How to design and create security features

Abstract

A method is provided for designing at least a region of a printed image within a security feature. The security feature includes an array of optical elements overlaying the printed image. The method includes designing an icon matrix including rows and columns of pixels having pixel values ​​representing an icon seen by a user of the security feature, determining a desired gap size to provide a desired magnification of the icon, and generating an array of two-dimensional matrices of pixels, the array including a sequence of repeated matrix sets, each set including a first number of matrices of a first type having a first size and a second number of matrices of a second type having a second size, the first type matrices and second type matrices being based on the icon matrix, and the first number, second number, first size, and second size are selected such that the average size of each matrix in the set is displaced from the modal matrix size by the desired gap size. A printed image of the security feature is also provided.

Description

[Technical field]

[0001] Many documents contain security features that aid in identifying counterfeit or forged documents. Many of these documents contain security features that utilize micro-optics, and such features are typically difficult to copy due to the precision required to produce a reliable counterfeit.

[0002] Security features used on these documents often include an array of micro-optical elements that overlay a printed image made up of pixels. One such example of a security feature that uses micro-optical elements is a Moire magnifier, where the printed image includes a series of icons printed approximately under each lens of a micro-optical element. Different repeat lengths (pitches) of the icons and lenses create a mismatch, where adjacent portions of the icon are magnified by adjacent lenses, providing the viewer with a magnified view of the icon. [Background technology]

[0003] The present invention generally relates to the design of micro-optical based security features that are based on the principle of moire magnification. Moire magnification is described in detail in Kamal et al., "Properties of moire magnifiers," Optical Engineering 37(11) 3007-3014, the disclosure of which is incorporated herein by reference. A prior art moire magnifier based security feature is shown in plan view in FIG. 1A and in side cross-sectional view in FIG. 1B. The security feature includes a regular two-dimensional array of substantially identical printed micro-images, or icons 110. These icons typically have dimensions up to about 250 μm. In general, the printed icons are made up of a large number of printed pixels 130, as shown in FIG. 1B. Each pixel has a pixel value (or pixel values) that determines the color of the icon at that time. A two-dimensional array of micro-optical elements 120, e.g., a two-dimensional array of micro-lenses, overlays the printed icons. The repeat length or pitch 125, 126 of the optical elements is similar (but not identical) to the pitch 115, 116 of the printed icon. When viewed through the two-dimensional array of optical elements, one or more magnified versions of the icon are produced. As described herein, the degree of magnification varies depending on how much the pitch of the icon array and the pitch of the optical element array differ from one another. Note that typically, but not necessarily, the optical element pitch 125 and printed icon pitch 115 in the horizontal direction are the same as the respective optical element pitch 126 and printed icon pitch 116 in the vertical direction.

[0004] Generally, each optical element (e.g., microlens) has the same optical properties. By providing a slight mismatch between the pitch of the icon and the pitch of the microlens array, each microlens images a different portion of the corresponding printed icon. Essentially, successive optical elements image successive portions of the icon to build a magnified image of the icon, each time the mismatch is equal to an integer number of lenses. The gray dashed box 150 in FIG. 1A shows a repeating pattern that defines the boundary where the mismatch between the icon 110 and the optical elements 120 has accumulated to the width of one microoptical element 120. As a result of successive optical elements imaging successive portions of the icon, the viewer sees a magnified version of the icon 160, as depicted in FIG. 1C. As the viewer tilts the security feature, different portions of the icon appear magnified by each lens, so that as the security feature is tilted, the magnified icon appears to "shift" relative to the plane of the microlenses. This gives the effect of depth, as the magnified image of the icon appears to be on a different plane than the microlenses.

[0005] From the above, it is clear that the magnification in a Moire magnifier depends on the degree of mismatch between the pitch of the optical elements and the pitch of the icon. As will now be explained with reference to a specific example, as the pitch mismatch decreases, higher magnification is achieved.

[0006] For example, the security feature may have a width W of 70 μm beneath the array of microlenses. I Considering the inclusion of an icon with a width W of 70 μm, each microlens L and are positioned exactly adjacent to each other, i.e. with a pitch P of 70 μm. L where the pitch of the icon array P I is 72.5μm, that is, each icon is P I -W IConsider the resulting magnification when adjacent microlenses are spaced apart by Δ=P I -P L =P I -W I = 2.5 μm. After 28 microlenses, the cumulative offset reaches 28Δ = 70 μm, which is the size of the icon. So in effect, the next microlens (i.e., the 29th microlens) images the same part of the icon as the first microlens. To the viewer, the icon is displayed across 28 microlenses, so the magnification factor M is 28x.

[0007] The apparent size of the icon to the viewer is M·W I = 28 · 70 μm = 1.96 mm. It will be appreciated that because the apparent size of the icon is much larger than the size of the microlens viewed through it, it gives the viewer the appearance that the icon is positioned on an imaginary plane which appears to be moving away from the viewer relative to the plane of the security feature. Summary of the Invention [Problem to be solved by the invention]

[0008] As can be seen from the above, the magnification ratio M is M=P L / Δ. Thus, to increase the apparent magnification (and hence the apparent separation between the plane of the virtual icon and the plane of the security feature), the difference between the icon pitch and the icon width must decrease, i.e., the spacing between adjacent printed icons must decrease.

[0009] It will also be appreciated that by making the icon pitch smaller than the icon width, the sign of the magnification is reversed. In effect, this gives the visual appearance that the icons are positioned on an imaginary plane that appears to move closer to the viewer relative to the plane of the security feature.

[0010] It is known in the art to provide the required difference in pitch in various ways. For example, the difference in pitch can be obtained by printing the icons at the same pitch as the lenticular array, but then slightly rotating the lenticular array relative to the underlying printed image. This effectively reduces the pitch of the lenticular array compared to the pitch of the underlying image. Alternatively, the pitch of the underlying printed image can be different from the pitch of the lenticular array, and an angular offset between the lenticular array and the printed image is used to vary the effective difference in pitch (and therefore the magnification) between the icons and the lenticular array. A problem with this method, however, is that the difference in pitch applied by the angular offset is necessarily constant across the security feature, making it difficult to provide contrasting areas of magnification / apparent depth across the security feature. Furthermore, it can be difficult to align the microlens array and the printed image with the required angular offset and with the required precision.

[0011] Another approach is to print an array of icons with a small distance between each other, increasing the icon pitch compared to the lens pitch (as shown in FIG. 1B). In the example above, the icon array could be printed with 2.5 μm between each icon. Alternatively, the icons could be printed with a reduced spacing of 2.5 μm, giving M a negative value. The problem with this approach, however, is that it is limited by the precision of the printing process. Ultimately, the minimum difference in pitch that can be achieved is limited by the resolution of the printing process, and in the prior art, very high resolution printing processes are required to achieve high apparent magnification on physically thin security features.

[0012] It is these and other problems that the present invention seeks to address. [Means for solving the problem]

[0013] One aspect of the invention provides a method of designing at least a region of a printed image within a security feature, the security feature comprising an array of optical elements overlaying the printed image, the method comprising: designing an icon matrix comprising rows and columns of pixels having pixel values ​​representing an icon seen by a user of the security feature, determining a desired gap size to provide a desired magnification of the icon, and generating an array of two dimensional matrices of pixels, the array comprising a sequence of repeated matrix sets, each set comprising a first number of matrices of a first type having a first size and a second number of matrices of a second type having a second size, the first type matrices and the second type matrices being based on the icon matrix, the first number, the second number, the first size, and the second size being selected such that an average size of each matrix in the set is displaced from the modal matrix size by the desired gap size.

[0014] Advantageously, this allows the effective mismatch between the pitch of the icons and the pitch of the overlaid optical elements to be controlled by a printing process having a print resolution no higher than that required in the prior art, without the need to rotationally offset the optical elements relative to the printed image. The achievable magnification is no longer limited by the minimum print resolution or by the precision of the rotational offset between the array of optical elements and the underlying image.

[0015] In one embodiment, the step of determining the desired gap dimension includes calculating a gap size that produces the desired magnification effect when an array of repeated matrices corresponding to the icon matrix are viewed through an array of optical elements with the repeated matrices spaced apart by the gap size.

[0016] In one embodiment, the first type of matrix corresponds to an icon matrix.

[0017] That is, in this embodiment, the first type matrix may be an icon matrix having the same dimensions as the icon matrix, while the second type matrix may be a modified version of the icon matrix such that it has a different size. For example, the pixel values ​​of the second type matrix may correspond to an image that is a scaled version of the icon matrix, and may be either larger or smaller than the icon matrix. Alternatively, the second type matrix may be a cropped version of the icon matrix, i.e., may correspond to the icon matrix except that one or more columns and / or rows of pixels have been removed. Alternatively, the second type matrix may be a version of the icon matrix with additional padding or white space, i.e., may correspond to the icon matrix except that it has one or more additional columns and / or rows of pixels.

[0018] Alternatively, each of the first and second matrices can be derived separately from the icon matrix, for example, the first and second matrices can each be scaled versions of the same icon matrix with different scale factors such that they have different sizes.

[0019] In various embodiments, the second type matrix includes at least one additional column or at least one less column than the first type matrix.

[0020] In various embodiments, the second type matrix includes at least one additional column or at least one less column than the first type matrix.

[0021] In various embodiments, the second number is one.

[0022] A further aspect of the invention provides a method of designing a print image within a security feature, the method comprising: dividing the print image into a plurality of regions; providing a first region of the plurality of regions with a first icon design associated with the region and a desired first magnification ratio associated with the region; and designing the first region according to any of the methods disclosed above, wherein the icon matrix represents the first icon design and the desired magnification ratio is the desired first magnification ratio.

[0023] Advantageously, this allows certain regions of the security feature to be provided with a visual effect of magnification, while other regions can be provided with a different visual effect. In particular, since the method of providing the effect of magnification does not depend on, for example, the rotation of the micro-optical element array relative to the printed image, the visual effect provided throughout the security feature is not limited by the difference in pitch being determined (at least in part) by the angular offset between the micro-optical element array and the printed image, as is the case with moire magnifiers such as those of the prior art. For example, regions of different signs and higher magnifications can be provided throughout the security feature. In general, using the method of the present invention, it is possible to provide almost any combination of magnifications throughout the image. In various embodiments, this allows for the design of security features where different optical effects within the security feature enhance its visual distinctiveness, thereby improving its effectiveness as an easily identifiable authentication security feature.

[0024] In one embodiment, the method further includes providing, for a second region of the plurality of regions, a second icon design associated with the second region of the plurality of regions and a second desired magnification factor associated with the second region, and designing the second region according to a method as described in any preceding claim, wherein the icon matrix represents the second icon design, the desired magnification factor is the second desired magnification factor, the second desired magnification factor differs from the first desired magnification factor, and a size of the modal matrix at the first region is the same as a size of the modal matrix at the second region.

[0025] Advantageously, this allows different areas of the security feature to be provided with different magnification factors.

[0026] In one embodiment, the second icon design is different from the first icon design.

[0027] Advantageously, this allows different areas of the security feature to be given different icon designs, each associated with a different magnification factor.

[0028] In various embodiments, the method further includes providing a region corresponding to a static design element in a further region of the plurality of regions, wherein a size of the static design element relative to the optical element results in the pixels under each optical element in the security feature within the region corresponding to the static design element being substantially uniform.

[0029] Advantageously, this allows both magnified and non-magnified static areas to be provided within the security feature.

[0030] In various embodiments, the method further includes providing a further region of the plurality of regions corresponding to an animated design element, in which the print image is designed such that each lens overlays a pixel matrix, each pixel being associated with a particular frame of the animation within a series of frames of the animation.

[0031] Advantageously, this allows both magnified and non-magnified animated regions to be provided within the security feature.

[0032] A further aspect of the invention provides a method of producing a security feature comprising printing a print image designed according to any of the methods described above.

[0033] In one embodiment, the method further includes placing an array of optical elements over the printed image, each optical element being substantially the same size as the modal matrix.

[0034] A further aspect of the invention provides a printed image for a security feature, the security feature including an array of optical elements overlaying the printed image, at least one region of the printed image including an array of two dimensional matrices of pixels including a sequence of repeated sets, each set including a first number of matrices of a first type having a first size and a second number of matrices of a second type having a second size, the first type matrices and the second type matrices being based on icon matrices including rows and columns of pixels having pixel values ​​representing an icon seen by a user of the security feature, the first number, second number, first size, and second size being selected such that when the printed image is viewed through the array of optical elements, the average size of each matrix in the set is displaced from the modal matrix size by a desired gap size to provide a desired magnification of the icon.

[0035] A further aspect of the invention provides a security feature that includes a printed image and an array of identical optical elements overlaying the printed image.

[0036] A further aspect of the present invention provides a security document that includes a security feature.

[0037] A further aspect of the invention provides a non-transitory computer readable medium storing computer readable instructions that, when executed, cause a machine having a processor to perform any of the methods described above. [Brief description of the drawings]

[0038] [Figure 1A] 1 shows a prior art moire magnifier. [Figure 1B] 1 shows a prior art moire magnifier. [Figure 1C] 1C illustrates the apparent magnification of the icons within the Moire Magnifier of FIGS. 1A and 1B. [Diagram 2] 4 illustrates security features of the present invention. [Diagram 3] 1A-C illustrate the visual effects provided by a security feature in one embodiment of the present invention, including areas having different apparent magnifications. [Figure 4] 6A and 6B show the visual effects provided by a security feature in another embodiment of the invention having both magnified and non-magnified areas. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0039] Certain exemplary embodiments are described to provide a general understanding of the principles of the structure, function, manufacture, and use of the devices, systems, and methods disclosed herein. One or more examples of these embodiments are illustrated in the accompanying drawings. Those skilled in the art will appreciate that the devices, systems, and methods specifically described herein and shown in the accompanying drawings are non-limiting exemplary embodiments, and the scope of the invention is defined only by the claims. Features illustrated or described in connection with one exemplary embodiment may be combined with the features of other embodiments. Such modifications and variations are intended to be included within the scope of the present invention.

[0040] Moire magnification by modifying icon matrix size In one embodiment, the present invention provides a method for designing a printed image for use in a security feature that relies on designing a printed image of a security feature having an effective pitch that is not determined by the physical separation of icons or the rotation of a micro-optical array relative to the icons, but instead is determined by providing a printed image that includes repetitions of icon sets, each set including icons of slightly different sizes, thereby providing an effective difference in icon pitch compared to lens pitch.

[0041] The present invention can be understood from FIG. 2, which shows a cross-sectional view of a series of printed icons 210, 211 beneath a series of microlenses 220 spaced at a pitch 225. It will be appreciated that each icon 210, 211 is comprised of a number of pixels 230. It will be further appreciated that each icon is a two-dimensional matrix of pixels, with only one dimension being shown in FIG. 2 for ease of understanding. In a security feature of the present invention, the number of pixels 230 varies between matrices associated with a particular icon 210, 211. For example, it can be seen that the matrix for icon 211 has one more pixel than the matrix for icon 210. In this manner, the size of the matrices corresponding to the icons can be varied to allow for useful differentiation in icon pitch compared to lens pitch.

[0042] Each icon is designed as a two-dimensional matrix of pixels. The number of pixels in the icon design determines the size of the icon after it is printed. For example, if an icon is designed as a 28x28 pixel icon matrix, and each pixel is printed as a 2.5μm square, the resulting icon size is 70μm.

[0043] Rather than providing an array of icon matrices of the same size, in the present invention, the print image is designed as an array of repeated matrix sets. Each set contains a number of matrices corresponding to the icon matrix (28 pixels wide in the above example) and at least one matrix of a different size than the icon matrix. Thus, the average size of the matrices is different from the size of the icon matrix (which is the modal size of the matrix). By design, the modal size of the matrix corresponds to the pitch of the optical elements in the array. The average size of the matrix determines the effective pitch of the icons in the print image. In comparison to the prior art print image designs described in the Background section above, once printed, the average matrix size of the present invention is equal to the icon pitch and the modal matrix size of the present invention is equal to the icon size. That is, the difference between the modal print matrix size and the average print matrix size is the magnification factor M=P L This corresponds to the quantity Δ in the calculation of Δ / Δ.

[0044] Taking the above example, the array of matrices can be grouped into a set of three matrices, two of which are designated as iconic matrices (i.e., 28 pixels wide) and the width of the third is increased by one pixel, giving the following sequence: ...,28,28,29,28,28,29,... In this case, the average icon width across the rows and columns of the entire array is 28.33 pixels. When printed at 2.5 μm per pixel, this corresponds to an average row and column size of 70.83 μm, with a modal or icon row size of 70 μm. By design, the modal row and column size corresponds to the pitch of the lens elements in the overlaying lens array.

[0045] As a result, the effective pitch of the icon array differs from the pitch of the lens elements by 0.83 μm. This gives M=P L / Δ=+84x magnification, which gives the visual effect of the icon being enlarged to 84 times its original size and placed on a plane that moves away from the viewer compared to the plane of the security feature itself.

[0046] It will be appreciated that the second matrix may be one pixel less than the icon matrix (rather than one additional pixel) such that the average matrix size, and therefore the effective pitch of the icon array, is less than the pitch of the lens elements. In such a case, the sign of the magnification is reversed, giving the visual effect of the plane moving closer to the viewer.

[0047] Although the above examples have been described with respect to adding or deleting columns of pixels from the matrix, it will be appreciated that in some embodiments rows of pixels are added or deleted, while in other embodiments both rows and columns are deleted.

[0048] The pixel values ​​of the first type matrix and the second type matrix can be determined in various ways. For example, the pixel values ​​of the second type matrix may correspond to an image that is a scaled version of the icon matrix, either larger or smaller than the icon matrix. Alternatively, the second type matrix may be a cropped version of the icon matrix, i.e., it may correspond to the icon matrix except that one or more columns and / or rows of pixels have been removed. Alternatively, the second type matrix may be a version of the icon matrix with additional padding or white space, i.e., it may correspond to the icon matrix except that it has one or more additional columns and / or rows of pixels.

[0049] Alternatively, rather than the first matrix type being an icon matrix, each of the first and second matrices can be derived separately from an icon matrix design, for example, the first and second matrices can each be scaled versions of the same icon matrix with different scale factors such that they have different sizes.

[0050] In contrast to prior art security features, the effective difference between icon pitch and lens pitch is no longer determined by the minimum print resolution, but instead by the average matrix size in a repeated sequence, which may contain more icon matrices, resulting in an even smaller difference between the average matrix size and the modal matrix size.

[0051] Furthermore, because the effective difference between icon pitch and lens pitch is achieved by print design rather than by a difference in orientation between the printed image and the lens array, different effective pitch differences (and therefore different magnification effects) can be imparted to various areas of the security feature.

[0052] It is desirable for a security feature to provide a distinctive and complex visual effect. The more distinctive the visual effect, recognizable by a viewer of a security device, the easier it is to verify whether a given document is genuine. The more complex the visual effect, the more difficult it may be to create a counterfeit copy of the security feature.

[0053] Security features that exhibit varying degrees of magnification within the design As mentioned above, the above-described methods allow security features to be designed such that different regions across the image can have different effective magnifications. In one aspect of the invention, a printed image can be designed such that different regions of the security feature exhibit different apparent magnifications, thus providing a particularly distinctive and complex visual design.

[0054] For example, referring to Figures 3A-3C, the design 300 can be separated into a first central portion 310 surrounded by a second frame portion 320. As a first example shown in Figure 3B, the central portion 310 can have a first design with a magnification factor of "positive" sign (in the convention above) such that it appears as a plane moving away from the viewer, i.e., "behind" the plane of the security feature. The frame portion 320, although having a "positive" sign, can have a smaller magnification factor than the central portion, such that it appears to be in a plane moving away from the viewer, but at a depth closer to the plane of the security device than the central portion. In this way, the frame portion appears to float "above" the central portion.

[0055] As a further example shown in Figure 3C, the second portion may be designed to have a magnification factor of a different sign to the first portion, for example the frame portion may be designed to have a "negative" signed magnification factor and therefore appear above a plane approaching the viewer, i.e. "above" the plane of the security feature.

[0056] As another example shown in Figure 4, the design can be further enhanced by printing a portion of the image that does not appear to be magnified at all and therefore appears to be in the plane of the security feature itself. As shown, the design 400 may include a first central portion 410 with a positive sign magnification such that it appears to be on a plane moving away from the viewer. This is surrounded by a second frame portion 420 that has a "negative" sign magnification and therefore appears to be on a plane moving closer to the viewer. A third portion 440 has no apparent magnification whatsoever and is therefore designed to appear to be on the plane 430 of the security feature itself, between the planes of the first portion 410 and the second portion 420.

[0057] One way to provide the apparent no magnification portion 440 is to design the printed image as a design feature that is large compared to the microlenses. In the above example, the no magnification portion 440 is a macro-scale circular design in the center of the image. Because the design is large compared to the microlenses, the pixels under each microlens will be substantially uniform (i.e., substantially all pixels under the microlens will have substantially the same pixel value), and thus the appearance of the image at that microlens will not appear to change with changing viewing angles. Thus, the no magnification portion appears as a static image in the plane 430 of the security device.

[0058] A further way in which such a design can be augmented is by designing the print image to have portions that result in animated objects that are in the plane of the security feature. Referring again to FIG. 4, this can be achieved by designing the print image such that a region 440 of the print image that corresponds to the non-magnified portion of the design provides a non-magnified animated design. In this case, within region 440, the pixels below each lens each correspond to a different "frame" of the animation, and the pixels of the different frames of the animation are interlaced below the lenses. That is, the non-magnified portion of the design spans multiple lenses, and the matrix below each lens might be, for example, a 28x28 matrix of pixels. This might be conceptually divided into a 14x14 matrix of "design" pixels (i.e., each pixel is twice the height and width of a print pixel). The non-magnified portion of the design is designed to have 14x14=196 frames of animation. For each frame of the animation, each lens is associated with a particular pixel value, and that pixel value is assigned to the corresponding frame pixel below that lens. In this way, pixel values ​​of the images corresponding to different frames of the animation are interlaced across the area of ​​the design that corresponds to the animated object.

[0059] Thus, when a user views this portion of the security feature from different angles, they see different sets of interlaced pixels, which correspond to particular frames of the animation. For example, different frames of the animation may cause the non-magnified portion of the design to display different colors to the user, such that as the user changes the angle at which they view the design, the non-magnified portion of the design cycles through different colors. Alternatively, each frame may be a frame of a simple motion animation in which the non-magnified portion of the image appears to move when the security feature is tilted.

[0060] Method for creating a printed image, security feature, or security document - Patents.com In another embodiment, a method of generating a print image on a security feature is disclosed, the method including designing a print image on the security feature according to any of the methods detailed herein and fabricating the security feature.

[0061] To produce a security feature, typically an image is printed. An array of micro-optical elements (such as microlenses) is overlaid onto the printed image. Alternatively, the image may be printed on the back side of the substrate and on the front side is an array of micro-optical elements. Still alternatively, the printed image may be printed through the micro-optical array using a laser printing process. Still alternatively, the security feature can be produced by embossing features on the back side of the substrate and filling the features with ink to provide the printed image.

[0062] In another embodiment, a security feature is disclosed that includes a printed image, the printed image designed according to any of the methods detailed herein. In some embodiments, the security feature may further include an array of optical elements. In another embodiment, a security document may include a security feature disclosed herein. In some embodiments, the security document may be a banknote. In other embodiments, the security document may be a passport, a driver's license, an ID card, or any other government document.

[0063] Computer Readable Instructions In another embodiment, a non-transitory computer readable medium is disclosed that stores computer readable instructions that, when executed, cause a machine with a processor to perform any of the methods disclosed herein.

Claims

1. 1. A method of designing at least a region of a printed image within a security feature, comprising the steps of: the security feature includes an array of optical elements overlaying the printed image; The method comprises: designing an icon matrix including rows and columns of pixels having pixel values ​​representing a user-visible icon of said security feature; determining a desired gap size to provide a desired magnification of the icon; generating an array of two-dimensional matrices of pixels, the array including a sequence of repeated sets of matrices; Including, determining the desired gap size includes calculating a gap size, the gap size being an amount of deviation of an average size of each matrix in the set from a modal matrix size; Each set includes a first type matrix and a second type matrix; the first type matrix and the second type matrix are based on the icon matrix, and the first type matrix corresponds to the icon matrix; the number of matrices of the first type, the number of matrices of the second type, the size of the first type matrices, and the size of the second type matrices are selected such that an average size of a matrix in each of the sets of matrices of the first and second types is displaced from a modal matrix size by the desired gap size, a pitch of an array of optical elements is equal to the modal matrix size, and the modal matrix size is equal to the size of the icon matrix; The method, wherein the second type matrix includes at least one additional column than the first type matrix, or the second type matrix includes at least one less column than the first type matrix.

2. The method of claim 1, wherein the gap size produces a desired magnification effect when an array of repeated matrices corresponding to the icon matrices are viewed through the array of optical elements with the repeated matrices separated by the gap size.

3. 3. The method of claim 1, wherein the second type matrix includes at least one additional row than the first type matrix.

4. 3. The method of claim 1, wherein the second type matrix contains at least one less row than the first type matrix.

5. The method according to claim 1 , wherein the number of matrices of the second type is one.

6. The method according to claim 1 , wherein the sizes of the matrices of the first type are identical to each other.

7. 1. A method of designing a print image within a security feature, comprising: Dividing the print image into a plurality of regions, and for a first region of the plurality of regions, providing a first icon design associated with the region and providing a first desired magnification factor associated with the region; Designing the first region according to the method of any one of claims 1 to 6, wherein the icon matrix represents the first icon design and the desired magnification is the first desired magnification; The method comprising:

8. With respect to a second region of the plurality of regions, providing a second icon design associated with a second region of the plurality of regions and providing a second desired magnification associated with the second region; designing the second region according to the method of any one of claims 1 to 7, wherein the icon matrix represents the second icon design and the desired magnification is the second desired magnification; Further comprising: The method of claim 7 , wherein the second desired magnification factor is different from the first desired magnification factor, and the modal matrix size of the first region is the same as the modal matrix size of the second region.

9. The method of claim 8 , wherein the second icon design is different from the first icon design.

10. 10. The method of claim 7, further comprising providing a region in a further region of the plurality of regions corresponding to a static design element, the size of the static design element relative to the optical element resulting in the pixels under each optical element in the security feature in the region corresponding to the static design element being substantially uniform.

11. A method according to any of claims 7 to 10, further comprising providing in a further region of the plurality of regions a region corresponding to an animated design element, in which in the region corresponding to the animated design element the printed image is designed such that each lens overlays a matrix of pixels, each pixel being associated with a particular frame of an animation within a sequence of frames of the animation.

12. A method of producing a security feature comprising printing a print image designed according to any of claims 1 to 11.

13. The method of claim 12 , further comprising: disposing an array of optical elements over the printed image, each optical element being substantially the same size as the modal matrix size.

14. a printed image of a security feature, the security feature including an array of optical elements overlaying the printed image; at least one region of the printed image includes an array of two-dimensional matrices of pixels including a sequence of repeated sets of matrices, each set including a first type of matrix and a second type of matrix; the first type matrix and the second type matrix are based on an icon matrix including rows and columns of pixels having pixel values ​​representing a user-visible icon of the security feature, the first type matrix corresponding to the icon matrix; the number of matrices of the first type, the number of matrices of the second type, the size of the matrices of the first type, and the size of the matrices of the second type are selected such that an average size of the matrices in each of the sets of matrices of the first and second types is displaced from a modal matrix size by a desired gap size to provide a desired magnification of the icon when the printed image is viewed through the array of optical elements, the pitch of the array of optical elements being equal to the modal matrix size, and the modal matrix size being equal to the size of the icon matrix; the matrix of the second type includes at least one additional column than the matrix of the first type, and the matrix of the second type includes at least one less column than the matrix of the first type; A printed image of said security feature, wherein said gap size is the amount of deviation of the average size of each matrix in a set from a modal matrix size.

15. 15. The printed image of claim 14, wherein the matrix of the second type includes at least one additional row than the matrix of the first type.

16. 15. The printed image of claim 14, wherein the matrix of the second type includes at least one less row than the matrix of the first type.

17. The print image according to any one of claims 14 to 16, wherein the number of matrices of the second type is one.

18. The print image according to any one of claims 14 to 17, wherein the sizes of the first type matrices are the same as each other.

19. The print image of any one of claims 14 to 18, wherein the print image includes a plurality of regions, the at least one region is a first region of the plurality of regions, the icon matrix in the first region is a first icon matrix, and the desired magnification ratio in the first region is a desired first magnification ratio.

20. 20. The print image of claim 19, wherein the plurality of regions includes a second region, the icon matrix in the second region is a second icon matrix, the desired magnification in the second region is a second desired magnification, and the modal matrix size in the second region is the same as the modal matrix size in the first region.

21. 21. The printed image of claim 20, wherein the second icon design is different from the first icon design.

22. 22. The printed image of any of claims 19 to 21, further comprising an area corresponding to a static design element, the size of the static design element relative to the optical element resulting in the pixels under each optical element in the security feature within the area corresponding to the static design element being substantially uniform.

23. 23. A printed image as described in any one of claims 19 to 22, further comprising an area corresponding to an animated design element, wherein in the area corresponding to the animated design element, the printed image is designed such that each lens overlays a pixel matrix, each pixel being associated with a particular frame of animation within a sequence of frames of the animation.

24. The print image according to any one of claims 14 to 23, an array of identical optical elements overlaying said printed image; Security features, including:

25. A security document including the security feature of claim 24.

26. 26. The security document of claim 25, wherein the security document is one of a banknote, a passport, a driver's license, and an identity card.

27. A non-transitory computer readable medium storing computer readable instructions that, when executed, cause a machine including a processor to perform the method of any of claims 1-11.

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