CA2923132C

CA2923132C - Pixel mapping and printing for micro lens arrays to achieve dual-axis activation of images

Info

Publication number: CA2923132C
Application number: CA2923132A
Authority: CA
Inventors: Mark A. Raymond; Hector Andres Porras Soto
Original assignee: Lumenco LLC
Current assignee: Lumenco LLC
Priority date: 2013-09-04
Filing date: 2014-02-27
Publication date: 2020-09-08
Anticipated expiration: 2034-02-27
Also published as: CA2923132A1; MX2016002927A; PH12016500422A1; WO2015034551A1; RU2661743C2; CN108638690B; EP3042238A4; EP3042238A1; BR112016004827A8; RU2016112319A; CN108638690A; JP6349401B2; JP2016539378A; MX359175B; AU2014315695A1; ZA201602171B; KR20160068758A; AU2014315695B2; CN105683815B; CN105683815A

Abstract

A visual display assembly adapted for use as an anti-counterfeiting device on paper currency, product labels, and other objects. The assembly includes a film of transparent material including a first surface including an array of lenses and a second surface opposite the first surface. The assembly also includes a printed image proximate to the second surface. The printed image includes pixels of frames of one or more images interlaced relative to two orthogonal axes. The lenses of the array are nested in a plurality of parallel rows, and adjacent ones of the lenses in columns of the array are aligned to be in a single one of the rows with no offset of lenses in adjacent columns/rows. The lenses may be round-based lenses or are square-based lenses, and the lenses may be provided at 200 lenses per inch (LPI) or a higher LPI in both directions.

Description

PIXEL MAPPING AND PRINTING FOR MICRO LENS ARRAYS
TO ACHIEVE DUAL-AXIS ACTIVATION OF IMAGES
CROSS-REFERENCE TO RELATED APPLICATIONS
BACKGROUND
1. Field of the Description.
[0001] The present invention relates, in general, to combining printed images with lens arrays to display three dimensional (3D) images with or without motion, and, more particularly, to a method of pixel mapping, providing arrangements of pixels, and imaging that is adapted for use with arrays of square, round, parallelogram, or hexagonal-based micro lenses to provide enhanced 3D imagery with fuller volume and/or with multi-directional motion.

2. Relevant Background.
[0002] There are presently many applications where it is desirable to view a printed image via an array of lenses. For example, anti-counterfeiting efforts often involve use of an anti-counterfeiting device or element that is made up of an array of lenses and an image printed onto the back of the lens array or onto an underlying substrate or surface (e.g., a sheet of paper or plastic). The anti-counterfeiting element may be used to display an image that is chosen to be unique and be an indicator that the item carrying the anti-counterfeiting element is not a counterfeit. The anti-counterfeiting market is rapidly growing worldwide with anti-counterfeiting elements placed on a wide range of items such as upon currency (e.g., on a surface of a paper bill to help prevent copying) and on labels for retail products (e.g., labels on clothing showing authenticity).

[0003] In this regard, moire patterns have been used for years in anti-counterfeiting elements with arrays of round lenses and with arrays of hexagonal arrays (or round and hexagonal lens arrays).

Typically, the printed images provided in an ink layer under these lens arrays are small, fine images relative to the size of the lenses. A moire pattern is provided in the printed images in the form of a secondary and visually evident superimposed pattern that is created when two identical patterns on a surface are overlaid while being displaced or rotated a small amount from each other.
[0005] In such moire pattern-based anti-counterfeiting elements, some of the images may be printed in a frequency slightly more or less frequent than the one-to-one dimension of the lenses in two axes, and some of the images may be printed slightly differently relative to each other. Figure 1 illustrates an exemplary assembly 100 that may be used as an anti-counterfeiting element making use of magnification of moire patterns. The assembly 100 includes a lens array 110 made up of side-by-side, parallel columns (or rows) 112 of round lenses 114, and it can be seen that the columns 112 are offset from each other (by about 50 percent) such that pairs of adjacent lenses 114 in the columns are not aligned (e.g., a lens in a next column is positioned in the space between two lenses in the previous column).
[0006] A printed image 120 is provided in a layer of ink underneath the lens array 110 (on a back, planar surface of the lens array 110). The result, which is difficult to see in Figure 1, is a magnified moire pattern that provides the illusion of depth of field to a viewer via the lenses 112 of the array 110 or, in some cases, the sense that the images are moving (motion or animation of the displayed items). Typically, the thickness of each of the lenses 112 is in the range of 0.5/1000 to 5/1000 inches (or 12 to about 125 microns), and the frequency of these lenses 112 in an array 110 is about 400 X 400 to over 1000 X 1000 per inch.
[0007] While helpful to reduce counterfeiting, use of moire patterns with magnifying round lens arrays has not been wholly satisfactory for the anti-counterfeiting market.
One reason is that the effects that can be achieved with moire patterns are limited. For example, one cannot take a photograph and display 3D with a moire pattern. Generally, the moire patterns are used in the security and/or anti-counterfeiting industry in very fine lenses with focal lengths of about 20 to 75 microns and frequencies of over 500 lenses per inch in one axis or more than 250,000 lenses per square inch. As a result, the images underlying the lenses in the lens array are typically printed at least at 12,000 DPI (dots per inch) and may even be provided at over 25,000 DPI. These micro-lens arrays are generally closely nested as shown in element 200 with its array 210 in Figure 2. The array 210 uses hexagonal lenses that are provided in offset and overlapping columns 212 (e.g., side-by-side lenses 214 are not aligned in a row and are positioned to fill or be nested into space between two lenses of adjacent columns 212) to focus on and magnify an image or moire pattern 220 in an underlying ink layer.
[0008] One problem or issue with the use of such an array 210 and images 220 is that the element 200 is relatively easy to reverse engineer, which limits its usefulness as an anti-counterfeiting element. Particularly, the patterns 220 underlying the lenses 214 can be seen with an inexpensive and readily available microscope, which allows one to determine the frequency of the images and patterns. In addition, the lenses 214 can be cast and re-molded, which leaves printing the identified images as the only hurdle for successfully copying the element 200 (and then counterfeiting a piece of currency or a label for a product). Unfortunately, printing the image 220 is becoming easier to accomplish due to high resolution lasers and setters and other printing advances. Typically, for an element 200, the micro-lenses are printed using an emboss and fill technology, which limits the printing to one color due to the fact that the process tends to be self-contaminating after one color and also due to the fact that the process is difficult to control from a relative color-to-color pitch in the emboss-and-fill printing process.
[0009] Hence, there remains a need for advancements in the design and fabrication of assemblies or elements that combine a lens array with a printed image (layer of ink containing images/patterns) to display imagery. Such improvements may allow new anti-counterfeiting devices or elements to be produced for use with currency, labels, credit/debit cards, and other items, and these anti-counterfeiting devices preferably would be much more difficult if not nearly impossible to duplicate or copy. Further, there is a growing demand for such anti-counterfeiting devices to provide a surprising or "wow factor" with their displayed imagery such as images that float above and/or below a focal plane (e.g., more true 3D displays).
SUMMARY
[0010] Briefly, the inventors recognized that it may be beneficial to provide a different nesting of lenses in an array that can then be combined with an image having dual-axis interlacing. For example, the lenses may be circular or square-based lenses that have their centers aligned such that the array is made up of parallel rows and columns of lenses (e.g., without having adjacent lenses being offset from each other as seen in the arrays of Figures 1 and 2). The image is printed from a print file generated from a matrix of frames of images taken from a plurality of points of view (POVs) along both a first axis (X axis) and also along a second axis (Y axis).
The frames are interlaced in both directions to provide a pixel mapping to the lenses of the array.
[0011] More particularly, a visual display assembly is provided that is useful as an anti-counterfeiting device on paper currency, product labels, and other objects.
The assembly includes a film of transparent material including a first surface including an array of lenses and a second surface opposite the first surface. The assembly also includes a printed image proximate to the second surface. The printed image includes pixels of frames of one or more images interlaced relative to two orthogonal axes (printed from a file generated using dual-axis interlacing rather than single axis interlacing as in conventional lenticular printing). The lenses of the array are nested in a plurality of parallel rows, and adjacent ones of the lenses in columns of the array may be aligned to be in a single one of the rows (e.g., no offsetting of adjacent lenses may be useful in some cases).
[0012] To provide the lens array, the lenses may be round-based lenses, square-based, or hexagonal-based lenses. The lenses of the array are provided at 200 LPI (or a higher LPI) as measured along both of the two orthogonal axes. The lenses may each have a focal length of less than 10/1000 inches. In some embodiments, the frames each include a different point of view (POV) of the one or more images. In such cases, the frames include images from at least three POVs along a first of the two orthogonal axes, and the frames further include images from at least two additional POVs corresponding to each of the three POVs along the second of the two orthogonal axes.
[0013] In the assembly, the printed image may be adapted such that an image displayed from a normal POV includes a first set of symbols and a second set of symbols, and, in an image displayed when the assembly is rotated from the normal POV about a first axis, the first and second sets of symbols move in opposite directions. Further, the printed image may be adapted such that in an image displayed, when the assembly is rotated from the normal POV about a second axis orthogonal to the first axis, the first and second symbols move in a single direction that is orthogonal to the second axis.

4 [0014] In other assemblies, the printed image can be adapted such that an image displayed from a normal POV includes a first set of symbols and a second set of symbols, and, in an image displayed when the assembly is rotated from the normal POV about a first axis, the first and second sets of symbols can move in a single direction that is parallel to the first axis of the assembly. In such embodiments of the assembly, the printed image is adapted such that in an image displayed when the assembly is rotated from the normal POV about a second axis orthogonal to the first axis, the first and second symbols move in a single direction that is parallel to the second axis.
[0015] Another visual effect is achieved in other embodiments of the assembly.
Particularly, the printed image may include a wallpaper pattern (e.g., with icons, logos, and other symbols) and an overlay pattern. Then, the printed image may include mapped pixels such that the wallpaper pattern is visible from a plurality of POVs (when the assembly is rotated/tilted to differing angles relative to a viewer's line of sight), and the overlay pattern has a range of differing visibilities over the plurality of POVs. For example, the differing visibilities may include the overlay being invisible (or only faintly visible) to a viewer along a normal POV of the assembly while rotating or tilting the assembly away further and further from normal (in any direction in some cases) causes the darkness or brightness of the overlay pattern to increase until it is fully visible (or as dark or bright in color as it can be such as at some more extreme angle relative to normal such as an angle in the range of 45 to 60 degrees or the like).
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] Fig. 1 is a top view of an assembly used as an anti-counterfeiting element or device with a lens array made up of side-by-side and vertically offset columns of round lenses (e.g., lenses are not arranged in linear rows in the array) overlying a printed moire pattern;
[0017] Fig. 2 is a top view, similar to that of Fig. 1, showing an assembly used as an anti-counterfeiting element or device with a lens array made up of side-by-side and vertically offset columns of hexagonal lenses (e.g., lenses not arranged in linear rows and tightly nested in abutting contact) overlying a printed moire pattern;

[0018] Figs. 3A and 3B illustrate a top and sectional view taken at line 3B-3B, respectively, of an item such a piece of paper currency or a product label with an anti-counterfeiting device based on a round lens array;
[0019] Figs. 4A and 4B illustrate a top and sectional view taken at line 4B-4B, respectively, of an item such as a paper currency or label with an anti-counterfeiting device or element provided on a surface that is based on a square lens array;
[0020] Fig. 5 shows a process of obtaining frames or images associated with differing points of view taken of a scene along the horizontal or X-axis;
[0021] Fig. 6 shows a process of obtaining frames or images associated with differing points of view taken of the scene of Fig. 5 along the vertical or Y-axis;
[0022] Fig. 7 illustrates a larger set of frames or images obtained by taking differing viewpoints of a scene at each point along the X-axis (or Y-axis), e.g., multiple sets of frames to provide height;
[0023] Fig. 8 illustrates an image provided by an exemplary interlaced file for one row of a matrix of frame files associated with multiple points of view (e.g., a vertically combined file);
[0024] Fig. 9 illustrates an image provided by a combination print file (or two-way interlacing file or X and Y axis combination file) for use with a lens array of the present description;
[0025] Fig. 10 illustrates a side-by-side comparison of an image of an original combination print file and an image of a combination print file adjusted (enlarged) as discussed in the description;
[0026] Figs. 11 and 12 illustrate views of two exemplary assemblies viewed from differing POVs, with the assembly being useful as anti-counterfeiting devices for currency or the like that are configured with a lens array and printed image to provide differing motion effects;
[0027] Fig. 13 illustrates a number of views of another exemplary lens/printed image (ink layer) assembly (or anti-counterfeiting device) from a number of differing POVs;
[0028] Fig. 14 illustrates a normal (or orthogonal/plan) view and tilted left and right views of another lens/printed image assembly (anti-counterfeiting device);

[0029] Fig. 15 illustrates an assembly (e.g., an anti-counterfeiting device in the form of a label) incorporating a micro lens array provided over an ink layer containing a dual-axis interlaced set of images as described herein;
[0030] Fig. 16 is a functional block diagram or schematic of a system for use in manufacturing anti-counterfeiting devices or lens/printed image assemblies of the present description;
[0031] Fig. 17 illustrates a flow diagram of Oa pixel adjustment method according to the present description and as may be implemented with the system of Fig. 16;
[0032] Fig. 18 provides a schematic and a print file (pixel mapping) showing a process of providing dual-axis interlacing of image frames to achieve visual effects described herein;
[0033] Figs. 19-21 are plots showing ray tracing for assemblies of the present description, e.g., for a lens array combined with a dual-axis interlaced image;
[0034] Fig. 22 is plot of an off-axis ray tracing;
[0035] Fig. 23 is a spot diagram corresponding to an off-axis analysis of Fig.
22;
[0036] Figs. 24 and 25 are two additional spot plots or diagrams for a round-based lens (or spherical lens);
[0037] Fig. 26 is a plot of a ray tracing for the lens associated with the plots of Figures 24 and 25;
[0038] Figs. 27-29 illustrate, similar to Figures 11 and 12, another exemplary assemblies viewed from differing POVs, with the assemblies being useful as an anti-counterfeiting device for currency or other objects that are configured with a lens array and printed image to provide differing motion effects (dual-axis activation);
[0039] Fig. 30 illustrates another assembly that may be used as an anti-counterfeiting device with a background pattern pushed back from foreground images in all POVs;

[0040] Fig. 31 illustrates a top of an item such a piece of paper currency or a product label with an anti-counterfeiting device based on a hexagonal-based lens array (or array of hexagon lenses in a nested pattern); and [0041] Fig. 32 illustrates a top of an item such a piece of paper currency or a product label with an anti-counterfeiting device based on a round or circular-based lens array (or array of round lenses in a nested pattern).
DETAILED DESCRIPTION
[0042] Briefly, the present description is directed toward designs for assemblies of lens arrays combined with printed images provided in an ink layer. The assemblies can be used, for example but not as a limitation, as anti-counterfeiting elements or devices. The lens arrays differ from those shown in Figures 1 and 2, in part, because the lenses are arranged in columns that are not vertically offset such that the lenses are provided in parallel columns and also in parallel rows (e.g., pairs of adjacent lenses in side-by-side columns are aligned with their center axes being collinear). The lenses may be round-based, square-based, parallelogram-based, or hexagonal-based lenses, and the underlying image has its pixels mapped and arranged such that the micro lens arrays produce a 3D
displayed image with full volume and, in some cases, with multi-directional motion or animation.
[0043] In an embodiment shown in Figures 3A and 3B, an item 300 (such as a piece of paper currency, a label for a product, or the like) is provided with an anti-counterfeiting element or device in the form of a lens array (round lens array) 310 covering or provided on top of a layer of ink 320 providing a printed image. As shown, the item 300 includes a substrate or body 305 such as a sheet of paper or plastic (e.g., paper to be used as currency or paper/plastic to be used for a product label).
On a surface 307 of the substrate/body 305, an image is printed via a layer of ink 320, and a lens array 310 is provided on an exposed surface of the ink layer 320 (e.g., the ink layer 320 and its pattern/image may be printed onto the substrate surface 307 or onto the back surface of the lens array 310).
[0044] As shown, the lens array 310 is made up of a plurality of lenses 314 that each have a round base 317 abutting the surface 321 of the ink layer 320 and have a dome-shaped cross section as seen in Figure 3B. The round-based lenses or round lenses 314 are arranged in a number of columns 312 that are parallel as shown by parallel vertical or Y-axes 313 (axes passing through the center of the lenses 314 in columns 312) in Figure 3A. Further, the lenses 314 are arranged such that pairs of lenses 314 in adjacent ones of the columns 312 are in contact or proximate at least at the bases 317 (as seen in Figures 3A and 3B). Still further, the columns 312 are not vertically offset as seen in arrays 110, 210 of Figures 1 and 2 such that pairs of adjacent lenses 314 arc aligned in rows as can be seen by parallel horizontal or X-axes 315 passing through centers of lenses 314 in the array 310 (e.g., the lenses 314 of the array 310 are both vertically and horizontally aligned due to the specific nesting shown in Figure 3A).
[0045] In an embodiment shown in Figures 4A and 4B, an item 400 (such as a piece of paper currency, a label for a product, or the like) is provided with an anti-counterfeiting element or device in the form of a lens array (e.g., square-based lens array) 410 covering or provided on top of a layer of ink 420 providing a printed image. As shown, the item 400 includes a substrate or body 405 such as a sheet of paper or plastic (e.g., paper to be used as currency or paper/plastic to be used for a product label). On a surface 407 of the substrate,/body 405, an image is printed via a layer of ink 420, and a lens array 410 is provided on an exposed surface of the ink layer 420 (e.g., the ink layer 420 and its pattern/image may be printed onto the substrate surface 407 or onto the back surface of the lens array 410).
[0046] As shown, the lens array 410 is made up of a plurality of lenses 414 that each have a square base 417 abutting the surface 421 of the ink layer 420 and may have a dome-shaped cross section as seen in Figure 4B. The square-based lenses or square lenses 414 are arranged in a number of columns 412 that are parallel as shown by parallel vertical or Y-axes 413 (axes passing through the center of the lenses 414 in columns 412) in Figure 4A. Further, the lenses 414 are arranged such that pairs of lenses 414 in adjacent ones of the columns 412 are in contact or proximate at least at the bases 417 (as seen in Figures 4A and 4B). Still further, the columns 412 are not vertically offset as seen in arrays 110, 210 of Figures 1 and 2 such that pairs of adjacent lenses 414 are aligned in rows as can be seen by parallel horizontal or X-axes 415 passing through centers of lenses 414 in the array 410 (e.g., the lenses 414 of the array 410 are both vertically and horizontally aligned due to the illustrated nesting of the lenses 414).

[0047] In the lens arrays 310, 410, the lenses may be provided at a frequency of as few as 150 lenses per linear inch in both the X and Y axes or up to about 4000 lenses per linear inch on each of the X and Y axes. Note, the lenses are nested as shown in Figures 3A and 4A so that there is little or no interference from the adjoining or adjacent lenses when an image in ink layers 320, 420 is viewed by a viewer of the items 300, 400. Both stacked square-based and round-based lenses 414, 314 may be used to support the interlacing process described herein for providing the image/pattern in ink layer 320, 420. In some cases, the square-based lenses 414 may be preferred as these produce a fuller or full-filled image.
[0048] The ink layers 320, 420 are adapted or designed for use with the lens arrays 310, 410 to provide full volume 3D displayed images with or without multi-directional motion or animation.
Particularly, images are interlaced, similar to lenticular images, in the X-axis and also then in the Y-axis to create full volume 3D interlaced images. The lenses 314, 414 have a point focus for a viewer, and the resulting image (displayed image from light reflected from the ink layers 320, 420 via the lens arrays 310, 410) viewed by the viewer is a 3D image in all directions, regardless of the viewer's viewpoint.
[0049] At this point, it may be useful to compare and contrast the effects that can be produced with a pixel mapping arrangement in ink layers 320, 420 combined with the lens arrays 310, 410 versus a conventional moire pattern-based assembly (see those shown in Figures 1 and 2) with the following effect listing: (1) float is provided by both moire and pixel mapping according to the present description; (2) float height is limited to 100 percent with moire patterns while 150 percent float can be achieved with pixel mapping-based embodiments; (3) 1-directional motion is provided by both techniques; (4) on-off is available/achievable only with pixel mapping techniques; (5) animation is also only available with the pixel mapping-based embodiments; (6) zoom cannot be provided using moire patterns but can be provided with pixel mapping; (7) true 3D is provided only with the pixel mapping-based embodiments described herein; (8) movement in opposite directions is also achievable only with the pixel mapping-based embodiments of the present description; (9) one image up/one side is another effect available only with the use of the pixel mapping-based embodiments; and (10) full volume 3D is only available via the use of the lens arrays and pixel mapping taught herein. As a result of some or all of these effects or aspects of the two techniques, the moire pattern-based anti-counterfeiting devices are easily reverse engineered while the pixel mapping-based anti-counterfeiting devices are impossible or nearly impossible to reverse engineer.
[0050] With a general understanding of the lens arrays and their configurations understood, it may be useful to discuss pixel arrangement, imaging, and mapping for circular-based and square-based lenses (e.g., design of the ink layers of the assemblies shown in Figures 3A-4B). Traditional lenticular printing (interlaced printing of images for use with lenticular lens arrays) uses a certain number of files that are created from different points of view (or viewpoints) in order to get a 3D
effect. For example, a point of view in a single plane is moved to the left or to the right to create a next point of view. Traditional lenticular printing also uses different frames from a sequence of images to create some motion or animation or other visual effects. Once generated, the set of frames or files are combined in an interlaced file that is then printed onto the back of a lenticular lens array or onto a substrate upon which the lenticular lens array can be applied. The process to create the final file from the original frames is called "interlacing" (e.g., the process of striping and arranging printed information to a given pitch to match a particular lenticular lens array).
[0051] The interlacing on traditional lenticular material has just one direction, and the interlacing depends on the lens direction so that the striping is either horizontal or vertical. This process combines the frames so that the observer can see the effect working either horizontally or vertically (but not both) according to the lens direction. Figure 5 illustrates a process 500 in which a set of files of a single image or scene 540 viewed from three different viewpoints 510, 520, and 530 (such as -45 degrees, orthogonal, and +45 degrees or the like) are obtained for use in printing. The viewpoints 510, 520, and 530 are views from the same scene taken along the horizontal or X-axis.
The frames or viewpoints 510, 520, 530 resulting from the points of views are slightly different and are then combined in an interlacing process. When this frame of interlaced images is combined with a sheet of lenticular material and viewed, the frame can generate depth perception or a 3D
effect.
[0052] As shown in Figures 3A-4D, circular and square-based lenses may be used in a lens array with a printed image, and these lenses allow the effects to work in two directions concurrently, e.g., in the horizontal and vertical directions at the same time. The fact that the visual effects are created in all directions also demands that a more complete set of frames or views from the same scene be provided in the printed image (or ink layer) used with round or square lens arrays. With this recognition by the inventors, the inventors developed a new process (described below) for interlacing (or, more accurately, mapping, arranging, and imaging pixels) these sets of frames from a single scene.
[0053] For example, circular, hexagonal, parallelogram-type, or round-based lens arrays (in contrast to cylindrical lenses or elongated lenticules) allow one to have not only one set of points of view as shown in Figure 5 that may be useful with traditional lenticular lenses but to also have different sets of points of view from differing heights (or along the vertical or Y-axis).
Figure 6 shows a process 600 for obtaining additional frames or views from the scene 640 (which may be the same as scene/image 540). As shown, frames 610, 620, 630 from three different viewpoints (e.g., +45 degrees relative to orthogonal to the Y-axis, orthogonal to the Y-axis, and -45 degrees relative to the Y-axis or the like) are obtained from an image 640 of a single scene.
[0054] One of the main differences between the presently described process and traditional lenticular printing, though, is the fact that now two or more sets of points of views or frames corresponding to such viewpoints are combined in an image file for printing.
In other words, the interlacing is performed for view points along the vertical and along the horizontal axis. This means that, instead of interlacing one sequence of frames, the new interlacing process (or print file generation process) involves intelligently mapping a matrix of frames corresponding to differing viewpoints taken along both the X and Y-axes. In the present example, as shown in diagram 700 of Figure 7, there are three sets 710, 720, 730 that each contains three frames 712, 714, 716, 722, 724, 726, 732, 734, 736. This may be thought of as selecting each horizontal or X-axis point of view (as shown in Figure 5) and then generating two additional vertical or Y-axis points of view for a single scene (as shown in Figure 6) (or vice versa).
[0055] Figures 5-7 provide a simple example, but many other numbers of points of view may be utilized. For example, a traditional lenticular printing may involve use of 10 frames corresponding with 10 different view points along the X-axis (or Y-axis). In contrast, the presently described interlacing or image printing process would involve 10 sets of 10 frames each so that the total number of frames provides a matrix of 100 frames. According to the present description, the interlacing or printing process then involves mapping and imaging each of the 100 frames in individual pixels.
[0056] At this point, it may be useful to describe in more detail the mapping and imaging of X and Y-axes pixels to obtain an image file that can be printed for use with one of the lens arrays described herein (such as for use on currency or a product label as part of an anti-counterfeiting device). The matrix of frame files (e.g., the matrix 700 of frame files of Figure 7) is preferably combined in order to generate the file to print and that, when printed and used with a predefined/particular lens array, can generate a desired visual effect. For example, if one were to assume the use of six frames for each set of frames (instead of three as shown in sets 710, 720, 730 in Figure 7), the matrix of frames would be (with the frame number providing the set number and the frame within that set):
Frame 11 Frame 12 Frame 13 Frame 14 Frame 15 Frame 16 Frame 21 Frame 22 Frame 23 Frame 24 Frame 25 Frame 26 Frame 31 Frame 32 Frame 33 Frame 34 Frame 35 Frame 36 Frame 41 Frame 42 Frame 43 Frame 44 Frame 45 Frame 46 Frame 51 Frame 52 Frame 53 Frame 54 Frame 55 Frame 56 Frame 61 Frame 62 Frame 63 Frame 64 Frame 65 Frame 66 [0057] A first step in mapping/imaging can be to combine each row of frames from the matrix (e.g., as if vertical lenses were being used). In this way, a sequence of combined pixels is produced in the X axis from the same scene but from slightly different heights or points of view (from the Y axis).
For example, the combining may start by interlacing the six frames from the first row of the matrix, interlacing the six frames from the second row, and so on until there is one interlaced file for each row of the matrix of frame files (images of a scene from differing points of view). It may be useful to name the image sequences on a sequence from the top to the bottom of the matrix, and the first interlaced file may be IF 01", which is a result from the first row, and so on until we have a sixth interlaced file of "IF 06" from the sixth row for the exemplary (but not limiting) matrix provided above. Figure 8 illustrates an image 800 using the images from the matrix 700 of Figure 7 for one of the rows of the matrix. The resulting file providing image 800 is a combination of slices 810 from each frame in the particular row (interlaced image stripes or slices 810).
[0058] A second step in mapping/imaging is to combine these vertically combined files (X axis) into one final file to use in printing. The information that is useful or even needed is one horizontal slice to concurrently or simultaneously create the effect in the other direction. A second mapping process (horizontal) is performed, but this time using the previously generated vertical pixel files as the input to create the bi-directional (X and Y axis) frames.
[0059] In this second step it is desirable that: (1) the pixels in the files are vertically combined in the same sequence previously defined; (2) the files are regenerated with the horizontal information pursuant to the pixel map and, therefore, to create the print file; and (3) the result is a bi-directional pixel map with all of the 3D or motion information in both directions, which means that, instead of having stripes or slices, the final file has squares with the data from the matrix arranged in a way that is similar to the frames in the matrix. With regard to this third item, it may be important to note that when combined with the round, hexagonal, parallelogram, or square-based lenses of an array, an image printed from this file will allow any viewpoint to be achieved/displayed to a viewer and will allow motion to be presented in any direction.
[0060] Figure 9 illustrates an image 900 that may be printed for use with a round, hexagonal, parallelogram, or square-based lens array from a final print file output from this second mapping/imaging step. In this final linear image 900, one can see interlacing in a vertical direction with slices/stripes 912 and also in the horizontal direction with slices/stripes 914. The exploded and/or enlarged portion 910 is useful for showing this two-way interlacing and also for showing the "square" composition (see, for example, square 916) of this final print file (two axis combination file).
[0061] Mapping and imaging can also be performed using both the X axis and the Y axis to achieve a motion effect. In traditional lenticular printing, the idea is to get a loop in an interlaced print image with the sequence of frames that describes or provides motion. This "loop" concept is also useful for the printing described herein but, again, with circular, hexagonal, parallelgram, or square-based lenses (or other arrays of lenses), one processes a matrix of frames. In order to get the loop sequence in all directions, the matrix typically should be arranged in a way that a loop sequence is viewed in each row and also in each line/column of the matrix simultaneously.
For instance, if the input for printing is a sequence of six frames, the matrix of the 6 X 6 frames may be arranged as:
Frame 5 Frame 6 Frame 1 Frame 2 Frame 3 Frame 4 Frame 6 Frame 1 Frame 2 Frame 3 Frame 4 Frame 5 Frame 1 Frame 2 Frame 3 Frame 4 Frame 5 Frame 6 Frame 2 Frame 3 Frame 4 Frame 5 Frame 6 Frame 1 Frame 3 Frame 4 Frame 5 Frame 6 Frame 1 Frame 2 Frame 4 Frame 5 Frame 6 Frame 1 Frame 2 Frame 3 [0062] The arrangement provided in this matrix allows, when used to create a printed image, one to see a loop (through a circular or square-based lens array) in both directions (X and Y axis). The printed image also may produce little to no distortion by providing each row and each column so as to be slightly out of phase relative to the other nearby rows and columns. The interlacing process based on this matrix would then be the same as described above to obtain or produce a final interlaced file (also sometimes called an X and Y axes pixel file).
[0063] In order to create a quality image in micro lens printing (printing for use with the lens arrays shown herein), the optical pitch of the lens should precisely match the plate-making, proofing, or digital output device in two axes. In other words, the number of frames in both the X axis and the Y
axis multiplied by the number of lenses should be equal (precisely equal in some cases) to the DPI
(dots per inch) of the output device of the lenses' optical pitch. The exact lens LPI number that comes out of the construction of the sheets of lens array material is what is called mechanical pitch, but, depending on the viewing distance, those lenticules will focus on a different frequency meaning that when one combines the number of lines per inch of a certain frame there will not be a match with the number of lenticules per inch. Hence, a calibration process may be used (called a pitch test) to better determine the exact number of lines per inch that focus in that particular lens sheet or film at a given distance and for a particular printing device.
[0064] Stated differently, the X-axis frame count multiplied by the number of lenses (optical pitch) should be equal to the resolution of the output device (this should also hold true for the Y-axis).
One challenge is that the DPI generated during printing, even when carefully engineered, may not match the optical pitch of the printed lens. This may be due to distortion in the web or sheet process and/or due to typical shrinkage or expansion and distortion in the manufacture of a film. Even if the film is made precisely to match the optical pitch of the output device, the pitch may change significantly as the film is printed due to cylindrical distortion that is common in all printing processes (e.g., flexo, gravure, offset, letterpress, holography, emboss and fill, and the like). Also, the distortion may be greater in the repeat direction of the web or sheet around the cylinder.
[0065] In the past, adjusting a file to match the target pitch and DPI was done in traditional linear lenticular optics with software tools such as Adobe PhotoShop or the like, and this process works well in a linear lens as may be used in a relatively course lens array.
However, in a micro lens as used in the arrays discussed here (e.g., lenses provided at more than 200 LPI
in any direction), the results using these conventional software tools or by simply allowing the rip in the image or place setter to make the adjustments are unsatisfactory as there may be severe quality problems. These quality problems may arise because the attempt to match the resolution, while it may work in some cases, often creates a corrupted file in which the image slices do not accurately stay in their channels relative to the lens array.
[0066] Again, this problem does not arise when using a thick lens array, but it is a problem that has to be addressed when using a micro lens array as taught herein because, otherwise, the image may become muddy or the printed image may not work at all to achieve the desired 3D or motion effects due to the rays in the channels mixing to the viewer. Such results are often due to uneven image slices and the interpolation of the files in the process. When examining the files microscopically after the adjustments made by the rip or other traditional graphic programs are used, one can see the interlaced slices are no longer uniform. Therefore, the images mix relative to the lens focus (e.g., one image may mix with another image (Image 2 mixes with Image 4 and so on), which significantly reduces the quality of the image provided to or viewed by a viewer). Hence, when one considers this problem or challenge in the context of dual X-axis and Y-axis, full volume interlacing, the problem/challenge is significantly compounded and the output can be particularly messy such that the displayed image is not pleasing or even understandable for a viewer.
[0067] In some cases, the desired optical pitch may be within some range of target (such as within 3 percent of the target). In these cases, devices (such as a VMR (Variable Main-scan Resolution) from Kodak or the like) may be used to adjust the files to a precise number.
However, since this process only works in one axis, it is not very useful for X-axis and Y-axis or full volume interlacing as discussed herein. For the imagery to work and be adjusted properly to print the film in nearly any condition, the inventors recognized that the pitch should be adjusted precisely using other techniques/tools so that the output device can run at the parent resolution in both axes without adversely effecting the integrity of the X and Y-axes interlaced image. The channels in both axes preferably stay precisely as planned in the file relative to the target optical pitch of the lens.
Alternatively, the file can be "scaled" to the target number by interlacing the file in both axes at the closest whole integer. Such scaling may be performed either above or below the target optical pitch resulting in a DPI higher or lower than the target DPI. By either manual or automated software, pixels can be added or subtracted throughout the file image.
[0068] It was previously mentioned that the number of frames used in the combined image multiplied by the optical pitch should be equal to the exact resolution of the output device in both directions. This may be stated as: NF x OP = DOR, where NF is the number of frames, OP is the optical pitch, and DOR is the device output resolution. One typical situation in this regard is that, despite the fact that the number of frames can be chosen, the number of frames has to be an integer.
Further, the number of lenses per inch may vary from time-to-time because of the production batch of the lenses and ambient conditions when printing. As a result, one option to make the above equation work properly is to combine the images by choosing an integer number of frames and an optical pitch (even if is not the required one) that is close enough to obtain the exact resolution of the output device. Then, a correction can be made on the file in a way such that the pitch is adjusted without changing the resolution.

10069l Due to the complexity of this process, it may be useful to describe an exemplary (but not limiting) process of how these techniques can be successfully implemented to provide a printed image for use with a lens array of the present description. For example, a 2400 DPI output device may be used for printing a combined X-axis and Y-axis file, and the printed image is intended for use with a 240 LPI lens (mechanical) that has a 239.53 optical pitch. This means that it is desirable to combine 10 frames at 240 LPI to obtain the 2400 DPI needed for the assembly (e.g., an anti-counterfeiting device). So, the challenge presented is how to adjust the 240 LPI interlaced image to 239.53 without modifying the size of the file and losing the pixel integrity or changing the resolution.
[0070] To make this adjustment, it may be useful to enlarge the size of the file such as by 0.196 percent (i.e., from 240.0 divided by 239.53) while also keeping the same pixel size. To this end, a calculated number of pixel columns may be inserted that are in precise positions throughout the width of the file. In this particular example, if the file is 1 inch wide, the file has a total of 2400 pixels. Following this example further, one would need to insert 5 (4.7 rounded up to 5) pixels to decrease the interlaced LPI count while keeping the same resolution or pixel size. A software routine (or smart algorithm) may be implemented in a computer system (e.g., software or code stored in memory may be executed by a processor computer to cause the computer to perform the described functions on an image file stored in memory or accessible by the processor/computer) that acts to choose the right places to add or clone pixels or to take out the needed number of columns of pixels without distorting the images.
[0071] Figure 10 provides a side-by-side comparison 1000 showing an image 1010 provided by an original combination (or dual axis) print file and an image 1020 provided by the same print file after adjustment. The adjustment, in this example, was an enlargement of 0.7 percent via Adobe Photoshop. The image comparison 1000 shows how a simple pitch adjustment can ruin the pixel integrity if using a simple single axis or other traditional size adjustment technique. As will be understood from Figure 10, the image 1020 after adjustment is no longer pristine and the focus of the lenses of an array will likely yield a blurry image or an image that simply does not contain the targeted or desired visual effects (such as 3D in two directions or motion).
The adjustment involving enlargement using one axis or an automatic adjustment through the rip acts to mix the images viewable by a viewer in an inconsistent way.
[0072] For example, ray mixing to the viewer occurs when the images of the matrices described above are reproduced or adjusted using Adobe Photoshop or other automatic processes. This is because the pixels are no longer uniform in both axes. Therefore, the lenses of an array (e.g., circular or square-based lenses) focus on inconsistent numbers, and the rays mix to the viewers.
Instead of the viewer receiving all number "3's," the viewer may receive information under number "l's" and "4's" or the like at the same time. The viewing result or displayed image is of poor quality. The pixels' height and width are no longer the uniform exact height and width needed to achieve a good result as each pixel can vary in the printed image. The result is that the lenses focus on different images (rather than on the specific intended pixels), and the image is no longer pristine and, in many cases, is not even viewable.
[0073] Figures 11 and 12 illustrate two exemplary assemblies useful as anti-counterfeiting devices for currency or the like that are configured with a lens array and printed image to provide differing motion effects. Particularly, the sets 1100 and 1200 of diagrams in Figures 11 and 12 are useful for showing how the round, hexagon, parallelogram, or square-based lens arrays when combined with a printed image with the dual-axis interlacing/combination described herein can be effectively used to provide selected motion effects. Due in part to the complex interlacing process that provides pixel mapping, the assemblies shown in Figures 11 and 12 are particularly useful as anti-counterfeiting devices (which may be applied to currency, product labels, and other objects/items) as they are very difficult to reproduce.
[0074] In the diagrams 1100 of Figure 11, a plan or orthogonal view 1110 of a lens/image assembly according to the present description is shown. The viewer is able to observe or view an original image with rows of two differing icons with the icons all being stationary or non-moving. In diagram or view 1120, the assembly is tilted or angled to the right (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 1110 such as a matrix similar to that shown in Figure 7) is configured to cause the rows of different icons to move in opposite directions. For example, rows with padlock icons move to the right while company logos/icons move to the left. In contrast, in diagram or view 1122, the assembly is tilted or angled to the left (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames is configured to cause the rows of different icons again to move in opposite directions. For example, rows of padlock icons may move to the left while the company logos/icons concurrently move to the right.
In other words, the printed image is adapted to provide animation of the original image when the lens/printed image (or ink layer) is viewed from differing angles or points of view (e.g., the assembly or anti-counterfeiting device shown in view 1110 is pivoted about a first or vertical axis).
[0075] Significantly, the assembly of an array of lenses with an ink layer providing a dual-axis interlaced image provides animation or motion in more than one direction. In diagram or view 1124, the assembly is tilted or angled upward (e.g., through or to an angle of 15 to 45 degrees or the like by pivoting about a second or horizontal axis of the assembly), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 1110 such as a matrix similar to that shown in Figure 7) is configured to cause the rows of different icons to move in a single direction (e.g., all move upward). In contrast, in diagram or view 1126, the assembly is tilted or angled downward (e.g., through or to an angle of 15 to 45 degrees or the like about a horizontal axis of the assembly), and the interlacing of the matrix of frames is configured to cause the rows of different icons again to move in a single direction (e.g., all move downward). In other words, the printed image is adapted to provide animation of the original image when the lens/printed image (or ink layer) is viewed from differing angles or points of view (e.g., the assembly or anti-counterfeiting device shown in view 1110 is pivoted about a second or horizontal axis).
[0076] In the diagrams or views 1200 of Figure 12, a plan or orthogonal view 1210 of a lens/image assembly according to the present description is shown. The viewer is able to observe or view an original image with rows of two differing icons with the icons all being stationary or non-moving.
In diagram or view 1220, the assembly is tilted or angled to the right (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 1210 such as a matrix similar to that shown in Figure 7) is configured to cause the rows of different icons to move in a single direction (rather than in opposite directions as shown in 1120 of Figure 11). For example, rows with padlock icons and company logos/icons all move downward when the assembly (or anti-counterfeiting device) is tilted to the right. In contrast, in diagram or view 1222, the assembly is tilted or angled to the left (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames is configured to cause the rows of different icons again to move in a single direction such as upward.
In the embodiment shown in Figure 12, the printed image is adapted to provide animation of the original image when the lens/printed image (or ink layer) is viewed from differing angles or points of view (e.g., the assembly or anti-counterfeiting device shown in view 1210 is pivoted about a first or vertical axis). The animation as shown can be in a direction that is transverse relative to the pivoting directions.
[0075] Significantly, as discussed relative to Figure 11, the assembly of an array of lenses with an ink layer providing a dual-axis interlaced image provides animation or motion in more than one direction. In diagram or view 1224, the assembly is tilted or angled upward (e.g., through or to an angle of 15 to 45 degrees or the like by pivoting about a second or horizontal axis of the assembly), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 1210 such as a matrix similar to that shown in Figure 7) is configured to cause the rows of different icons to move in single direction but one that differs from that found during left or right tilting (e.g., all move or scroll to the right). In contrast, in diagram or view 1226, the assembly is tilted or angled downward (e.g., through or to an angle of 15 to 45 degrees or the like about a horizontal axis of the assembly), and the interlacing of the matrix of frames is configured to cause the rows of different icons again to move or scroll in a single direction (e.g., all move to the left). In other words, the printed image is adapted to provide animation of the original image when the lens/printed image (or ink layer) is viewed from differing angles or points of view (e.g., the assembly or anti-counterfeiting device shown in view 1210 is pivoted about a second or horizontal axis).
[0076] Figure 13 illustrates a set of images or views 1300 of another lens/printed image (ink layer) assembly as may be seen by a viewer in differing positions or with the assembly tilted or moved to change the viewing angle for the viewer. The assembly may take the form of an array of round, hexagonal, parallelogram, or square-based micro lenses overlying a dual-axis interlaced image (printed onto the back, planar surface of the lens array or on a substrate (e.g., paper currency, a plastic card, a paper or plastic label, or the like) upon which the lens array is later attached). The plastic card, a paper or plastic label, or the like) upon which the lens array is later attached). The interlaced image is printed using a print file that is generated as discussed above to combine a matrix of frames (e.g., sets of 2 to 4 or more frames of a single image/scene taken at differing POVs relative to the horizontal and vertical axes) to provide pixel mapping.
[0079] In Figure 13, image or view 1310 shows a straight-on or orthogonal view of the assembly or anti-counterfeiting device 1300, and the image is a company logo in this example. Image or view 1320 is visible to a viewer when the assembly is tilted up as shown with arrow 1321 (the planar assembly is rotated upward about a horizontal or first axis of the assembly).
As shown, view/image 1320 shows additional information relative to the original image seen in view 1310 such as the bottom side of the logo or object that has been the subject of the interlaced image file. Another image or view 1322 is visible by a viewer when the assembly is rotated or tilted to the right as shown with arrow 1323 (the planar assembly is rotated or tilted about a vertical axis (e.g., a second axis orthogonal or at least transverse to the first axis of the assembly)).
More information or imagery is visible in the view 1322 such as the left side of the logo or other object that was the subject of the interlaced image file.
[0080] Further, another view or image 1324 is viewed when the assembly is rotated or tilted 1325 downward (rotated about a horizontal or first axis), and, in this view 1324, information not seen in the other views is presented such as the top side of the logo or other imaged object. View or image 1326 provides more information or portions of the target object such as the right side of the logo/target object, and the view 1326 is visible when the assembly is rotated or tilted 1327 about a vertical or the second axis of the assembly.
[0081] Figure 14 illustrates a set of views/images 1400 of another embodiment or implementation of a lens/printed image assembly (or anti-counterfeiting device) 1410. As shown in view/displayed imagery 1412, the assembly 1410 (a micro lens array as described herein positioned over a dual-axis interlacing of a matrix of frames corresponding to differing images of a scene/object from differing points of view) is seen from a point of view that is normal or orthogonal to a front surface 1411 of the assembly 1410. In some embodiments, the front surface 1411 is provided by the outer surfaces of an array of round, hexagonal, parallelogram, or square-based lenses. As shown, the viewer can see a background that contains a static wallpaper pattern (of icons and padlocks). The icons/image components may appear very deep in the plane of the film and may be visible in each viewing angle (e.g., are visible in views 1414, 1416 when the assembly 1410 is tilted right or left). The overlay pattern is in the plane of the film but is not visible (or only slightly visible) when viewed straight on as shown in view 1412 (but can be seen in views 1414 and 1416).
[0082] View 1416 is useful for showing a display provided by the interlaced image of assembly 1410 when the assembly is tilted at a shallow angle (tilted or rotated slightly to the left about a vertical axis). When tilted at a shallow angle (e.g., up to about 15 degrees or the like), the overlay pattern is only visible in black on the area of the film or front surface 1411 of the assembly 1410 that is closest to the viewer. The printed image may be configured such that tilting slightly (e.g., less than about 15 degrees) in any side direction (up, down, left, or right or rotating of the assembly 1410 about either the vertical or horizontal axis) causes the overlay pattern to gradually become visible (appears black in this example). The pattern is an "overlay" that appears to be on the top of or covering over the icons or wallpaper pattern in the plane of the film (or outer surface 1411 of the assembly 1410).
[0083] At shallow angles, the overlay is first visible on the portion of the film or assembly 1410 closest to the viewer. When the assembly 1410 is tilted further away from the viewer (such as to angles of about 30 to 45 degrees or more), more and more of the overlay pattern gradually becomes visible until the entire overlay pattern is visible when the assembly 1410 is viewed via surface 1411 at a predefined more extreme angle (e.g., an angle of 45 to 60 degrees or more relative to the normal view 1412). This can be seen in extreme angle view 1414 of Figure 14 where the assembly 1410 is rotated about a vertical axis (e.g., to the right) more than about 60 degrees.
In view 1414, the overlay pattern is fully visible over the wallpaper pattern with the icons (logos and padlocks in this example) over the entire surface 1411 of the assembly/film 1410.
[0084] Figure 15 illustrates an assembly 1510 of another embodiment of the present description.
The assembly 1510 may be configured for use as an anti-counterfeiting device or label with a body/substrate, an ink layer providing a printed image with dual-axis interlacing of a matrix of differing POV frames as discussed herein, and an array of round, hexagonal, parallelogram, or square-based lenses for viewing the printed image. For example, the assembly 1510 may be a label (e.g., a 2-inch by 1 inch or other sized label) that may be printed down a web on 1.125-inch centers or the like during its manufacture. The assembly 1510 includes a front or upper surface 1512 (e.g., a thin lens array formed of transparent or at least translucent plastic or similar material) through which an interlaced image (image built using the pixel mapping taught herein) may be viewed as shown. The printed image may include a void or blank space as shown with white (or other-colored) box 1513, which may be used for printing (e.g., flcxo) barcodcs and/or human-readable text, which may be added offline or in later processing (e.g., via thermal transfer printing).
[0085] The assembly/label 1510 has a printed image that has been specifically designed to provide a number of images and effects to make it more difficult to reproduce and to allow a viewer to readily verify its authenticity. For example, the printed image presents a gray background 1516 (e.g., that may be subsurface printed (e.g., flexo)) upon which icons or symbols 1514, 1517 (colored and/or black) may be printed or layered. The symbol 1517 may take the form of a boundary (e.g. a circle) in which a second symbol or text is provided such as text (e.g., "OK") that should be completely inside the boundary to show the label 1510 is not a counterfeit or is authentic.
[0086] The printed interlaced image may also include devices/components for further allowing a viewer to check the authenticity of the label 1510. For example, a magnifying glass image 1520 may be incorporated into printing plates used to fabricate the assembly/label 1510 and appear on the plane of the film or surface 1512. One or more of the icons/symbols 1523, 1525 may be provided within the image 1520 such as under the glass of the magnifying glass of image 1520. Then, the printed image may be configured such that, when a viewer looks through the glass area of image 1520, the icons 1523 appear black and the icons 1525 appear blue, which may be a different color than these icons 1514, 1517 appear in the rest of the label 1510 (e.g., reverse the coloring of these icons when viewed under the glass image 1520). Further the icons 1523 and 1525 under the magnifying glass image 1520 may appear to be somewhat larger in size than the corresponding wallpaper/background versions of these icons 1514, 1517.
[0087] The wallpaper icons 1530 may be designed to move in opposite (or the same) directions when the assembly 1510 is tilted about a first axis (e.g., the assembly/label is rotated/tilted to the left or right) while moving in the same (or opposite) directions when the assembly 1510 is tilted about a second axis (e.g., the assembly/label is rotated/tilted upward or downward).
In contrast in some embodiments of the label 1510, the corresponding icons/symbols 1523, 1525 under the magnifying glass image 1520 may be designed to move differently than those icons 1530 that are not under the glass. For example, the icons 1523, 1525 may move together in a single direction under the glass image 1520 while the icons 1530 move, as shown with arrows 1531, in opposite directions when the assembly 1510 is rotated/tilted about a particular axis.
[0088] The printed image under the lens array of assembly 1510 may include a further element (e.g., a boxed/bordered display) 1540 to enhance security (or limit counterfeiting efforts further).
The element 1540 may include a border 1549, which may be formed of a pattern that is difficult to reproduce such as a 0.15-mm (or other size) microtext border containing one or more intentional misspellings (e.g., the border appears solid to the naked eye of a viewer but misspelled words are evident under a microscope). In the normal view as shown in Figure 15, a first image 1541 is displayed but, as shown in the exploded view, a second image 1542 is displayed in the element 1540 when the assembly 1510 is rotated 1543 about a first axis (e.g., rotated right or left about a vertical axis of assembly 1510). To further enhance security, a third image 1544 may be displayed in the element 1540 when the assembly 1510 is rotated 1545 in another direction (e.g., rotated up or down about a horizontal axis of assembly 1510).
[0089] Figure 16 illustrates a system 1600 adapted for use in fabricating an assembly such as an anti-counterfeiting device as described herein. The system 1600 includes an imaging workstation 1610 with a processor 1612 for executing code or software programs to perform particular functions. The workstation 1610 may take the form of nearly any computer device with the processor 1612 acting to manage operation of input and output devices 1614 such as devices for allowing an operator of the station 1610 to view and input data useful by the mapping and imaging module 1620 to create a print file 1648 communicated as shown at 1675 to a print controller 1680.
The CPU 1612 also manages memory 1630 accessible by the mapping and imaging module 1620.
[0090] The mapping and imaging module 1620 performs the functions useful in performing the functions and processes described herein such as for generating frame sets 1640 from an original image 1632, creating a frame matrix 1646 from these image sets 1640, and producing a bidirectional bit map or print file 1648 (i.e., print file using pixel mapping) from the frame matrix 1646. For example, the memory 1630 may be used to store an original image 1632 that may include a background 1634 as well as one or more icons/symbols 1636 that may be provided as wallpaper (e.g., these elements may be layered over the background 1634).
[0091] The module 1620 may act to generate a number of sets of frames 1640 from the original image 1632, and each of the sets 1640 may include 2 to 10 or more frames from differing points of view of the original image (e.g., see the sets of frames shown in Figure 7 that provide differing POV
frames along two axes (X and Y axis frames/images of a base or original image 1632)). The module 1620 may generate a frame matrix 1646 as discussed above to properly map the pixels to provide proper X and Y axis interlacing with or without a motion effect. From the matrix 1648, a bidirectional pixel map or print file 1648 is generated by combining the rows and columns of the matrix 1646 with proper sequencing (with all 3D and/or motion information in both directions such as with squares with the data from the matrix 1646 rather than stripes).
[0092] The mapping and imaging module 1620 may generate the print file 1648 based on a variety of imaging/mapping parameters 1650. For example, the lens array design information 1652 including whether the lenses are round, hexagonal, parallelogram, or square, the optical pitch 1654, and the LPI 1656 values may be taken as input by the module 1620 to create the print file 1648.
Further, the device output resolution 1670 may be used by the module 1620 to create the print file 1648 such as to set the number of frames in the sets 1640 or the like. The parameters 1650 may also include motion parameters 1660 to define how to animate the original image with tilting/rotating of an assembly such as by setting the direction of movement of the icons/symbols and how fast movement occurs (how much rotation needed to achieve a particular motion effect and so on). The parameters 1650 may also include color parameters 1666 such as whether or not icons/symbols change colors with rotation of an assembly with an image printed from file 1648 and what such colors should be in the displayed image.
[0093] Once a print file 1648 is created, the imaging workstation 1610 may communicate (in a wired or wireless manner such as over a digital communication network) this file 1648 to a print controller 1680 (e.g., another computer or computing device). The print controller 1682 may use this print file 1648 to fabricate a printing or embossing plate 1682, which can then be used to emboss a surface such as the planar/back side of a lens array with fabrication device 1684. This embossed surface can then be filled with one or more coatings/layers of ink to form a printed image in a lens array/printed image assembly (e.g., an anti-counterfeiting device).
The controller 1680 may also use the print file 1648 to provide a digital file 1670 to a color, digital printer 1674 for printing of the dual-axis interlaced image on a surface such as the planar back side of a lens array or on a side of a piece of paper currency or a product label over which a lens array is later applied to provide an anti-counterfeiting device on the currency/label.
[0094] At this point, it may be useful to describe techniques for performing pixel adjustment that may be performed (at least in part) by a software module/program such as the mapping and imaging module 1620 of Figure 16. Figure 17 illustrates with a flow diagram a pixel adjustment method 1700 according to the present description. The method 1700 includes at 1710 performing a print test (e.g., with components 1680 to 1684 of Figure 16) to determine the optical pitch, in the X axis and also in the Y axis, of a lens array, which as discussed above, may vary from design. At 1720, a target visual pitch is selected for a desired or input viewing distance (again, in the X and Y axes).
For example, as shown at 1730, the method 1700 may involve setting the target pitch at 416.88 for the X axis and 384.47 for the Y axis.
[0095] The method 1700 continues at 1740 with interlacing the X and Y axes in the pixel map.
This typically involves mapping at the nearest device output for the desired target pitch (e.g., 400 output is near to the pitches set at step 1730). In step 1750, the method 1700 includes calculating the difference between the device output and the target optical pitch. In this example, the difference in the X axis is +4.22 percent (i.e., Target Pitch of 416.88 divided by the device output of 400) and the difference in the Y axis is -3.9 percent (e.g., Target Pitch of 384.47 divided by the device output of 400).
[0096] At step 1760, the mapping and imaging module/software program acts to remove pixels based on the differences determined in step 1750. In this example, the module may remove 4.22 percent of the pixels by specifically targeting low information areas in the X
axis. The module may also act to add 3.9 percent pixels in the Y axis. Step 1770 of method 1700 further explains this process with the module acting to identify pixels with less information for removal (e.g., evenly in the X axis in this example) while the adding of pixels may be performed by blending pixels such as nearby (e.g., blending pixels are added in the Y axis). At 1780, plates are output based on the print file modified to provide pixel adjustment. In this working example, the plates for printing may be output at 4800 pixels in the X axis and 4800 pixels in the Y axis. At 1790, it is noted that the process 1700 retains integrity of the displayed image without blur, e.g., due to re-resolution pristine pixels.
[0097] Figure 18 is useful for further explaining the process of providing dual-axis interlacing for a lens array of the present description. A small lens array or lenslet 1810 is shown in a plan or top view that includes four lenses 1812, 1814, 1816, and 1818 (with a more typical array having many more lenses). As shown at 1815, the lenses 1812, 1814, 1816, and 1818 are round-based lenses in this non-limiting example. Underneath the lens array 1810, a dual-axis printed image (or ink layer with a printed image) can be provided with each of the boxes 1813 in the figure being used to represent a pixel. Further, each of these "pixels" 1813 can be considered to be a lens focus point.
[0098] The printed image provided in pixels 1813 when combined with lens array 1810 provides a display device that can be used to provide full 3D imagery as well as multi-directional motion. For example, each lens 1812, 1814, 1816, 1818 may be used to display a looping image. To this end, the diagonal sets of pixels 1830 shown with shading may be used to provide a 45 degree tilt loop sweep while the horizontal and vertical sets of pixels 1820 shown with "stars"
may be used to provide a side-to-side and up-and-down image loop.
[0099] With this in mind, graph 1850 is useful for illustrating how an arrangement of 7 pixels by 7 pixels provided under each lens 1812, 1814, 1816, and 1818 may be printed with dual-axis combined/interlaced images to provide these effects. In this example, four frames in the X axis are combined with four frames in the Y axis (e.g., "X=3" refers to a particular frame in the set of four frames along the X axis). A mapping and imaging module (such as module 1620) may be used to select the proper frames to generate such a matrix and/or print map, and a print file can be generated from this mapping for use in printing the dual-axis interlaced images in each pixel as shown in graph 1850 so as to provide the visual effects described with pixels 1820, 1830.
[00100] Figures 19-21 are plots 1900, 2000, and 2100 showing ray tracing for assemblies of the present description, e.g., for a lens array combined with a dual-axis interlaced image.
Particularly, Figure 19 illustrates a plot 1900 of a tracing of rays 1920 using an assembly 1910 (e.g., an anti-counterfeiting device) configured as described herein. As shown, the assembly 1910 includes a lens array 1912 of round-based lenses 1914 overlying an ink layer/printed image 1916 including a number of interlaces 1918 (7 images are interlaced using dual-axis interlacing).
[00101] The plot 1900 shows rays 1920 traced from idealized lenticular interlaced stripes 1918 in printed image/ink layer 1916. The order of the interlaces was modified so that to the viewer the image is properly interlaced. In this example, the radius of each lens 1914 was 1.23 mils, the lenses 1914 were provided at 408 LPI, the lenses 1914 were 3 mils thick, and the index of refraction was assumed to be 1.49. For clarity, only zero width interlaces were represented with 7 interlaces 1918 per sets of two lenses 1914. Tracings were made over a range of +30 degrees to -30 degrees with 5 degree steps showing the near lenticule region.
[00102] The plot 2000 is a filled-in ray trace showing a larger overall view of the plot 1900 of Figure 19. The interlaces for plot 2000 were taken to be 2 mils wide with 7 interlaces provided per set of two lenses. Five steps per interlace were traced, the range was +30 degrees to -30 degrees using 1 degree steps. The sequence of the interlaces was 6, 4, 2, 3, 7, 5, and 1. The plot 2100 is a trace done with a normal sequence of the interlaces (e.g., 1, 2, 3, 4, 5, 6, and 7) for a lens of radius 1.23 mils, lenses provided at 408 LPI, a lens thickness of 3 mils, and an index of refraction of 1.49.
The lens width was taken at 2 mils, and there were 7 interlaces provided for each set of two lenses.
Five steps were traced across each lens again with a range of +30 degrees to -30 degrees with 1 degree steps. In summary, the plots 1900, 2000, and 2100 show coding that is done by having multiple interlaces per multiple lenticules and the change in distribution to the viewer by changing the interlace sequence.
[00103] In analyzing use of the lens arrays of the present invention with dual-axis interlaced print images, it is useful to generate ray tracings and spot diagrams to check a planned array/image design. In this regard, Figure 22 is a plot 2200 of an off-axis ray tracing while Figure 23 is a corresponding spot diagram 2300 that may be generated to analyze a planned array/image design.
Further, Figures 24 and 25 are two additional spot plots or diagrams 2400 and 2500 for a round-based lens (or spherical lens), while Figure 26 is a plot 2600 of a ray tracing for the lens associated with the plots of Figures 24 and 25. The radius of the lens for these latter three figures was 5 units and the focal plane was about 10 units (e.g., the units may be any unit such as mils).

[00104] Although the invention has been described and illustrated with a certain degree of particularity, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the combination and arrangement of parts can be resorted to by those skilled in the art without departing from the spirit and scope of the invention, as hereinafter claimed.
[00105] The description teaches a display assembly (e.g., an anti-counterfeiting device) that includes an array of round or square lenses combined with an ink layer with a printed image/pattern.
The lens arrays are made up of nested round, hexagonal, parallelogram, or square lenses arranged as shown in the attached figures. The printed image/pattern provided in the ink layer (or layers) are aligned with the lens arrays (e.g., with the X and Y axes of the printed image), and the printed image/pattern is made up of vertically and horizontally mapped pixels (e.g., printed using a print file defining dual-axis interlacing (or interlacing in two axis) of frames of a matrix as discussed herein).
The pixels may be of any type and often are adapted to match the output device with the viewer's optical pitch in two axes. The lens arrays may be provided at 200 or more LPI
in both directions so as to provide 4000 lenses or more per square inch. The focal lengths of the lenses may vary, but some arrays have been implemented that have focal lengths of less than about 10/1000 inches for round and for square-based lenses.
[00106] The printing of the dual-axis interlaced image for use with a lens array may be performed using one or more colors using the pixel mapping provided in a generated print file. In some cases, diffractive techniques are used to create color with the separation of wave lengths, purposefully or accidentally, within the interlaced image in a round-based lens array. Particularly, the printing step involves printing of an X and Y pixel-imaged file or pixel map so as to produce a printing plate or a digital image, either of which may be used to provide an ink layer with a printed image/pattern that is useful in combination with the round and square-based lenses as nested in an array as described herein (e.g., printing on the back or planar surface of the lens material to provide the X and Y axis pixel mapped images). In other cases, an embossing plate is produced for use to emboss the back of the lens material (lens array). Then, the embossed back surface is filled with ink or metalized for use in holography in combination with a round or square-based lens array. In some cases, though, printing may also occur on the front or contoured surface of the lens array. For example, the printing may involve printing features, colors, or images directly on top of the lenses (i.e., the non-planar side of the lens array) in combination with printing on the back or planar side of the lenses using interlaced images.
[00107] A number of unique visual or display effects can be achieved with the printed image viewed through one of the lens arrays of the present description. For example, image mapping of the X and Y axes may be performed so that a wallpapered array of repeating icons (e.g., the company logos and padlocks of the exemplary figures) scroll or move across the substrate in opposite directions to each other when the substrate (or assembly or anti-counterfeiting device) is tilted left and right (rotated about a vertical or first axis) and in the same direction when the substrate is tilted up and down (rotated about a horizontal or second axis transverse to the first axis).
This effect may be called "Continuum Movement in Opposite Directions."
[00108] In other cases, the image mapping is performed so that a wallpapered array of repeating icons moves or scrolls up and down across the surface of the assembly/anti-counterfeiting device when the assembly/device is tilted left and right (icons all move in the same direction) and left and right when the assembly/device is tilted up and down (again, all icons move in the same direction) (e.g., tilt left causes all icons to scroll or move upward, tilt right causes all icons to scroll move down, tilt up causes all icons to scroll right, and tilt down causes all icons to scroll left). This effect may be labeled "Continuum Movement in Orthogonal Directions."
[00109] Image mapping of the X axis and Y axis pixels may be performed such that a volumetric icon or image like a company logo or a symbol has five viewable sides (e.g., a top side, a bottom side, a left side, a right side, and a face or front side). These five sides are viewable in three dimensions, with apparent depth and in full parallax, when the assembly/device is tilted or rotated in differing directs (orthogonal/normal view, tilt left, tilt right, tilt upward, and tilt downward or a positioning therebetween). The face of the 3D logo/symbol/icon may be a different color than the sides to create a more noticeable 3D effect, and this effect may be called "full volume 3D."
[00110] Another effect that can be achieved via the image mapping of the X
axis and the Y
axis described herein is to provide wallpaper with icons with another overlay pattern. Then, the overlay pattern may be provided in the print file and resulting printed image so that it is hidden from view when the assembly is viewed from certain POVs (such as a normal POV) but gradually becomes more and more visible (in the plane of the film and wallpaper pattern) on top of the icons/symbols/logos of the wallpaper (such as when moved to angles of 30 to 60 degrees or the like from normal). Further, it is not required that the entire printed image provide a single effect.
Instead, different zones or portions of the printed image may be used to provide differing visual effects (e.g., any of the effects described herein).
[00111]
Several means are available to implement the systems and methods discussed in this specification. These means include, but are not limited to, digital computer systems, microprocessors, application-specific integrated circuits (ASTC), general purpose computers, programmable controllers and field programmable gate arrays (FPGAs), all of which may be generically referred to herein as "processors." For example, in one embodiment, signal processing may be incorporated by an FPGA or an ASIC, or alternatively by an embedded or discrete processor. Therefore, other embodiments include program instructions resident on computer readable media which when implemented by such means enable them to implement various embodiments. Computer readable media include any form of a non-transient physical computer memory device. Examples of such a physical computer memory device include, but are not limited to, punch cards, magnetic disks or tapes, optical data storage systems, flash read only memory (ROM), non-volatile ROM, programmable ROM (PROM), erasable-programmable ROM (E-PROM), random access memory (RAM), or any other form of permanent, semi-permanent, or temporary memory storage system or device. Program instructions include, but are not limited to, computer-executable instructions executed by computer system processors and hardware description languages such as Very High Speed Integrated Circuit (VHSIC) Hardware Description Language (VHDL).
[00112] While Figures 11-15 illustrate a number of the effects that can be achieved using the pixel mapping techniques described herein in combination with arrays of micro lenses, it may be useful at this time to discuss these unique effects in more detail. Pixel mapping (or dual-axis interlacing) allows one to generate a print file with a plurality of pixels each generated with the specific purpose of allowing activation of an effect about one of two axes. In other words, activation in 2 axes requires or is at least enhanced by pixel mapping as taught herein. The "effects"
that can be achieved (including those shown in Figures 11-15) may be thought of as the same set of effects achieved in a single axis using lenticular lenses and interlacing of images in a single direction. These effects, however, can now be provided one (or two, three, or more) at a time in each direction using pixel mapping, and the anti-counterfeiting devices may use any combination of these effects (with one provided in each direction in many cases). The effects include 3D, motion, flip (change an image into another or modified image), animation, on/off (make an image appear and disappear with rotation about an axis or with "activation"), zoom, morph (like a flip but can view the transition to the new image), and color shift (change color as part of the activation).
[00113] As a first example, a lens array and printed image assembly may be designed and fabricated to provide 3D in one axis (such as in the X axis) and to provide an effect activation in the a second axis transverse (such as orthogonal) to the first axis (such as by providing activation in the Y axis). The 3D may be provided in a first axis of the assembly with patterns or elements in different layers (such as by having a foreground image over one or more background images).
Then, activation of additional effects may be provided in the second axis such as: (a) motion (e.g., elements moving or with displacement in the frame; (b) flip (e.g., an image "A" changing to image "B" for 2-image flip or more than two images may be used to provide more flipping); (c) animation (e.g., a sequence of frames may be used to describe or define animation of images); (d) on/off (e.g., single or multiple elements may be provided in the frames that appear or disappear depending on the viewing angle; (e) zoom (e.g., single or Multiple element enlarging or reducing of size of a displayed image may be provided that depends upon the viewing angle); (f) morph (e.g., effect can be like a flip from image "A" to image "B" but with transition frames included in between final images so that it is possible for viewer to see the transformation from image "A" to image "B"); and (g) color shift (e.g., single or multiple elements can change color with activation that may be triggered by rotation of assembly through multiple viewing angles or POVs).
[00114] With these combinations in mind, Figure 27 illustrates a set of views 2700 of an exemplary assembly viewed from differing POVs, with the assembly being useful as an anti-counterfeiting device for currency or other objects that are configured with a lens array and printed image to provide differing motion effects (dual-axis activation). In the diagrams or views 2700 of Figure 27, a plan or orthogonal view 2710 of a lens/image assembly according to the present description is shown. The viewer is able to observe or view an original image with rows of two differing icons 2712 with the icons 2712 all being stationary or non-moving.
Further, the original image includes an overlay image or foreground image 2714A (shown here as a checkmark) that appears to be in a different layer than the rows of icons 2712. Hence, the assembly is adapted to provide a 3D effect. In the figures, rows of two icons are shown, but it will be understood that this was done for ease of explanation only and not as a limitation. With rows of two icons understood and how they may be used to provide security with activation in two axes, it will be understood that each row may include two or more differing icons (rather than a single icon per row) and rows of a third, fourth, or more differing icon may be included in the assembly as desired to achieve a desired displayed image.
[00115] In diagram or view 2720, the assembly is tilted or angled to the right (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 2710 such as a matrix similar to that shown in Figure 7 is used in pixel mapping) is configured to cause the rows of different icons 2712 to move in opposite directions. For example, rows with padlock icons and/or logos 2712 move left and right when the assembly (or anti-counterfeiting device) is tilted to the right. In contrast, in diagram or view 2722, the assembly is tilted or angled to the left (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames is configured to cause the rows of different icons again to move in differing directions from each other and in the opposite direction as in view 2720 (icons 2712 that moved to the right now move to the left and vice versa).
[00116] In the embodiment shown in Figure 27, the printed image is adapted to provide animation of the original image when the lens/printed image (or ink layer) is viewed from differing angles or points of view (e.g., the assembly or anti-counterfeiting device shown in view 2710 is pivoted about a first or vertical axis). The animation as shown can be in a direction that is parallel to the pivoting directions. However, the print file is configured such that some images such as foreground or other layer image 2714A, remains in the same relative location, and this movement of background or other layer icons (as these moving icons 2712 could be foreground images and symbol/icon 2714A could be provided in the background layer) enhances or even provides the 3D
effect of the assembly.

[00117] Further, the 3D effect can be combined with additional effects when the assembly is activated in another or the second of two orthogonal axes. As shown, the assembly of an array of lenses with an ink layer presenting a dual-axis interlaced image provides animation and a 3D effect in one direction or when activated along one axis and flipping (or morphing) in a second direction or when activated along a second axis. In diagram or view 2724, the assembly is tilted or angled upward (e.g., through or to an angle of 15 to 45 degrees or the like by pivoting about a second or horizontal axis of the assembly), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 2710 such as a matrix similar to that shown in Figure 7) is configured to cause the icons 2712 to stay the same or remain unchanged while the symbollicon 2714A in the other layer (foreground image) flips (or morphs) to a different image 2714B (here, a check mark flips into a star).
[00118] Similarly, in diagram or view 2726, the assembly is tilted or angled downward (e.g., through or to an angle of 15 to 45 degrees or the like about a horizontal axis of the assembly), and the interlacing of the matrix of frames is configured to cause the rows of icons 2712 to remain stationary while the foreground or other layer symbeicon 2714A flips (or morphs) into a different image 2714B (here the same image as when the assembly is tilted upward). In other words, the printed image is adapted to provide flipping of an image when the assembly is rotated about a second axis (such as about the horizontal or X-axis). Flipping is shown in Figure 27 for the effect provided when activated in the second direction but the effect may also be morphing, on/off, motion, animation, zoom, or color shift.
[00119] To further illustrate the many possible combinations, Figure 28 illustrates a set of views 2800 of an exemplary assembly viewed from differing POVs, with the assembly being useful as an anti-counterfeiting device for currency or other objects that are configured with a lens array and printed image to provide differing motion effects (dual-axis activation).
In the diagrams or views 2800 of Figure 28, a plan or orthogonal view 2810 of a lens/image assembly according to the present description is shown, and the assembly is configured to provide 3D
from all viewpoints (e.g., floating and/or depth) along with the same or different image elements having a Y-axis or X-axis activation (to have motion, to flip, to morph, or another of the effects achievable with interlacing of image frames). The viewer is able to observe or view an original image with rows of two differing icons 2812 with the icons 2812 all being stationary or non-moving. Further, the original image includes first and second overlay images or foreground images 2814A and 2816A
(shown here as the word "OK" and a check-nark symbol) that appear to be in a different layer than the rows of icons 2812. Hence, the assembly is adapted to provide a 3D effect.
[00120] In diagram or view 2820, the assembly is tilted or angled up (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 2810 such as a matrix similar to that shown in Figure 7 is used in pixel mapping) is configured to cause the rows of different icons 2812 to move in a single direction (e.g., all icons move downward or opposite the activation direction).
With this movement of the assembly (tilt up), the foreground images 2814A and 2816A remain unchanged (e.g., no flip at this point). The movement of the icons 2812 underneath (or over the top in some embodiments) the symbols 2814A, 2816A heightens the 3D effect achieved with the assembly.
[00121] In contrast, in diagram or view 2822, the assembly is tilted or angled downward (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames is configured to cause the rows of different icons again to move in a single direction (but this time upward or opposite the activation direction). Concurrently, though, a flip effect is also activated with the foreground symbol/icon 2814A flipping to an image as shown at 2814B
(e.g., from the word "OK" to the word "Yes"), while the other symbol/icon 2816A remains unchanged in this example. From the view 2822 to the view 2820, flipping will again occur as the symbol 2814B will change back or flip back to image 2814A (e.g., flipping effect is activated with rotation about the horizontal or X-axis of the assembly concurrently with the movement effect for icons 2812 (in a single direction in this non-limiting example)).
[00122] Further, the 3D effect can be combined with additional flip effects when the assembly is activated in another or the second of two orthogonal axes. As shown, the assembly of an array of lenses with an ink layer presenting a dual-axis interlaced image provides animation and a 3D effect in one direction or when activated along one axis and flipping (or morphing) in a second direction or when activated along a second axis. In diagram or view 2824, the assembly is tilted or angled to the left (e.g., through or to an angle of 15 to 45 degrees or the like by pivoting about a second or horizontal axis of the assembly), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 2810 such as a matrix similar to that shown in Figure 7) is configured to cause the icons 2812 to be placed in motion with the icons 2812 moving in the same direction (again opposite the activation direction and this is orthogonal to the earlier movement directions of views 2820 and 2822). Concurrently, the symbol/icon 2814A (or 2814B) in the other layer (foreground image) remains unchanged while the symbol/icon 2816A does not flip but is activated to have a morph effect in that it changes as shown at 2816B
to be spun to a new position (e.g., the checkmark in this example has a new orientation, which may also be considered an animation effect).
[00123] Similarly, in diagram or view 2826, the assembly is tilted or angled to the right (e.g., through or to an angle of 15 to 45 degrees or the like about a horizontal axis of the assembly), and the interlacing of the matrix of frames is configured to cause the rows of icons 2812 to again have a motion effect (move in single direction such as opposite the activation direction) while the foreground or other layer symbol/icon 2816A again is morphed (or animated) to spin into image 2816B. In other words, the printed image is adapted to provide 3D with foreground images that can be flipped, morphed, or animated with activation and such activation effects can be independent from each other and from the background images. Further, the printed image provides concurrent motion effects with background images, which are shown to be activated to move together in a single direction that is opposite the activation direction. With the icons 2812 moving in the directions shown, the result is a depth effect (e.g., 3D) where the icons 2812 appear to be pushed back from the foreground symbols/icons 2814A-2816B. This effect can also be combined with some layers being pushed toward the front or outward toward the viewer.
[00124] To still further illustrate the many possible combinations, Figure 29 illustrates a set of views 2900 of an exemplary assembly viewed from differing POVs, with the assembly being useful as an anti-counterfeiting device for currency or other objects that are configured with a lens array and printed image to provide differing motion effects (dual-axis activation).
In the diagrams or views 2900 of Figure 29, a plan or orthogonal view 2910 of a lens/image assembly according to the present description is shown, and the assembly is configured to provide activation in a first axis (such as the X-axis) that achieves orthogonal movement of the image elements combined with activation in a second axis (such as the Y-axis) of the same or different image elements. The viewer is able to observe or view an original image with rows of two differing icons 2912 with the icons 2912 all being stationary or non-moving. Further, the original image includes first and second overlay images or foreground images 2914A and 2916A (shown here as the word "OK" and a checkmark symbol) that appear to be in a different layer than the rows of icons 2912. Hence, the assembly is adapted to provide a 3D effect.
[00125] In diagram or view 2920, the assembly is tilted or angled to the right (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 2910 such as a matrix similar to that shown in Figure 7 is used in pixel mapping) is configured to cause the rows of different icons 2912 to move in a single direction (e.g., all icons move downward or orthogonal to the activation direction). With this movement of the assembly (tilt right), the foreground images 2914A and 2916A remain unchanged (e.g., no flip at this point). The movement of the icons 2912 underneath (or over the top in some embodiments) the symbols 2914A, 2916A heightens the 3D effect achieved with the assembly.
[00126] In contrast, in diagram or view 2922, the assembly is tilted or angled to the left (e.g., through or to an angle of 15 to 45 degrees or the like), and the interlacing of the matrix of frames is configured to cause the rows of different icons again to move in a single direction (but this time upward (which is opposite the movement shown in view 2920) and orthogonal to the activation direction). Concurrently, though, a flip effect is also activated with the foreground symbol/icon 2914A flipping to an image as shown at 2914B (e.g., from the word "OK" to the word "Yes"), while the other symbol/icon 2916A remains unchanged in this example. From the view 2922 to the view 2920, flipping will again occur as the symbol 2914B will change back or flip back to image 2914A (e.g., flipping effect is activated with rotation about the vertical or Y-axis of the assembly concurrently with the movement effect for icons 2912 (in a single direction in this non-limiting example)).
[00127] Further, the 3D effect can be combined with additional flip effects when the assembly is activated in another or the second of two orthogonal axes. As shown, the assembly of an array of lenses with an ink layer presenting a dual-axis interlaced image provides animation and a 3D effect in one direction or when activated along one axis and flipping (or morphing) in a second direction or when activated along a second axis. In diagram or view 2924, the assembly is tilted or angled upward (e.g., through or to an angle of 15 to 45 degrees or the like by pivoting about a second or horizontal axis of the assembly), and the interlacing of the matrix of frames (a set of different points of view (POVs) of the original image shown in view 2910 such as a matrix similar to that shown in Figure 7) is configured to cause the icons 2912 to be placed in motion with the icons 2912 moving in the same direction (again orthogonal to the activation direction which may be to the right as shown in this example) . Concurrently, the symbol/icon 2914A (or 2914B) in the other layer (foreground image) remains unchanged while the symbol/icon 2916A does not flip but is activated to have a morph effect in that it changes as shown at 2916B to be spun to a new position (e.g., the checkmark in this example has a new orientation, which may also be considered an animation effect).
[00128] Similarly, in diagram or view 2926, the assembly is tilted or angled downward (e.g., through or to an angle of 15 to 45 degrees or the like about a horizontal axis of the assembly), and the interlacing of the matrix of frames is configured to cause the rows of icons 2912 to again have a motion effect (move in single direction such as to the left and so as to move orthogonal to the activation direction (or the vertical or Y-axis of the assembly) while the foreground or other layer symbol/icon 2916A again is morphed (or animated) to spin into image 2916B.
[00129] Figure 30 illustrates another assembly 3010 useful as an anti-counterfeiting device that may be used on or with currency or the like. The assembly 3010 may be formed with a top or outer surface 3102, which may be provided with a lens array. The assembly 3010 may also include an ink layer(s) providing a printed image printed using a print file with pixel mapping as described herein to provide dual-axis activation (or activation of image effects such as 3D, motion, or the like) in two axes. Particularly, the printed image of assembly 3010 is adapted to allow viewing of a background image made up of a plurality of smaller symbols/icons 3014 (such as the checkmarks shown in Figure 30). The printed image of assembly 3010 also is adapted to allow viewing (through lens array/front surface layer 3012) a foreground image made up of one or more symbols/icons (which are typically larger than the background image elements 3014).

[00130] In some implementations of the assembly 3010, the printed image is pixel mapped to the lens array in a manner that full 3D is provided in all directions by providing the image elements 3014 and 3018 in 2 or more layers. As shown in Figure 30, the background image or pattern provided by symbols/icons 3014 is pushed back away from a viewer to appear to be behind the foreground image made up of symbols/icons 3018. The elements 3018 may be provided as larger elements, and they may be caused to appear to float in different levels relative to image elements 3014 from all view points. This may be achieved in part by causing the images 3018 to remain stationary during dual-axis activation (rotating of the assembly 3010 about the X and Y-axes) while the background images 3018 are caused to move (apply a motion effect to the image elements 3014).
[00131] Other assemblies may be created that include a print image formed using pixel mapping chosen to provide patterns or images that are activated in a first axis (e.g., the X-axis) with any of the effects listed or described herein. Further, the print image may be configured to provide a combination of the same image elements (e.g., an icon or symbol) or different image elements being activated in a second axis (e.g., the Y-axis) with any one of the effects listed or described (the same or differing effects). For example, the effects may include, but are not limited to: (a) a 3D layered effect (e.g., image elements displayed so as to appear in different layers with each layer being a flat image); (b) a 3D real effect (e.g., provide a picture or 3D element generated by 3D software or the like); (c) a motion effect (e.g., image elements that are moving or with displacement in the frame);
(d) a flip effect (e.g., an image "A" changing to an image "B" for 2-image flip or more than two images may be used in a flip effect); (e) animation (e.g., sequence of frames that describes or defines animation for one or more image elements); (f) an on/off effect (e.g., single or multiple image elements may be caused to appear or disappear depending on the viewing angle for the assembly); and (g) a zoom effect (e.g., single or multiple image elements may be enlarged or reduced in size depending on the viewing angle of the printed image through the array of round, hexagonal, parallelogram, or square-based micro lenses).
[00132] Figures 3A-4B provide examples of items formed using round-based and square-based lenses to form lens arrays. Further, these lens arrays were specifically patterned or arranged to not use offset or nested rows and columns of lenses (e.g., the lenses in adjacent rows and columns were aligned rather than offset). The use of pixel mapping as taught herein by the inventors has allowed anti-counterfeiting devices with lens array/printed image assemblies to be fabricated effectively with the use of lens arrays with offset/nested lenses and also with lens arrays that are configured to include hexagon lenses or hexagonal-based lenses. Hence, Figures 31 and 32 provide specific working examples of such implementations.
[00133] In an embodiment shown in Figure 31, an item 3100 (such as a piece of paper currency, a label for a product, or the like) is provided with an anti-counterfeiting element or device in the form of a lens array (array of hexagonal-based lenses) 3110 covering or provided on top of a layer of ink 3120 providing a printed image. As shown, the item 3100 includes a substrate or body 3105 such as a sheet of paper or plastic (e.g., paper to be used as currency or paper/plastic to be used for a product label). On a surface of the substrate/body 3105, an image is printed via a layer of ink 3120, and a lens array 3110 is provided on an exposed surface of the ink layer 3120 (e.g., the ink layer 3120 and its pattern/image may be printed onto the substrate surface or onto the back surface of the lens array 3110).
[00134] As shown, the lens array 3110 is made up of a plurality of lenses 3114 that each have a hexagonal base abutting the surface of the ink layer 3120 and have a dome-shaped cross section and/or one two or more facets/sides. The hexagonal-based lenses or round lenses 3114 are arranged in a number of columns 3112 that are parallel as shown by parallel vertical or Y-axes 3113 (axes passing through the center of the lenses 3114 in columns 3112) in Figure 31.
Further, the lenses 3114 are arranged such that pairs of lenses 3114 in adjacent ones of the columns 3112 are in contact or proximate at least at the bases. Still further, the columns 3112 are vertically offset such that pairs of adjacent lenses 3114 in a particular column 3112 are spaced apart. Then, the array 3110 is configured to have parallel rows of lenses 3114, each abutting their neighboring lenses in such rows (or nearly contacting each other at the bases), as can be seen by parallel horizontal or X-axes 3115 passing through centers of lenses 3114 in the array 3110, and the rows are shown to be abutting each other and to also be offset (e.g., to have a horizontal offset as well as vertical offset). In this way, the lenses 3114 may be tightly nested in the pattern shown in Figure 31 (note, the array 3110 may be rotated for use such as rotation of 90 degrees such that the "columns"
become "rows" and vice versa).

[00135] In an embodiment shown in Figure 32, an item 3200 (such as a piece of paper currency, a label for a product, or the like) is provided with an anti-counterfeiting element or device in the form of a lens array (array of round-based lenses) 3210 covering or provided on top of a layer of ink 3220 providing a printed image. As shown, the item 3200 includes a substrate or body 3205 such as a sheet of paper or plastic (e.g., paper to be used as currency or paper/plastic to be used for a product label). On a surface of the substrate/body 3205, an image is printed via a layer of ink 3220, and a lens array 3110 is provided on an exposed surface of the ink layer 3220 (e.g., the ink layer 3220 and its pattern/image may be printed onto the substrate surface or onto the back surface of the lens array 3210).
[00136] As shown, the lens array 3210 is made up of a plurality of lenses 3214 that each has a round or circular base abutting the surface of the ink layer 3220 and have a dome-shaped cross section and/or one two or more facets/sides. The round lenses 3214 are arranged in a number of columns 3212 that are parallel as shown by parallel vertical or Y-axes 3213 (axes passing through the center of the lenses 3214 in columns 3212) in Figure 32. Further, the lenses 3214 are arranged such that pairs of lenses 3214 in adjacent ones of the columns 3212 are in contact or proximate at least at the bases. Still further, the columns 3212 are vertically offset such that pairs of adjacent lenses 3214 in a particular column 3212 are spaced apart. Then, the array 3210 is configured to have parallel rows of lenses 3214, each abutting their neighboring lenses in such rows (or nearly contacting each other at the bases), as can be seen by parallel horizontal or X-axes 3215 passing through centers of lenses 3214 in the array 3210, and the rows are shown to be abutting each other and to also be offset (e.g., to have a horizontal offset as well as vertical offset). In this way, the lenses 3214 may be tightly nested in the pattern shown in Figure 32 (note, the array 3210 may be rotated for use such as rotation of 90 degrees such that the "columns" become "rows" and vice versa).
[00137] As discussed in the initial portion of this document, moire patterns have been used in conjunction with round and hexagonal lens arrays for many years. Typically the printed images are small fine images relative to the size of the lenses. Some of the images are printed in a frequency slightly more frequent or less than the one to one dimension of the lenses in two axes and some are printed slightly differently relative to each other. The result is a moire pattern that shows the illusion of depth of field with the lenses to the viewer or shows motion of the items to the viewer.
Typically, these lens arrays combined with printing of an image are used in the anti-counterfeiting market for labels and currency. The thickness of the lenses is under 5/1000-inch and down to about .5/1000-inch (i.e., 125 microns to about 12 microns). The frequency of these lenses is about 400 X
400 to over 1000 X 1000 per inch.
[00138] While useful to a point, the effects one can achieve with moire patterns are limited.
For example, one cannot take a photograph and display 3D with a moire pattern.
Typically, the moire patterns are used in the security industry in very fine lenses with focal lengths of about 20 to 75 microns and frequencies of over 500 lenses per inch in one axis (or more than 250,000 per square inch). The printed images underlying the lenses are typically at least 12,000 DPI and may go to over 25,000 DPI, with the micro-lens arrays being closely nested (e.g., as shown in Figures 1 and 2). In other cases, these lenses can be quite course at 30 lenses in a linear inch with focal lengths of more than 0.125 inches or even 0.25 inches and only about 900 lenses per square inch.
[00139] One significant problem with the use of moire images is that they can be relatively easily reverse engineered. It is easy to see the patterns underlying the lens with a cheap microscope and determine the frequency of the images and patterns. In addition, the lenses can be cast and re-molded making counterfeiting possible. The relative difficulty in reverse engineering comes in printing the images, but this is also getting easier to achieve due to high-resolution lasers and setters.
[00140] Typically, the micro-lenses are printed using an emboss-and-fill technology. This generally limits the printing to one color due to the fact that the process tends to be self-contaminating after one color, as well as the fact that the process is difficult to control from a relative color-to-color pitch in the emboss and fill printing process. Some have implemented a motion technology that uses emboss-and-fill, high-resolution printing that is one color due to the fact the web or sheet is pre-embossed, flood coated with an ink and wiped clean (absent the embossed areas) and a blade leaves ink residue and contaminants making additional colors challenging. Another problem relative to the general web stretch and movement is that the small optical pitch differences needed for magnifying moires are difficult to achieve due to differences in run tensions between colors.

[00141] Hence, the inventors determined that there was a need for anti counterfeiting devices that are much more difficult, if not impossible to duplicate. Preferably, it was determined that these devices should also be designed to have the "wow" factor for overt display of images floating above the focal plane and below the focal plane.
[00142] Printed lens arrays can be difficult to print in either sheet or web form (especially web form) in offset, gravure, flexo or any other method. Some of the problems lie with the devices that make plates or "plate-setters" as well as the physical ability to print a very small dot or image. This fact when combined with the registration inaccuracies in equipment, film stretch, and other variables make it impossible or difficult to print very high resolution images needed in micro-lens arrays in 4-color process or with any real accuracy. These facts limit what can be done in printed micro lenses.
[00143] General print accuracies limitations found in press manuals can be found as follows (color to color registration): (1) Best Sheetfed Press (Heidelberg or Komori)-8 microns; (2) Best Currency Press (Sheet only-KBA Notsys)-4 to 6 microns; (3) Best Web (Gravure or Flexo)-150 plus microns; and (4) Best Central Impression Web -50 microns. Further, physics dictates that the thinner the substrate or lens array used (needed for security and anti counterfeiting) the finer or smaller the lens array is for the target thickness and focal length relationship. The basic formula is the following: (A) Chord Width=C; (B) Radius of Lens= R; (C) Focal Length=F
(or lens thickness);
and (D) LPI= Lens frequency or number of lenses in a lineal inch. Then, basic lens physics indicates: R>.5(C). Further, F=1.5(C) (as an approximation).
[00144] For example, a currency thread can be printed in multiple colors in patterns and plain colors at about 25 microns. The minimum realistic LPI in both directions to make this possible is about 1200 LPI, which requires a minimum of 5 pixels for decent 3D or animation. Therefore, 5 X
1200 = 6000 DPI in both directions. However, much better quality dictates 10 images and about 12,000 DPI. Non-registering patterns and so forth can be printed showing motion and 3D in multiple colors. However, the registration requirements for printing color to color, 4¨color process, or registering colors together at this level is impossible or at least extremely difficult with past technology. The lens width or chord width (C) in this case is about 21 microns. Since one pixel is needed for each frame and 5 frames are needed for each lens, the print requirement for even a single color is difficult. Looking at the discussion above, the best web presses register color to color at about 50 microns. The registration requirement for 4-color process or other tight multiple color processes with a chord width of about 21 microns (5 frames, each at 4.2 microns) is about 2-3 microns. Unfortunately, this has proven difficult to impossible to achieve with current technology.
[00145] Producing non-holographic imagery (printed imagery) in registration in even one axis is impossible with current technology with more than one color. Obviously, photographs in motion or 3D are impossible under lens arrays regardless of the print technology. The practical limitation with today's technology in web is really non-existent (the thickness of the material would necessarily be over 15/1000" and about 100 LPI to possibly register color to color, and would not practically wind in a web). Therefore, printed and registered color would be limited to sheet fed offset technology (not practical for banknotes or labels for security).
[00146] A novel way to address this problem is needed for the technology to advance beyond traditional printing. In the microwave part of the spectrum, where there are few losses, patterned and perforated metal films or films coated with metal on the sub-wavelength scale achieve spectral selectivity by balancing the transmission and reflective characteristics of the surface. For optical frequencies, where joule losses are important, the planned structure of a metal film (without perforation) or a violation of continuity is sufficient to provide or achieve substantial modification of reflectivity. By engineering the geometry of the structure imposed or embossed onto the surface, one can dramatically change the "perceived" color of the metal without the use of chemicals, thin-film coating, or diffraction effects.
[00147] This novel selective frequency effect underlies plasmonic joule losses in continuous elements of the patterns ("intaglio" and "bas relief') in the metamaterials to distinguish both the raised and indented portions of the structures, and it is specific to the optical part of the spectrum.
Such a technology has the advantage of maintaining the integrity of the metal structures on the surfaces and is scalable for high production techniques and fabrication.
[00148] The highest possible resolution for printed color images is determined by the diffraction limit of visible light. To hit the "limit," individual color elements, which are or may be considered "pixels," with a pitch of 250 nm (e.g., a pitch of less than 10,000 nanometers (or 10 microns) such as in the range of 200 to 300 nanometers or less than about 300 nm) are required or desired for making the effective print resolution (often given as dots per inch (DPI)) at about 100,000 DPI (or a range of 10,000 to 125,000 DPI or at least about 10,000 DPI
in some cases while others may use at least 75,000 DPI). Color information can be encoded in the dimensional parameters of the metal nano structures so that tuning their plasmonic resonance determines the color of the individual pixels. This type of color mapping produces images with sharp color differences as well as fine tonal variations. The method can be used for large volume color printing without ink via nanoimprint lithography.
[00149] This technology can be used to reproduce the entire spectrum of visible colors from distinct colors to RGB blends and CMYK process colors for the reproduction of photographs or other images. It is important to note that, unlike diffraction imagery, the resulting colors from the manipulation of the balance of reflected and transmitted waves are largely insensitive to viewing angle. Therefore, since combining these nanostructures tuned to produce color pixels simulating up to 100,000 DPI with lens arrays as described herein using both moire and interlaced images results in incoming light (due to the lens focus) of different entry angles, the resulting color back to the viewer is not distorted or changed as it is with diffraction patterns.
Interlaced images with lenses that focus on individual pixels or groups of pixels remain as designed when presented or reflected back to the viewer and color remains unchanged. The resulting color is largely unaffected due to the incoming angle.
[00150] For the above reasons, combining lens arrays as described herein with this "plasmonic resonance" technology makes the ideal, or at least a very useful, combination for thin film 4-color processes and for providing combined and registered color for lens arrays for uses in security, branding, and other applications. For the first time, one can use the dramatic color effects that can be produced in a single step intaglio/bas relief metamaterial. It can be applied equally to a bulk and thin film surface and can be implemented into a single step process.
The mapping of the pixels can be done post interlacing or mapping of the 3D or animated image.
The images can be interlaced first and then converted at the pixel level to the proper conversion method (continuous intaglio or bas relief) to simulate the desired color.

[00151] An example of the astounding depth of features and animation that can occur is illustrated by the conventional counterpart (traditional print combined with these lenses) that would be at 75 microns. Even in the proofing environment (images impossible to register and print in production), a maximum of 6 images for a 400 LPI lens (bi-directional round or square based lens) by 6 images could be achieved at about 2400 DPI. Conversely, the plasmonic resonance system described above allows a very sharp focusing lens to be designed that will provide the pixels at 75 microns. Rather than a 6 by 6 frame pattern (36 images in a lens), a 250 image by 250 image pattern could be achieved at 100,000 DPI with 62,500 views or image frames in process colors, straight colors (PMS equivalents), or RGB colors. Hence, plasmonic resonance facilitates larger frame patterns than the 6 by 6 patterns such as 7 by 7 frame patterns (49 image frames) up to 250 by 250 frame patterns (62,500 image frames).
[00152] The lens array can then be cast, extruded, or laminated to the nano-bas relief or embossed film that contains the imagery or the nano-bas relief structures. The optical pitch of the lens can be designed and fabricated to match the exact resonance of the color pixels generated by the nano-bas relief structures or the inverse. The optical pitch can be scaled to match the lens array exactly by the systematic removal of pixel sets (formed by sets of nano structures) or addition of nanostructures formulated in blending (non-interfering) colors or pixels so that the exact resolution of the device writing the file is matched without interpolation down to about 250 nanometers.
[001531 Using plasmonic resonance or continuous metal frequency for creating imagery using interlaced files allows the finite adjustment of a file down to the combined nanopost combination creating color resonance at the 250 rim level. This pixel "replacement"
represents a final pixel, and therefore, the adjustment to match the optical pitch (imagery) to the microlens goes down to about 250 mn. This is ideal for creating a precise match between the micro lens and the image itself, as it allows a finite adjustment without using ancillary programs that cause averaging and distortion in the file.
[00154] With regard to general interlacing for all lens arrays using continuous metal frequency technology, images may be created in a normal way using photographs, Adobe's Photoshop Illustrator, or any number of programs. The color file is then separated into color zones via color separation software that may be in RGB or CMYK for the images. This is done at a very high resolution so that the pixels may be broken down to make color builds at up to about 100,000 DPI, with about 250 nm per pixel. The shapes of the nanoposts are then formed to match the appropriate color given the plasmonic resonance associated with that color when matching the wave length to the electron. This can be done in the color separation software.
[00155] The individual color selections for those pixels are then translated into the appropriate physical shapes of the micro-structures (nanoposts) to create the proper color to the viewer.
However, before the final selection of the shapes, the files are interlaced for 3D and/or animation down to the possible level of one pixel per frame or 250 nm depending upon the size of the file and or micro lens. The files are then interlaced to match the lenses, whether round, square, hexagonal, linear, parallelogram-type, or aspheric lenses are used in the lens array. The pixels are then translated (after interlacing) with software that identifies the colors and the pixels and provides the necessary data to create the nanoposts or micro-embossing file containing X, Y
and Z coordinates.
[00156] With regard to lens application and general manufacturing, after the files are created with the interlaced images and converted into embossing files, a plastic substrate may be embossed first and then metalized appropriately, with the exact metamaterials used varying from application to application. The materials may be individually conductive materials or combinations of conductive materials such as gold, aluminum, silver and so forth. These materials may be vapor coated with layers of 2 to 50 or more nanometers of material. Conversely, the film itself may be pre-coated with the metamaterials and post-embossed with the nano-structures.
[00157] The lenses (again, any of the previously mentioned types/shapes may be used) may be applied after the process of metallization and embossing or even before.
The lens array is formed on or as part of the film and the metallization occurs, and this is followed by embossing on the planar side of the lens. However, when the lens is applied afterward, the adhesive and or stamping process and associated hot melt adhesive and the index of refraction should be taken into account to calculate the appropriate focal lengths.
[00158] In summary, the lens or array of micro lenses: (1) may be applied after the production of the substrate, embossing, and metallization; (2) may be embossed with the lens array first extruded or cast first and then embossed with the nano-interlaced images (then metalized with the metamaterials); and (3) may be made, metalized, and then embossed on the backside (planar side).

PROGRAM LISTING OR SUBROUTINE FOR RAY TRACING FOR DUAL-AXIS
INTERLACING AND ROUND OR SQUARE-BASED LENS ARRAYS
Sub Intersect_Nearest_Surface(xs, ys, zs, elx, ely, elz, xi, yi, zi, enx, eny, enz, gnfound, snfound, surftypefound, success) 'finds surface nearest to starting point of ray.
'inputs 'xs,ys,zs starting point of ray ' c 1 x,c 1 y,c 1 z direction cosines of ray 'xi,yi,zi intersection point of ray 'returns 'gnfound,snfound group number, surface number found 'surfacetypefound of nearest surface.
'sucess (if found) Dim intplaneflag, IntSphere5flag, IntCylinderFlag, IntEllipsoidFlag As Boolean Dim icolor, k As Integer Dim surftypetemp As String Dim intsphere3planeflag As Boolean Dim gn, sn, gntemp, sntemp As Integer Dim distance As Double Dim xitemp, yitemp, zitemp As Double Dim enxtemp, enytemp, enztemp As Double Dim xp, yp, zp As Double Dim XP1, YP1, ZP1 As Double 'Dim enx, eny, enz As Double Dim enxx, enyy, enzz As Double Dim enxplane, enyplane, enzplane As Double Dim xc, yc, zc, rr As Double Dim x0, yO, z0 As Double Dim Tx, ry, rz As Double 'Dim rxl, ryl, rzl, rx2, ry2, rz2 As Double 'Dim xil, yil, zil, xi2, yi2, zi2 As Double Dim gx, gy, gz As Double Dim a, b, c, xvertex As Double Dim riml, toll, sl As Double toll = 0.0001 'go through all the surfaces that have been defined, intersect each one and find the surface nearest to the starting point of the 'incident ray.
success = False distance = 10 A 10 For gn = GroupStart To GroupEnd Step GroupStep For sn = SurfaceStart(gn) To SurfaceEnd(gn) Step SurfaceStep 'plane surface If SurfaceType(gn, sn) = 1 Then xp = x(gn, sn) yp = y(gn, sn) zp = z(g-n, sn) enx = Xdir(gn, sn) eny = Ydir(gn, sn) cnz = Zdir(gn, sn) Call intplanc2(xs, ys, zs, clx, cly, clz, xp, yp, zp, cnx, cny, cnz, xi, yi, zi, intplaneflag) If intplaneflag = True Then sl = Scir((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If s 1 < distance And sl > toll Then distance = s 1 xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz surftypetemp = "Plane"
gntemp = gn sntemp = sn End If End If 'intplane=true End If 'spherical surface If SurfaceType(gn, sn) = 2 Then xc = x(gn, sn) ye = y(gn, sn) zc = z(gn, sn) rr = r(gn, sn) XP1 = XPlane(gn, sn) YP1 = YPlane(gn, sn) ZP1 = ZPlane(gn, sn) enxplane = ENXP(gn, sn) enyplane = ENYP(gn, sn) enzplane = ENZP(gn, sn) Call IntSphere5(xs, ys, zs, elx, ely, elz, xc, ye, zc, rr, Tx, ry, rz, xi, yi, zi, IntSphere5flag) 'Call IntSphere3_Plane_Divide(xs, ys, zs, elx, ely, elz, xc, ye, zc, rr, XP1, YP1, ZP1, enxplane, enyplane, enzplane, Tx, ry, rz, xi, yi, zi, intsphere3planeflag) 'Call IntSphere2(xs, ys, zs, elx, ely, elz, xc, ye, zc, rr, Tx, ry, rz, xi, yi, zi, intsphereflag) If IntSphere5flag = True Then 'If IntSphere5flag = True Then '= 1 Or intsphereflag = 2 Then sl = Sqr((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) s 1 < distance And sl > tol I Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = rx '999999?999?99999 enytemp = ry enztemp = rz surftypetemp = "Sphere"
gntemp = gn sntemp = sn End If 'If intsphereflag = 2 Then sl = Sqr((xi2 - xs) A 2 + (yi2 - ys) A 2 + (zi2 - zs) A 2) ' If s1 < distance And sl > toll Then distance = sl ' xitemp = xi2 yitemp = yi2 ' zitemp = zi2 enxtemp = rx2 ,?799799?799?7997 enytemp = ry2 enztemp = rz2 surftypetemp = "Sphere"
gntemp = gn sntemp = sn ' End If 'End If 'intsphereflag=2 'End If 'intsphere=1 or 2 End If 'intsphere <>0 End If 'spherical surface 'cylinder surface If SurfaceType(gn, sn) = 3 Then x0 = x(gn, sn) y0 = y(gn, sn) z0 = z(gn, sn) gx = Xdir(gn, sn) gy = Ydir(gn, sn) gz = Zdir(gn, sn) rr = r(g-n, sn) Call intcylindcr(xs, ys, zs, clx, cly, clz, x0, yO, zO, gx, gy, gz, rr, xi, yi, zi, cnx, cny, enz, IntCylinderFlag) If IntCylinderFlag = True Then sl = Scir((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If s 1 < distance And sl > toll Then distance = s 1 xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz surftypetemp = "Cylinder"
gntemp = gn sntemp = sn End If End If End If 'Aperture If SurfaceType(gn, sn) = 4 Then xp = x(gn, sn) yp = y(gn, sn) zp = z(gn, sn) enx = Xdir(gn, sn) eny = Ydir(gn, sn) enz = Zdir(gn, sn) Call intplane(xs, ys, zs, elx, ely, elz, xp, yp, zp, enx, eny, enz, xi, yi, zi, intplaneflag) If intplaneflag = True Then s I = Sqr((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If s 1 < distance And sl > toll Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz surftypetemp = "Aperture"
gntemp = gn sntemp = sn End If End If End If 'Ellipsoid If SurfaceType(gn, sn) = 5 Then a = ax(gn, sn) b = by(gn, sn) c = cz(gn, sn) xvertex = x(gn, sn) riml = RimLocation(gn, sn) toll = 0.000001 '.00001 seems to give consistant results Call IntEllipsoid(a, b, c, xvertex, riml, xs, ys, zs, elx, ely, elz, xi, yi, zi, enx, eny, enz, IntEllipsoidFlag) If IntEllipsoidFlag = True Then sl = Sqr((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If sl < distance And sl > toll Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz surftypetemp = "Ellipsoid"
gntemp = gn sntemp = sn End If End If End If 'Spline If SurfaceType(gn, sn) = 6 Then MsgBox ("Trace main does not support spline") End If Next sn Next gn 'Target plane xp = XTarget yp = 0#
zp = 0#
enx = 1#
eny = 0#
enz = 0#
Call intplane(xs, ys, zs, elx, ely, elz, xp, yp, zp, enx, eny, enz, xi, yi, zi, intplaneflag) If intplaneflag = True Then sl = Scir((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If s 1 < distance And s 1 > toll Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz gntemp = 0 sntemp = 0 surftypetemp = "Target"
End If End If 'plot boundaries 'right side xp = BoundaryRight yp = 0#
zp = 0#
enx = 1#

eny = 0#
enz = 0#
Call intplane(xs, ys, zs, elx, ely, elz, xp, yp, zp, enx, eny, enz, xi, yi, zi, intplaneflag) If intplaneflag = True Then sl = Sqr((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If s 1 < distance And s 1 > toll Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz gntemp = 0 sntemp = 0 surftypetemp = "Boundary"
End If End If 'left side xp = BoundaryLeft yp = 0#
zp = 0#
enx = -1#
eny = 0#
enz = 0#
Call intplane(xs, ys, zs, elx, ely, elz, xp, yp, zp, enx, eny, enz, xi, yi, zi, intplaneflag) If intplaneflag = True Then sl = Sqr((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If s 1 < distance And s 1 > toll Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enz temp = enz gntemp = 0 sntemp = 0 surftypetemp = "Boundary"
End If End If 'top side xp = 0#
yp = BoundaryTop zp = 0#
enx = 0#
cny = 1#
cnz = 0#
Call intplane(xs, ys, zs, elx, ely, elz, xp, yp, zp, enx, eny, enz, xi, yi, zi, intplaneflag) If intplaneflag = True Then sl = Sqr((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) Tf s 1 < distance And s 1 > tol 1 Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz gntemp =0 sntemp = 0 surftypetemp = "Boundary"
End If End If 'bottom side xp = 0#
yp = BoundaryBottom zp = 0#
enx = 0#
eny = -1#
enz = 0#
Call intplane(xs, ys, zs, elx, ely, elz, xp, yp, zp, enx, eny, enz, xi, yi, zi, intplaneflag) If intplaneflag = True Then sl = Sqr((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If s1 < distance And sl > toll Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz gntemp = 0 sntemp = 0 surftypetemp = "Boundary"
End If End If 'front side xp = 0#
yp = 0#
zp = 10 A 6 enx = 0#
eny = 0#
enz = -1#
Call intplane(xs, ys, zs, elx, ely, elz, xp, yp, zp, enx, eny, enz, xi, yi, zi, intplaneflag) If intplaneflag = True Then sl = Sqr((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If s 1 < distance And s 1 > toll Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz gntemp = 0 sntemp = 0 surftypetemp = "Boundary"
End If End If 'back side xp = 0#
yp = 0#
zp = -10 A 6 enx = 0#
eny = 0#
enz = 1#
Call intplane(xs, ys, zs, elx, ely, elz, xp, yp, zp, enx, eny, enz, xi, yi, zi, intplaneflag) If intplaneflag = True Then sl = Sqr((xi - xs) A 2 + (yi - ys) A 2 + (zi - zs) A 2) If s 1 < distance And s 1 > toll Then distance = sl xitemp = xi yitemp = yi zitemp = zi enxtemp = enx enytemp = eny enztemp = enz gntemp = 0 sntemp = 0 surftypetemp = "Boundary"
End If End If 'final report If distance < 10 A 9 Then success = True xi = xitemp yi = yitemp zi = zitemp enx = enxtemp eny = enytemp enz = enztemp gnfound = gntemp snfound = sntemp surftypefound = surftypetemp End If If gnfound = GroupEnd And snfound = SurfaceEnd(gnfound) Then surftypefound = "Final Surface"
End If End Sub **************************************************************************
*******************************************************
Sub IntSphere5(xs, ys, zs, elx, ely, elz, xc, ye, zc, r, Tx, ry, rz, xi, yi, zi, IntSphere5flag) 'xs,ys,zs is starting point of ray 'elx,ely,elz are direction cosines of ray 'xc,yc,zc is center of circle 'r is radius of sphere 'rx,ry,rz are direction cosines of radius at intersection 'xi,yi,zi is intersection of ray on sphere 'intsphereflag = true if intersection found Dim sl, s2, s3, xl, x2 As Double Dim LL, Li, L2 As Double IntSphere5flag = False s 1 = 2# * ((xs - xc) * e 1 x + (ys - ye) * e ly + (zs - zc) * e 1 z) s3 = s 1 A 2 - 4# * s2 'there is no intersection If s3 <0 Then Exit Sub End If 'there is only one intersection If s3 = 0# Then LL -s 1 / 2#
GoTo IntSphere250 End If 'there are two intersections Li = (-Si + Sqr(s3)) / 2#
L2 = (-sl - Sqr(s3)) / 2#
'check for + L and - L for the side of sphere to choose ( compare where xc and xi is) If Li <0# And L2 <0# Then Exit Sub 'no intersection End If If Ll > 0# And L2 > 0# Then If Ll > L2 Then 1=L1 Else 1=L2 End If 'End If If Li > 0# Then xi = xs + Li * clx yi = ys + L 1 * ely zi = zs + Li * el z If r > 0# Then If xi <= xc Then LL = Li End If End If If r < 0# Then If xi >= xc Then LL = Li End If End If End If If L2> 0# Then xi = xs + L2 * elx yi = ys + L2 * c ly zi = zs + L2 * c I z If r > 0# Then If xi <= xc Then LL = L2 End If End If If r < 0# Then If xi >= xc Then LL = L2 End If End If End If IntSphere250:
'Ifl <=0 Then ' Exit Sub 'End If xi = xs + LL * el x yi ys + LL * ely zi = zs + LL * clz rx = (xi - xc) / r ry = (yi - yc) / r rz = (zi - zc) / r sl =rx^ 2 +ry^2 +rzA2 'MsgBox ("Sum of squares of normal direction cosines "& sl ) IntSphere5flag = True End Sub

Claims

What we claim is:

1. A visual display assembly useful as an anti-counterfeiting device on paper currency, product labels, and other objects, comprising:
a film comprising a first surface including an array of lenses and a second surface opposite the first surface; and an image layer proximate to the second surface, the image layer comprising pixels of frames of images interlaced relative to two orthogonal axes, wherein the image layer is adapted to display an image including a set of symbols.
wherein the set of symbols is activated with a first display effect when the assembly is rotated from a normal POV about a first axis, wherein the set of symbols is activated with a second display effect when the assembly is rotated from the normal POV about a second axis orthogonal to the first axis, wherein the image layer comprises a film with a surface comprising metal or clear film nanostructures formed to provide the pixels of the frames of the images interlaced relative to two orthogonal axes, wherein the metal nanostructures are formed to encode color information in dimensional parameters of the metal nanostructures to define color of each of the pixels of the frames of the images, wherein the first and second display effects are each selected from the group of display effects consisting of: 3D layered, 3D real, motion, flip, animation, morph, on and off, and zoom, and wherein the first display effect includes moving a first subset of the symbols in a first direction and a second subset of the symbols in a second direction opposite the first direction.

2. The assembly of claim 1 wherein the frames correspond to a matrix with up to 62,500 image frames.

3. The assembly of claim 1, wherein the first and second directions are both orthogonal to the first axis.

4. The assembly of claim 1. wherein the set of symbols include a foreground symbol and a plurality of background symbols appearing in a layer offset and behind the foreground symbol and wherein the foreground symbol remains stationary during the first display effect while the background symbols are moved relative to the foreground symbol.

5. The assembly of claim 4, wherein the background symbols remain stationary during the second display effect while the foreground symbol is activated to flip or morph between a first image and a second image differing from the first image.

6. The assembly of claim 1, wherein the lenses are round-based lenses, square-based lenses, hexagonal-based, or parallelogram-type lenses.

7. The assembly of claim 6, wherein the lenses of the array are provided at 200 or more LPI as measured along a row of lenses in either or any direction.

8. The assembly of claim 1, wherein the frames each comprises a different point of view (POV) of the one or more images.

9. The assembly of claim 1, wherein the film comprises a non-bas relief or embossed film that includes the metal or clear film nanostructures.

10. The assembly of claim 1, wherein the metal or clear film nanostructures are provided at a pitch of less than 10,000 nanometers.

11. The assembly of claim 10, wherein the metal or clear film nanostructures provide an effective print resolution of at least 10,000 dots per inch.

12. The assembly of claim 1, wherein the film comprises a layer of gold, aluminum, silver, or polymer in which the nanostructures are formed.

13. A visual display assembly useful as an anti-counterfeiting device on paper currency, product labels, and other objects, comprising:
a film comprising a first surface including an array of lenses and a second surface opposite the first surface; and an image layer proximate to the second surface, the image layer comprising pixels of frames of images interlaced relative to two orthogonal axes, wherein the image layer is adapted to display an image including a set of symbols.
wherein the set of symbols is activated with a first display effect when the assembly is rotated from a normal POV about a first axis, wherein the set of symbols is activated with a second display effect when the assembly is rotated from the normal POV about a second axis orthogonal to the first axis, wherein the image layer comprises a film with a surface comprising metal or clear film nanostructures formed to provide the pixels of the frames of the images interlaced relative to two orthogonal axes, wherein the metal nanostructures are formed to encode color information in dimensional parameters of the metal nanostructures to define color of each of the pixels of the frames of the images, wherein the first and second display effects are each selected from the group of display effects consisting of: 3D layered, 3D real, motion, flip, animation, morph, on and off, and zoom, and wherein an optical pitch of the array of lenses matches a resonance of color pixels provided by the metal or clear film nanostructures.

14. A method of fabricating an anti-counterfeiting device, comprising:
generating a print file defining dual-axis interlacing of a matrix of image frames;

providing a transparent film comprising an array of lenses on a first surface;
and based on the print file, printing an ink layer or providing a thin metal film with nanostructures on a second surface opposite the first surface, wherein the lenses of the array are round, hexagonal, or square-based lenses that are nested in the array, wherein the generating of the print file comprises providing pixel mapping of interlaced images that when viewed through the array of lenses provide image elements that are first activated to provide a first display effect when the anti-counterfeiting device is rotated about a first axis and that are activated to provide a second display effect when the anti-counterfeiting device is rotated about a second axis that is transverse to the first axis, and wherein the generating of the print file defining dual-axis interlacing of a matrix of image frames comprises mapping pixels to two or more of the lenses in the array in a non-sequential process.

15. The method of claim 14, wherein the generating of the print file includes combining the image frames from rows of the matrix to obtain vertical pixel files comprising pixels in the X axis and then combining the vertical pixel files to obtain the print file.

16. The method of claim 14, wherein generating of the print file comprises adjusting a size of the print file to match an optical pitch of the array of lenses.

17. The method of claim 14, wherein the thin metal film comprises a non-bas relief or embossed film fabricated to include the nanostructures.

18. The method of claim 14, wherein the nanostructures are provided at a pitch of less than 300 nanometers.

19. The method of claim 1 8 , wherein the nanostructures provide an effective print resolution of at least 10,000 dots per inch.

20. The method of claim 14, wherein the first and second display effects are each selected from the group of display effects consisting of: 3D layered, 3D real, motion, flip, animation, morph, on and off, and zoom; and wherein the first display effect is used to activate a first set of the image elements and the second display effect is used to activate a second set of the image elements that differs from the first set of the image elements.

21. The method of claim 20, wherein the image frames comprise images from a plurality of points of view relative to a horizontal axis and to a vertical axis.

22. The method of claim 21, wherein the generating of the print file includes combining the image frames from rows of the matrix to obtain vertical pixel files comprising combining pixels in the X axis and then combining the vertical pixel files to obtain the print file.

23. The method of claim 20, wherein the non-sequential process is performed based on a viewing distribution for the lenses of the array and wherein the lenses of the array are non-linear lenses with square, hexagonal, or circular bases.

24. The method of claim 14, wherein the image frames comprise images from a plurality of points of view relative to a horizontal axis and to a vertical axis.

25. The method of claim 14, wherein the non-sequential process is performed based on a viewing distribution for the lenses of the array and wherein the lenses of the array are non-linear lenses with square, hexagonal, or circular bases.

26. The method of claim 14, wherein the first and second display effects are each selected from the group of display effects consisting of: 3D layered, 3D real, motion, flip, animation, morph, on and off, and zoom.

27. The method of claim 26, wherein the first display effect differs from the second display effect.

28. The method of claim 26, wherein the first display effect is used to activate a first set of the image elements and the second display effect is used to activate a second set of the image elements that differs from the first set of the image elements.

29. A method of fabricating an anti-counterfeiting device, comprising:
generating a print file defining dual-axis interlacing of a matrix of image frames;

providing a transparent film comprising an array of lenses on a first surface;
and based on the print file, printing an ink layer or providing a thin metal film with nanostructures on a second surface opposite the first surface, wherein the lenses of the array are round, hexagonal, or square-based lenses that are nested in the array, wherein the generating of the print file comprises providing pixel mapping of interlaced images that when viewed through the array of lenses provide image elements that are first activated to provide a first display effect when the anti-counterfeiting device is rotated about a first axis and that are activated to provide a second display effect when the anti-counterfeiting device is rotated about a second axis that is transverse to the first axis, wherein the nanostructures are formed to encode color information in dimensional parameters of the nanostructures to define color of each of the pixels of the frames of the images, wherein the first and second display effects are each selected from the group of display effects consisting of: 3D layered, 3D real, motion, flip, animation, morph, on and off, and zoom, and wherein the generating of the print file includes combining the image frames from rows of the matrix to obtain vertical pixel files comprising combining pixels in the X axis and then combining the vertical pixel files to obtain the print file.

30. The method of claim 29, wherein an optical pitch of the array of lenses matches a resonance of color pixels provided by the nanostructures.

31. The method of claim 29, wherein the image frames comprise images from a plurality of points of view relative to a horizontal axis and to a vertical axis.

32. The method of claim 29, wherein the first display effect differs from the second display effect.

33. The method of claim 29, wherein the first display effect is used to activate a first set of the image elements and the second display effect is used to activate a second set of the image elements that differs from the first set of the image elements.

34. The method of claim 29, wherein the thin metal film comprises a non-bas relief or embossed film fabricated to include the nanostructures.

35. The method of claim 29, wherein the nanostructurcs are provided at a pitch of less than 300 nanometers and wherein the nanostructures provide an effective print resolution of at least 10,000 dots per inch.

36. A visual display assembly useful as an anti-counterfeiting device on paper currency, product labels, and other objects, comprising:
a film comprising a first surface including an array of lenses and a second surface opposite the first surface; and an image layer proximate to the sccond surface, the image layer comprising pixels of frames of images interlaced relative to two orthogonal axcs, wherein the image layer is adapted to display an image including a set of symbols, wherein the set of symbols is activated with a first display effect when the assembly is rotated from a normal POV about a first axis, wherein the set of symbols is activated with a second display effect differing from the first display effect when the assembly is rotated from the normal POV
about a second axis orthogonal to the first axis, and wherein the first display effect includes concurrently moving a first subset of the symbols in a first direction and a second subset of the symbols in a second direction opposite the first direction.

37. The assembly of claim 36, wherein the first and second directions are both orthogonal to the first axis.

38. The assembly of claim 36, wherein the set of symbols include a foreground symbol and a plurality of background symbols appearing in a layer offset and behind the foreground symbol and wherein the foreground symbol remains stationary during the first display effect while the background symbols are moved relative to the foreground symbol.

39. The assembly of claim 38, wherein the background symbols remain stationary during the second display effect while the foreground symbol is activated to flip or morph between a first image and a second image differing from the first image.

40. The assembly of claim 36, wherein the lenses are round-based lenses, square-based lenses, hexagonal-based, or parallelogram-type lenses.

41. The assembly of claim 40, wherein the lenses of the array are provided at 200 or more LPI as measured along a row of lenses in either or any direction.

42. The assembly of claim 36, wherein the frames each comprises a different point of view (POV) of the one or more images.

43. The assembly of claim 36, wherein the image layer comprises a printed ink layer or a film with a plurality of metal nanostructures or clear film nanostructures.

44. The assembly of claim 36, wherein the image layer comprises a film with a surface comprising metal or clear film nanostructures formed to provide the pixels of the frames of the images interlaced relative to two orthogonal axes.

45. The assembly of claim 44, wherein the film comprises a non-bas relief or embossed film that includes the metal or clear film nanostructures.

46. The assembly of claim 45, wherein the metal or clear film nanostructures provide an effective print resolution of at least 10,000 dots per inch.

47. The assembly of claim 46, wherein the metal nanostructures are formed to encode color information in dimensional parameters of the metal nanostructures to define color of each of the pixels of the frames of the images.

48. The assembly of claim 47, wherein an optical pitch of the array of lenses matches a resonance of color pixels provided by the metal or clear film nanostructures.

49. The assembly of claim 44, wherein the film comprises a layer of gold, aluminum, silver, or polymer in which the nanostructures are formed.

50. The assembly of claim 44, wherein the frames correspond to a matrix with up to 62,500 image frames.

51. The assembly of claim 44, wherein the metal or clear film nanostructures are provided at a pitch of less than 10,000 nanometers.

52. An apparatus adapted to protect against counterfeiting, comprising:
a film comprising a first surface including an array of lenses and a second surface opposite the first surface;
a printed image proximate to the second surface, the printed image comprising pixels of frames of images arranged according to pixel mapping configured to provide dual-axis activation; and a substrate with a surface upon which the printed image and the film are supported, wherein the dual-axis activation comprises producing a first display effect when the apparatus is rotated about a first axis and a second display effect differing from the first display effect when the apparatus is rotated about a second axis transverse to the first axis, wherein the first and second display effects are each selected from the group of display effects consisting of: 3D layered, 3D real, motion, flip, animation, morph, on and off, and zoom, and wherein the dual-axis activation comprises displaying an image with a first layer of images and a second layer of images and wherein the first layer of images appear to float in a different level than the second layer of images from a plurality of POVs.

53. The apparatus of claim 52, wherein the first and second display effects comprise causing a set of image elements to move in a direction opposite a direction of the rotation of the apparatus.

54. The apparatus of claim 53, wherein the first display effect further comprises causing a foreground image element to flip from a first symbol to a second symbol differing from the first symbol.

55. The apparatus of claim 53. wherein the second display effect further comprises causing a foreground image element to have motion or to be animated in a manner independent from the set of image elements.

56. The apparatus of claim 52, wherein the first and second display effects comprise causing a set of image elements to move in a direction orthogonal to a direction of the rotation of the apparatus.

57. The apparatus of claim 56, wherein the first display effect further comprises causing a foreground image element to flip from a first symbol to a second symbol differing from the first symbol.

58. The apparatus of claim 56, wherein the second display effect further comprises causing a foreground image element to have motion or to be animated in a manner independent from the set of image elements.

59. An apparatus adapted to protect against counterfeiting, comprising:
a film comprising a first surface including an array of lenses and a second surface opposite the first surface;
a printed image proximate to the second surface, the printed image comprising pixels of frames of images arranged according to pixel mapping configured to provide dual-axis activation; and a substrate with a surface upon which the printed image and the film are supported, wherein the dual-axis activation comprises producing a first display effect when the apparatus is rotated about a first axis and a second display effect differing from the first display effect when the apparatus is rotated about a second axis transverse to the first axis, wherein the first and second display effects are each selected from the group of display effects consisting of: 3D layered, 3D real, motion, flip, animation, morph, on and off, and zoom, and wherein the first and second display effects comprise causing a set of image elements to move in a direction opposite a direction of the rotation of the apparatus or a direction orthogonal to a direction of the rotation of the apparatus.

60. The apparatus of claim 59, wherein the dual-axis activation comprises displaying an image with a first layer of images and a second layer of images and wherein the first layer of images appear to float in a different level than the second layer of images from a plurality of POVs.

61. The apparatus of claim 59, wherein the first display effect further comprises causing a foreground image element to flip from a first symbol to a second symbol differing from the first symbol.

62. The apparatus of claim 59, wherein the second display effect further comprises causing a foreground image element to have motion or to be animated in a manner independent from the set of image elements.

63. The apparatus of claim 59, wherein the first display effect further comprises causing a foreground image element to flip from a first symbol to a second symbol differing from the first symbol.

64. The apparatus of claim 59, wherein the second display effect further comprises causing a foreground image element to have motion or to be animated in a manner independent from the set of image elements.