# Patent

## Title
Methods of making a master and replicas thereof

## Abstract

The invention relates to methods of making a master and replicas thereof including tooling and retroreflective sheeting. The invention further relates to the corresponding master, tooling and in particular retroreflective sheeting. The method comprises forming V-shaped grooves in a substrate (e.g. metal plate) wherein the intersections of three grooves form cube-corner elements. The cube-corner elements are substantially the same size throughout the array. The master as well as corresponding tooling and sheeting preferably have an average groove spacing within the range of about 0.0005 inches (0.0127 mm) to about 0.007 inches (0.1778 mm) throughout the array and more preferably an average groove spacing of less than about 0.004 inches (0.1016 mm).

## Background
FIELD OF THE INVENTION
The invention relates to methods of making a master and replicas thereof including tooling and retroreflective sheeting. The invention further relates to the corresponding master, tooling and in particular retroreflective sheeting. The method comprises forming V-shaped grooves in a substrate (e.g. metal plate) wherein the intersections of three grooves form cube-corner elements. The cube-corner elements are substantially the same size throughout the array. The master as well as corresponding tooling and sheeting preferably has an average groove spacing within the range of about 0.0005 inches (0.0127 mm) to about 0.007 inches (0.1778 mm) throughout the array and more preferably an average groove spacing of less than about 0.004 inches (0.1016 mm).
BACKGROUND OF THE INVENTION
Retroreflective cube-corner sheeting is commonly employed for various decorative and safety purposes. Cube-corner sheeting is often preferred for such uses as traffic signs, pavement markings, vehicle markings and personal safety articles, in view of its high retroreflected brightness. Since its inception, various improvements have been made, such as described by the patent literature that relates to cube-corner retroreflective sheeting.
More recently for example, U.S. Pat. No. 6,206,525 teaches retroreflective sheeting for forming orientation free cones of reflected light encompassing a 0.5 degree angle of observation formed of small metal backed cube-corner prisms in an array in which the size of the prisms are in a range between 0.0005 inch to 0.003 inches on center. The array is formed by casting transparent plastic prisms in a mold formed by ruling three sets of grooves which intersect at an angle. The grooves are spaced apart in the range of 0.0005 inch to 0.003 inches on center. Before or after formation, the prisms are coated with a reflective material such as a metal. The main disadvantage of very small prisms is described as being that it is very difficult to rule an array of 0.002′′ on center prisms over a large area, as the ruling cutting diamond wears out. However, very small prisms are described as having advantages as well, including increased flexibility.
SUMMARY OF THE INVENTION
The present inventors have found that when very small cube-corner prisms are formed from a master having precisely positioned V-shaped intersecting grooves, retroreflective masters and retroreflective replicas thereof such as retroreflective sheeting can exhibit a moiré-like pattern. It is surmised that the occurrence of such moiré-like pattern is caused from optical interference between neighboring cubes (i.e. group of cubes wherein the incident light is coherent). The presence of this moiré-like pattern in the sheeting can detract from the appearance of retroreflective articles comprising such retroreflective sheeting and in particular can diminish the legibility of traffic signs comprising such sheeting.
The present inventors have discovered methods of making a master as well as the corresponding tooling and retroreflective sheeting that minimize and eliminate the occurrence of such moiré-like pattern.
In preferred embodiments, the method comprises forming three sets of V-shaped grooves in a substrate such that the intersections form an array of cube-corner elements. The grooves in each set have average groove spacings ranging from 0.0005 inches (0.0127 mm) to 0.0070 inches (0.1778 mm). The grooves are formed such that the groove position of at least every 10th groove in at least one set is varied from an adjacent parallel groove by a magnitude ranging from about 50 nm to about {fraction (1/10)}th of the average groove spacing.
Also disclosed are methods of making a master wherein the grooves in each set are formed with a groove position precision ranging from about +/−10 nm to about +/−500 nm for a distance of 10 consecutive grooves and at least every 10th groove in at least one of the three sets is varied from an adjacent parallel groove by a magnitude ranging from about 15 nm to about {fraction (1/10)}th of the average groove spacing.
Also disclosed are methods of making a master comprising cube corner elements wherein the elements have a lateral dimension in plan view ranging from 0.0005 inches (0.0127 mm) to 0.0070 inches (0.1778 mm) throughout the array and at least 10% of neighboring cubes are formed such the cubes are randomly shifted in phase by at least {fraction (1/10)}th of a wavelength of visible light. In preferred embodiments a higher percentage of neighboring cubes are shifted in phase and/or the magnitude of the shift in phase is greater.
The magnitude of groove position variation is typically less than {fraction (1/15)}th of the average groove spacing, preferably less than {fraction (1/20)}th, more preferably less than {fraction (1/50)}th, even more preferably less than {fraction (1/75)}th of the average groove spacing, and most preferably about {fraction (1/100)}th or less of the average groove spacing. When the minimum magnitude of groove position variation is at least 200 nm, the grooves are formed with a precision at least as precise as +/−100 nm, whereas for embodiments wherein the minimum magnitude of groove position variation is at least 400 nm, the groove precision is at least as precise as +/−200 nm. The frequency of groove position variation is typically at least every 7th groove, preferably at least every 5th groove, more preferably at least every 3rd groove, and most preferably each groove position is varied throughout the array.
A random or pseudo-random process is preferably used to generate the magnitude of groove position variation. The groove position is varied by altering the groove spacing and/or the groove depth. The cube-corner elements may be canted or uncanted. The groove angle precision is typically at least as precise as +/−2 arc minutes, preferably at least as precise as +/−1 arc minute, and more preferably at least as precise as +/−1⁄2 arc minute. For embodiments wherein the master is retroreflective, the master is substantially free of a moiré-like pattern.
Also disclosed are methods of making retroreflective sheeting comprising providing a tooling that would result in the occurrence of a moiré-like pattern and tiling one or more tooling such that each tile is less than about 1⁄4inch (6.35 mm) in at least one dimension.
Also disclosed are methods of making a tooling comprising providing any of such masters, electroplating the master forming a negative tooling, removing the tooling from the master, optionally electroplating the negative tooling forming a positive tooling, and optionally electroplating the positive or negative tooling forming a multigenerational tooling.
Also disclosed are methods of making a retroreflective sheeting comprising providing such toolings having a microprismatic surface, casting a fluid resin composition on the microprismatic face of the tooling, allowing the composition to harden forming a sheet, and removing the tooling. In an alternate embodiment, a retroreflective sheeting may be formed by providing the tooling having a microprismatic surface, providing a moldable substrate, and contacting the microprismatic surface of the tooling to the substrate such that a replica of the microprismatic surface is imparted on the substrate, and removing the tooling. The resin composition or moldable substrate is typically transparent, such as polycarbonate. The method may optionally further comprise applying a reflective coating to the hardened resin or moldable substrate replica.
In other aspects, the invention relates to retroreflective sheeting comprising a polymeric sheet having an array of cube-corner elements. The elements are formed from intersecting V-shaped grooves. The grooves preferably have an average groove spacing ranging from 0.0005 inches (0.0127 mm) to 0.007 inches (0.1778 mm) and the sheeting is substantially free of a moiré-like pattern. A continuous land layer preferably connects the elements.



DESCRIPTION OF THE DRAWINGS
FIG. 1 depicts a magnified plan view of a portion of a master comprising three sets of V-shaped parallel grooves. An actual 6-inch-square (15.24-centimeter-square) master having a groove spacing of 0.004 inches (0.1016 mm) would have 1500 cube-corner elements along the width totaling over 2 million for the entire area. This figure also depicts a magnified plan view of a portion of retroreflective sheeting formed from a tool that was a negative replica of the master.
FIG. 2 depicts a photograph of a tooling that was a negative replica of a master having a constant groove spacing of less than 0.003500 inches (0.088900 mm) throughout the array wherein the grooves were cut with a precision at least as precise as +/−100 nm. The photograph was taken with an Olympus C700 digital camera using the flash at a distance of about 10 feet (3 meters).
FIG. 3 depicts a photograph of a tooling that was a negative replica of a master wherein the grooves were cut with a precision at least as precise as +/−100 nm and 90% of the groove spacings were randomly varied, the average groove spacing being the same as in FIG. 2 and the magnitude of variation within the range of +/−{fraction (1/100)}th of the average groove spacing.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention relates to methods of making a master and replicas thereof including tooling and retroreflective sheeting. The invention further relates to the corresponding master, tooling and in particular retroreflective sheeting. The occurrence of a moiré-like pattern in a retroreflective master, tooling or sheeting is substantially reduced, preferably minimized, and more preferably eliminated in the retroreflective sheeting. As used herein “substantially free of a moiré-like pattern” refers to an observation that is similar to that depicted in FIG. 3 in comparison to FIG. 2 when evaluated by shining the light from an ordinary flash light held near an observer's eyes at about the position of the nose at a distance from a retroreflective master or replica of up to about twenty feet, illuminating the retroreflective master or replica approximately normal to its plane.
The master is preferably manufactured with a groove-forming machine that employs a direct machining technique that comprises forming a pattern of grooves that mutually intersect to form cube-corner elements. The grooved substrate is referred to as a master from which a series of replicas may be formed. Examples of direct machining techniques include flycutting, milling, grinding and ruling such as described in U.S. Pat. Nos. 4,588,258 (Hoopman) and 3,712,706 (Stamm), which disclose single or multiple passes of a machine tool having two opposing cutting surfaces for cutting grooves to form cube-corner optical faces in a substrate.
Any substrate suitable for forming directly machined groove sets may be employed in the method of making the master of the invention. Suitable substrates should machine cleanly without burr formation, exhibit low ductility and low graininess and maintain dimensional accuracy after groove formation. A variety of machinable plastics or metals may be utilized. Suitable plastics comprise thermoplastic or thermoset materials such as acrylics or other materials. Machinable metals include aluminum, brass, electroless nickel alloys, and copper. Preferred metals include non-ferrous metals. Preferred machining materials are typically chosen to minimize wear of the cutting tool during formation of the grooves.
The diamond tools suitable for directly machining the groove sets are of high quality such as diamond tools that can be purchased from K&Y Diamond (Mooers, N.Y.) or Chardon Tool (Chardon, Ohio). In particular, suitable diamond tools are scratch free within 10 mils of the tip, as can be evaluated with a 2000× white light microscope. Typically, the tip of the diamond has a flat portion ranging in size from about 0.00003 inches (0.000762 mm) to about 0.00005 inches (0.001270 mm). Further, the surface finish of suitable diamond tools preferably have a roughness average of less than about 3 nm and a peak to valley roughness of less than about 10 nm. The surface finish can be evaluated by forming a test cut in a machinable substrate and evaluating the test cut with a micro-interferometer, such as can be purchased from Wyko (Tucson, Ariz.), a division of Veeco.
Although the method of making a master in accordance with the present invention is directed toward direct machining methods, the tooling and retroreflective sheeting could be derived from a master manufactured by other methods as well wherein the precise formation of retroreflective cube-corner elements would result in the occurrence of such moire-like pattern in the absence of the present invention. The resulting cube corner elements in plan view may have other shapes that are non-triangular including but not limited to trapezoids, rectangles, quadrilaterals, pentagons, or hexagons.
In the method of making the master of the invention, a plurality of V-shaped grooves are formed in a substrate (e.g. metal plate). As used herein, “cutting angle” refers to the relative orientation of the groove sets with respect to each other. “Groove spacing” refers to the distance (e.g. in the x-direction) between the nadir of a groove and the nadir of an adjacent parallel groove, the nadir being the lowest point of the groove. “Groove depth” refers to the distance (e.g. in the y-direction) between the top surface of the substrate (e.g. plate) and the nadir of the groove. “Groove position” refers to the two-dimensional position of the groove relative to the surface of the master (e.g. x, y coordinates). The third dimension of the groove (e.g. z-direction) is typically constant, extending from an outer edge of the master plate to an opposing outer edge. Accordingly, changing the groove spacing, the groove depth, or combination thereof can alter the groove position. “Groove half-angle” refers to the angle formed on either side of the V-shaped groove. The groove half angles are measured relative to a reference plane that is aligned with the cutting direction and normal to the plane of the substrate. The “groove angle” is the sum of adjacent half angles sharing the same nadir.
Typically, a first set of parallel grooves are formed in a plane, as depicted by grooves 1, 1 to 1, 20 of FIG. 1; a second set of parallel grooves are formed in the plane at a cutting angle relative to the first set, as depicted by grooves 2, 1 to 2, 31 of FIG. 1; and a third set of parallel grooves are formed in the plane at a cutting angle relative to the first set, as depicted by grooves 3, 1 to 3, 31 of FIG. 1. Each set comprises a plurality of adjacent parallel grooves. As used herein “adjacent parallel groove” refers to the groove on either side in the same set. For example, an adjacent parallel groove with respect to groove 1, 2 is groove 1, 1 or 1, 3.
Each groove within a set as well as each set of grooves is typically formed at a common depth. The cutting angle is typically about 60° and specifically chosen to be a specified angle within the range from about 45° to about 75°. The groove angles for each groove set intersection are chosen such that the dihedral angles are about 90°, forming cube-corner elements. In the case of uncanted cubes, the nominal groove angle is the same for all three sets. Alternatively, the cube-corner elements may be canted, the groove and cutting angles being chosen such that the optical axes of the elements are tilted. An example of forward canting is described in U.S. Pat. No. 4,588,258 (Hoopman). Further, the canted or uncanted cubes may be formed such that the groove angle is varied slightly (e.g. +/−10 arc minutes) to control the spread of retroreflected light. As depicted by FIG. 1, the three sets of intersecting grooves result in an array of cube-corner elements arranged in a uniform pattern. The array preferably has substantially the maximum number of elements per area of cube-corner elements.
The V-shaped grooves are formed with a diamond-tooling machine that is capable of forming each groove with fine precision. Moore Special Tool Company, Bridgeport, Conn.; Precitech, Keene, N.H.; and Aerotech Inc., Pittsburg, Pa., manufacture suitable machines for such purpose. Such machines typically include a laser interferometer-positioning device. A suitable precision rotary table is commercially available from AA Gage (Sterling Heights, Mich.); whereas a suitable micro-interferometer is commercially available from Zygo Corporation (Middlefield, Conn.) and Wyko (Tucson, Ariz.) a division of Veeco. The precision (i.e. point to point positioning) of the groove spacing and groove depth is preferably at least as precise as +/−500 nm, more preferably at least as precise as +/−250 nm and most preferably at least as precise as +/−100 nm. The precision of the groove angle is at least as precise as +/−2 arc minutes (+/−0.033 degrees), more preferably at least as precise as +/−1 arc minute (+/−0.017 degrees), and most preferably at least at precise as +/−1⁄2 arc minute (+/−0.0083 degrees). Further, the resolution (i.e. ability of groove forming machine to detect current axis position) is typically at least about 10% of the precision. Hence, for a precision of +/−100 nm, the resolution is at least +/−10 nm. Over short distances (i.e. 10 adjacent parallel grooves), the precision is approximately equal to the resolution.
In order to consistently form a plurality of grooves of such fine accuracy over duration of time, the temperature of the process is maintained within +/−0.1° C. and preferably within +/−0.01° C. Further, to maintain groove angle tolerances, all the grooves in the master are preferably initially rough cut to a depth about 10 microns shallower than the final depth and then finish cut in alternating directions. As depicted in FIG. 1, the first groove 1, 1 (i.e. first set, first groove) is finish cut. The second groove is skipped and the third groove 1, 3 is finish cut in the same manner except in the opposite direction. The fourth groove was skipped and the fifth groove 1, 5 was finish cut in the first direction, etc. until the last groove at the bottom of the plate was formed. Then the alternating (i.e. skipped even numbered) grooves were finish cut from bottom to top in the same manner. The second and third groove sets are then cut in the same fashion.
The applicants have found that when small cubes are formed in a master with such precision, the retroreflective replicas thereof (i.e. tooling and sheeting) exhibit a moiré-like pattern. For instances wherein the master is made from a suitable substrate such that the master itself is retroreflective (e.g. transparent plastic), the master will also exhibit this moiré-like pattern. For embodiments wherein a tooling is formed from a master, the pattern is replicated during the manufacture of the tooling. Further, the pattern is then replicated again when retroreflective sheeting is formed from such tooling. Thus, for embodiments wherein a negative copy tool is employed to form a positive copy retroreflective sheeting, the surface of the retroreflective sheeting is substantially the same as the master from which it was derived.
Without intending to be bound by theory, it is surmised that the presence of such moiré-like pattern is an interference effect caused by coherence of incident light illuminating on and reflecting from neighboring cubes. The area over which the light is coherent defines the size of the neighborhood and is greater than the aperture size of the cubes. The aggregate of cubes that define that neighborhood all affect the incoming light identically. Neighboring cubes have within some small fraction of a wavelength of visible light an identical, repeating geometry. The reflected electric field of the light is theorized to only differ by the position of the cubes, the sum of the fields from individual cubes giving rise to the observed moiré-like pattern.
For reasons not fully understood, the occurrence of this moiré-like pattern was not readily evident in larger cubes, having a groove spacing of 0.01 inches (0.254 mm) for example. Accordingly, the methods and articles of the present invention are primarily directed to relatively small cubes, having an average groove spacing (i.e. pitch) in the range of 0.0005 inches (0.0127 mm) to 0.007 inches (0.1778 mm). Further, it is surmised that the severity of the occurrence of this moiré-like pattern tends to increase as the pitch decreases. Thus, the invention is most useful for methods of making masters and corresponding articles wherein the average groove spacing is less than 0.004 inches (0.1016 mm), and preferably less than 0.0035 inches (0.0889 mm).
Regardless of the technique employed in making the retroreflective elements, the lateral dimension of the elements (i.e. size of the elements as measured between opposing sides or features) preferably ranges from 0.0005 inches (0.0127 mm) to 0.007 inches (0.1778 mm). The lateral dimension of the elements is preferably less than 0.004 inches (0.1016 mm) and more preferably less than 0.0035 inches (0.0889 mm).
The applicants have discovered that the occurrence of such pattern can be diminished or eliminated by introducing a certain magnitude and frequency of groove position variability into the method of making the master wherein the variability is intentional and controlled. In doing so, one can minimize or eliminate the moiré-like pattern without sacrificing the retroreflected brightness. Altering the groove spacing, the groove depth, or combination thereof can vary the groove positions.
In contrast to forming cube-corner elements having substantially different sizes, as described in U.S. Pat. No. 6,168,275 for example, in the present invention the variation is relatively small such that the cube-corner elements of the master, tooling and sheeting are substantially the same size throughout the array, meaning that the smallest cube is at least 85% and preferably at least 90% of the size in comparison to the largest cube. In another regard, the active aperture of each cube is substantially the same as a corresponding cube in comparable sheeting wherein the only substantial difference being that the comparable sheeting employs a constant groove position throughout the array. For example, whereas in a comparable sheeting the grooves would have a common depth and constant spacing throughout the array [e.g. 0.003500 inch (0.088900 mm)], the sheeting of the invention would have an average groove spacing of 0.003500 inch (0.088900 mm) with the actual groove spacing varying from the average by a magnitude in the range of +/−0.000035 inch (0.000889 mm). In the present invention, the active aperture of the varied cube corner element (e.g. cube formed by the intersection of grooves 1,2; 2, 20; and 3,2) has substantially the same active aperture as the same cube corner element formed by the same intersections of the comparable sheeting having groove positions wherein groove position is constant. The effective area (i.e. active aperture) for a single or individual cube corner element may be determined by, and is equal to, the topological intersection of the projection of the three cube corner surfaces on a plane normal to the refracted incident ray with the projection of the image surfaces of the third reflection on the same plane. One procedure for determining effective aperture is discussed for example by Eckhardt, Applied Optics, v. 10 n. 7, Jul. 1971, pp. 1559-1566. Straubel U.S. Pat. No. 835,648 also discusses the concept of effective area or aperture.
The magnitude of the groove position variation ranges from greater than the precision of the groove-forming machine (i.e. +/−the resolution) to about {fraction (1/10)}th of the average groove spacing of the groove set. Accordingly, the magnitude of purposeful variation described herein is greater than the variation present as a result of machining tolerances. Further, however, the variation is substantially smaller than the variation employed for forming cube-corner elements that are substantially different in size. The magnitude of variation is at least 15 nm, preferably at least 25 nm, more preferably at least 50 nm and more preferably at least 100 nm, to insure that the variation is sufficiently large to shift the reflected light out of phase to the extent that can be detected by the human eye. For less precise groove forming machines, the minimum magnitude of variation is typically at least about 200 nm and preferably at least about 400 nm. At variations of greater than {fraction (1/10)}th of the target average groove spacing, the cube-corner elements are no longer substantially the same in size and geometry. Further, the cube-corner elements on at least one side of the groove have a substantially reduced active aperture, which can cause diminished retroreflected brightness at certain angles, particularly when the groove position variation is present at a high frequency, such as in the case wherein all the groove spacings are randomly varied throughout the array. Typically, however, the magnitude of the groove position variation is less than about {fraction (1/15)}th of the groove spacing, preferably less than about {fraction (1/20)}th, more preferably less than about {fraction (1/50)}th, and even more preferably less than about {fraction (1/75)}th, and most preferably about {fraction (1/100)}th or less to effectively eliminate the occurrence of the moiré-like pattern, without significantly affecting the retroreflected brightness.
In order to obtain a perceptible reduction of the occurrence of the moiré-like pattern, at least every 10th groove in at least one of the three sets is varied to the magnitude just described, meaning that throughout the array there are no more than 9 consecutive parallel grooves in a groove set have identical depths (e.g. 0.001500 inches (0.0381)) and a constant groove spacing (e.g. 0.003200 inches (0.08128 mm))+/−the precision. For a further reduction, at least every 8th groove in at least one set, preferably at least every 7th groove in at least one set, and more preferably at least every 6th groove in at least one set is varied. For an appreciable reduction, however, at least every 5th groove in at least one set, preferably at least every 4th groove, and more preferably at least every 3rd groove spacing is varied. In order to obtain a substantial reduction, the variation is introduced at a frequency such that every other groove or every groove position is varied.
It is surmised that varying the groove position at the frequency just described in at least two sets is more preferred than introducing such variation in only a single groove set. Further, introducing such variation in all three sets is surmised most preferred. Accordingly, the present invention describes 1000 combinations of groove position variation frequencies.
Upon introducing sufficient variation, a significant portion of neighboring cubes are shifted in phase such that the portion affected no longer affects the incident light identically. Typically at least 10% of neighboring cubes are randomly shifted in phase in the medium in which the light travels. In instances where the light travels through the microprismatic substrate, the medium and microprismatic substrate are one in the same. For other constructions, where light is retroreflected from the microstructured surface of the substrate, the medium is the material adjacent to the microstructured surface. Preferably, the shifting is random since it is surmised that shifting neighboring cubes in phase in a regular pattern may give rise to a different optical interference pattern. The percentage of cubes that are shifted in phase is related to the frequency at which the groove position variation is introduced. Since higher frequencies of groove position variation is preferred to obtain a significant reduction in the occurrence of the moiré-like pattern, it is also preferred that at least 20%, more preferably at least 30%, even more preferably at least 40%, and even more preferably at least 50% of neighboring cubes are formed such that the cubes are shifted in phase. To eliminate the occurrence, it is preferred that at least 60%, more preferred that at least 70%, even more preferred that at least 80% and most preferred that 90% or greater of the neighboring cubes are shifted in phase.
Although the magnitude of variation can be introduced in a repeating pattern, it is preferred that the magnitude of the variation is generated with a random or pseudo-random process. Various computer software programs are available that are suitable for generating random numbers within a specified range such as computer software commercially available under the trade designation “Microsoft Excel 97 SR-2”. The following general formula can be used to generate random numbers within a specific range of numbers:

RND*(UL−LL)+LL;

wherein RND is a random number between 0 and 1, UL is the upper limit of the range, and LL is the lower limit of the range. For example for a target constant groove spacing of 0.00320000 inches (0.081280 mm) the upper limit may be 0.000032 inches (0.00082 mm, i.e. {fraction (1/100)}th of the target groove spacing), and the lower limit is −0.000032 inches. Therefore, the formula can be written as RND*(0.000032-−0.000032)+−0.000032, or RND*(0.000064)−0.000032.

Typically, the grooves are formed with a diamond tool in the substrate such that the groove spacing, groove depth, and groove angle are uniform throughout each groove. Accordingly, the magnitude of the groove position variation is the same throughout the groove. Alternatively, however, the grooves may be scallop cut or cut irregularly, either randomly or in a repeating pattern such that the groove position may vary from cube to cube or vary along the boundaries of a single cube. Alternatively, preformed grooves of a master that result in retroreflective sheeting having such moiré-like pattern, may be altered to the magnitude and frequency just described. For example, the grooves may be recut such that the groove position is modified. Typically, however, this is less preferred in view of the additional machining involved.
Depending on the substrate into which the grooves were formed, the master itself may be useful as a retroreflective article such as in the case wherein grooves are formed in a suitable transparent plastic substrate. Typically, however, the master itself is not retroreflective such as in the case of employing a metal plate as the substrate. To form a master tool of suitable size for forming retroreflective sheeting, a plurality of toolings (also referred to as tiles) are formed by electroplating the grooved surface of the master to form negative copies, subsequently electroplating the negative copies to form positive copies, electroplating the positive copies to form a second generation negative copies, etc. Electroplating techniques are generally known, such as described in U.S. Pat. Nos. 4,478,769 and 5,156,863 to Pricone et al. Tiling such toolings together can then assemble a master tool of the desired size.
It is appreciated that the tiling process may also be suitable for introducing groove position variation at the interface between seamed tiles. Typically, however, tiles are relatively large in size such that groove position variation as a result of tiling is too infrequent to sufficiently diminish the occurrence of the moiré-like pattern. However, provided that the tiles are sufficiently small, less than about 1⁄4′′ (0.635 cm), the moiré-like pattern could be diminished as a result of tiling as well. This approach is less preferred due to the additional manufacturing time needed for such “micro” tiling. Further, groove position variation as a result of tiling does not affect the occurrence of the moiré-like pattern within the tile (i.e. sub-array).
The retroreflective sheet is preferably manufactured as an integral material, i.e. wherein the cube-corner elements are interconnected in a continuous layer throughout the dimension of the mold, the individual elements and connections there between comprising the same material. The surface of the sheeting opposing the microprismatic surface is typically smooth and planar, also being referred to as the “land layer”. This land layer typically has a thickness ranging from about 0.001 inches (25 microns) to about 0.006 inches (150 microns) and is preferably at least 0.002 inches (50 microns) to 0.003 inches (75 microns). Manufacture of such sheeting is typically achieved by casting a fluid resin composition onto the master tool and allowing the composition to harden to form a sheet.
Optionally, however, the grooved master(s) or positive copy(s) thereof can be used as an embossing tool to form retroreflective articles, such as described in JP 8-309851 and U.S. Pat. No. 4,601,861 (Pricone). Alternatively, the retroreflective sheeting can be manufactured as a layered product by casting the cube-corner elements against a preformed film as taught in PCT application No. WO 95/11464 and U.S. Pat. No. 3,684,348, or by laminating a preformed film to preformed cube-corner elements. In doing so the individual cube-corner elements are interconnected by the preformed film. Further, the elements and film are typically comprised of different materials.
Suitable resin compositions for the retroreflective sheeting of this invention are preferably transparent materials that are dimensionally stable, durable, weatherable, and readily formable into the desired configuration. Examples of suitable materials include acrylics, which have an index of refraction of about 1.5, such as Plexiglas brand resin manufactured by Rohm and Haas Company; polycarbonates, which have an index of refraction of about 1.59; reactive materials such as thermoset acrylates and epoxy acrylates; polyethylene based ionomers, such as those marketed under the brand name of SURLYN by E. I. Dupont de Nemours and Co., Inc.; (poly)ethylene-co-acrylic acid; polyesters; polyurethanes; and cellulose acetate butyrates. Polycarbonates are particularly suitable because of their toughness and relatively higher refractive index, which generally contributes to improved retroreflective performance over a wider range of entrance angles. These materials may also include dyes, colorants, pigments, UV stabilizers, or other additives. A specular reflective coating such as a metallic coating can be placed on the backside of the cube-corner elements. The metallic coating can be applied by known techniques such as vapor depositing or chemically depositing a metal such as aluminum, silver, or nickel. A primer layer may be applied to the backside of the cube-corner elements to promote the adherence of the metallic coating. In addition to or in lieu of a metallic coating, a seal film can be applied to the backside of the cube-corner elements; see, for example, U.S. Pat. Nos. 4,025,159 and 5,117,304. The seal film maintains an air interface at the backside of the cubes that enables total internal reflection at the interface and inhibits the entry of contaminants such as soil and/or moisture.
An adhesive layer also can be disposed behind the cube-corner elements or the seal film to enable the cube-corner retroreflective sheeting to be secured to a substrate. Suitable substrates include wood, aluminum sheeting, galvanized steel, polymeric materials such as polymethyl methacrylates, polyesters, polyamids, polyvinyl fluorides, polycarbonates, polyvinyl chlorides, polyurethanes, and a wide variety of laminates made from these and other materials.
The retroreflective sheeting is useful for a variety of uses such as traffic signs, pavement markings, vehicle markings and personal safety articles, in view of its high retroreflected brightness. The coefficient of retroreflection, RA, as measured as recommended by CIE publication No. 54 at −4° entrance, 0° orientation, 0.2° observation is typically at least about 100 candela per lux per square meter, preferably at least about 300 candela per lux per square meter, and more preferably at least about 800 candela per lux per square meter. The sheeting is advantageous, particularly in comparison to the cube-corner sheeting having relatively larger cubes in view of its ease in manufacturing.
Objects and advantages of the invention are further illustrated by the following examples, but the particular materials and amounts thereof recited in the examples, as well as other conditions and details, should not be construed to unduly limit the invention.
EXAMPLES
Comparative Example A
A master was prepared using a 9-inch (22.86 cm) diameter by about 1 inch thick block comprised of machinable metal. The block was machined to have a 4.75 inch (12.06 cm) square portion raised by about 0.005 inches (0.127 mm). The block was positioned on a groove-forming machine having a groove space and groove depth precision (i.e. point-to-point positioning) at least as precise as +/−100 nm and a resolution (i.e. ability of the laser interferometer positioning device to detect current axis position) of at least +/−10 nm.
Several diamond tools, which can be purchased from K&Y Diamond (Mooers, N.Y.) or Chardon Tool (Chardon, Ohio), were inspected to insure that each tool was suitable. Each diamond tool was evaluated with a 2000× white light microscope to insure that within 10 mils (250 microns) of the diamond tip the surface was scratch free. The surface finish of each diamond tool was also inspected by forming a test cut in a machinable substrate and evaluating the test cut with a micro-interferometer obtained from Wyko under the trade designation “RST” to ensure that the roughness average was less than 3 nm and that the peak to valley roughness was less than 10 nm. The tip of the diamond had a flat portion ranging in size from 0.00003 inches (0.00076 mm) to 0.00005 inches (0.001270 mm). A suitable diamond tool was fixed on the groove-forming machine so that V-shaped grooves could be formed into the raised center portion of the block. While forming each groove in the test block and master block, the temperature of the groove forming machine, block, and diamond tool was maintained at 20° C.+/−0.01° C. The diamond tool was adjusted by making cuts in a 1 inch cube test block. The cuts in the test block were made by iteratively adjusting the diamond tool to adjust the groove angle to a tolerance of +/−30 arc seconds (0.008 degrees) and measuring the resultant angles on a precision rotary table and micro-interferometer to optically reference the plane of the groove surfaces. A suitable precision rotary table is commercially available from AA Gage (Sterling Heights, Mich.); whereas a suitable micro-interferometer is commercially available from Zygo Corporation (Middlefield, Conn.) and Wyko (Tucson, Ariz.) a division of Veeco.
To maintain groove angle tolerances on the master, a diamond tool that was about 1° smaller than the smallest target groove angle was used to sequentially rough cut each groove in all three sets. Each groove was rough-cut back and forth to a depth that was 10 microns shallower than the target depth and a peak to valley surface finish of 0.000002 inches (0.000051 mm). To minimize diamond wear, the finish grooves were cut in the master in alternating directions to a peak to valley surface finish of 0.000001 inches (0.000025 mm). The first groove was finish cut in a first direction. The second groove was skipped and the third groove was finish cut in the same manner except in the opposite direction. The fourth groove was skipped and the fifth groove was finish cut in the first direction, etc., until the last groove at the bottom of the plate was formed. The diamond tool was then inspected for wear, as previously described, to insure that the average surface roughness continued to be no more than 3 nm and that the groove angle had not changed by more than 30 arc seconds (0.008 degrees). Then the alternating (i.e. skipped even numbered) grooves were finish cut from bottom to top in the same manner. The second and third groove sets were cut in the same fashion, inspecting the diamond tool prior to cutting the alternating grooves. In addition, the diamond tool was replaced and adjusted by use of the test block after each groove set.
For each of the comparative examples, the grooves were formed with constant groove spacing in each set throughout the array. For Comparative Example A, the first groove set is cut in the master plate with a pitch (i.e. groove spacing) of 0.003200 inches (0.081280 mm), a groove angle of 67.301 degrees and a cutting angle of 0 degrees. The second groove set is cut in the master plate having a pitch of 0.003102 inches (0.078791 mm), a groove angle of 72.081 degrees and a cutting angle +61 degrees (relative to the first direction), respectively. The third groove set is cut having a pitch, groove angle and cutting angle of 0.003102 inches (0.078791 mm), 72.081 degrees and −61 degrees (relative to the first direction), respectively. The groove depth for the first, second, and third directions was chosen such that the height of each cube was about 0.001476 inches (0.037490 mm).
The master was removed from the groove-forming machine. Toolings were made from the master by nickel electroforming the master as described in U.S. Pat. Nos. 4,478,769 and 5,156,863. Multigenerational positive and negative copies were formed such that the tools had substantially the same degree of precise cube formation as the master. An electroformed negative tool was used to impart the pattern of the tool onto a polycarbonate film having a thickness of approximately 200 microns and having an index of refraction of about 1.59. The negative tool was observed to have a moiré-like pattern, as depicted by FIG. 2. The tool was used in a compression molding press with the pressing performed at a temperature of approximately 375° F. (191° C.) to 385° F. (196° C.), a pressure of approximately 1600 psi, and a dwell time of 20 seconds. The molded polycarbonate was then cooled to about 200° F. (100° C.) over 5 minutes. The resulting sheeting had a structured surface comprising a plurality of cube-corner elements having a constant groove spacing with the base of the elements being integrally connected in the same plane in a continuous land layer, such land layer being substantially smooth and flat on the opposing surface such that the presence of the land layer does not detract from the retroreflective properties of the sheeting.
Retroreflective sheeting having a constant groove spacing of less than 0.003500 inches (0.088900 mm), prepared in same manner described in Comparative Example A, was evaluated by shining light from an ordinary flashlight held out from an observer's nose, illuminating the retroreflective sheeting normal to its plane. From a distance of about two feet, the light that retroreflected from the sheeting exhibited a moiré-like pattern when viewed by that same observer's eyes. The moiré-like pattern was retroreflected also as seen by that observer's eyes when the flashlight was replaced by the light specified as CIE Standard Illuminant A. The moiré-like pattern was clearly visible at distances of about 100 feet. The coefficient of retroreflection, RA, was measured as recommended by CIE publication No. 54 at −4° entrance, 0° orientation, 0.2° observation. The average of 9 spot readings over the entire area of the sample was 764 candles per lux per square meter with a standard deviation of 36 candles per lux per square meter.
Comparative Example B
The cube-corner surface of the retroreflective sheeting of Comparative Example A was coated with aluminum by vapor deposition at a thickness of about 950 angstroms.
The resulting retroreflective sheeting was evaluated in the same manner as Comparative Example A. The light that retroreflected from the sheeting was observed to exhibit the moiré-like pattern. The coefficient of retroreflection, RA, was measured as recommended by CIE publication No. 54 at −4° entrance, 0° orientation, 0.2° observation. The average of 9 spot readings over the entire area of the sample was 1085 candela per lux per square meter with a standard deviation of 37 candles per lux per square meter.
Comparative Example C
A master was made in the same manner as described in Comparative Example A. A positive copy tooling was used to form sheeting from that tooling. The cube-corner structured surface of this negative copy sheeting was coated with aluminum by vapor deposition.
The resulting retroreflective sheeting was evaluated in the same manner as Comparative Example A. The light that retroreflected from the sheeting was observed to exhibit the moiré-like pattern. The coefficient of retroreflection, RA, was measured as recommended by CIE publication No. 54 at −4° entrance, 0° orientation, 0.2° observation. The average of 9 spot readings over the entire area of the sample was 1950 candela per lux per square meter with a standard deviation of 98 candles per lux per square meter.
Example 1
Three sets of grooves were made using the same cutting angles, groove angles, and groove depth as described in Comparative Example A, with the only difference being that the groove spacing was precisely varied. A random number generating computer software package commercially available from Microsoft under the trade designation “Microsoft Excel 97 SR-2” was used to generate the magnitude of the groove spacing variation within a specified range. The following equation was used:

=IF(MOD(A3, 10)=0, 0,(RAND( )*(0.00003—(−0.00003))+(−0.00003))*25.4)

The function acts on the input from cell “A3”. If A3 is exactly divisible by ten the output is zero. If A3 is not exactly divisible by ten the output is a random number between 0.00003 and −0.00003. The multiplicative factor of 25.4 converts the random numbers into position in millimeters. This function generated a list of random numbers, the first 1260 of such random numbers are set forth in Tables I to IV as follows.
The odd columns show the index (i.e. cell “A3” in equation) input to the “MOD” function of the equation. The even columns are the random numbers generated by the equation. This formula was selected such that every 10th groove in all three sets would have a “perfect” intersection rather than randomly varied groove intersections. By doing so, the master could be inspected with a microscope in order to easily verify that the actual groove spacing was as intended.










TABLE I







index
Random #



















1
−0.00023



2
0.00002



3
−0.00076



4
−0.00001



5
−0.00006



6
0.00028



7
−0.0001



8
−0.00028



9
0.00011



10
0



11
0.00005



12
−0.00036



13
−0.00016



14
−0.00004



15
−0.00051



16
−0.00074



17
0.00031



18
−0.00074



19
−0.00039



20
0



21
−0.00049



22
0.00004



23
0.00027



24
−0.00054



25
0.00048



26
−0.00053



27
−0.00047



28
0.00066



29
0.00001



30
0



31
−0.00019



32
−0.00026



33
0.00051



34
0.00057



35
−0.00018



36
−0.00023



37
0.00011



38
−0.00028



39
−0.00043



40
0



41
−0.00026



42
−0.00075



43
−0.00062



44
−0.00004



45
−0.00005



46
−0.00053



47
−0.0005



48
−0.00058



49
−0.00003



50
0



51
0.00016



52
−0.00022



53
0.00053



54
0.00048



55
−0.00024



56
−0.00025



57
0.00058



58
0.00057



59
0.0006



60
0



61
−0.0001



62
0.00025



63
−0.00047



64
0.00066



65
0.00028



66
−0.00028



67
−0.00008



68
−0.00056



69
0.00052



70
0



71
0.00035



72
0.00062



73
−0.00002



74
0.00054



75
0.00055



76
0.00021



77
0.00035



78
0.00035



79
0.00014



80
0



81
0.0006



82
−0.00034



83
−0.00036



84
−0.00069



85
0.00042



86
−0.00048



87
−0.00064



88
−0.00001



89
0.00023



90
0



91
0.00038



92
−0.00062



93
−0.0006



94
0.00005



95
−0.0001



96
−0.00061



97
0.00038



98
0.00068



99
−0.00036



100
0



101
−0.00037



102
0.00028



103
−0.00022



104
0.00064



105
0.00014



106
0.00021



107
−0.00071



108
0.00055



109
0.00069



110
0



111
−0.00033



112
0.00022



113
−0.00017



114
−0.00024



115
0.00019



116
0.00003



117
−0.00014



118
0.00074



119
−0.00075



120
0



121
0.00008



122
0



123
−0.00014



124
0.00025



125
−0.00026



126
−0.0006



127
0.00074



128
0.00024



129
0.00046



130
0



131
0.00064



132
0.00039



133
−0.00032



134
−0.00039



135
0.00053



136
−0.00075



137
−0.00008



138
0.00066



139
0.00032



140
0



141
0.00045



142
−0.00057



143
0.00009



144
0.00057



145
0.00024



146
−0.00073



147
−0.00059



148
0.00022



149
0.00026



150
0



151
0.00026



152
0.00004



153
−0.00067



154
0.00029



155
−0.00075



156
−0.00075



157
0.00004



158
0.00009



159
0.00013



160
0



161
−0.00023



162
0.00068



163
−0.00037



164
−0.00056



165
0.00002



166
−0.00013



167
0.00053



168
0.00055



169
−0.0004



170
0



171
−0.00044



172
−0.00066



173
0.00057



174
−0.00044



175
0.00046



176
0.00033



177
0.00015



178
0.00008



179
−0.00003



180
0



181
0.00025



182
−0.00034



183
0.0007



184
0.00039



185
0.00074



186
0.00006



187
0.0007



188
0.00066



189
0.00042



190
0



191
−0.00019



192
−0.0007



193
−0.00043



194
0.00028



195
−0.00017



196
−0.00067



197
−0.00002



198
−0.00064



199
−0.0002



200
0



201
0.00037



202
−0.00056



203
0.00054



204
−0.00031



205
0.00056



206
−0.00039



207
0.00075



208
0.00051



209
0.00008



210
0



211
−0.00072



212
0.00056



213
0.00011



214
0.00069



215
0.0003



216
0.00017



217
0.00051



218
0.00059



219
0.00072



220
0



221
−0.00048



222
−0.00011



223
0.0001



224
0.00003



225
−0.00014



226
−0.00031



227
0.00004



228
0.00044



229
0.00002



230
0



231
−0.00057



232
0.00059



233
0.00047



234
0.00022



235
−0.00012



236
0.0003



237
−0.00001



238
−0.00028



239
0.0006



240
0



241
0.00034



242
0.00059



243
0.0002



244
−0.00034



245
−0.00035



246
−0.00069



247
−0.00062



248
−0.00018



249
−0.00053



250
0



251
−0.00063



252
0.00052



253
−0.00019



254
0.00031



255
0.00042



256
−0.00015



257
0.00052



258
−0.0003



259
0.00044



260
0



261
0.00045



262
−0.0004



263
−0.00031



264
−0.00042



265
−0.00075



266
−0.00034



267
−0.00039



268
−0.00001



269
0.0006



270
0



271
−0.00026



272
0.00005



273
0.0006



274
0.00011



275
−0.00069



276
−0.00056



277
0.00041



278
−0.00061



279
0.00039



280
0



281
0.00059



282
0.00038



283
−0.00064



284
0.00073



285
0.0002



286
−0.00013



287
0.00053



288
0.00046



289
−0.00026



290
0



291
0.00032



292
0.00027



293
−0.00049



294
0.00021



295
0.00008



296
0.00049



297
−0.0005



298
−0.0002



299
−0.00039



300
0



301
0.00012



302
−0.00044



303
−0.00012



304
0.0001



305
0.00049



306
0.00023



307
−0.00017



308
0.00026



309
−0.00031



310
0



311
0.00076



312
−0.00029



313
−0.00074



314
−0.00016



315
0.00001




















TABLE II







Index
Random #



















316
0.00067



317
−0.0003



318
−0.00028



319
0.00061



320
0



321
−0.00008



322
−0.00034



323
−0.0004



324
0.00031



325
−0.00053



326
−0.00035



327
0.00002



328
0.00013



329
−0.00044



330
0



331
−0.00026



332
0.00038



333
0.00046



334
−0.0006



335
0.00017



336
0.00053



337
−0.0002



338
0.00067



339
0.0005



340
0



341
−0.00044



342
−0.0002



343
0.00009



344
−0.00022



345
−0.00022



346
−0.00065



347
−0.00072



348
−0.00011



349
0.00006



350
0



351
0.00033



352
−0.00012



353
−0.00033



354
0.00051



355
−0.00023



356
−0.00017



357
−0.00007



358
−0.00039



359
0.00068



360
0



361
0.00039



362
−0.00042



363
−0.00045



364
−0.00026



365
−0.00058



366
−0.00027



367
−0.00033



368
0.00035



369
−0.00033



370
0



371
−0.00056



372
0.00061



373
0.00008



374
−0.00024



375
0.00038



376
0.00001



377
0.00016



378
0.00046



379
−0.0007



380
0



381
−0.00009



382
0.00052



383
0.00024



384
0.00044



385
−0.00041



386
0.0002



387
0.00042



388
0.00066



389
0.00001



390
0



391
0.00013



392
−0.00072



393
−0.00003



394
0.00016



395
0.00047



396
−0.00022



397
0.0001



398
0.00053



399
0.00027



400
0



401
0.00032



402
0.00074



403
−0.00025



404
0.00062



405
−0.00017



406
0.00057



407
−0.00047



408
0.00067



409
0.00057



410
0



411
−0.00063



412
−0.00014



413
0.00071



414
−0.00041



415
−0.0004



416
−0.00014



417
0.00052



418
−0.00051



419
0.0004



420
0



421
0.00047



422
0.00071



423
0.00049



424
0.00067



425
−0.00071



426
0.00052



427
0.00011



428
0.00033



429
−0.00036



430
0



431
−0.00056



432
0.00068



433
−0.00066



434
−0.00058



435
−0.00042



436
0.00064



437
0.00071



438
0.00005



439
0.00035



440
0



441
0.00023



442
−0.00061



443
0.00025



444
0



445
−0.00075



446
−0.00049



447
0.00058



448
0.00038



449
−0.00046



450
0



451
−0.00059



452
−0.00035



453
−0.00063



454
0.00066



455
0.00004



456
−0.00031



457
−0.00038



458
0.00063



459
−0.00023



460
0



461
0.00015



462
0.00033



463
0



464
0.00055



465
−0.00012



466
−0.00056



467
−0.00075



468
−0.00045



469
0.00045



470
0



471
−0.00002



472
−0.00037



473
0.0001



474
0.00075



475
−0.00002



476
−0.00014



477
−0.00021



478
0.00067



479
0.00068



480
0



481
0.00045



482
0.0006



483
0.00063



484
−0.00057



485
0.00018



486
0.00056



487
−0.00076



488
−0.00024



489
−0.00024



490
0



491
0.00014



492
−0.00037



493
0.00042



494
0.0003



495
0.00049



496
−0.00042



497
−0.00036



498
−0.00048



499
0.00025



500
0



501
0.00034



502
0.00056



503
−0.00058



504
−0.00066



505
0.0006



506
−0.00069



507
−0.00015



508
−0.00047



509
0.00066



510
0



511
−0.00026



512
0.00036



513
−0.00056



514
−0.00043



515
0.00045



516
−0.00021



517
0.00033



518
−0.00019



519
0.00045



520
0



521
0.00071



522
−0.00016



523
−0.00027



524
−0.00011



525
0.00013



526
−0.0001



527
−0.00038



528
0.00045



529
−0.00034



530
0



531
−0.00025



532
0.00049



533
−0.00019



534
−0.00059



535
0.00057



536
0.00037



537
0.00071



538
0.00048



539
−0.00045



540
0



541
0.00008



542
−0.00016



543
−0.00072



544
−0.0005



545
0.00004



546
0.00029



547
0.00056



548
0.00025



549
−0.00044



550
0



551
0.00018



552
0.00015



553
0



554
−0.00035



555
0.00028



556
−0.00058



557
0.00016



558
−0.00053



559
0.00037



560
0



561
−0.00025



562
−0.00041



563
0.00031



564
0.00029



565
−0.0005



566
−0.00042



567
0.00074



568
−0.00054



569
−0.00005



570
0



571
0.00065



572
0.00063



573
−0.00065



574
0.00038



575
−0.00047



576
0.00001



577
−0.0002



578
−0.00029



579
−0.00025



580
0



581
−0.00002



582
−0.00016



583
−0.00022



584
−0.00003



585
0.00013



586
−0.00014



587
0.00018



588
0.00055



589
0.00026



590
0



591
0.00032



592
0.00035



593
0.00056



594
−0.00008



595
−0.00038



596
0.00011



597
−0.00054



598
−0.00052



599
0.00029



600
0



601
0.00015



602
−0.00045



603
−0.00013



604
−0.00026



605
−0.00064



606
−0.00051



607
0.00029



608
0.00003



609
−0.00021



610
0



611
0.00001



612
−0.0007



613
0.00055



614
0.00042



615
−0.00062



616
−0.00025



617
0.00068



618
−0.00073



619
−0.00005



620
0



621
−0.00048



622
0.00055



623
0.00075



624
0.00006



625
−0.00042



626
0.00052



627
0.00076



628
−0.00075



629
0.00076



630
0




















TABLE III







index
Random #



















631
0.00024



632
−0.00043



633
0.00075



634
−0.00056



635
−0.00051



636
0.00028



637
−0.00033



638
0.00026



639
−0.0002



640
0



641
−0.00032



642
−0.00042



643
−0.00059



644
−0.00058



645
−0.00057



646
−0.00068



647
0.00035



648
−0.00025



649
0.00015



650
0



651
−0.00001



652
−0.00033



653
0.00048



654
−0.00052



655
−0.00003



656
0.00026



657
0.00033



658
0.00073



659
−0.00071



660
0



661
0.00011



662
−0.00014



663
0.00011



664
0.00006



665
−0.00012



666
−0.00061



667
−0.0002



668
0.00062



669
0.00015



670
0



671
0.00051



672
−0.00021



673
−0.00058



674
0.00015



675
−0.00056



676
0.00009



677
−0.00043



678
0.00006



679
0.00076



680
0



681
0.00008



682
0.00066



683
−0.00038



684
−0.00054



685
−0.0002



686
0.00002



687
−0.00041



688
−0.00066



689
0.00048



690
0



691
−0.00046



692
−0.00036



693
−0.00057



694
0.00046



695
−0.00043



696
0.00053



697
−0.00046



698
0.00046



699
−0.00022



700
0



701
−0.00016



702
−0.00071



703
−0.0001



704
0.00015



705
0.00015



706
0.00049



707
0.00036



708
0.00022



709
0.00035



710
0



711
−0.00075



712
−0.00075



713
0.00058



714
0.00037



715
−0.00055



716
−0.00056



717
−0.00057



718
−0.00022



719
0.00038



720
0



721
−0.00062



722
−0.00045



723
−0.00005



724
0.00004



725
−0.00041



726
−0.00016



727
0.00033



728
0.00075



729
0.00072



730
0



731
0.00016



732
−0.00071



733
−0.0004



734
−0.00034



735
−0.00021



736
−0.00028



737
−0.00028



738
0.00068



739
0.00046



740
0



741
0.00018



742
0.00059



743
0.00024



744
−0.00037



745
0.00008



746
−0.00029



747
−0.00011



748
−0.00054



749
0.00024



750
0



751
0.0005



752
0.00023



753
−0.00035



754
0.0003



755
0.00049



756
−0.00015



757
0.0007



758
0.0002



759
−0.00018



760
0



761
0.00009



762
−0.00054



763
0.0006



764
0.00065



765
−0.00032



766
0.00055



767
−0.00028



768
0.00045



769
−0.00002



770
0



771
0



772
−0.00075



773
0.00023



774
0.00048



775
0.00047



776
−0.00022



777
−0.00015



778
0.00052



779
0.00035



780
0



781
−0.00049



782
−0.00071



783
0.00019



784
0.00064



785
0.00076



786
−0.00033



787
0.00003



788
−0.00053



789
−0.00062



790
0



791
0.00071



792
−0.00046



793
0.00005



794
0.00074



795
0.00034



796
−0.00057



797
−0.00009



798
−0.00018



799
0.00021



800
0



801
−0.00055



802
−0.00063



803
0.00058



804
−0.00008



805
0.00074



806
−0.00037



807
−0.00009



808
−0.00009



809
0.00033



810
0



811
0.00046



812
−0.00063



813
0.00065



814
−0.00036



815
0.00005



816
−0.00076



817
−0.00002



818
0.00055



819
0.00048



820
0



821
0.00054



822
−0.00017



823
−0.00073



824
0.00012



825
−0.00021



826
−0.00057



827
−0.00037



828
−0.00022



829
−0.00027



830
0



831
0.00057



832
0.00016



833
0.00009



834
0.00072



835
−0.00053



836
0.00071



837
−0.00024



838
0.00019



839
−0.0001



840
0



841
0.00026



842
0.00036



843
−0.00036



844
−0.00005



845
−0.00059



846
0.00049



847
−0.00055



848
−0.00059



849
0.00035



850
0



851
−0.00029



852
0.00043



853
0.00035



854
0.00071



855
0.00045



856
0.00004



857
−0.00003



858
−0.00038



859
−0.00031



860
0



861
0.00036



862
0.0006



863
0.00045



864
0.00055



865
−0.00007



866
−0.00074



867
0.00031



868
0.0004



869
0.00039



870
0



871
0.00002



872
0.00036



873
−0.0003



874
−0.00059



875
0.00063



876
−0.00028



877
−0.00057



878
−0.00037



879
0.00014



880
0



881
0.00047



882
−0.00011



883
0.00042



884
−0.00054



885
−0.00001



886
0.0003



887
0.00018



888
−0.00008



889
−0.00029



890
0



891
−0.00006



892
−0.00059



893
−0.00049



894
−0.0001



895
−0.00025



896
−0.00008



897
0.0002



898
−0.00014



899
−0.00044



900
0



901
0.00042



902
−0.00036



903
−0.00057



904
−0.00023



905
0.00058



906
−0.00022



907
−0.0007



908
0.00062



909
0.00012



910
0



911
−0.00037



912
−0.00067



913
0.00031



914
−0.00055



915
0.00019



916
−0.00003



917
0.00022



918
−0.00015



919
−0.00019



920
0



921
−0.00065



922
0.00062



923
−0.00005



924
−0.00063



925
−0.0007



926
0.0004



927
−0.00059



928
0.00069



929
0.00008



930
0



931
−0.0007



932
−0.00066



933
0.00072



934
−0.00015



935
−0.00031



936
0.00062



937
−0.00062



938
0.00027



939
−0.00029



940
0



941
0.00074



942
−0.00057



943
0.00075



944
−0.00019



945
−0.0007




















TABLE IV







Index
Random #



















946
0.00036



947
0.00014



948
0.00034



949
0.00044



950
0



951
0.00065



952
0.00066



953
0.00004



954
0.00057



955
−0.00033



956
−0.00016



957
−0.00004



958
0.00031



959
0.00002



960
0



961
0.00045



962
−0.00027



963
−0.00061



964
−0.00041



965
0.00026



966
0.00063



967
−0.00071



968
0.00067



969
0.00031



970
0



971
0.00023



972
−0.00012



973
0.00034



974
0.00066



975
−0.00069



976
0.00067



977
−0.00001



978
−0.00026



979
−0.00015



980
0



981
−0.00069



982
−0.00036



983
−0.00053



984
0.00058



985
−0.00032



986
−0.00068



987
0.00011



988
−0.00067



989
−0.00036



990
0



991
−0.00003



992
−0.00058



993
0.00018



994
0.00059



995
0.00056



996
−0.00029



997
−0.00057



998
−0.00071



999
0.00021



1000
0



1001
0.00014



1002
−0.00053



1003
−0.00002



1004
0.00065



1005
0.0005



1006
−0.00035



1007
−0.00031



1008
0.0007



1009
−0.00058



1010
0



1011
−0.00019



1012
−0.00058



1013
0.00011



1014
−0.0003



1015
0.00013



1016
−0.0002



1017
0.0007



1018
0.00067



1019
0.00001



1020
0



1021
−0.00056



1022
−0.00043



1023
−0.00038



1024
0.00066



1025
−0.00029



1026
−0.00071



1027
0.00064



1028
0.00066



1029
−0.00034



1030
0



1031
−0.0001



1032
0.0002



1033
−0.0004



1034
0.00071



1035
−0.00025



1036
0.00018



1037
0.00069



1038
0.00071



1039
−0.0002



1040
0



1041
−0.00006



1042
−0.00056



1043
0.0003



1044
0.00074



1045
−0.00058



1046
0.00003



1047
0.00041



1048
0.0003



1049
0.00029



1050
0



1051
0.00045



1052
−0.00006



1053
−0.00054



1054
0.00002



1055
0.00025



1056
−0.00003



1057
−0.00047



1058
−0.00008



1059
0.00023



1060
0



1061
0.00011



1062
0



1063
−0.00029



1064
−0.0004



1065
−0.00012



1066
0.00046



1067
0.00019



1068
0.00058



1069
0.00045



1070
0



1071
0.00046



1072
−0.00012



1073
0.00003



1074
−0.00025



1075
0.00067



1076
0



1077
0.00059



1078
−0.00039



1079
−0.00074



1080
0



1081
−0.00045



1082
−0.00016



1083
0.00064



1084
−0.00069



1085
0.00046



1086
−0.00031



1087
−0.00045



1088
−0.00027



1089
0.00013



1090
0



1091
−0.00057



1092
−0.00048



1093
−0.00069



1094
0.00056



1095
0.00017



1096
−0.00037



1097
−0.0002



1098
0.00038



1099
0.00026



1100
0



1101
0.00043



1102
−0.00012



1103
−0.00013



1104
−0.00045



1105
0.00057



1106
−0.00047



1107
0.00021



1108
0.0005



1109
0.0005



1110
0



1111
−0.00011



1112
−0.00068



1113
0.00024



1114
0.0007



1115
0.00016



1116
−0.00041



1117
0.00019



1118
0.00034



1119
0.00038



1120
0



1121
−0.00033



1122
−0.00057



1123
0.00006



1124
−0.00003



1125
−0.00056



1126
0.00005



1127
−0.0002



1128
−0.00054



1129
−0.00056



1130
0



1131
0.00062



1132
−0.00002



1133
0.00018



1134
−0.00073



1135
−0.00028



1136
0.00031



1137
−0.00051



1138
0.00046



1139
0.00076



1140
0



1141
0.00019



1142
−0.00064



1143
−0.0003



1144
0.0003



1145
−0.00039



1146
−0.00022



1147
0.00015



1148
0.00001



1149
0.00075



1150
0



1151
−0.00043



1152
0.00021



1153
0.00024



1154
0.00025



1155
0.00076



1156
−0.0003



1157
−0.00055



1158
−0.00066



1159
0.00056



1160
0



1161
0.00051



1162
−0.00046



1163
0.00006



1164
−0.00051



1165
−0.00015



1166
0.00063



1167
0.00048



1168
0.00007



1169
0.00021



1170
0



1171
−0.00028



1172
0.00047



1173
0.00075



1174
−0.0004



1175
0.00072



1176
−0.00021



1177
0.00066



1178
−0.00015



1179
0.0005



1180
0



1181
−0.00041



1182
0.00005



1183
0.00014



1184
−0.00044



1185
0.00022



1186
−0.00009



1187
0.00025



1188
−0.00058



1189
0.00001



1190
0



1191
−0.00009



1192
0.00045



1193
−0.00043



1194
0.00006



1195
−0.00036



1196
0.00038



1197
0.00007



1198
0.00046



1199
0.00055



1200
0



1201
−0.00014



1202
0.0001



1203
−0.00013



1204
−0.00061



1205
−0.00011



1206
−0.00018



1207
−0.00064



1208
−0.00039



1209
0.00018



1210
0



1211
0.00037



1212
−0.00021



1213
−0.00006



1214
−0.00022



1215
0.00019



1216
−0.00076



1217
0.00019



1218
−0.00013



1219
0.0001



1220
0



1221
−0.00012



1222
−0.00026



1223
−0.00009



1224
−0.00028



1225
−0.00035



1226
0.00055



1227
0.00036



1228
−0.00036



1229
−0.00033



1230
0



1231
−0.00058



1232
−0.00018



1233
0.00023



1234
−0.00065



1235
−0.00036



1236
−0.00056



1237
0.00033



1238
0.00022



1239
−0.00044



1240
0



1241
0.00004



1242
−0.00002



1243
0.00032



1244
0.00072



1245
0.0002



1246
−0.00011



1247
−0.00005



1248
0.00019



1249
−0.00015



1250
0



1251
−0.00064



1252
−0.00005



1253
0.00046



1254
0.00075



1255
−0.00038



1256
0.00005



1257
−0.00037



1258
0.00052



1259
−0.00052



1260
0










After the master was rough cut as previously described, the grooves were fine cut in alternating directions in the same manner as Comparative A. For the first set of grooves, the magnitude of the groove spacing variation for each groove corresponded to the random number indicated in the even columns for index 20 through 743. Hence, the first groove had a groove spacing of 0.003200 inches (0.081280 mm) with a variation of 0, the third groove had a groove spacing of 0.003200 inches (0.081280 mm)−0.00049000 mm=0.003181 inches (0.080797 mm), the fifth groove had a groove spacing of 0.003200 inches (0.081280 mm)+0.00004000 mm=0.003202 inches (0.813308 mm), etc. After fine cutting the 743rd groove at the bottom of the plate, the alternating (i.e. skipped even numbered) grooves were finish cut from bottom to top in the same manner using the random number indicated in the even columns of the tables for index 20 through 743. The second and third sets of grooves were cut in the same manner, the magnitude of the groove spacing variation for each groove corresponding to the random number indicated in the even columns for index 21 through 1041.
The master was removed from the groove-forming machine. Toolings were made from the master in the same manner as described in Comparative Example A. The negative tool was observed not to have a moiré-like pattern, as depicted by FIG. 3. Cube-corner sheeting was then prepared from the toolings in the same manner as described in Comparative Example A. The resulting sheeting was then evaluated in the same manner as described in Comparative Example A. The coefficient of retroreflection, RA, was measured as recommended by CIE publication No. 54 at −4° entrance, 0° orientation, 0.2° observation. The average of 9 spot readings over the entire area of the sample was 995 candles per lux per square meter with a standard deviation of 7 candles per lux per square meter. The difference in RA in comparison to Comparative Example A is due in part to the moiré-like pattern interfering with the retroreflection and in part to the cubes of Comparative Example A having a different average groove spacing. The relatively large standard deviation of Comparative Example A in comparison to Example 1 is surmised to be caused by the moiré-like pattern interfering with the ability to measure the retroreflection.
Example 2
The cube-corner surface of the retroreflective sheeting of Example 1 was coated with aluminum by vapor deposition. The resulting retroreflective sheeting was evaluated in the same manner as Comparative Example A. The light that retroreflected from the sheeting was observed not to exhibit the moiré-like pattern. The coefficient of retroreflection, RA, was measured as recommended by CIE publication No. 54 at −4° entrance, 0° orientation, 0.2° observation. The average of 9 spot reading over the entire area of the sample was 1679 candela per lux per square meter with a standard deviation of 7 candles per lux per square meter.
Example 3
A master was made in the same manner as described in Example 1. A positive copy tooling was used to form sheeting in the same manner described in Comparative Example A. The cube-corner structured surface of this negative copy was coated with aluminum by vapor deposition in the same manner as described in Comparative Example B. The resulting retroreflective sheeting was evaluated in the same manner as Comparative Example A. The light that retroreflected from the sheeting was observed not to exhibit the moiré-like pattern. The coefficient of retroreflection, RA, was measured as recommended by CIE publication No. 54 at −4° entrance, 0° orientation, 0.2° observation. The average of 9 spot readings over the entire area of the sample was 2075 candela per lux per square meter with a standard deviation of 11 candles per lux per square meter.

## Claims

1. A method of making a master for producing retroreflective sheeting substantially free of a reflected moiré-like pattern by forming three sets of V-shaped grooves in a substrate such that the intersections form an array of cube-corner elements; wherein the grooves in each set are formed at a position having an average groove spacing ranging from 0.0005 inches (0.0127 mm) to 0.0070 inches (0.1778 mm) and the grooves are formed such that the groove position of at least every 10th groove in at least one set is varied from an adjacent parallel groove by a magnitude ranging from about 15 nm to about {fraction (1/10)}th of the average groove spacing.

2. The method of claim 1 wherein the magnitude is less than {fraction (1/15)}th of the average groove spacing.

3. The method of claim 1 wherein the magnitude is less than {fraction (1/20)}th of the average groove spacing.

4. The method of claim 1 wherein the magnitude is less than {fraction (1/50)}th of the average groove spacing.

5. The method of claim 1 wherein the magnitude is less than {fraction (1/75)}th of the average groove spacing.

6. The method of claim 1 wherein the magnitude is about {fraction (1/100)}th or less of the average groove spacing.

7. The method of claim 1 wherein the grooves arc formed with a groove position precision that is at least as precise as +/−10 nm for a distance of 10 consecutive grooves.

8. The method of claim 1wherein the magnitude of groove position variation is at least 200 nm.

9. The method of claim 8 wherein the grooves are formed with a groove position precision that is at least as precise as +/−100 nm.

10. The method of claim 1 wherein the magnitude of groove position variation is at least 400 nm.

11. The method of claim 10 wherein the grooves are formed with a groove position precision that is at least as precise as +/−200 nm.

12. A method of making a master for producing retroreflective sheeting free of a moiré-like pattern by forming three sets of V-shaped grooves in a substrate much that the intersections form an array of cube-corner elements; wherein the grooves in each set are formed with a groove position precision ranging front about +/−10 nm to about +/−500 nm for a distance of 10 consecutive grooves and the groove position of at least every 10th groove in at least one of the three sets is varied from an adjacent parallel groove by a magnitude ranging from about 15 nm to about {fraction (1/10)}th of the average groove spacing.

13. The method of claim 12 wherein the magnitude is less than {fraction (1/15)}th of the average groove spacing.

14. The method of claim 12 wherein the magnitude is less than {fraction (1/20)}th of the average groove spacing.

15. The method of claim 12 wherein the magnitude is less than {fraction (1/30)}th of the average groove spacing.

16. The method of claim 12 wherein the magnitude Is less than {fraction (1/17)}th of the average groove spacing.

17. The method of claim 12 wherein the magnitude is about {fraction (1/100)}th or less of the average groove spacing.

18. The method of claim 12 wherein the magnitude of groove position variation is at least 200 nm.

19. The method of claim 12 wherein the magnitude of groove position variation is at least 400 nm.

20. The method of claim 1 wherein at least every 7th groove position is varied.

21. The method of claim 1 wherein at least every 5th groove position is varied.

22. The method of claim 1 wherein at least every 3rd groove position is varied.

23. The method of claim 1 wherein substantially all the groove positions are varied.

24. The method of claim 20 wherein at least two sets are varied.

25. The method of claim 21 wherein at least two sets are varied.

26. The method of claim 22 wherein at least two sets are varied.

27. The method of claim 23 wherein at least two sets are varied.

28. The method of claim 20 wherein each of the three sets are varied.

29. The method of claim 21 wherein each of the three sets are varied.

30. The method of claim 22 wherein each of the three sets are varied.

31. The method of claim 23 wherein each of the three sets are varied.

32. The method of claim 1 wherein the magnitude is generated by a random or pseudo-random process.

33. The method of claim 1 wherein the varied groove position has a constant groove depth and varied groove spacing.

34. The method of claim 1 wherein the varied groove position has a constant groove spacing and varied groove depth.

35. The method of claim 1 wherein the varied groove position has varied groove spacing and varied groove depth.

36. The method of claim 1 wherein the cube-corner elements are uncanted.

37. The method of claim 1 wherein at least a portion of the cube-corner elements are canted.

38. The method of claim 1 wherein the grooves are formed with a groove angle precision that is at least as precise as +/−2 arc minutes.

39. The method of claim 1 wherein the grooves are formed with a groove angle position that is at least as precise as +/−1 arc minute.

40. The method of claim 1 wherein the grooves are formed with a groove angle precision that is at least as precise as +/−1⁄2arc minute.

41. The method of claim 1 wherein the master is retroroflective.

42. The method of claim 41 wherein light reflected from the master is substantially free of a moiré-like pattern.

43. A method of making a tooling comprising providing a muster according to claim 1;
electroplating the master forming a negative tooling; 
removing the tooling from the master; and 
optionally electroplating the negative tooling at least once forming at least one positive tooling; 
optionally electroplating the positive or negative tooling forming a multigenerational tooling.

44. A method of making a retroreflective sheeting comprising providing a tooling having a microprismatic surface according to claim 43;
casting a fluid rosin composition on the microprismatic surface of the tooling; 
allowing the composition to harden forming a sheet; and 
removing the tooling.

45. The method of claim 44 wherein the resin composition is transparent.

46. The method of claim 44 wherein the resin composition is polycarbonate.

47. A method of making a retroreflective sheeting comprising
providing a tooling having a microprismatic surface according to claim 44; 
providing a moldable substrate; 
contacting the microprismatic surface of the tooling to the substrate such that a replica of the microprismatic surface is imparted on the substrate; and 
removing the tooling.

48. The method of claim 47 wherein the moldable substrate is transparent.

49. The method of claim 48 wherein the moldable substrate is polycarbonate.

50. The method of claim 44 further comprising applying a reflective coating to the substrate.

51. Retroreflective sheeting comprising a polymeric sheet having an array of cube-corner elements, the elements formed from three sets of parallel intersecting V-shaped grooves, wherein the grooves in each set are formed at a position having an average groove spacing ranging from 0.0005 inches (0.0127 mm) to 0.007 inches (0.1778 mm) and the groove position of at least every 10th groove in at least one of the three sets differs from an adjacent parallel groove by a magnitude ranging from about 50 nm to about {fraction (1/10)}th of the average groove spacing.

52. The retroreflective sheeting of claim 51 wherein the magnitude is learn than {fraction (1/15)}th of the average groove spacing.

53. The retroreflective sheeting of claim 51 wherein the magnitude is less than {fraction (1/20)}th of the average groove spacing.

54. The retroreflective sheeting of claim 51 wherein the magnitude is less than {fraction (1/50)}th of the average groove spacing.

55. The retroreflective sheeting of claim 51 wherein the magnitude is less than {fraction (1/75)}th of the average groove spacing.

56. The retroreflective sheeting of claim 51 wherein magnitude is about {fraction (1/100)}th or less of the average groove spacing.

57. The retrorefloctive sheeting of claim 51 wherein the magnitude of groove position variation is at least 200 nm.

58. The retroreflective sheeting of claim 51 wherein the magnitude of groove position variation is at least 400 nm.

59. The retroreflective sheeting of claim 51 wherein at least every 7th groove position is varied.

60. The retroreflective sheeting of claim 51 wherein at least every 5th groove position is varied.

61. The retroreflective sheeting of claim 51 wherein at least every 3rd groove position is varied.

62. The retroreflective sheeting of claim 51 wherein substantially all the groove positions are varied.

63. The retroroflective sheeting of claim 51 wherein the groove position has a constant groove depth and differs in groove spacing.

64. The retroreflective sheeting of claim 51 wherein the groove position has a constant groove spacing and differs in groove depth.

65. The retroroflective sheeting of claim 51 wherein the groove position differs in groove spacing and differs in groove depth.

66. The retroreflective sheeting of claim 51 wherein the cube-corner elements are uncanted.

67. The retroreflective sheeting of claim 51 wherein at least a portion of the cube-corner elements are canted.

68. The retroreflective sheeting of claim 51 wherein the sheeting is substantially free of a moiré-like pattern.