrate foil 20 and the focal length of the microlenses 22 are coordinated with each other such that the motif layer 26 is located approximately the lens focal length away. The substrate foil 20 thus forms an optical spacing layer that ensures a desired constant spacing of the microlenses 22 and of the motif layer having the micromotif image portions 28, 28′, 28″.
Due to the slightly differing lattice parameters, the viewer sees, in each case, when viewing from above through the microlenses 22, a somewhat different sub-region of the micromotif image portions 28, 28′, 28″, such that, overall, the plurality of microlenses 22 produces a magnified image of the micromotif elements formed from the micromotif image portions. Here, the resulting moiré magnification depends on the relative difference between the lattice parameters of the Bravais lattices used. If, for example, the grating periods of two hexagonal lattices differ by 1%, then a 100× moiré magnification results. For a more detailed description of the operating principle and for advantageous arrangements of the motif grids and the microlens grids, reference is made to German patent application 10 2005 062 132.5 and international application PCT/EP2006/012374, the disclosures of which are incorporated herein by reference.
Now, the distinctive feature of the present invention consists in that the micromotif elements of the motif layer 26 that correspond to the moiré image elements of the magnified moiré image are larger than the dimension of a lattice cell 24 of the motif layer 26 and thus, due to the occurring overlaps, can not simply be arranged periodically repeated in the motif layer. Rather, according to the present invention, the micromotif elements are broken down in a suitable manner into micromotif image portions that are each accommodated within one of multiple spaced-apart lattice cells 24 and that, taken together, form the respective micromotif element. Here, the breakdown of a micromotif element into micromotif image portions and the distribution of the image portions to lattice cells must be done according to certain rules if the image portions are to be composed, correctly and without gaps, to form a high-contrast, magnified moiré image element for the viewer.
With the described breakdown of larger motifs according to the present invention, especially particularly thin moiré magnifiers can be manufactured: for technical reasons, the thickness of a moiré magnifier arrangement is approximately equal to the line screen of the motif grid. Since, according to the background art, the motifs must each fit in a motif lattice cell, customarily, it is not possible to make the thickness smaller than the smallest possible technically realizable motif size. This obstacle is overcome according to the present invention in that the motif extends across multiple lattice cells.
For example, there is a method in the background art to produce motifs that are just 10 μm in size and suitable for moiré magnifiers; the resolution of the method is not sufficient for smaller motifs. Such a 10 μm motif just fits in a 10 μm grid such that, customarily, no moiré magnifiers that are thinner than 10 μm can be manufactured with this method. According to the present invention, however, a 10 μm motif can be accommodated broken down into four lattice cells of a 5 μm grid, and a 5-μm-thin moiré magnifier thus manufactured. Of course, the 10 μm motif according to the present inventive method can also be accommodated broken down into more than four lattice cells and, in this way, practically arbitrarily thin moiré magnifiers manufactured.
To explain the approach according to the present invention, the required variables will first be defined and briefly described with reference to
The arrangement of the micromotif image portions in the motif plane 32 is described by a two-dimensional Bravais lattice whose unit cell can be represented by vectors {right arrow over (u)}1 and {right arrow over (u)}2 (having the components u11, u21 and u12, u22). In compact notation, the unit cell can also be specified in matrix form by a motif grid matrix (below also often simply called motif grid):
In the same way, the arrangement of microlenses in the lens plane 34 is described by a two-dimensional Bravais lattice whose unit cell is specified by the vectors {right arrow over (w)}1 and {right arrow over (w)}2 (having the components w11, w21 and w12, w22). The unit cell in the moiré image plane 36 is described with the vectors {right arrow over (t)}1 and {right arrow over (t)}2 (having the components t11, t21 and t12, t22).
designates a general point in the motif plane 32,
a general point in the moiré image plane 36. To be able to describe, in addition to vertical viewing (viewing direction 35), also non-vertical viewing directions of the moiré-type magnification arrangement, such as the general direction 35′, between the lens plane 34 and the motif plane 32 is additionally permitted a displacement that is specified by a displacement vector
in the motif plane 32. Analogously to the motif grid matrix, the matrices
(referred to as the lens grid matrix or simply lens grid) and
are used for the compact description of the lens grid and the image grid.
In the lens plane 34, in place of lenses 22, also, for example, circular apertures can be used, according to the principle of the pinhole camera. Also all other types of lenses and imaging systems, such as aspherical lenses, cylindrical lenses, slit apertures, circular or slit apertures provided with reflectors, Fresnel lenses, GRIN lenses (Gradient Refractive Index), zone plates (diffraction lenses), holographic lenses, concave reflectors, Fresnel reflectors, zone reflectors and other elements having a focusing or also a masking effect, can be used as microfocusing elements in the focusing element grid.
In principle, in addition to elements having a focusing effect, also elements having a masking effect (circular or slot apertures, also reflector surfaces behind circular or slot apertures) can be used as microfocusing elements in the focusing element grid.
When a concave reflector array is used, and with other reflecting focusing element grids used according to the present invention, the viewer looks through the in this case partially transmissive motif image at the reflector array lying therebehind and sees the individual small reflectors as light or dark points of which the image to be depicted is made up. Here, the motif image is generally so finely patterned that it can be seen only as a fog. The formulas described for the relationships between the image to be depicted and the moiré image apply also when this is not specifically mentioned, not only for lens grids, but also for reflector grids. It is understood that, when concave reflectors are used according to the present invention, the reflector focal length takes the place of the lens focal length.
If, in place of a lens array, a reflector array is used according to the present invention, the viewing direction in
The moiré image lattice results from the lattice vectors of the motif plane 32 and the lens plane 36 in
=·(−)−1
and the image points of the moiré image plane 36 can be determined with the aid of the relationship
{right arrow over (R)}=·(−)−1·({right arrow over (r)}−{right arrow over (r)}0)
from the image points of the motif plane 32. Conversely, the lattice vectors of the motif plane 32 result from the lens grid and the desired moiré image lattice through
=·(+)−1·
and
{right arrow over (r)}=·(+)−1·{right arrow over (R)}+{right arrow over (r)}0.
If the transformation matrix =·(−)−1 is defined that transitions the coordinates of the points in the motif plane 32 and the points in the moiré image plane 36,
{right arrow over (R)}=·({right arrow over (r)}−{right arrow over (r)}0) and {right arrow over (r)}=−1·{right arrow over (R)}+{right arrow over (r)}0,
then, from two of the four matrices , , , in each case, the other two can be calculated. In particular:
=·=·(−)−1·=(−)· (M1)
=·(+)−1·=−1·=(−−1)· (M2)
=·(−)−1·=(−)−1·=(−)−1·· (M3)
=·(−)−1=(+)·−1=·1 (M4)
applies, designating the identity matrix.
As described in detail in the referenced German patent application 10 2005 062 132.5 and the international application PCT/EP2006/012374, the transformation matrix describes both the moiré magnification and the resulting movement of the magnified moiré image upon movement of the moiré-forming arrangement 30, which derives from the displacement of the motif plane 32 against the lens plane 34.
The grid matrices T, U, W, the identity matrix I and the transformation matrix A are often also written below without a double arrow if it is clear from the context that matrices are being referred to.
The design of moiré-type magnification arrangements normally starts from a magnified moiré image as the target motif that is visible when viewed, the desired magnification factor and the desired movement behavior of the moiré images when the arrangement is tilted laterally and when tilted forward/backward. The desired magnification and movement behavior of the target motif can be combined in the transformation matrix .
Also the arrangement of the microlenses can, as in the present example, be specified via the lens grid matrix . Alternatively, also only certain limitations or conditions can be placed on the lens arrangement, and the required lens arrangement calculated together with the motif image.
For illustration,
The magnification and movement behavior is specified in the exemplary embodiment in the form of the transformation matrix
which describes a pure magnification by a factor of 7. Let it be emphasized here that, to illustrate the inventive principle, deliberately simple exemplary embodiments are described that allow for good and approximately true-to-scale graphical depiction. For this, in this and in the following examples, simple and high-symmetry lattice arrangements and simple transformation matrices are chosen.
From the cited specifications, the micromotif to be introduced into the motif plane is obtained in the manner described above by applying the inverse matrix −1 to the target motif. Also the motif grid in which the micromotif elements must be arranged is defined by the given specifications and results according to relationship (M2) through
=(−−1)·. (B1-2)
a) shows the thus-calculated micromotif element 50 to be introduced and the motif grid 52, which, for the chosen specifications, likewise depicts a simple square lattice. In addition, a portion of the lens grid 42 is drawn in with dotted lines. As can be seen in
L
U=6/7*LW,
as yielded by the relationships (B1-1) and (B1-2).
As can further be seen in
To eliminate these overlaps and facilitate the depiction of a gapless, high-contrast moiré image having non-overlapping moiré image elements, according to the present invention, uniform motif subsets of the micromotif element arrangement 66 in
Here, the fact that the identified motif subsets are all to be “uniform” meant that the motif subsets together with the corresponding lens subsets of the lens grid 42 each form moiré-type magnification arrangements that, according to the above-indicated relationships between the image points of the moiré image plane and the image points of the motif plane
{right arrow over (R)}=·(−)−1·({right arrow over (r)}−{right arrow over (r)}0) and {right arrow over (R)}=·({right arrow over (r)}−{right arrow over (r)}0),
lead to the same target motif.
To determine such uniform motif subsets in the concrete exemplary embodiment, first, a superlattice grid of the motif grid 52 is identified in which the micromotif elements 50 can be arranged without overlaps. A superlattice grid is understood here to be a grid whose unit cell includes multiple lattice cells of the motif grid.
If the micromotif element 50 is now arranged repeatedly in the motif plane with the periodicity of the motif superlattice grids 62, so in the exemplary embodiment with the periodicity length LU′, then, in accordance with the choice of the superlattice grid 62, no more overlaps of the micromotif elements 50 result, as shown in
L
U
*L
U=¼LU′*LU′
includes only one fourth of the original elements.
b) shows a portion of the motif superlattice grid 62 and of the motif grid 52 drawn in with dotted lines again in detail. To the right of the two singled-out lattice cells 64 of the motif superlattice grid 62, the lattice vectors {right arrow over (u)}1 and {right arrow over (u)}2 of the motif grid 52 are drawn in.
As evident from
With reference to a superlattice cell 64, the four subgrids 52-1, 52-2, 52-3 and 52-4 exhibit an offset that is described in each case by a subgrid displacement vector v1, v2, v3, or v4 (
v1=0;
v2=u1;
v3=u2; and
v
4
=u
1
+u2.
Likewise drawn in in
Through the above-indicated relationship (M3), a superlattice grid 72 of the lens grid 42 corresponds to the superlattice grid 62 of the motif grid 52. In the exemplary embodiment, in which each superlattice cell 64 of the motif superlattice grid 62 consists of 2×2 lattice cells 54 of the motif grid 52, the lens superlattice grid 72 is formed from superlattice cells 74 that likewise consist of 2×2 lattice cells 44 of the lens grid 42. The periodicity length LW′ of the lens superlattice grid 72 is thus twice as large in both directions as the periodicity length LW of the lens grid 42.
This lens superlattice grid 72, which forms the starting point for the further approach, is depicted in
Analogously to the breakdown of the motif grid 52 in
As now explained with reference to
First, the first subgrid 42-1 is selected, as shown in
Then, as shown in
This approach is then repeated with the third subgrid 42-3 and the fourth subgrid 42-4, the motif image element arrangement 66 in
It is understood that, for another choice of superlattice, also another number and arrangement of the subgrids can result. For example, in a lens and motif superlattice composed of 2×3 lattice cells, there are 6 subgrids whose offset can be expressed in each case by subgrid displacement vectors v1 to v6. Accordingly, 6 intersections of the subgrids are then produced with the appropriately displaced motif image element arrangements.
Lastly, the four sectional images 80-1, 80-2, 80-3 and 80-4 are composed in accordance with the relative position of the subgrids 42-1, 42-2, 42-3 and 42-4 such that the finished motif image 82 illustrated in
If this motif image 82 is now viewed with the lens array in
Example 2 starts, like example 1, from the target motif 40 in the form of the letter “P” specified in
In example 2, the magnification and movement behavior is specified by the transformation matrix
with which, in addition to a magnification, also an approximately orthoparallactic movement effect is described.
As in example 1, from the transformation matrix A and the lens grid matrix W is first obtained, with the aid of the inverse matrix A−1, the micromotif element to be introduced into the motif plane, and the motif grid U.
Also in example 2, the chosen specifications lead to a micromotif element 90 (
To eliminate these overlaps and to depict a gapless, high-contrast moiré image having non-overlapping moiré image elements, a superlattice grid of the motif grid U is identified in which the micromotif elements 90 can be arranged free of overlaps.
Then the motif grid is broken down into four subgrids and the subgrid displacement vectors vj (j=1 . . . 4) for the offset of the appropriate subgrid determined.
Further, the lens superlattice grid corresponding to the motif superlattice grid is determined and likewise broken down into four subgrids. One of these four subgrids 94-j is depicted in
Now, analogously to the approach described for
If this motif image 95 is now viewed with the lens array in
With the magnification and movement matrix A applied in example 2, an approximately orthoparallactic movement effect is achieved: when the moiré arrangement consisting of the motif image 95 in
Example 3 illustrates an alternative and particularly simple method to accommodate large image motifs in a moiré magnifier arrangement. For example, an entire alphabet can be accommodated in a moiré magnifier, the approach being explained for the first letters of the alphabet based on
a) shows a motif layer 100 composed of motifs “A”, “B”, “C” that, combined with the appropriate lens grid, yields the magnified moiré image 108 in
With reference to the example 4 illustrated in
Let a denote the lens spacing in the hexagonal lens grid in
If m is the desired moiré magnification factor, then a vertical movement in the moiré image upon tilting laterally is described by the movement matrix
An opposite vertical movement in the image upon tilting laterally while maintaining the movement direction upon tilting vertically is described by the movement matrix
For the motif arrangements for the motif letters “A” (202-A) and “C” (202-C) in the fields 204-A and 204-C of the motif layer 200 (
For the motif arrangement for the motif letters “B” (202-B) in the field 204-B in
For grid arrangements chosen in this way, when tilted laterally in the tilt direction 210 (to the top right, to the bottom left), the letters “A” (206-A) and “C” (206-C) in
If the letters are to move oppositely also when tilted vertically, the following movement matrix is applied. A particular effect in such opposite movements is that the letters assemble into an easily perceptible sequence (e.g. a word, in the exemplary embodiment “ABC”) only in certain tilt directions.
These movement sequences are cited merely by way of example. Other movement sequences in arbitrary directions upon tilting can be calculated in accordance with the teaching of PCT/EP2006/012374, the disclosure of which is incorporated herein by reference. Also, the movement direction and/or magnification can change locally, the regional widths and regional limits being adjusted accordingly.
As set forth in the application PCT/EP2006/012374, already mentioned multiple times, and also incorporated in the present description in this respect, it is possible to use, in the moiré magnifier, motif lattice cells that are extended infinitely in one direction (e.g. vertically) and that have arbitrarily long motifs. In other directions (e.g. laterally), the lattice cell size is limited. Here—as explained in PCT/EP2006/012374—either cylindrical lenses or two-dimensional lens arrays can be used.
If, in one direction, a larger motif having 1:1 imaging is present, it is possible to apply the approach of example 1, modified accordingly.
For examples 1 to 5, for illustration, deliberately simple examples were chosen that allow for good and approximately true-to-scale drawing. Simple, very symmetrical lattice arrangements W (hexagonal or square) were chosen, and simple magnification and movement matrices A (only magnification or magnification with rotation). The present invention comprises, of course, for the matrix W, all two dimensional Bravais lattices, especially also those of low symmetry, and for A, all two-dimensional matrices, i.e. all products of magnification, mirroring, rotating and shear mapping, as explained in detail in, for example, the publication PCT/EP2006/012374, which, in this respect, is incorporated in full in the present application.
Number | Date | Country | Kind |
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10 2007 029 203.3 | Jun 2007 | DE | national |
This application is a continuation of U.S. application Ser. No. 12/665,072 with filing or 35 USC 371(c) date of Dec. 17, 2009, which is the U.S. National Stage of International Application No. PCT/EP2008/005173, filed Jun. 25, 2008, which claims the benefit of German Patent Application DE 10 2007 029 203.3, filed Jun. 25, 2007; all of which are hereby incorporated by reference in their entireties to the extent not inconsistent with the disclosure herewith.
Number | Date | Country | |
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Parent | 12665072 | Dec 2009 | US |
Child | 14102223 | US |