Method of manufacturing an asymmetric cube corner article

A method is disclosed for manufacturing a cube corner article comprising the steps of providing a machinable substrate material suitable for forming reflective surfaces, and creating a plurality of geometric structures including cube corner elements in the substrate. The step of creating the cube corner elements comprises directly machining at least three sets of parallel grooves in the substrate so that only one side of at least one groove in at least one groove set forms cube corner element optical surfaces.

FIELD OF INVENTION 
This invention relates to retroreflective articles having prismatic 
retroreflective elements. 
BACKGROUND 
Many types of retroreflective elements are known, including prismatic 
designs incorporating one or more raised structures commonly known as cube 
corners. Retroreflective sheeting which employs cube corner type 
reflecting elements is well known. Cube corner reflecting elements are 
trihedral structures which have three approximately mutually perpendicular 
lateral faces meeting in a single corner. Light rays are typically 
reflected at the cube faces due to either total internal reflection or 
reflective coatings. The manufacture of directly machined arrays 
comprising retroreflective cube corner elements has many inefficiencies 
and limitations. Total light return and percent active aperture are 
adversely affected by these limitations, and overall production costs 
versus performance are often higher relative to the new class of articles 
and methods of manufacture taught below. The asymmetric arrays of this 
invention permit excellent manufacturing flexibility and production of 
cube corner element designs which are highly tailorable to particular 
needs. 
SUMMARY OF INVENTION 
The invention comprises a method of manufacturing a retroreflective cube 
corner article comprising the steps of providing a machinable substrate 
material suitable for forming reflective surfaces, and creating a 
plurality of geometric structures including cube corner elements in the 
substrate. The step of creating the cube corner elements comprises 
directly machining at least three sets of parallel grooves in the 
substrate so that only one side of at least one groove in at least one 
groove set forms cube corner element optical surfaces. The invention also 
includes retroreflective replicas of an article manufactured according to 
this method. 
The invention also includes a method of manufacturing an article having a 
plurality of geometric structures including cube corner elements formed by 
directly machining three sets of parallel grooves into a machinable 
substrate. A first groove set of parallel grooves is directly machined 
along a first path in the substrate. A second groove set of parallel 
grooves is directly machined along a second path in the substrate. A third 
groove set comprising at least one additional groove is directly machined 
along a third path in the substrate. Only one side of at least one groove 
in at least one groove set forms cube corner element optical surfaces. 
The invention also comprises a retroreflective cube corner article which is 
a replica of a machined substrate in which a plurality of geometric 
structures including cube corner elements are directly machined. Each cube 
corner element is bounded by a groove from each of three sets of parallel 
grooves. Only one side of at least one groove in at least one groove set 
forms cube corner element optical surfaces. The article exhibits 
asymmetric entrance angularity when rotated about an axis within the plane 
of the substrate. 
The invention also comprises a retroreflective article which is a replica 
of a directly machined substrate having a plurality of geometric 
structures including directly machined canted cube corner elements. The 
cube corner elements are arranged between a plurality of grooves in the 
substrate which intersect at angles of other than 90.degree.. Each cube 
corner element has a symmetry axis, and the symmetry axis of substantially 
every one of the cube corner elements in the article is in substantially 
parallel relation to each other. 
The invention also comprises a retroreflective cube corner element 
composite sheeting comprising a plurality of zones of retroreflective cube 
corner elements in an ordered array within each zone. The array of each 
zone comprises a replica of a directly machined substrate in which a 
plurality of cube corner elements are machined in the substrate. Each cube 
corner element is bounded by a groove from each of three sets of parallel 
grooves in the substrate, and only one side of at least one groove in at 
least one groove set forms cube corner element optical surfaces. 
The invention also comprises a retroreflective cube corner element 
composite sheeting comprising a plurality of zones of retroreflective cube 
corner elements in an ordered array within each zone. The array of each 
zone comprises a replica of a directly machined substrate in which a 
plurality of cube corner elements are machined in the substrate between a 
plurality of grooves which intersect at angles of other than 90.degree.. 
Each cube corner element has a symmetry axis, and the symmetry axis of 
substantially every one of the cube corner elements within each zone is in 
substantially parallel relation to each other.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
The manufacture of retroreflective cube corner element arrays is 
accomplished using molds made by different techniques, including those 
known as pin bundling and direct machining. Molds manufactured using pin 
bundling are made by assembling together individual pins which each have 
an end portion shaped with features of a cube-corner retroreflective 
element. U.S. Pat. No. 3,926,402 (Heenan et al) and U.S. Pat. No. 
3,632,695 (Howell) are examples of pin bundling. 
The direct machining technique, also known generally as ruling, comprises 
cutting portions of a substrate to create a pattern of grooves which 
intersect to form cube corner elements. The grooved substrate is referred 
to as a master from which a series of impressions, i.e. replicas, may be 
formed. In some instances, the master is useful as a retroreflective 
article, however replicas, including multi-generational replicas, are more 
commonly used as the retroreflective article. Direct machining is an 
excellent method for manufacturing master molds for small micro-cube 
arrays. Small micro-cube arrays are particularly beneficial for producing 
thin replica arrays with improved flexibility, such as continuous rolled 
goods for sheeting purposes. Micro-cube arrays are also more conducive to 
continuous process manufacturing. The process of manufacturing large 
arrays is also relatively easier using direct machining methods rather 
than other techniques. One example of direct machining is shown in U.S. 
Pat. No. 4,588,258 (Hoopman). 
FIG. 1 illustrates a method by which directly machined masters of 
conventional cube arrays are manufactured. A directly machinable substrate 
20 receives a plurality of parallel grooves 23, arranged in two 
non-parallel sets. Grooves through directly machinable substrate 20 are 
formed by a machine tool with two opposing cutting surfaces for cutting 
cube corner optical faces. Examples of shaping, ruling, and milling 
techniques suitable for forming directly machined grooves are discussed in 
U.S. Pat. No. 3,712,706 (Stamm). The two groove sets 23 produce the 
partial cube shapes 39 depicted in the sectional views of FIG. 2 and FIG. 
3. Machine tool 26, such as that shown in FIG. 4, is typically mounted on 
a post 35 and has a cutting surface 29 on each side of a tool central axis 
32. 
In FIGS. 1-4, partial cube shapes 39 are shown as rhombus shaped structures 
formed in substrate 20. At least two grooves 23 in both non-parallel 
groove sets are required to produce shapes 39. A third groove 41, as shown 
in sectional view dashed lines in FIG. 5, is required to produce 
conventional cube corner elements. Portions of a conventional cube array 
42 after completion of the three groove sets are shown in FIGS. 6 and 7. 
Both sides of all grooves 23, 41 form cube corner element optical surfaces 
in array 42. An equilateral triangle is formed at the base of each cube 
corner reflecting element 44, 45. The grooves 23 and 41 mutually intersect 
at representative locations 43. Another example of this grooving is shown 
in U.S. Pat. No. 3,712,706 (Stamm). U.S. Pat. Nos. 4,202,600 (Burke et al) 
and 4,243,618 (Van Arnam) also disclose, and incorporate by reference, the 
triangular based corner reflecting elements or prisms shown in Stamm. The 
Burke et al patent discloses tiling of these prisms in multiple 
differently oriented zones to produce an appearance of uniform brightness 
to the eye when viewed at a high angle of incidence from at least a 
minimum expected viewing distance. 
Conventional retroreflective cube corner element arrays are derived from a 
single type of matched pairs, i.e. geometrically congruent cube corner 
retroreflecting elements rotated 180.degree.. These matched pairs are also 
typically the same height above a common reference plane. One example of 
this matched pair derivation is shown in FIG. 6 with matched shaded pair 
of cube corner retroreflecting elements 44, 45. Other examples of this 
fundamental matched pair concept relating to conventional cube arrays is 
shown in U.S. Pat. No. 3,712,706 (Stamm), U.S. Pat. No. 4,588,258 
(Hoopman), U.S. Pat. No. 1,591,572 (Stimson) and U.S. Pat. No. 2,310,790 
(Jungersen). U.S. Pat. No. 5,122,902 (Benson) discloses another example of 
matched pairs of cube corner retroreflecting elements having coincident 
base edges, although these may be positioned adjacent and opposite to each 
other along a separation surface. 
Another type of matched pair of cube corner elements is disclosed in German 
patent reference DE 42 42 264 (Gubela) in which a structure is formed 
having a micro-double triad and two single traids within a rhombic body. 
The structure is formed in a work piece using turning angles of 60 degrees 
and grinding directions which do not cross each other at one point, 
resulting in only two of the directions having a common point of 
intersection. 
The above examples of cube corner element retroreflective arrays comprise 
non-canted cubes which have individual symmetry axes 46, 47 that are 
perpendicular to a base plane 48, as shown in FIG. 7. The symmetry axis is 
a central or optical axis which is a trisector of the internal or dihedral 
angles defined by the faces of the element. However, in some practical 
applications it is advantageous to cant or tilt the symmetry axes of the 
matched pair of cube corner retroreflective elements to an orientation 
which is not perpendicular to the base plane. The resulting canted 
cube-corner elements combine to produce an array which retroreflects over 
a wide range of entrance angles. This is taught in U.S. Pat. No. 4,588,258 
(Hoopman), and is shown in FIGS. 8 and 9. The Hoopman structure is 
manufactured with three sets of parallel V-shaped grooves 49, 50, 51 that 
intersect to form matched pairs of canted cube corner elements 53, 54 in 
array 55. Both sides of all grooves 49, 50, 51 form cube corner element 
optical surfaces in array 55. 
FIG. 9 illustrates the symmetry axis 57 for cube corner element 53, and the 
symmetry axis 58 for cube corner element 54. The symmetry axes are each 
tilted at angle o with respect to a line 60 that lies normal to a base 
plane 63, or the front surface, of the element. The base plane is usually 
co-planar or parallel with the front surface of a sheeting comprising the 
cube corner element array. Cube corner elements 53, 54 are geometrically 
congruent, exhibit symmetric optical retroreflective performance with 
respect to entrance angle when rotated about an axis within the plane of 
the substrate, and have symmetry axes which are not parallel to each 
other. Entrance angle is commonly defined as the angle formed between the 
light ray entering the front surface and line 60. 
Canting may be in either a forward or backward direction. The Hoopman 
patent includes disclosure of a structure having an amount of cant up to 
13.degree. for a refractive index of 1.5. Hoopman also discloses a cube 
with a cant of 9.736.degree.. This geometry represents the maximum forward 
cant of cubes in a conventional array before the grooving tool damages 
cube optical surfaces. The damage normally occurs during formation of a 
third groove when the tool removes edge portions of adjacent elements. For 
example, as shown in FIG. 8, for forward cants beyond 9.736.degree., the 
cube edge 65 is formed by the first two grooves 49, 50 and is removed by 
forming the primary groove 51. U.S. Pat. No. 2,310,790 (Jungersen) 
discloses a structure which is canted in a direction opposite that shown 
in the Hoopman patent. 
For these conventional arrays, optical performance is conveniently defined 
by the percent of the surface area that is actually retroreflective, i.e. 
which comprises an effective area or active aperture. The percent active 
aperture varies as a function of the amount of canting, refractive index, 
and the entrance angle. For example, shaded areas 68 of FIG. 10 represent 
the active apertures of the individual cube corner retroreflective 
elements in array 42. The active apertures shown in FIG. 10 are a uniform 
hexagonal size and shape. The percent active aperture of this equilateral 
60.degree.-60.degree.-60.degree. base angle geometry array at a zero 
entrance angle is about 67 percent, which is the maximum possible for a 
conventional three groove set array. 
At non-zero entrance angles, conventional arrays display, at most, two 
different aperture shapes of roughly similar size. These result from the 
single type of geometrically congruent matched pairs of conventional cube 
corner elements. Canted conventional cube corner arrays exhibit similar 
trends, although the shape of the aperture is affected by the degree of 
canting. 
As discussed in U.S. Pat. No. 5,171,624 (Walter), diffraction from the 
active apertures in nearly orthogonal conventional cube corner arrays 
tends to produce undesireable variations in the energy pattern or 
divergence profile of the retroreflected light. This results from all the 
active apertures being roughly the same size in conventional arrays and 
therefore exhibiting roughly the same degree of diffraction during 
retroreflection. 
Some conventional cube corner arrays are manufactured with additional 
optical limitations, perhaps resulting from canting or other design 
features, to provide very specific performance under certain 
circumstances. One example of this is the structure disclosed in U.S. Pat. 
No. 4,349,598 (White). FIGS. 11 and 12 schematically depict, in side and 
plan views respectively, White's extreme backward cant associated with one 
geometric limit of a conventional cube design. In this design, cube 
structure 73 is derived from a matched pair of cube corner elements 74, 75 
with symmetry axes 77, 78. Cube corner elements 74, 75 are each canted in 
a backward direction to the point that each of the base triangles is 
eliminated, resulting in two vertical optical faces 79, 80. This occurs 
when the cube peaks 81, 82 are directly above the base edges 83, 84 and 
the base triangles have merged to form a rectangle. Only two groove sets 
are required, using tools with opposing cutting surfaces, to create this 
cube structure in a substrate. One groove set has a 90.degree. V-shaped 
cut 85 and the other groove set has a rectangular cut shaped as a channel 
86. Both sides of all grooves 85, 86 form cube corner element optical 
surfaces in array 73. In the White design, the pair of cube corner 
reflecting elements are specifically arranged to provide a high active 
aperture at large entrance angles. 
A further modification to the conventional cube corner arrays and to the 
White design is disclosed in U.S. Pat. No. 4,895,428 (Nelson et al). The 
cube structure 87 disclosed by Nelson et al, shown in the side view of 
FIG. 13 and the plan view of FIG. 14, is derived by reducing the length of 
the White element 73 and by eliminating one of the cube vertical optical 
faces 79, 80. Like the White design, manufacture of the Nelson et al 
structure also requires only two groove sets 88, 89. Both sides of all the 
grooves 88 form cube corner element optical surfaces in array 87. Nelson 
must also have at least one vertical retroreflective face. This is 
accomplished by replacing the tool for cutting the White rectangular 
channel with an offset tool. The Nelson et al tool forms a 
non-retroreflective surface 90, using a tool relief surface, and a 
vertical retroreflective surface 92 using the tool vertical sidewall. 
Conventional cube corner retroreflective element designs include structural 
and optical limitations which are overcome by use of the asymmetric cube 
corner retroreflective element structures and methods of manufacture 
described below. Use of this new class of asymmetric retroreflective cube 
corner element structures and manufacturing methods permits diverse cube 
corner element shaping. For example, cubes in a single array may be 
readily manufactured with raised discontinuous geometric structures having 
different heights and non-vertical optical surfaces. Non-vertical cube 
surfaces are more easily metalized, processed, and replicated. Use of 
asymmetric methods and structures also permits manufacture of cubes which 
have highly tailorable asymmetric optical performance. For example, at 
many entrance angles, including at zero entrance angle, asymmetric 
structures outperform conventional structures by exhibiting higher percent 
active apertures or by providing improved divergence profiles, or both. 
Asymmetric manufacturing techniques also produce enhanced optical 
performance resulting from closely spaced intermixed cubes with different 
active aperture shapes and sizes. This presents more uniform appearances 
of asymmetric arrays over a wide range of viewing distances under both day 
and night observation conditions. These advantages of asymmetric cube 
corner elements enhance the usefulness of articles having these elements. 
Such articles include, for example, traffic control materials, 
retroreflective vehicle markings, photoelectric sensors, directional 
reflectors, and reflective garments for human or animal use. 
Half of the cubes in conventional arrays derived from matched pairs of 
cubes are frequently not actively retroreflecting light at a given 
entrance angle. Asymmetric cubes are not derived from the simple matching 
of pairs of cubes or from a modification of conventional pairs of cubes. 
Therefore, asymmetric arrays permit placement of optically active cubes in 
the areas which, if conventional, would not be optically active. 
Use of asymmetric cube corner element articles eliminates a structural 
requirement in some conventional cube corner elements for at least one 
vertical optical face in each cube corner element. This provides 
significant advantages due to the additional care and related cost which 
is required to manufacture vertical optical faces. 
Asymmetric cube corner element arrays may be of simple or composite 
construction. Manufacture of asymmetric cube corner element master arrays, 
as well as multi-generational replicas, results in diverse and highly 
adaptable optical performance and cost efficiencies. These and other 
advantages are described more fully below. 
A substrate suitable for forming retroreflective surfaces according to this 
invention may comprise any material suitable for forming directly machined 
grooves or groove sets. Suitable materials should machine cleanly without 
burr formation, exhibit low ductility and low graininess, and maintain 
dimensional accuracy after groove formation. A variety of materials such 
as machinable plastics or metals may be utilized. Suitable plastics 
comprise thermoplastic or thermoset materials such as acrylics or other 
materials. Suitable metals include aluminum, brass, nickel, and copper. 
Preferred metals include non-ferrous metals. Preferred machining materials 
should also minimize wear of the cutting tool during formation of the 
grooves. 
FIG. 15 discloses a method by which directly machined masters of asymmetric 
cube corner element arrays are manufactured. A directly machined substrate 
100 receives a plurality of parallel grooves arranged in two non-parallel 
sets, which may have variable spacing between grooves. Grooves may be 
formed using either single or multiple passes of a machine tool through 
substrate 100. Each groove is preferably formed by a machine tool which 
has only one side configured for cutting a retroreflective non-vertical 
optical surface and which is maintained in an approximately constant 
orientation relative to the substrate during the formation of each groove. 
Each groove forms the side surfaces of geometric structures which may 
include cube corner optical or non-optical elements. 
A more detailed description of a method of manufacturing an asymmetric cube 
corner element array is to directly machine a first groove set 104 of 
parallel grooves 106 cut into substrate 100 along a first path. A second 
groove set 107 of parallel grooves 108 is then directly machined along a 
second path in substrate 100. The machining of the first and second groove 
sets, also referred to as the two secondary grooves or secondary groove 
sets, creates a plurality of rhombus or diamond shaped partial cube 
sub-elements 109, depicted in shaded highlight in one instance for ease of 
recognition. Each partial cube sub-element comprises two orthogonal 
optical faces 110, as shown in FIGS. 15, 17 and 19. Preferably, only one 
side of grooves 106 and 108 form the orthogonal faces 110 on partial cube 
sub-element 109. The secondary grooves intersect at locations 114. 
Asymmetric arrays may be compared to conventional arrays at this point of 
manufacture by comparing analogous views of Figures i and 15, 2 and 19, 3 
and 17, and 5 and 18. After formation of the secondary grooves, a third or 
primary groove set, which may contain as few as one groove, is cut along a 
third path in substrate 100. In FIG. 18, a representative primary groove 
116, which in this example mutually intersects the secondary grooves 106 
and 108, is shown in dotted lines. A more detailed discussion of such 
primary groove(s) is found below in relation to groove set 128 and 
groove(s) 130 depicted in the array embodiment of FIG. 20. 
Each of the secondary grooves 106, 108 are preferably formed using a novel 
half angle tool 118, shown in one embodiment in FIG. 16. The half angle 
tool 118 is typically mounted on a post 174 with a post axis 119 Half 
angle tool 118 comprises a cutting surface 120 for cutting retroreflective 
optical surfaces into substrate 100, and a relief surface 122. Relief 
surface 122 may actually cut substrate 100, but it will preferably not cut 
or shape optical surfaces which provide retroreflection. The relief angle 
X may be any angle, although a preferred range of angles is between 
0.degree. and 30.degree.. In FIGS. 15, and 17-23 relief angle X is 
0.degree.. The tool side angle Y shown in FIG. 16 is non-zero and 
preferably specified to create orthogonal or nearly orthogonal cube 
optical surfaces. This provides a preferred machine tool which has only 
one side configured for cutting an optical surface of a cube corner 
element. 
As shown in FIG. 16, the half angle tool 118 is typically mounted offset on 
the post axis 119 with tool side angle x not equal to relief angle y. In 
this case, the tool axis is set perpendicular to the substrate during 
direct machining. Alternatively, the half angle tool 118 may be mounted 
centered on the post axis 119. Tool side angle x will equal relief angle y 
in this case, and the tool axis 119 is tilted relative to the substrate 
during direct machining. Intermediate combinations of offset tool mounting 
and tilting of the post during direct machining may also be beneficially 
utilized to produce the desired groove side and relief angles in the 
substrate. In FIGS. 15, and 17--23, groove side angle for secondary 
grooves 106, 108, is the same. However, different groove side angles may 
be used provided corresponding variations in relative secondary groove 
orientation is utilized to maintain orthogonal or nearly orthogonal 
partial cube sub-element surfaces. 
After formation of the secondary grooves, a third or primary groove set 
128, which may contain as few as one groove 130, is preferably cut using a 
pass along a third path in substrate 100. The addition of a plurality of 
parallel primary grooves 130 is shown in FIGS. 20 and 21. Third groove set 
128 is cut through partial cube sub-elements so that non-canted individual 
cube corner elements 134, 135, 136, with cube peaks 137, 138, 139 are 
formed by the intersections of the primary groove(s) with the orthogonal 
faces of the partial cube sub-elements. Primary grooves 130 may intersect 
the secondary grooves either individually or at the locations of the 
secondary groove intersections. Another embodiment of this method of 
manufacturing asymmetric cube corner elements is to directly machine three 
non-parallel sets of grooves into substrate 100 in any order using at 
least one machine tool configured similarly to half angle tool 118. 
The invention also comprises a retroreflective cube corner article which is 
a replica of a directly machined substrate in which a plurality of 
geometric structures including cube corner elements are machined in the 
substrate. In this embodiment of the invention, each cube corner element 
is bounded by at least one groove from each of three sets of parallel 
grooves in the substrate. Only one side of at least one groove in at least 
one groove set forms cube corner element optical surfaces. It is 
recognized that grooves or groove sets in a method of forming cube corner 
elements according to this invention may comprise a different scope and 
meaning from grooves or groove sets which bound or form a cube corner 
element in known articles. For example, in known articles, multiple passes 
of a machine tool may be required to form a single groove. 
Other embodiments of this method include creation of an article, or 
replicas of the article, which further modify the shape of the 
retroreflected light pattern. These embodiments comprise at least one 
groove side angle in at least one set of grooves which differs from the 
angle necessary to produce an orthogonal intersection with other faces of 
elements defined by the groove sides. Similarly, at least one set of 
grooves may comprise a repeating pattern of at least two groove side 
angles that differ from one another. Shapes of grooving tools, or other 
techniques, may create cube corner elements in which at least a 
significant portion of at least one cube corner element optical face on at 
least some of the cubes are arcuate. The arcuate face may be concave or 
convex. The arcuate face, which was initially formed by one of the grooves 
in one of the groove sets, is flat in a direction parallel to said groove. 
The arcuate face may be cylindrical, with the axis of the cylinder 
parallel to said groove, or may have a varying radius of curvature in a 
direction perpendicular to said groove. 
FIG. 20 further discloses asymmetric cube array 141 in which primary 
grooves 130 do not pass through the secondary grooves 106, 108 at the 
mutual intersection locations 114 of the secondary grooves. Primary 
grooves 130 are equally spaced and centered on secondary groove 
intersection locations 114. Array 141 presents yet another novel feature 
of asymmetric cube corner technology. In particular, a method is disclosed 
for manufacturing a cube corner article by directly machining three 
non-parallel non-mutually intersecting sets of grooves. Preferably, these 
sets intersect at included angles less than 90.degree.. It is recognized 
that certain machining imprecisions may create minor, unintentional 
separation between grooves at intersections. However, this invention 
involves intentional and substantial separation. For example, a separation 
distance between the intersections of the grooves within two groove sets 
with at least one groove in a third groove set which is greater than about 
0.01 millimeters would likely provide the advantages of this feature. 
However, the precise minimum separation distance is dependent on the 
specific tooling, substrate, process controls, and the desired optical 
performance sought. 
Non-mutually intersecting groove sets create individual cube corner 
elements with different active aperture sizes and shapes. Arrays may even 
be formed with cube corners created by a combination of mutually and 
non-mutually intersecting groove sets. The position of the groove sets is 
controlled to produce maximum total light return over a desired range of 
entrance angles. Also the distance between grooves in at least one groove 
set might not be equal to the distance between grooves in at least another 
of the groove sets. It is also possible to machine at least one set of 
parallel grooves into a substrate in a repeating fashion with the set 
comprising a distance between grooves which is optionally variable at each 
machining of the set. Also, a portion of any one of the grooves may be 
machined to a depth that is different from at least one other groove 
depth. 
FIGS. 21 and 22 illustrate the multiple cube surfaces which are formed 
during direct machining of a groove in substrate 100. Groove 108 is formed 
by machining surfaces 147 on numerous cube corner elements. Groove 106 is 
formed by machining surfaces 150, and groove 130 is formed by the 
machining of surfaces 153. FIGS. 20-22 show how the tool(s) used with the 
methods of this invention form more than one optical surface 
simultaneously. FIG. 21 shows that the plurality of optical surfaces and 
cube peaks 137, 138, 139 are created at different heights above a common 
reference plane 154. Asymmetric cube corner element arrays are preferably 
formed using at least three sets of parallel grooves where only one side 
of at least one groove in at least one of the groove sets forms cube 
corner element optical surfaces. 
FIG. 23 is a plan view of a portion of asymmetric retroreflective cube 
corner element array 141 depicted in FIG. 22 with shaded areas 155, 156, 
157 representing three different active apertures, intermixed and arranged 
in close proximity and corresponding to cube types 134, 135, and 136. A 
conventional non-canted cube corner element array with an equilateral base 
triangle, at 0.degree. entrance angle, provides a maximum of only about 67 
percent active aperture. However, a non-canted asymmetric cube corner 
element array similar to that shown in FIGS. 22 and 23 may have a percent 
active aperture greater than 70 percent and possibly as high as about 92 
percent at 0.degree. entrance angle. 
FIGS. 15 and 17-23 disclose arrays manufactured with a half angle tool 118 
with a relief angle X equal to zero. The tool axis 124 was set 
perpendicular to the substrate during direct machining. A non-zero relief 
angle X was used to machine array 158 in FIG. 24 and to produce 
non-vertical non-reflective relief surfaces 160. This relief angle 
selection flexibility provided by asymmetric array manufacturing methods 
permits controllable selection of percent active aperture loss due to 
increased relief angles. Also, non-vertical relief surfaces 160 are quite 
helpful during the manufacture and mechanical separation of replicas since 
interlocking vertical faces are eliminated. 
The effect that relief angles have on the formation of active apertures is 
shown in FIG. 25, in which differently sized shaded areas 155, 161, 162 
denote the active apertures at 0.degree. entrance angle. In this 
non-canted geometry with a 3.degree. relief angle, it is possible to 
achieve 84 percent active aperture using the asymmetric cube design. 
Further, multiple differently sized apertures are intermixed and arranged 
in close proximity in array 158. This example of an asymmetric array 
highlights at least one other important distinction over conventional 
arrays. The asymmetric arrays of this invention permit manufacture of near 
vertical faces which are not retroreflective optical faces. This allows 
excellent manufacturing flexibility and permits production of cube corner 
element designs which are highly tailorable to particular needs. 
FIGS. 26 and 27 illustrate an asymmetric array 165 with the symmetry axis 
canted forward by 21.78.degree.. This amount of forward canting is beyond 
the 9.736.degree. limit associated with conventional cube arrays. Each of 
the primary grooves 167 has a 4.degree. relief angle, and each of the 
secondary grooves 169, 170 has a 20.degree. relief angle. The secondary 
groove intersection locations 171 are designed with a spacing distance 
D.sub.1. Primary grooves 167 are equally spaced, also with the distance 
D.sub.1, and are positioned at 0.155D.sub.1 from each adjacent 
intersection location 171. This pattern is repeated in other partial cube 
sub-elements. In the array of FIG. 26, there are three different cube 
types depicted by numerals 172, 173, and 174 respectively. Trihedron 177 
is an example of a structure formed by asymmetric cube corner element 
technology which is not retroreflective because the three faces are not 
orthogonal. 
FIG. 27 shows the multiple differently sized and shaped active apertures 
184, 185, 186, intermixed and arranged in close proximity, and 
corresponding to the three cube types numbered 172, 173, and 174 at a 
60.degree. entrance angle and a refractive index of 1.59. Total percent 
active aperture for array 165 is roughly 59 percent under these 
conditions. This design is useful in applications requiring high 
brightness at high entrance angles, for example, in pavement markers, 
roadway dividers, barriers, and similar uses. 
FIGS. 28 and 29 are side section views of canted asymmetric array 165. FIG. 
28 shows cube 172 with a symmetry axis 188. FIG. 29 shows cubes 173, 174 
with symmetry axes 189, 190 respectively. Although the shape of each of 
the retroreflective cubes 172, 173, 174 differs, the symmetry axes 188, 
189, 190 are essentially parallel. FIG. 29 illustrates the ray path of a 
light ray 187 entering array 165 at a 60.degree. entrance angle. 
The novel entrance angularity performance of canted asymmetric cube designs 
results in part from the common orientation of the symmetry axes for the 
different types of cube corner elements within each asymmetric array. This 
is in contrast with the non-parallel symmetry axes of canted conventional 
cube designs. Therefore, another embodiment of this invention comprises an 
article that is constructed from a machinable substrate which has a 
plurality of directly machined geometric structures including 
retroreflective cube corner elements arranged between a plurality of 
grooves in the substrate. Each of the grooves intersects other grooves at 
included angles other than 90.degree., and each cube corner element has a 
symmetry axis which is in substantially parallel relation to the other 
symmetry axes. The cant of each cube corner element is preferably within a 
range of angles between about backward 35.degree. and forward 54.degree.. 
Retroreflective replicas, including multi-generational replicas, of this 
article may be made which have the same inventive features as the master 
article machined from the substrate, and it is recognized that all of the 
replicas are within the scope of this invention as well as the master 
article. 
The invention permits numerous combinations of structures previously 
unknown and not possible within the art of retroreflective cube corner 
element design and manufacture. FIGS. 30 and 31 disclose, in plan and 
sectional views, asymmetric cube corner element array 191. Array 191 
comprises a plurality of cube corner elements each formed from primary and 
secondary grooves intersecting with included angles 82.degree., 
82.degree., and 16.degree.. Primary grooves are equally spaced through 
array 191, with some of the primary grooves mutually intersecting the 
secondary grooves at locations 194. In this embodiment, the primary 
grooves 195 have a 30.degree. relief angle, and the secondary grooves 196, 
197 have a 3.degree. relief angle. Numerous different retroreflective cube 
corner elements 198, 199, 200, 201, 202, 203, and 204 are created, 
comprising cube corner elements at different relative heights and with 
either three or four sides in this view. These features were simply not 
possible using previous manufacturing technologies. 
With light ray 208 entering array 191 at a 60.degree. entrance angle and a 
refractive index of 1.59, the array demonstrates an exceptional 63 percent 
active aperture as schematically shown in FIG. 32. This percent active 
aperture represents the combined Optical performance of multiple 
differently sized and shaped apertures 212, 213, 214, 215, 216, 217, and 
218, intermixed and arranged in close proximity, and corresponding to the 
different types of retroreflective cube corner elements 198, 199, 200, 
201, 202, 203, and 204. Array 191 is also useful in applications requiring 
high brightness at high entrance angles such as pavement or channel 
markers, roadway dividers, barriers, and similar uses. 
As discussed above, many limiting cases of conventional cube corner element 
design are surpassed through use of asymmetric methods of manufacture. In 
some asymmetric designs, cube surfaces having some conventional cube 
geometries may occur as part of a plurality of cube types in a single 
array. However, the normal limits of conventional cube shapes and 
performances are not similarly bounded using asymmetric methods and 
structures. 
Another advantage of arrays having asymmetric cube design is the improved 
entrance angularity in one direction of the array. The design may be 
specifically tailored to provide peak light return at a desired entrance 
angle. FIG. 33 is a representative graph depicting percent active 
area/aperture 228 versus entrance angle for an asymmetric retroreflective 
cube corner element array shown in FIG. 26 with a refractive index of 
1.59. The asymmetrical optical performance based on entrance angle 
provides efficiencies and other advantages not previously possible in the 
field of retroreflective cube corner element design and use. Therefore, 
another embodiment of this invention comprises a retroreflective article 
or replica which exhibits asymmetric entrance angularity when rotated 
about an axis within the plane of the substrate from which it is machined. 
Preferably the article is manufactured by directly machining a substrate 
to create cube corner elements between three non-parallel sets of parallel 
grooves. 
FIG. 34 provides further illustration of the asymmetric optical performance 
of this class of articles. In the graph of FIG. 34, the optical 
performance is represented by percent active area/aperture data lines 
versus entrance angle, and is shown for both conventional and asymmetric 
designs for a refractive index of 1.59. Data line 232 depicts the 
performance of a conventional 55.degree.-55.degree.-70.degree. geometry 
array as shown in FIG. 8; and line 235 depicts a conventional non-canted 
60.degree.-60.degree.-60.degree. geometry array as shown in FIG. 6. In 
contrast, line 244 depicts a non-canted asymmetric array as shown in FIG. 
24. A comparison between conventional geometry data lines 232, 235 and 
asymmetric geometry data line 244 demonstrates that higher active aperture 
percents are achievable with an asymmetric structure. The asymmetric array 
well exceeds the limits of conventional array percent active apertures at 
entrance angles up to about 25.degree.. 
This asymmetric geometry is particularly beneficial for use in applications 
requiring retroreflective sheeting having substantial total light return, 
such as traffic control materials, retroreflective vehicle markings, 
photo-electric sensors, internally illuminated signs, and reflective 
garments. The enhanced optical performance and design flexibility 
resulting from asymmetric techniques relates directly to improved product 
performance and marketing advantage. 
Total light return for retroreflective sheeting is derived from the product 
of percent active aperture and retroreflected light ray intensity. For 
some combinations of cube geometries, entrance angles, and refractive 
index, significant reductions in ray intensity may result in relatively 
poor total light return even though percent active aperture is relatively 
high. One example is retroreflective cube corner element arrays which rely 
on total internal reflection of the retroreflected light rays. Ray 
intensity is substantially reduced if the critical angle for total 
internal reflection is exceeded at one of the cube faces. Metallized or 
other reflective coatings on a portion of an array may be utilized 
advantageously in such situations. A portion, in this context, may 
comprise all or part of an array. 
The structure of asymmetric cube corner element arrays relying on total 
internal reflection is such that total internal reflection breakdown will 
occur for all cubes simultaneously. This contrasts with conventional 
arrays, based on matched pairs of cubes, where total internal reflection 
breakdown occurs for only half of the cubes for a given cube geometry, 
entrance angle, and refractive index. Asymmetric cube corner element 
arrays relying on total internal reflection may therefore be beneficially 
designed as directional retroreflectors for applications such as marine 
channel markers and passive airport runway markings. 
Composite tiling is the technique for combining zones of cube corner 
elements having different orientations. This is used with conventional 
arrays to provide sheeting with a uniform appearance at high angles of 
incidence regardless of orientation. However, composite tiling permits 
further modification to optical performance of asymmetric arrays, as well 
as to arrays comprising non-triangular based cube corner prisms. 
Referring to FIG. 35, composite array 252 comprises several zones of 
asymmetric arrays 165, as shown in FIG. 26. Each of the zones 165 may have 
a similar size and shape, but each zone is oriented in a 180.degree. 
relation to adjacent zones. FIG. 36 shows the effect of this particular 
composite tiling arrangement on percent active aperture. Data line 228 
represents the percent active aperture versus entrance angle for array 
165. In contrast, data line 260 illustrates a substantially constant value 
for percent active aperture versus entrance angle for composite array 252 
over an extremely wide range of entrance angles. The combined optical 
effect of numerous zones 165 in a composite array is useful for 
applications requiring roughly constant brightness over a wide range of 
entrance angles. Data line 260 also illustrates that composite tiled zones 
of asymmetric cube corner elements can provide symmetric entrance 
angularity during rotation about an axis within the plane of the composite 
array. 
The zones of asymmetric arrays may be different sizes and may also be 
oriented other than 180.degree. relative to adjacent zones. The size of 
the zones should be selected according to the requirements of particular 
applications. For example, traffic control applications may require zones 
which are sufficiently small that they are not visually resolvable by the 
unaided human eye at the minimum expected viewing distance. This provides 
a composite array with a uniform appearance. Alternatively, channel 
marking or directional reflector applications may require zones which are 
sufficiently large that they can be easily resolved by the unaided human 
eye at maximum required viewing distance. 
FIG. 37 is a side section view of one embodiment of the present invention. 
This view shows part of an asymmetric array 264 which is similar to array 
141 shown in FIG. 21, although this embodiment of the invention may also 
be used with other array configurations. FIG. 37 further illustrates the 
advantages of asymmetric manufacturing methods in providing geometric 
structures at different heights above a common reference plane. These 
structures may comprise individual retroreflective cube corner elements 
268, 269, non-retroreflective pyramids, frustums, posts 282, or other 
structures positioned above common reference plane 274. 
Cube peaks 271, 272, or other features machined from the original 
substrate, may also be truncated for specialized effect or use. Truncation 
may be accomplished by various techniques, including, for example, 
controlling depth of cut of the grooves, or further removal of substrate 
material after formation of the primary and secondary grooves. 
Retroreflective directly machined cube corner articles are often designed 
to receive a sealing film which is applied to the retroreflective article 
in order to maintain a low refractive index material, such as air, next to 
the retroreflective elements for improved performance. In conventional 
arrays this medium is often placed in direct contact with the cube corner 
elements in ways which degrade total light return. However, using 
asymmetric constructions, a sealing medium 280 may be placed on the 
highest surface 283 of the array without contacting and degrading the 
optical properties of lower retroreflective cube corner elements. The 
highest surface may comprise cube corner elements, non-retroreflective 
pyramids, frustums, posts, or other structures. In FIG. 37, the highest 
surface 283 has been truncated. Although slight height variations may 
result from slight non-uniformity of groove positions or included angle of 
cube corner elements due to machining tolerances or intentional inducement 
of non-orthogonality, these variations are not analogous to the variations 
disclosed and taught in this invention. For arrays using a sealing medium, 
the truncated surfaces may be used both to hold the medium above the cube 
corner elements as well as to increase the light transmissivity of the 
sheeting. Light transmissivity of the sheeting may be increased through 
use of a transparent or partially transparent sealing medium. 
FIG. 38 is a side view of another embodiment of the present invention. This 
view shows part of an asymmetric array 285 similar to a portion of array 
264 in FIG. 37 but including the use of a separation surface 288. The 
lateral faces 292, 293 of geometric structures 295, 296 form the boundary 
edges 299, 300 for the separation surface. The lateral faces may be either 
cube corner element optical surfaces or relief surfaces. The separation 
surface 288 may have flat or curved portions when taken in cross section. 
Separation surfaces may be advantageously utilized to increase light 
transmission or transparency in sheeting, including flexible sheeting, 
utilizing asymmetric retroreflective cube corner element arrays. For 
example, this is particularly useful in articles such as automotive signal 
light reflectors, which are normally manufactured using injection molding. 
In the embodiment shown in FIG. 38, separation surfaces are shown in 
combination with truncated surfaces of highest surfaces 283, although 
either feature may be utilized independently. Separation surface 288 may 
be formed using a machining tool with a flat or curved tip, or by further 
removal of material from a replica of the asymmetric cube corner element 
array master. 
Suitable materials for retroreflective articles or sheeting of this 
invention are preferably transparent materials which are dimensionally 
stable, durable, weatherable, and easily replicated into the desired 
configuration. Examples of suitable materials include glass; 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 taught in 
U.S. Pat. Nos. 4,576,850, 4,582,885 and 4,668,558; polyethylene based 
ionomers, such as those marketed under the brand name of SURLYN by E. I. 
Dupont de Nemours and Co., Inc.; polyesters, polyurethanes; and cellulose 
acetate buryrates. 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. Transparency of the 
materials ensures that the separation or truncated surfaces will transmit 
light through those portions of the article or sheeting. 
The incorporation of truncated or separation surfaces does not eliminate 
the retroreflectivity of the article, but rather it renders the entire 
article partially transparent. In some applications requiring partially 
transparent materials, low indices of refraction of the article will 
improve the range of light transmitted through the article. In these 
applications, the increased transmission range of acrylics (refractive 
index of about 1.5) is desirable. 
In fully retroreflective articles, materials having high indices of 
refraction are preferred. In these applications, materials such as 
polycarbonates, with refractive indices of about 1.59, are used to 
increase the difference between the indices of the material and air, thus 
increasing retroreflection. Polycarbonates are also generally preferred 
for their temperature stability and impact resistance. 
FIGS. 39 and 40 illustrate an asymmetric array 305 comprising a plurality 
of cube corner elements each formed from primary and secondary grooves 
intersecting with included angles 74.degree., 74.degree., and 32.degree.. 
Each of the primary grooves 308 has a 30.degree. relief angle and each of 
the secondary grooves 309, 310 has a 3.degree. relief angle. The secondary 
groove intersection locations 313 are designed with a spacing D2. Three 
primary grooves are positioned in the partial cube sub-element with 
varying spacing at 0.20D.sub.2, 0.55D.sub.2, and 0.83D.sub.2 from the 
secondary groove intersections 313. This pattern is repeated in other 
partial cube sub-elements. 
In the array of FIG. 39, there are six different cube types depicted by 
numerals 316, 317, 318, 319, 320, and 321. Trihedrons 325, 326 are 
examples of structures which are not retroreflective because the three 
faces are not orthogonal. FIG. 40 shows, for entrance angle 60.degree. and 
refractive index 1.59, the six active apertures 329, 330, 331, 332, 333, 
and 334, intermixed and arranged in close proximity, and associated with 
cube types numbered 316 through 321, respectively. Percent active aperture 
is roughly 63 percent for array 305. The active aperture shapes in this 
design have roughly equal dimensions both parallel and perpendicular to 
the primary grooves even at a 60.degree. entrance angle. These roughly 
circular aperture shapes produce light return patterns which are 
relatively circular and not significantly distorted due to diffraction. In 
contrast, conventional arrays specifically designed for high entrance 
angle high brightness applications exhibit highly elongated aperture 
shapes which significantly distort light return patterns. The asymmetric 
array 305 is particularly useful in applications requiring high brightness 
at high entrance angles, such as pavement or channel markers, roadway 
dividers, barriers, and similar uses. 
Various modifications and alterations of this invention will become 
apparent to those skilled in the art without departing from the scope and 
spirit of this invention.