U.S. patent number RE40,455 [Application Number 11/515,509] was granted by the patent office on 2008-08-12 for retroreflective articles having microcubes, and tools and methods for forming microcubes.
This patent grant is currently assigned to Avery Dennison Corporation. Invention is credited to Liviu A. Coman, Dennis I. Couzin, Sidney A. Heenan.
United States Patent |
RE40,455 |
Heenan , et al. |
August 12, 2008 |
**Please see images for:
( Certificate of Correction ) ** |
Retroreflective articles having microcubes, and tools and methods
for forming microcubes
Abstract
A method for tooling a pattern of retroreflective microcubes,
which pattern can be subdivided into smaller increments within
which there are straight line tooling paths, none of which pass
through an otherwise solid part of the incremental pattern. The
tooling paths within the various increments need not be parallel to
a common plane. Various adaptions of the method enable the tooling
of a number of specific microcube shapes and for modifying such
optical properties of the microcubes as entrance angularity,
incidence angularity, orientation angularity, observation
angularity, percent active aperture and retroreflectance. Specific
techniques govern the pre-selection of cube parameters such as cube
axis cant, cube apex decentration, and cube boundary proportions,
which parameters can be adjusted independently of each other.
Designs tooled by the method can have 100% active aperture at near
zero degrees entrance angle. The method involves providing a
plurality of plates of micro thickness, each plate having at least
one end comprised of a material that can be tooled with polished
surfaces by means of an appropriate tool, tooling on said end of
each plate an increment of the pattern, and assembling the plates
together in various ways to form a master. Retroreflective articles
made by means of this technique are expected to provide superior
performance when used in pavement markers, highway signs and other
applications.
Inventors: |
Heenan; Sidney A. (Park Ridge,
IL), Coman; Liviu A. (Deerfield, IL), Couzin; Dennis
I. (Berlin, DE) |
Assignee: |
Avery Dennison Corporation
(Pasadena, CA)
|
Family
ID: |
24629539 |
Appl.
No.: |
11/515,509 |
Filed: |
August 31, 2006 |
Related U.S. Patent Documents
|
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
|
08655595 |
May 30, 1996 |
6015214 |
|
|
Reissue of: |
09453327 |
Dec 2, 1999 |
06767102 |
Jul 27, 2004 |
|
|
Current U.S.
Class: |
359/530; 428/172;
359/529 |
Current CPC
Class: |
G02B
5/124 (20130101); B29D 11/00605 (20130101); B29C
33/42 (20130101); B29C 33/301 (20130101); B29C
39/00 (20130101); Y10T 428/24612 (20150115); B29C
43/00 (20130101); B29C 2059/023 (20130101); B29L
2011/0091 (20130101); Y10T 428/249921 (20150401); B29C
33/3842 (20130101) |
Current International
Class: |
G02B
5/124 (20060101) |
Field of
Search: |
;359/529-530 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
|
|
|
|
|
|
|
785139 |
|
May 1968 |
|
CA |
|
1917292 |
|
Oct 1970 |
|
DD |
|
2317871 |
|
Oct 1974 |
|
DD |
|
4236799 |
|
Oct 1992 |
|
DE |
|
92171796 |
|
Dec 1992 |
|
DE |
|
92171796 |
|
Jun 1993 |
|
DE |
|
4236799 |
|
May 1994 |
|
DE |
|
4236799 |
|
May 1994 |
|
DE |
|
4236799 |
|
May 1994 |
|
DE |
|
4410994 |
|
Oct 1995 |
|
DE |
|
0844056 |
|
May 1998 |
|
EP |
|
0885705 |
|
Dec 1998 |
|
EP |
|
875008 |
|
Jul 2002 |
|
EP |
|
844056 |
|
Apr 2003 |
|
EP |
|
885705 |
|
May 2003 |
|
EP |
|
1289029 |
|
Feb 1962 |
|
FR |
|
269760 |
|
Apr 1927 |
|
GB |
|
423464 |
|
Jan 1934 |
|
GB |
|
423464 |
|
Feb 1935 |
|
GB |
|
WO 9418581 |
|
Aug 1994 |
|
WO |
|
WO 9418581 |
|
Aug 1994 |
|
WO |
|
WO 9511463 |
|
Apr 1995 |
|
WO |
|
WO 9511463 |
|
Apr 1995 |
|
WO |
|
WO 9511465 |
|
Apr 1995 |
|
WO |
|
WO 9511465 |
|
Apr 1995 |
|
WO |
|
WO 9511467 |
|
Apr 1995 |
|
WO |
|
WO 9511467 |
|
Apr 1995 |
|
WO |
|
WO 9511470 |
|
Apr 1995 |
|
WO |
|
WO 9511470 |
|
Apr 1995 |
|
WO |
|
WO 9704939 |
|
Feb 1997 |
|
WO |
|
WO 9704939 |
|
Feb 1997 |
|
WO |
|
WO 9704940 |
|
Feb 1997 |
|
WO |
|
WO 9704940 |
|
Feb 1997 |
|
WO |
|
WO 9727035 |
|
Jul 1997 |
|
WO |
|
WO 9727035 |
|
Jul 1997 |
|
WO |
|
WO 9901269 |
|
Jan 1999 |
|
WO |
|
WO 9901269 |
|
Jan 1999 |
|
WO |
|
WO 9901273 |
|
Jan 1999 |
|
WO |
|
WO 9901273 |
|
Jan 1999 |
|
WO |
|
WO 9901274 |
|
Jan 1999 |
|
WO |
|
WO 9901274 |
|
Jan 1999 |
|
WO |
|
WO 9901275 |
|
Jan 1999 |
|
WO |
|
WO 9901275 |
|
Jan 1999 |
|
WO |
|
Other References
Applied Optics, "Photometry and Colorimetry of Retroreflection:
State-of-Measurement-Accuracy Report, " Apr. 1, 1981, p. 1266, vol.
20, No. 7. cited by other .
Applied Optics, "Making Masters for Corner Cube Reflectors," Apr.
15, 1981. pp. A80, 1267-1268, vol. 20, No. 8. cited by
other.
|
Primary Examiner: Phan; James
Attorney, Agent or Firm: Christie, Parker & Hale,
LLP.
Parent Case Text
This is a divisional of copending application(s) U.S. Ser. No.
08/655,595 filed on May 30, 1996 now U.S. Pat. No. 6,015,214.
Claims
What is claimed is:
1. An article comprising an array of microcubes, at least one of
said microcubes being non-hexagonal, such that for every plane in
space there are two adjacent microcubes for which at the place of
the adjacency none of the face edges is parallel to that plane,
said at least one microcube having a projected area of less than 1
mm.sup.2, said at least one microcube being canted
edge-more-parallel.
2. The article of claim 1 wherein said array is
retroreflective.
3. The article of claim 2 wherein said article comprises
retroreflective sheeting.
4. The article of claim 3 wherein at least one microcube of said
array has a projected area of about 1 mm.sup.2 or less.
5. The article of claim 4 wherein at least one microcube of said
array has a projected area of about 0.35 mm.sup.2 or less.
6. The article of claim 5 wherein at least one microcube of said
array has a projected area of about 0.04-0.12 mm.sup.2.
7. The article of claim 3 wherein said sheeting comprises a polymer
resin.
8. The article of claim 7 wherein said polymer resin is selected
from the group consisting of acrylic, polycarbonate, vinyl,
polyester, and polyethylene.
9. The article of claim 7 wherein said microcubes are formed by
embossing.
10. The article of claim 7 wherein said microcubes are formed by
casting.
11. The article of claim 3 wherein said sheeting is
transilluminated.
12. The article of claim 1 in which at least one microcube of said
array is canted.
13. The article of claim 12 in which at least one microcube in said
array is edge-more-parallel.
14. The article of claim 13 wherein retroreflectance in the plane
of symmetry of the microcubes of said array is substantially
constant and is greater than about 50% for all entrance angles less
than about 30.degree..
15. The article of claim 12 in which not all the cube axes in said
array are parallel to each other.
16. The article of claim 15 in which some adjacent cubes are
alternately face-more-parallel and edge-more-parallel.
17. The article of claim 12 in which said array is a
retroreflective part of a pavement marker.
18. The article of claim 1 wherein said article is a master for use
in the production of a tool for making a retroreflective
article.
19. The article of claim 1 wherein said article is an electroform
for use in the production of a tool for making a retroreflective
article.
20. The article of claim 1 wherein said microcubes of said array
are of unequal sizes.
21. An article comprising an array of microcubes, at least one of
said microcubes being non-hexagonal such that for every plane in
space there are two adjacent microcubes for which at the place of
the adjacency none of the face edges is parallel to that plane,
.Iadd.said at least one microcube having a projected area of less
than 1 mm.sup.2, .Iaddend.in which array at least one said
microcubes is canted, said array being formed of a material having
a refractive index n, and the cant of at least one microcube in
said array does not exceed about tan.sup.-1 {square root over
(2)}-sin.sup.-1(1/n).
22. An article comprising an array of rectangular microcubes, at
least some of which have no dihedral face-edges collinear with any
dihedral faces-edges of any adjacent microcubes, at least one of
said rectangular microcubes having a projected area of less than 1
mm.sup.2, said at least one microcube being canted
edge-more-parallel.
23. A pavement marker for establishing on a finished roadway
surface a marking visible from an oncoming vehicle, said pavement
marker comprising a base member adapted to be mounted on the
finished roadway surface, and a retroreflective signal means, said
retroreflective signal means comprising an array of microcubes of
claim 22.
24. The pavement marker of claim 23 wherein the retroreflective
signal means front surface is sloped about 30.degree.-40.degree.
with respect to the road surface and comprises an array of canted
rectangular microcubes, the cube axis cant being in the range of
about -5.degree. to -13.degree..
25. The pavement marker of claim 24 having horizontal entrance
angularity up to at least about 30.degree..
26. An article comprising an array of microcubes in which every
region of three by three microcubes is nonrulable and in which at
least one microcube in a said region of three by three microcubes
is rectangular, said at least microcube having a projected area of
less than 1 mm.sup.2, said at least one microcube being canted
edge-more-parallel.
.Iadd.27. An article comprising an array of microcubes, at least
one of said microcubes being rectangular such that for every plane
in space there are two adjacent microcubes for which at the place
of the adjacency none of the face edges is parallel to that plane,
said at least one microcube having a projected area of less than 1
mm.sup.2, in which array at least one of said microcubes is canted,
said array being formed of a material having a refractive index n,
and the cant of at least one microcube in said array does not
exceed about tan.sup.-1 {square root over (2)}-sin.sup.-1
(1/n)..Iaddend.
.Iadd.28. The article of claim 27 in which a plurality of
microcubes in said array are male microcubes and said array of
microcubes is nonrulable..Iaddend.
.Iadd.29. The article of claim 27 in which a plurality of said
microcubes of said array have a projected area of about 0.35
mm.sup.2 or less..Iaddend.
.Iadd.30. The article of claim 27 in which a plurality of said
microcubes of said array have a projected area of 0.12 mm.sup.2 or
less..Iaddend.
.Iadd.31. The article of claim 27 in which the article comprises
retroreflective sheeting..Iaddend.
.Iadd.32. The article of claim 27 in which one or more microcubes
within said array have substantially 100% active aperture for
incidence angles of about zero degrees..Iaddend.
.Iadd.33. The article of claim 27 in which said array comprises at
least three consecutive rows of said microcubes..Iaddend.
.Iadd.34. The article of claim 27 in which said array of microcubes
comprises rows of said microcubes in which each row of microcubes
is a replica of a structure that has been ruled on the end of a
microthick plate..Iaddend.
.Iadd.35. The article of claim 27 in which said array comprises
rows of rectangular microcubes, in which each row is a replica of a
structure that has been ruled on the end of a microthick plate by a
bevel face formed along the end of the plate and a plurality of
v-grooves substantially perpendicular to the bevel
face..Iaddend.
.Iadd.36. The article of claim 35 in which adjacent rows of said
microcubes correspond to adjacent plates oriented 180.degree. to
each other..Iaddend.
.Iadd.37. The article of claim 35 in which said array comprises
microcubes present as opposed paired microcubes, and in which said
array comprises pairs of rows of rectangular microcubes in which
each pair of rows is a replica of a structure that has been ruled
on the end of a microthick plate by a v-groove extending along the
center of the plate end, with opposed pairs of v-grooves extending
substantially perpendicular to the center v-groove..Iaddend.
.Iadd.38. The article of claim 27 in which said array comprises an
array of male microcubes for which every three by three subarray of
said microcubes is nonrulable..Iaddend.
.Iadd.39. The article of claim 38 in which the article comprises
retroreflective sheeting..Iaddend.
.Iadd.40. The article of claim 39 in which one or more microcubes
within said array have substantially 100% active aperture for
incidence angles of about zero degrees..Iaddend.
.Iadd.41. The article of claim 40 in which a plurality of said
microcubes of said array have a projected area of about 0.35
mm.sup.2 or less..Iaddend.
.Iadd.42. The article of claim 40 in which a plurality of said
microcubes of said array have a projected area of 0.12 mm.sup.2 or
less..Iaddend.
.Iadd.43. The article of claim 38 in which said array comprises at
least three consecutive rows of said microcubes..Iaddend.
.Iadd.44. The article of claim 38 in which said array of microcubes
comprises rows of said microcubes in which each row of microcubes
is a replica of a structure that has been ruled on the end of a
microthick plate..Iaddend.
.Iadd.45. The article of claim 44 in which said array comprises
rows of rectangular microcubes in which each row is a replica of a
structure that has been ruled on the end of a microthick plate by a
bevel face formed along the end of the plate and a plurality of
v-grooves substantially perpendicular to the bevel
face..Iaddend.
.Iadd.46. The article of claim 45 in which adjacent rows of said
microcubes correspond to adjacent plates oriented 180.degree. to
each other..Iaddend.
.Iadd.47. The article of claim 44 in which said array comprises
microcubes present as opposed paired microcubes, and in which said
array comprises pairs of rows of rectangular microcubes in which
each pair of rows is a replica of a structure that has been ruled
on the end of a microthick plate by a v-groove extending along the
center of the plate end, with opposed pairs of v-grooves extending
substantially perpendicular to the center v-groove..Iaddend.
.Iadd.48. The article of claim 38 in which said array of male
microcubes comprises at least three consecutive rows of said
microcubes in which each row of microcubes is a replica of a
structure that has been ruled on the end of a microthick plate
having a thickness of less than 1 mm..Iaddend.
.Iadd.49. The article of claim 34 in which the microthick plate has
a thickness of (a)-(b): (a) less than 1 mm, or (b) 0.012 inch
(0.305 mm) or less..Iaddend.
.Iadd.50. The article according to claim 44 in which the microthick
plate has a thickness of (a)-(b): (a) less than 1 mm, or (b) 0.012
inch (0.305 mm) or less..Iaddend.
.Iadd.51. The article of claim 48 in which the microthick plate has
a thickness of 0.012 inch (0.305 mm) or less..Iaddend.
.Iadd.52. The article of claim 27 in which a plurality of said
microcubes are male microcubes at least some of which have no
dihedral face edges collinear with any dihedral face edges of any
adjacent microcubes..Iaddend.
Description
BACKGROUND OF THE INVENTION
This invention relates to tools for making microcube
retroreflective elements for use in manufacturing retroreflective
articles, and in particular, retroreflective sheeting; to articles
and sheeting having microcubes; and to methods of making such tools
and articles; This invention further relates to tools, articles,
and methods wherein said microcubes may have boundary shapes other
than triangular.
Microcube retroreflective sheeting is now well-known as a material
for making reflective highway signs, safety reflectors, reflective
vests and other garments, and other safety-related items. Such
retroreflective sheeting typically comprises a layer of a clear
resin, such as for example, an acrylic or polycarbonate or vinyl,
having a smooth front surface and a plurality of retroreflective
microcube elements on the reverse surface. Light incident on the
smooth front surface passes through the sheeting, impinges on the
retroreflective elements, and is reflected back out through the
smooth front surface in a direction nominally 180.degree. to the
direction of incidence.
The reverse surface of the resin layer bearing the microcubes may
be further provided with additional layers, such as metallization,
which enhances the entrance angularity of the sheeting, or
hydrophobic silica, adhesives, release liners, or other layers
which otherwise contribute to the functionality of the
sheeting.
Cube corner retroreflectors have been used on automobiles and for
highway markings since the early 1900's. These prior art devices
were based on macrocube corner elements made by the pin making art.
From the use of macrocubes, a number of optical principles
involving cube corner technology have been published, and some have
been patented. Generally, these principles have involved changes in
the size, shape or tilt of the cube faces, or of the included
dihedral angles between faces, to achieve desired retroreflector
performance. These known optical principles have included:
increasing the efficiency of the retroreflector at large
observation angles by changing one or more of the three dihedral
angles of the cube, as taught in Heenan U.S. Pat. No. 3,833,285;
increasing the efficiency of the retroreflector at large incident
angles by including the cube axis with respect to the normal (often
called "angled reflex"), taught, for example, in Leray patents U.S.
Pat. No. 2,055,928 and Br. U.S. Pat. No. 423,464, and in Heenan
U.S. Pat. No. 3,332,327; increasing entrance angularity in one or
more planes by including in the array cubes with cube axis cant, as
taught in Heenan U.S. Pat. No. 3,873,184 and Heenan U.S. Pat. No.
3,923,378, and, in particular, by positioning one face of each of
the oppositely oriented cubes more parallel to the front face of
the reflector, as taught in U.S. Heenan et al U.S. Pat. No.
3,541,606 to increase entrance angularity in, two planes at right
angles to each other; increasing uniformity of retroreflectance
versus orientation by rotating some cubes by varying degrees about
a normal to the front surface of the article, and also by
assembling them in arrays of variant dispositions, as in Uding
Canadian Pat. No. 785,139; and by angling the cube axis in
combination with multiple rotations, as in U.S. Pat. No.
3,923,378.
While these retroreflective optic design principles are well-known
in the cube corner art, in more recent years some have attempted to
patent them again in microcube sheeting technology, apparently
because those persons either did not know what was done in prior
macrocube technology, or chose either to ignore or to limit the
applicability of the prior art teachings when applied to microcube
retroreflective sheeting.
Prior to applicants' present invention, virtually all microcube
sheeting has been limited to the use of microcubes made by ruling
along parallel planes. This limitation is a result of the microcube
dimensions being smaller than the dimensions obtainable by the
cutting, polishing and lapping techniques used in the pin making
art. The need to use traditional ruling techniques has inhibited
the application of known optical principles to microcubes, and has,
with one exception, further generally limited percent active
aperture to less than 100%.
The present invention is a major advance in microcube sheeting
technology. It enhances both the applicability to microcubes of
prior known retroreflective optic principles and the
manufacturability of microcubes of different base configurations.
Before detailing these advances, further background information is
provided.
Retroreflective sheeting and methods of forming the microcube
retroreflective elements in such sheeting are disclosed, for
example in U.S. Pricone et al. Pat. No. 4,486,363, assigned to the
common assignee herein, and incorporated herein by reference in its
entirety. As disclosed in such patent, the resinous layer of the
sheeting may be on the order of 0.01 inch (0.25 mm) thick or less,
and the retroreflective elements formed in the reverse face of the
resinous layer comprise triangular microcubes such as are known in
the manufacture of flexible retroreflective sheeting.
To manufacture such microcube sheeting, generally a master plate of
retroreflective triangular microcubes is made by ruling a pattern
of retroreflective cube corners into a planar surface of the plate.
This is taught generally by Stamm U.S. Pat. No. 3,712,706; is
mentioned in U.S. Pat. No. 5,122,902; and is also taught in detail
in U.S. Pat. No. 4,478,769, assigned to the applicants' assignee
and incorporated herein by reference in its entirety.
As shown in FIGS. 1A, 2 and 3 of the '769 patent, the planar
surface of a master plate is ruled with a diamond tool which cuts a
series of precise parallel V-shaped grooves. To rule equilateral
triangular microcubes, three sets of parallel grooves intersecting
one another at angles of 60.degree. are made; each groove also will
have an included angle of substantially 70.53.degree., and will be
ruled to a groove depth determined by the height of the microcubes
desired. This automatically results in an array of oppositely
oriented pairs of equilateral triangular microcubes on the face of
the master.
The ruled master may then be used to make a series of duplicates,
such as by electroforming, and the duplicates are assembled
together to form a single "mother" tool. The assembled "mother"
tool is used to electroform molds, which are then assembled and
ultimately used to form a tool capable of providing the microcube
retroreflective elements on the sheeting, such as by embossing,
casting, or other means known in the art. A continuous embossing
method is disclosed in the aforementioned U.S. Pat. No. 4,478,769;
a casting technique for forming microcubes is disclosed, for
example, in Rowland U.S. Pat. Nos. 3,684,348 and 3,689,346.
As will be described hereafter, triangular microcubes having bases
other than equilateral triangles have been used in an effort to
achieve enhanced entrance angularity by use of the well known
optical principles taught in macrocube technology. Thus, as taught
in applicants' assignee's commonly assigned patent Montalbano U.S.
Pat. No. 4,633,567, variations of the triangular microcube may be
achieved by changing the tool ruling angles (thus, canting the cube
axis), thereby adopting and applying some of the prior optical
principles to microcube technology. For example, it is possible to
achieve arrays having different entrance angularity or orientation
angularity (c.f. Rowland U.S. Pat. No. 3,684,348, col. 10, 11, 1-18
and Montalbano U.S. Pat. No. 4,633,567, col. 6, 11, 4-36).
As previously noted, U.S. Pat. No. 3,833,285, discloses that the
observation angularity of cube corner retroreflection can be
increased in one plane by increasing (or decreasing) one of the
three dihedral angles of the cubes; U.S. Pat. Nos. 3,873,184 and
3,923,378, disclose an array of retroreflective elements wherein
the cube axes of neighboring cubes are inclined with respect to
each other and oppositely oriented such that the entrance
angularity is increased; U.S. Pat. No. 3,541,606 discloses that if
one cube face of each of the oppositely oriented cubes is "more
parallel" to the front surface, entrance angularity is increased in
two planes at right angles to each other. Each of the foregoing
patents is incorporated herein by reference.
The identical optical principles used in macrocubes for enhancing
retroreflectivity have also been applied to the triangular
microsized cubes such as are used in retroreflective sheeting.
Thus, U.S. Pat. No. 4,588,258 to Hoopman discloses a
retroreflective article with purportedly novel wide angularity
wherein an array of triangular microcube elements comprises sets of
matched pairs with the cube axes of the cubes in each pair being
tilted toward one another; but this simply duplicates the
face-more-parallel structure disclosed, for example, in applicants'
assignee's prior U.S. Pat. No. 3,541,606, U.S. Pat. No. 3,923,378
or U.S. Pat. No. 3,873,184 patents. Moreover, the Hoopman matched
pairs of triangles are inherent when ruling triangles, which at the
time of Hoopman's application was the only technique used for
manufacturing microcubes.
Similarly, U.S. Pat. No. 4,775,219 to Appeldorn, et al., discloses
a retroreflective article of modified observation angularity having
an array of microcube retroreflective elements formed by three
intersecting sets of parallel V-shaped grooves, wherein at least
one of the sets includes, in a repeating pattern, at least two
groove side angles that differ from one another. The Appeldorn
article merely achieves, in an obvious manner, the identical
principle taught years ago in applicants' commonly assigned U.S.
Pat. No. 3,833,285.
However, all triangular cubes, while providing adequate
retroreflectance, suffer the known disadvantage that inherently by
their geometry no more than 66% of their area can be
retroreflective for any particular incidence angle. In an attempt
to overcome this deficiency of triangular cubes, the Minnesota
Mining and Manufacturing Company, in a series of published PCT
applications (WO 95/11463; WO 95/11465; WO 95/11467; WO 95/11470),
has disclosed arrays of microcubes including some non-triangular
cubes, and techniques for ruling such arrays. However, the
disclosed arrays have cubes of greatly different heights (which may
pose manufacturing problems) and greatly varying aperture size
(affecting diffraction and impacting on retroreflectivity). At
best, the disclosed arrays provide calculated percent effective
aperture (at 0.degree. incidence) of 91%, which appears to fall to
about 87% when manufacturing draft is considered (see, e.g., WO
95/11470, FIG. 12). If the cubes are canted by the disclosed ruling
technique, the efficiency drops even further. The very nature of
forming these cubes by intersecting ruled grooves parallel to a
single plane inherently limits the results which can be
obtained.
The advantages of the techniques and articles of the present
invention, as compared to those obtained by the earlier, triangular
microcubes or even by the more recent ruled mixtures of triangular
and non-triangular cubes, are shown in the drawings of this
application and are more specifically described hereinafter.
Unlike triangular cube corners, hexagonal and rectangular cube
corners have the advantage that 100% of their area can be
retroreflective even at large incidence angles. Also unlike
triangular microcubes, however, hexagonal and rectangular
microcubes are not defined by continuous straight lines that extend
along a planar surface, and therefore cannot be ruled with
intersecting sets of parallel lines all parallel to a common plane.
Thus, with the sole exception of the rectangular cubes disclosed in
U.S. Pat. Nos. 4,349,598 and 4,895,428 (wherein one of the active
cube faces is perpendicular to the reflector front surface) it is
not possible to cut or rule a master containing all hexagonal or
all rectangular microcubes by ruling straight lines in a single
flat surface. Moreover, because of the geometric limitations
inherent in ruling the cubes for the U.S. Pat. No. 4,349,598 and
U.S. Pat. No. 4,895,428 patents, the cube structures disclosed
therein are not useful where the primary light source will
generally be at a near-zero incidence angle, such as in highway
sign sheeting.
Processes for making tools having macrocubes are known in the prior
art. Such tools are typically made by assembling a cluster of metal
pins, each pin having a single cube corner machined and polished on
one end. Hexagonal pins typically may have a dimension across
parallel flats on the order of about 0.10 inch (2.5 mm).
Rectangular pins have a short dimension of about 0.070 inch (1.8
mm) and a long dimension of about 0.120 inch (3.0 mm). A cluster of
such pins is then used as a master to electroform a mold. These
larger cubes, because of their height, are too large for use in the
manufacture of thin flexible retroreflective sheeting requiring
microcubes, but do find utility where larger (and thus taller)
retroreflective elements are acceptable, such as in molded plastic
reflectors for roadway markers, automobile taillights, and the
like.
Because of manufacturing limitations, the smallest pin known to
applicants has a cube shape about 0.040'' square. Microcubes as
used in flexible retroreflective sheeting generally are no greater
than about 0.016 inch (0.4 mm) on a side, and in applicants'
assignee's commercial sheeting products, the longest edge of the
cube shape is about 0.010 inches (0.25 mm).
The term microcube (or a cube of small dimensions), has been used
in patents of others to describe or claim sheeting products
produced from tools made directly or indirectly from ruled masters,
as opposed to retroreflector articles comprising macrocubes
typically formed by grouping pins (or by other techniques used to
form the larger cubes).
For tooling hexagonal cubes, as alternative to the "pin cluster"
manufacturing technique is shown in Applied Optics, vol. 20, no. 8,
Apr. 15, 1981, pages 296-298. It is there stated that one way to
achieve hexagonal cube corners is to accurately machine and polish
grooves in the edge surfaces of a stack of flat plates and to
assemble the plates at a desired angle. The reference shows a
photograph of several flat plates with grooves cut in one edge,
stacked one atop the other and with adjacent plates shifted with
respect to one another so that the grooves are offset. The tilted
stack of plates so assembled results in a set of hexagonal cubes
which may be used as a master for electroforming molds. However,
this technique was disclosed decades earlier by applicants'
assignee's founder and was stated to be an unsatisfactory technique
for tooling retroreflectors, see U.S. Pat. No. 1,591,572 (FIG. 16,
p. 5, 11, 85-99).
Heretoforer, the above-described "stacked plates" method of forming
macrocubes was not of practical interest for producing molds for
retroreflective products on a commercial scale. First, the molds
for macrocubes could be made satisfactorily by the aforementioned
clustering of hexagonal pins. Secondly, as observed in U.S. Pat.
No. 1,591,572, by using conventional machining and polishing
techniques, it was not possible to cut and polish
inside-intersecting faces with the precise angular tolerances and
sharp edges achievable with the pin technique. In particular, any
irregularities in the cube surfaces as might be caused by either
the cutting operation or the polishing operation could
disadvantageously increase the divergence of the retroreflected
light and thus diminish the effective retroreflectivity of the
cubes so formed. This recognized difficulty in polishing grooved
internal angles is highly exacerbated with microcubes because the
area that cannot be polished flat is a relatively greater
percentage of the resulting cube face area.
As part of the present application, applicants disclose a technique
for making and using thin plates that can be ruled without the need
of polishing and that can be assembled in various ways to achieve
microcube elements not previously available.
It is an object of the present invention to provide an array of
microcubes which cannot be produced by ruling in one plane.
It is a further object of the invention to provide an array of
microcubes in which the non-dihedral face-edges are not all
parallel to a common plane.
It is still another object of the invention to provide means for
interrelating three constructional parameters defining a hexagonal
microcube (i.e., slippage, groove depth, and plate thickness,
explained infra), by which the desired optical characteristics of
the microcube can be optimized.
It is still another object of the invention to provide a
retroreflective article and, in particular, retroreflective
sheeting, having a pattern of hexagonal retroreflective microcubes
having desired retroreflective characteristics.
It is another object of the instant invention to provide a method
of making a tool including two or more contiguous hexagonal
microcubes, which tool can be used for making a retroreflective
article and, in particular, retroreflective sheeting.
It is still another object of the invention to provide a method of
making a tool having a pattern of all hexagonal microcubes, which
tool is made in part by ruling a set of grooves into the ends of a
set of plates and then assembling the plates so as to define an
array of hexagonal microcubes having desired retroreflective
characteristics.
It is yet another object of the invention to provide an article
having hexagonal microcubes wherein all of the cube faces are
pentagonal; to provide a tool for making such an article; and to
provide methods for making such an article and such a tool.
It is yet another object of the invention to provide a
retroreflective article and, in particular, retroreflective
sheeting, having rectangular retroreflective microcubes in which no
dihedral face-edges of one cube are collinear with those of another
cube, and in particular, such an article in which the microcubes
provide desired retroreflective characteristics.
It is another object of the invention provide a tool having a
unique pattern of rectangular microcubes in which cube axis cant is
not constrained by the need for collinearity of dihedral face-edges
of adjacent cubes, which tool can be used for making a
retroreflective article and, in particular, retroreflective
sheeting.
It is another object of the instant invention to provide a method
of making a tool having a pattern of rectangular microcubes in
which dihedral face-edges are not collinear, which tool can be used
for making a retroreflective article having rectangular microcubes,
such as sheeting.
It is still another object of the invention to provide a method of
making a tool having a pattern of rectangular microcubes, which
tool is made in part by ruling grooves and bevels into plate ends
to provide a desired rectangular cube shape and pattern.
It is also an object of the invention to provide a method of making
rectangular microcube tools by means of assembling flat plates, on
one end of which the rectangular microcubes have been formed.
It is still another object of the invention to provide an article
having a pattern of retroreflective square microcubes, wherein the
microcubes in a square set of four cubes have cube axes canted in
four different directions.
It is yet another object of the invention to provide an article
having a pattern of retroreflective pentagonal microcubes; to
provide a tool for making such an article; and to provide methods
for making such an article and such a tool.
It is still another object of the invention to provide an article
having a pattern of pentagonal microcubes with canted cube axes,
and such an article having pentagonal microcubes with differently
canted cube axes, and tools for making such articles and methods
for making such tools and articles.
Still a further object of the invention is to provide a
retroreflective article having one or more triangular microcubes in
which the cube shape and the position of the projection of the cube
apex within the cube shape are independent of the cube axis
cant.
Yet a further object is to provide such a retroreflective article
in which adjacent triangular microcubes may have different degrees
of inclination of the cube axes and are not necessarily matched
pairs.
Other objects, advantages, and novel features of the instant
invention will be understood by those skilled in the art from the
following specification and the drawings appended hereto.
SUMMARY OF THE INVENTION
In accordance with the invention, methods are disclosed for making
a tool having a pattern of microcubes for use in making a
retroreflective article. A plurality of plates is provided, each
plate having two substantially parallel planar surfaces and at
least one end made of a material that can be cut by a cutting tool
that will produce an optical surface, as cut. The plate has a
micro-sized thickness "t", i.e., on the order of about one or two
microcube widths, depending upon the type of microcube-corner to be
tooled. The thickness need not be the same for all plates.
Many shapes of microcubes are manufacturable using the plate
process disclosed herein. Two shapes, hexagonal and rectangular,
are discussed in detail; other shapes are described more generally
to illustrate the versatility of the process.
Hexagonal Microcubes
To produce a pattern of hexagonal microcubes, the plates are
stacked one against another so that the set of ends of cuttable
material lies substantially in a single plane, which, in a
preferred form, is substantially perpendicular to the parallel
planar surfaces of each plate. A series of parallel V-shaped
grooves is ruled with a cutting tool into the set of cuttable ends.
The ruled grooves preferably have polished surfaces as cut and
therefore do not require subsequent lapping and polishing as do
pins used in making macrocubes.
In one embodiment of the invention, the direction of cutting the
grooves is nominally perpendicular to the planar surfaces of the
plates, the length "L" of each inclined surface of the groove
perpendicular to the direction of cutting is chosen to be equal to
the thickness "t" of the plate, and the included angle between the
inclined surfaces is about 90.degree., the included angle may be
varied from 90.degree. by tilting the cutting face of the cutting
tool with respect to the surface being cut.
The grooved plates are then offset from one another by half a
groove width horizontally and possibly, but not necessarily, by the
depth "d" of one groove vertically, so that the top edge of a
groove in one plate coincides with the bottom edge of a ruled
groove in the adjacent plate, thus creating two superimposed arrays
of hexagonal cube corners. One array consists of female (concave)
hexagonal cube corners, each comprised of the exposed planar
surface of one plate plus the two surfaces of one groove of the
next adjacent plate. The other array consists of male (convex)
hexagonal cube corners, each comprised of the exposed planar
surface of one plate plus two adjacent surfaces from adjacent
grooves in that same plate. For greater accuracy in the eventual
retroreflective article, the male cube corners are preferred,
because they avoid any plate-to-plate angular errors.
Rectangular Microcubes
To produce a pattern of rectangular microcubes, in one embodiment,
plates of a chosen thickness "t" are stacked alternately with
slightly shorter spacers. The assembly of plates and spacers is
tilted at a predetermined preferred angle, with one set of edges of
the cuttable ends lying in a plane parallel to the bed of the
ruling machine. The cuttable end of each plate is then bevel cut by
means of a cutting tool so that the beveled face is perpendicular
to the bed of the ruling machine. A series of grooves of desired
included angle is then cut by the cutting tool in a direction
substantially perpendicular to the beveled face. To crease an
electroforming master comprising rectangular microcubes, the
spacers are removed and the plates are then stacked together with
adjoining plates rotated 180.degree. with respect to each other
with the apices of the rectangular cube-corners all lying in the
same plane perpendicular to the plane of the sides of the plates
and with the apices of cubes in adjoining plates aligned parallel
to the grooves.
Manufacture of Article
The stack of grooved plates (for hexagonal cubes) or grooved and
beveled plates (for rectangular cubes) may then be used as a master
for electroforming a mold insert or for initiating a mothering
process to electroform a larger mold insert or an embossing belt,
as shown in patent U.S. Pat. No. 4,478,769 for the manufacture of
retroreflective articles and, in particular, retroreflective
sheeting, but now having a pattern of hexagonal or rectangular
microcubes. The use of hexagonal or rectangular microcubes instead
of triangular microcubes advantageously increases the active
aperture of the article as projected parallel to the principal
refracted ray from 66% or less to essentially 100%.
Glossary of Terms
For purposes of this application, Applicants are using certain
terms in a particular sense, as defined herein, and other terms in
accordance with industry accepted practice, such as current ASTM
definitions. Note that many of these definitions distinguish
between a cube and a cube shape, each of which is defined
herein.
Adjacent--for microcubes, having a portion of an edge of the shape
of one cube essentially coincident with a portion of an edge of the
shape of another cube.
Angle of incidence--the angle between the illumination axis and the
normal to the front surface of a retroreflector. See also "entrance
angle."
Array active aperture--the sum of the active apertures of the
individual microcube elements making up the array. (See also
"percent active aperture")
Contiguous microcubes--microcubes, a non-dihedral face-edge of one
of which is coincident with a non-dihedral face-edge of another
microcube. Compare, "adjacent cubes." Note that non-contiguous
microcubes may be adjacent. An array of contiguous microcubes is
one in which the non-dihedral face edges of each microcube (except
those at the perimeter of the array) are coincident with
non-dihedral face edges of another microcube.
Cube (also "cube corner")--an element consisting of three nominally
perpendicular faces, regardless of the size or shape of the faces;
often referred to in industry and literature as "corner cubes",
"trihedrals" or "tetrahedrons".
Cube area--the area enclosed by the cube shape.
Cube axis--a central axis that is the trisector of the internal
space defined by the three intersecting faces of a microcube. In
the art, sometimes called the "symmetry axis."
Cube axis cant--the angle between the cube axis and the principal
refracted ray. The sign of the cant is negative for
face-more-parallel and positive for edge-more parallel. A cube is
considered canted when the cube axis cant is not zero.
Cube diagonal--for certain cube corners, an imaginary line passing
through the apex of the cube corner at an angle such that in a
projection of the outline of the cube corner parallel to the cube
diagonal, every line through the apex terminating on both ends at
the cube shape will be bisected by the apex.
Cube perimeter--closed spatial curve comprising the non-dihedral
edges of the faces of a cube. In instances where there is an
uninterrupted surface shared by two or more microcubes, the
dividing lines between microcubes shall be considered to be the
shortest lines that can be drawn to complete the polygon (see e.g.
FIG. 27B).
Cube shape--the two-dimensional geometrical figure defined by the
projection of the cube perimeter in the direction of the principal
refracted ray. Thus, a triangular cube has a cube shape that is a
triangle, a hexagonal cube has a cube shape that is a hexagon, and
so forth.
Cube symmetry plane--a plane that divides a cube corner into mirror
images. Not all cube corners have a plane of symmetry.
Design ray--an imaginary line through the cube apex in a tool,
which ray is coincident with the principal refracted ray in the
article.
Dihedral face-edge--intersection of two faces of a single cube.
Entrance angle--the angle between the illumination axis and the
optical axis (retroreflector axis). Note the distinction between
entrance angle and angle of incidence. The angle of incidence is
always measured between the incident ray and the normal to the
surface (which may or may not be the retroreflector axis), whereas
the entrance angle is measured between the incident ray and the
retroreflector axis (which may or may not be the normal to the
surface). Entrance angle is a measure only of the amount by which
an incident ray is angled to the retroreflector axis, and is not
concerned with the normal; angle of incidence is a measure only of
the amount by which an incident ray is angled to the normal, and is
not concerned with the retroreflector axis. For example, a pavement
marker may be designed for the normal to the marker surface to be
angled 60.degree. to the optical axis; if light from an approaching
vehicle is incident upon that marker along the retroreflector axis,
the entrance angle is 0.degree. and the angle of incidence is
60.degree., if light from an approaching vehicle is incident on the
marker at a horizontal angle of 20.degree. with respect to the
retroreflector axis, the entrance angle is 20.degree. and the angle
of incidence is 61.98.degree.=[cos.sup.-1(cos 60)(cos 20)].
"Face-more parallel" and "edge-more parallel" refer to the
positioning of the cube relative to the principal refracted ray.
When the angles between the cube faces and the principal refracted
ray are not all equal to 35.26.degree., the cube is
"face-more-parallel" or "edge-more-parallel" depending upon whether
the face angle with respect to the principal refracted ray that is
most different from 35.26.degree. is respectively greater or less
than 35.26.degree.. In the case of sheeting or other
retroreflectors for which the principal refracted ray is nominally
perpendicular to the front surface of the retroreflector, then for
face-more-parallel microcubes the selected cube face will also be
more parallel to the reflector front surface than will any face of
an uncanted microcube.
Horizontal entrance angle--for pavement markers, the angle in the
horizontal plane between the direction of incident light and the
retroreflector axis.
Incidence angle--see, "angle of incidence."
Microcube (also "microcube corner")--a cube corner having a maximum
area of about 0.0016 square inches (1 mm.sup.2).
Non-dihedral face-edge--edge of a microcube face that is not a
dihedral face-edge, i.e., an edge that is a segment of the cube
perimeter.
Optical axis--a designated line segment from the retroreflector
center that is chosen centrally among the intended directions of
illumination, such as the direction of the road on which or with
respect to which the retroreflector is intended to be mounted.
Paired--oppositely oriented. Paired cubes, as used herein, refers
to oppositely oriented adjacent cubes. Paired arrays, as used
herein, refers to two arrays, the cube in one array being
oppositely oriented to the cubes of the other.
Percent active aperture--that portion of the projected area of an
array that is retroreflectively functional for a particular
selected direction of projection. (This definition assumes that the
rear surfaces of the cube are 100% reflective. This definition is
equivalent to that used in WO 95/11470, page 6, lines 23-25).
Principal incident ray--a light ray parallel to the optical axis,
chosen so that after refraction at the article's front surface, the
ray passes through the apex of the cube corner.
Principal refracted ray--the continuation of the principal incident
ray after refraction at the retroreflector front surface.
Retroreflectance--the product of percent active aperture times each
cube face's reflectivity times the square of the transmission (to
account for Fresnel transmission loss) of the front surface. (This
term differs from "total light return" as defined in WO95/11467,
page 17, lines 26 and 27, by inclusion in "retroreflectance" of the
Fresnel loss of the front surface.) Photometrically,
retroreflectance is the measure of the total retroreflection
accumulated over all appropriately small observation angles and all
rotation angles.
Retroreflector axis--same as "optical axis."
Rulable--capable of being generated by the repeated straight-line
motion of a shaped tool along paths parallel to a common plane.
Zone of reflectorization--the range of entrance angles in a given
entrance plane throughout which the retroreflector maintains a
given minimum retroreflectance.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective view of a steel block for forming
electroless nickel plates used in the present invention;
FIG. 2A is a cross section of the block of FIG. 1 in the direction
of the arrows 2--2 after deposition of an electroless nickel layer
on the top surface of the block;
FIG. 2B is a cross section of the block of FIG. 1 and the
electroless nickel deposit after machining one of the upper
edges;
FIG. 2C is a cross section of the block with the electroless nickel
plate separated and with electroless nickel residue remaining in
one of the block undercuts;
FIG. 3 is a perspective view of a stack of electroless nickel
plates before being ruled;
FIG. 3A is a view perpendicular to the face of one of the plates of
FIG. 3 showing an arrangement of dowel holes used in one method of
aligning plates for ruling and assembly of the electroform
master.
FIG. 4 is a perspective view of the same stack of plates after
being ruled with grooves;
FIG. 5 is a perspective view of the plates of FIG. 4 with adjacent
plates offset by one groove depth in the vertical direction and one
half groove width in the horizontal direction;
FIG. 6 is a side view of the stack of plates of FIG. 5 in the
direction of the arrows 6--6 and in which "L" (as shown in FIG. 4)
equals "t";
FIG. 6A is a view in the direction of the arrows 6A--6A of FIG.
6;
FIG. 6B is a view in the direction of the arrows 6B--6B of FIG. 6,
with different shading added to emphasize the offset between
adjacent plates;
FIG. 7A is a view of a portion of the front face of a cutting tool
used to rule grooves in the plate ends in accordance with the
instant invention, taken perpendicular to the face of the tool;
FIG. 7B is a view in the direction of the arrows 7B--7B of FIG. 7A
and illustrates a side view of the cutting tool of FIG. 7A;
FIG. 8A is a view of a portion of the front face of the cutting
tool as tilted for cutting a groove;
FIG. 8B is a side view of the cutting tool of FIG. 8A in the
direction 8B--8B of FIG. 8A, showing the tilt, e, of the face of
the tool and the direction of cutting;
FIG. 9 is a view of one complete groove as cut in a plate with
included groove angle C+.DELTA.C corresponding to the tilt, e, of
the cutting tool;
FIG. 10 is a side view of stacked plates similar to FIG. 6, but in
which "L" is greater than "t" and in which adjacent plates are
offset by one groove depth d in the vertical direction and one-half
groove width in the horizontal direction;
FIG. 10A is a view taken in the direction of the arrows 10A--10A in
FIG. 10, which direction is along the diagonal of the cubes formed
by the plates, which may also coincide with the principal refracted
ray;
FIG. 10B is a view taken in the direction of the arrows 10B--10B in
FIG. 10, which direction is perpendicular to the plane passing
through the cube apices;
FIG. 10C is a view taken perpendicular to the faces of the plates,
in which different shading has been added to emphasize the offset
between adjacent plates;
FIG. 11 is a side view of a stack of plates about to be ruled with
grooves but set at an angle to the cutting plane, the angle being
greatly exaggerated for the purpose of illustration;
FIG. 11A is a side view of the stack of plates of FIG. 11 after
ruling and after being offset with respect to adjacent plates by
one groove depth in the vertical direction and one-half groove
width in the horizontal direction;
FIG. 11B is a view taken perpendicular to the plane of the face of
the plate (along the arrows 11B--11B in FIG. 11A) illustrating that
the edges of the grooves are angled with respect to the
perpendicular to the face of the plate (only portions of the plates
being differently shaded for illustrative purposes);
FIG. 12 is a side view of a stack of plates with "L" equal to "t"
as in FIG. 6, but stacked with adjacent plates offset 1.64t
vertically and 0.707t horizontally;
FIG. 12A is a projection taken in the direction 12A--12A of FIG.
12, which direction is parallel to the cube diagonal;
FIG. 12B is a frontal view of the plates of FIG. 12;
FIGS. 12C and 12D illustrate the interrelationship of various cube
parameters for different incident rays;
FIG. 13 is a partial side view of an article comprising paired
arrays of hexagonal microcubes formed from stacked plates similar
to FIG. 12, in which d=0.55t and s=0.45t to provide 9.74.degree.
face-more-parallel microcubes;
FIGS. 14A and 14B are partial plan and side views respectively of a
plate before machining rectangular cubes;
FIG. 15 is a schematic side view of a section of a stack of
alternating plates and spacers tilted at angle X for machining a
bevel face with a cutting tool;
FIGS. 16A and 16B are partial plan and side views respectively of
the single plate of FIGS. 14A and 14B after machining of the bevel
face;
FIG. 17 is a view similar to FIG. 15 of a section of a stack of
alternating plates and spacers after machining the bevel faces,
with the spaces between plates filled with plastic in preparation
for machining grooves;
FIG. 18 is a view in the direction 18--18 on FIG. 17 of the stack
of plates and spacers after partial machining of groove faces and
showing a cutting tool moving toward the plane of the paper and
machining the grooves (and the next groove to be cut in dashed
lines);
FIG. 19 is a side view of the cross section of a single plate of
FIG. 18 at arrows 19--19;
FIG. 20 is a plan view in the direction of arrows 20--20 in FIG. 19
of a single plate after machining of the bevel faces and groove
faces and showing the rectangular outline of the microcube corners,
a typical microcube being shown in the dashed circle in FIG.
20;
FIG. 21 is a plan view of a stack of three plates machined as in
FIG. 20, assembled with adjacent plates oriented 180.degree. to
each other and ready for use as a master in electroforming, with a
typical individual cube indicated by three dotted faces;
FIG. 22 is a partial side view of a double thickness plate used in
an alternative inventive method of making rectangular microcubes,
after cutting a bevel face perpendicular to the plane of the bed of
the ruling machine, with the plates positioned at an angle
(90.degree.-X) to that plane;
FIG. 22A is a view of the cutting tool as positioned for cutting
the bevel face of FIG. 22;
FIG. 22B is a view in the direction of arrows 22B--22B of FIG. 22
showing the first bevel face and a temporary face machined in the
plate end by the cutting tool;
FIG. 22C shows the first bevel face and the temporary face in FIG.
22 filled in preparation for cutting grooves;
FIG. 23 shows the plate of FIG. 22 during cutting of groove faces
in a direction substantially perpendicular to the direction of the
first bevel cut by means of a second cutting tool;
FIG. 23A is a cross section through FIG. 23 at arrows 23A--23A, at
the root of the cut for the groove faces;
FIG. 23B is a view of FIG. 23A in the direction of arrows 23B--23B
after cutting of the groove faces to form a first row of
rectangular cubes, one of which is indicated by the dotted faces in
the dashed circle;
FIG. 24 is the side view of the plate of FIG. 23A repositioned for
cutting a second bevel face for a second row of cubes by means of
the first cutting tool, which, in effect, removes the temporary
face (as shown by dashed lines);
FIG. 25 shows a front view of the plate of FIG. 24 after cutting
the second bevel face for the second row of cubes and during
machining of new groove faces substantially perpendicular to the
second bevel face;
FIG. 25A is a cross section in the direction of the arrows 25A--25A
at the root of the cut for the groove faces of the second row of
cubes;
FIG. 25B is a plan view of a finished plate ready for use as an
electroforming master, taken in the direction 25B--25B of FIG. 25A
and showing the bevel faces and groove faces of the second row of
cubes, one such cube of the second row being indicated in the
dashed circle;
FIG. 26 is a plan view of two square microcubes;
FIG. 27 is a frontal view of a plate for forming the square
microcubes of FIG. 26, taken in the direction of cutting of the
groove faces, in which the groove roots define a plane parallel to
but offset above the intersection of the bevel faces;
FIG. 27A is a cross-section view in the direction of arrows
27A--27A of FIG. 27 taken through a groove root;
FIG. 27B is a view in the direction of arrows 27B--27B of FIG. 27A,
depicting a finished plate for use as an electroform master;
FIG. 27C is another partial side view of an article similar to FIG.
13, but depicting an array of rectangular microcubes made in a
manner similar to that of FIGS. 27 through 27B, but in which H=2W,
axes are canted, and apices are decentered;
FIG. 28 depicts rectangular cubes wherein three principal optical
parameters (apex decentration, boundary proportion, and axis cant)
have been modified for illustrative purposes; cube size is a fourth
parameter, not illustrated here;
FIG. 29 illustrates an improved rectangular cube, with
face-more-parallel when used, for example, in a pavement marker
with a 55.degree. incidence angle;
FIG. 29A is a projection of the cube of FIG. 29 parallel to the
principal refracted ray;
FIG. 30 is an illustrative rear isometric view of an array of cubes
of the type shown in the marker of FIG. 29;
FIG. 31 illustrates the tooling of triangular microcubes with bases
not all parallel;
FIG. 32 depicts an array of square microcubes providing four
orientations without slippage walls;
FIG. 33 is a plan view of a plate with a single row of square cubes
of the type shown in FIG. 32, with the three cutting steps
indicated;
FIGS. 34A and 34B are plan and side views respectively of a portion
of a plate having rectangular microcubes with the bevel face ruled
in a direction perpendicular to the front face of the plate, as
contrasted to the tooling method described in FIGS. 15-21, for
which the bevel face was ruled in a direction parallel to the front
face of the plate;
FIG. 35 illustrates in plan view an array of penta-face hexagonal
cubes with the end of one plate highlighted;
FIG. 36 illustrates an array of pentagonal microcubes made pursuant
to the plate technique of the present invention;
FIG. 36A illustrates two pentagonal microcubes with different
cants;
FIG. 37 is a graph of a family of curves comparing retroreflectance
of microcubes of various refractive indices versus incidence angle
from -90.degree. to +90.degree., for an array of hexagonal
microcubes where d/t=7071, s/t=0, of the type depicted in FIGS. 6
through 6B;
FIG. 38 is a graph of a family of curves of retroreflectance versus
incidence angle I from -90.degree. to +90.degree., for arrays of
unpaired hexagonal microcubes having refractive index=1.49 where
d/t is varied and s/t=0;
FIG. 39 is a graph of a family of curves of percent active aperture
(instead of retroreflectance) versus incidence angle I from
-90.degree. to +90.degree. for the same microcubes used for FIG.
38;
FIG. 40 is a graph comparing the efficiency of the paired arrays of
hexagonal microcubes and paired rectangular microcubes of FIGS. 13
and 27C, at entrance angles from 0.degree. to 70.degree., with
efficiency being shown as both percent active aperture and also as
retroreflectance;
FIG. 41 is a graph of curves of retroreflectance versus horizontal
entrance angle for the improved inventive rectangular microcubes of
FIGS. 29 and 30 as compared with rectangular microcubes of cube
axis cant=1.9.degree. for which the non-quadrilateral face is
perpendicular to the front surface of the reflector as in prior art
devices;
FIG. 42A through 42E depict a family of three curves of
retroreflectance versus entrance angle from 0.degree. to 70.degree.
for paired arrays of hexagonal microcubes of refractive index=1.59
for each of five cube axis cants compared with the retroreflectance
of a triangular microcube retroreflective article of Hoopman U.S.
Pat. No. 4,588,258;
FIG. 43 depicts curves of retroreflectance versus entrance angles
from 0.degree. to 60.degree. in a plane perpendicular to the plane
of symmetry of the cubes for paired canted rectangles and paired
arrays of canted hexagons compared with identically canted
Hoopman;
FIG. 44 is a graph showing percent active aperture versus entrance
angles from -20.degree. through 20.degree. for paired rectangles
and paired squares, both without cant, compared with arrays of
microcubes from FIG. 12 of prior publication W/O 95/11470.
FIG. 45 is a graph showing percent active aperture versus entrance
angles from -70.degree. through 70.degree. for paired canted
rectangular microcubes and paired arrays of canted hexagonal
microcubes, compared with FIG. 32 of prior publication WO
95/11463.
FIGS. 46a-c show the effect of diffraction on the pattern of
retroreflected light for three different size of hexagonal
microcubes.
These various figures, which are not to scale, are intended to be
merely illustrative and not limiting. The various graphs are
similarly not limiting but are for demonstrative and comparative
purposes. Other graphs and examples will be apparent from the
detailed descriptions which follow.
DETAILED DESCRIPTION OF THE INVENTION
The inventive method of making microcubes uses the principle of
ruling the ends of certain plates in a particular fashion and then
assembling these plates in a particular combination to form an
array of microcubes. An "array" as used in this patent application
shall mean a repeating pattern of geometrical elements, including
microcubes. Those skilled in the art will recognize that a
retroreflective article having desired performance characteristics
could be made from a component of different arrays. For example,
such an article could include different arrays each made by one or
more techniques of the instant invention, or such an article could
include a combination of arrays of the instant invention and arrays
made by prior art machining methods. Means for combining different
arrays in a single article are known to those skilled in the art,
and retroreflective articles having a plurality of arrays, one or
more of which is made in accordance with the instant invention, are
considered to be within the scope of the instant application. In
every instance where different arrays are combined, it shall be
understood that the specification and claims are relevant to that
array, or that portion of the array, that is made by the technique
of the instant invention.
The various examples discussed hereinafter demonstrate the advances
in this technology in their simplest form and also disclose
specific embodiments in which improved retroreflector performance
can be achieved in microcubes using the same optical principles as
have been employed in macrocubes.
All embodiments of the invention require the use of plates, which
differ somewhat for different types of microcubes. The plates are
of micro-sized thickness, on the order of about b 0.004-0.040
inches (0.1-1.00 mm). There are four basic types of plates. Plates
10, suitable for the tooling of hexagonal microcubes, with
rectangular cube faces, have flat and parallel faces and, uniquely,
one face of the plate becomes a face of the microcube, and
therefore, must have a polished surface. Plates 10 and 210,
suitable for tooling rectangular and triangular microcubes, have
flat and parallel faces and in a preferred form, neither face of
the plate becomes a face of the microcube. Plates 710 and 810,
suitable for tooling the pentagonal microcubes of FIG. 36, have one
flat face and one grooved face, neither of which becomes a face of
the microcube. Plates suitable for tooling the hexagonal microcubes
with pentagonal faces of FIG. 35, or for cutting two rows of
pentagonal microcubes on one plate, are grooved on both sides, the
groove spacing and groove angles being not necessarily the same for
both sides.
Method of Making Plates
The plates must be of a material that cuts cleanly when ruled, such
as with a diamond cutting tool as is known in the art. Electroless
nickel is a particularly suitable material for the rulable plates
used in the method of the instant invention.
Although the above-described plates may differ, the method of their
manufacture can be generally illustrated by the method of making
plates 10 used in the manufacture of hexagonal microcubes. For
purposes of illustration, plate 10 can have dimensions of about
1.0''.times.4.0'' and a thickness "t" of about 0.010''.
Referring to FIG. 1, a stainless steel block 601 is provided having
a flat top surface 602 of about 1.0''.times.4.0''. Block 601 may be
of grade 440C stainless. Grind and polish the surface 602 of block
601. Machine an undercut 603 on the two 0.75'' by 4.0'' side
surfaces tapering from zero at the polished face 602 to 0.005''
deep at 0.250'' down from the polished face 602. Passivate the
block 601 by immersion for 10 seconds in 30% nitric acid, for
example, and deposit electroless nickel 604, FIG. 2A, on the
polished top surface 602 of the stainless block to the thickness
desired plus approximately 0.002'', in this example to a total
thickness above the block of 0.012'' and also approximately 0.25''
down the sides of the block.
Machine the 1.0'' by 4.0'' surface 609 of the electroless nickel
604 with a diamond tool to the desired thickness, in this example
to 0.010''. Machine the sides of the block with diamond to cut away
electroless nickel at 605 (FIG. 2B) to the stainless at the top of
the undercut, freeing the 0.010'' thick electroless nickel plate
606FIG. 2C to be separated from the stainless block. Clean out the
undercuts in the block by picking out the loose wedge 607FIG. 2C of
electroless nickel in the undercut. Repeat the process to make as
many plates 606 as may be required. In the steps that follow, the
plates 606 will be identified as 10, 110 or 210 in the tooling of
hexagonal, single rectangular or double rectangular microcubes,
respectively.
In the tooling of hexagonal microcubes, a portion of the surface
608FIG. 2C of the electroless nickel plate 606 that was against the
polished surface of the stainless block will become one face of the
cube corner. Alternatively, the approximately 1.0'' by 4.0''
surface 609 of the electroless nickel can be provided with an
optical finish during the step of machining, the plate to size with
a diamond tool, in which instance, it will be unnecessary to polish
the face of the stainless steel block. For the tooling of
rectangular microcubes, it will be unnecessary to polish the face
of the stainless steel block before electroforming because neither
face of the plate becomes a face of a microcube.
Method of Making Hexagonal Microcubes
As shown in FIG. 3, the plates 10 are preferably flat and each has
at least one flat end 12 that is cuttable, such as by a diamond
cutting tool. The plates 10 are stacked together so that at least
one set of ends 12 lies within a plane. It will be understood that
the three plates shown in FIG. 3 are for clarity of the
illustration, and that more than three plates can be included in a
single stack. A series of V-grooves 14 are ruled into the set of
ends 12. FIG. 4 shows the same stack of plates 10 but with the
V-grooves 14 ruled into the straight ends 12. The grooves 14 are
preferably substantially parallel to one another and substantially
perpendicular to the front face of the stack of plates 10. The
V-shaped grooves have an included angle of substantially
90.degree., with each groove being defined by two top edges or
crests 20 and a bottom edge or root 21. For optimum efficiency, the
grooves 14 are spaced from one another so that they are separated
only by the top edges 20 of adjoining grooves; i.e., there are no
substantial flat surfaces between the grooves 14.
FIGS. 7A and 7B are front and side views, respectively, of a
portion of the cutting tool for ruling grooves, in which C is the
angle between cutting edges viewed perpendicular to the front face
of the tool. The angle C may be chosen to be smaller than the
desired included groove angle, C+.DELTA.C in FIG. 9, in order that
fine adjustment of that groove angle may be made by tilting the
tool by a relatively coarse amount "e" in FIG. 8B, where "e" is the
angle at which the face of the cutting tool is tilted from a
perpendicular to the direction of the cut such that
e=cos.sup.-1[(tan 0.5C)/tan 0.5(C+.DELTA.C)] Equation A:
FIG. 8A is a view of a portion of the front face of the cutting
tool tilted by the amount "e" of FIG. 8B, in which C+.DELTA.C is
the angle between cutting edges viewed parallel to the direction of
cutting. FIG. 9 shows the changed angle C+.DELTA.C in the cut
groove.
In order to define a pattern of hexagonal retro-reflective
microcubes the grooved plates 10 may be offset one from another as
shown in FIG. 5. Adjacent plates are offset from one another in the
horizontal direction by a distance "a", which as shown in FIG. 5 is
equal to one half the width of a groove. Adjacent plates are also
offset from one another in the vertical direction by a distance
"d", which as shown in FIG. 4 is equal to the depth of one groove.
The manner in which the plates are offset from one another is also
shown in FIG. 6B, wherein, alternating plates are shaded
differently for clarity. It will be understood that, throughout
this specification, "vertical" shall designate a direction
perpendicular to the plane of the roots of the grooves of a single
plate, and "horizontal" shall designate a direction perpendicular
to the vertical and in the plane of the plate.
With the plates offset in this manner, "male" microcubes are
defined by the inclined walls of adjacent grooves which meet at a
top edge 20 to form two faces 17 and 18 of the microcube, and the
front surface of the same plate which forms the third face 19 of
the microcube. It can be seen in FIG. 6A that all three faces 17,
18 and 19 of a single male cube (shown by dots) are formed on a
single plate 10. Female microcubes may be formed by the two faces
of a groove in one plate and the front surface of an adjacent
plate. An advantage of the male microcube is that the accuracy of
the angels between the faces of each microcube is dependent solely
on the accuracy of the groove ruling operation, and not on the
accuracy with which the plates are stacked and assembled in forming
the "master". The "master" of stacked and assembled plates may then
be subjected to an electroforming procedure to make tools, as will
be discussed in greater detail below.
The hexagonal outline of the cube corners produced by the method
described above, and the quadrilateral outline of the cube faces,
are both readily apparent in FIGS. 5 and 6A. In particular, it is
evident in FIGS. 5 and 6A that the hexagonal cube corners are not
defined by continuous straight lines which extend along the entire
surface of the ruled master, as is the case with triangular cube
corners, shown for example in FIG. 1A of the aforementioned patent
U.S. Pat. No. 4,478,769. Therefore, it is apparent that a tool
comprising only hexagonal microcube corners cannot be machined by
ruling three sets of parallel grooves as described in the '769
patent.
In the embodiment of FIGS. 5 and 6, the length of the sides of the
groove ("L" in FIGS. 4 and 6B) and the thickness of the plate ("t"
in FIGS. 3 and 6) are equal and the direction of the ruling is
perpendicular to the face of the plate 10. For this embodiment, the
cube axis is perpendicular to the plane of the cube apices and the
angle X in FIG. 6 is nominally 35.26.degree..
While in the foregoing example all the cube dihedral angles are
equal and all the cube faces are identical, it is recognized in the
art of cube corner retroreflectors that for some applications it
may be desirable to alter various optical properties of the
retroreflective article by making predetermined modifications to
the cube angles and the relative sizes and shapes of the respective
cube faces. Those modifications can be achieved using the methods
of the instant invention. Thus, for example, the thickness of the
plate "t" need not necessarily be equal to the length of the side
of the groove "L", the crest of one groove need not be coincident
with the root of a groove in an adjacent plate, and the direction
of ruling is not necessarily perpendicular to the face of the plate
10.
The inventive method as described allows the cube designer to
control certain retroreflective properties of the resulting array
of microcubes. For example, various angles of the principal
incident ray can be accommodated by varying the depth of the groove
relative to the thickness of the plates (FIG. 10), and/or by
tilting the bisector of the groove so that the lengths of the two
sides of a single groove are not the same (not illustrated) and/or
by changing the offset of adjacent plates (FIG. 12). In another
embodiment, the entrance angularity can be increased either in a
plane perpendicular to the cube symmetry plane by canting the cube
axis to face-more-parallel (FIGS. 41 and 43) or in a plane parallel
to the cube symmetry plane by using oppositely oriented pairs with
either face-more-parallel or edge-more-parallel cant (FIG. 42) or
in multiple planes parallel to and perpendicular to the symmetry
plane by combining oppositely oriented pairs with
face-more-parallel cant (FIGS. 43 and 45). In yet another
embodiment, the divergence of the retroreflected beam (i.e., the
observation angularity) can be increased in one plane or in
multiple planes by making the groove angle slightly greater or less
than 90.degree. and/or by making the path of the cutting tool
slightly angled to the normal to the face of the plates, as
illustrated by greatly exaggerated angle "b" in FIG. 11, where "b"
equals the small angle between the cutting path and the normal to
the front surface of the plate. In FIG. 11, angle "b" lies in a
vertical plane, but it could, by other shifts of the plates, lie in
any plane that includes the cutting path and the normal to the face
of the plates. FIG. 11A shows the adjacent plates of FIG. 11 offset
so that the crest of a groove in one plate is aligned with the root
of a groove in an adjacent plate. The manner in which the plates
are offset from one another is shown in FIG. 11B, wherein
alternating plates are shaded differently for clarity; FIG. 11B
also shows that, because of the exaggerated cutting angle, faces 17
and 18 are visible even though the view is perpendicular to face
19.
Those skilled in the art will recognize that the above variations
of the inventive method allowing for control of incidence
angularity, entrance angularity, and observation angularity, are
not necessarily mutually exclusive, and can be combined by one
skilled in the art to produce an array having a desired combination
of retroreflector performance characteristics.
Three constructional parameters determine the geometry and thus the
entrance angularity of a regular assembly of identical grooved
plates that produces an array of hexagon cube corners: plate
thickness t; groove depth d; and plate slip s. (See FIGS. 12C and
12D). Slip is the distance between the crests of one grooved plate
and the roots of the next adjacent plate. For the assembly of FIG.
6, the slip s=0; for the assembly of FIG. 12, the slip s does not
equal 0. The entrance plane is assumed to be parallel to a symmetry
plane of the cube corners.
Light incident on the front surface of an article at incidence
angle I will be retroreflected with 100% geometric efficiency
(i.e., percent active aperture equals 100%) if and only if the
following relation holds: .degree.'.times..times. .times..times.
##EQU00001## I' is the incidence angle after refraction by the
article's front surface. I'=sin.sup.-1(sinI/n), where n is the
refractive index of the material. I''=I for hollow retroreflectors.
I and I' are either negative or positive; negative and positive
values of I and I' are illustrated in FIGS. 12C and 12D,
respectively. Because cube size is being ignored in the following
discussion, the dimensions d and s have been relativised to t.
For every value of I, from -90.degree. to +90.degree., there are
solutions to Equation E for t, d, and s. For small values of slip
s/t, Equation E assures a unique ratio of groove depth to plate
thickness, the quantity d/t, for each incidence angle. For example,
Table B shows solutions when there is no slip, i.e., s/t=0, and
when the refractive index is 1.49.
TABLE-US-00001 TABLE B Tailoring of Plates to Incidence Angles,
Assuming s/t = 0, n = 1.49 d/t External Incidence Ratio of Depth to
Angle I Thickness -90.degree. 0.301 -80.degree. 0.307 -60.degree.
0.351 -40.degree. 0.434 -20.degree. 0.552 0.degree. 0.707
20.degree. 0.906 40.degree. 1.151 60.degree. 1.423 80.degree. 1.628
90.degree. 1.659
For large values of slip s/t, there are solutions to Equation E
only for the larger value of I. For example, Table C shows examples
when s/t=0.75, and when the refractive index is 1.49.
TABLE-US-00002 TABLE C Tailoring of Plates to Incidence Angles,
Assuming s/t = .75, n = 1.49 d/t External Incidence Ratio of Depth
to Angle I Thickness less than -40.degree. impossible -40.degree.
impossible -20.degree. 0.028 0.degree. 0.169 20.degree. 0.352
40.degree. 0.583 60.degree. 0.842 80.degree. 1.041 90.degree.
1.071
If the radio d/t is fixed, such as would be the case for a set of
fabricated plates, then there will be a range of incidence angles
for which it is possible to solve equation E with positive values
of s/f. For example, Table D was developed for d/t=0.707 and
refractive index 1.49.
TABLE-US-00003 TABLE D Slip for Utilization of Plates with d/t =
.707, n = 1.49 s/t External Incidence Ratio of Slip to Angle I
Thickness less than 0.degree. impossible 0.degree. 0 20.degree.
.262 40.degree. .581 60.degree. .932 80.degree. 1.199 90.degree.
1.239
The solution with d/t=0.707 and s/t=0 appearing both in Tables B
and D corresponds to the embodiment previously discussed, for which
L equals t and adjacent plates are offset in the vertical direction
by the groove depth d as in FIG. 6, so that the crest of a groove
in one plate is aligned with the root of a groove in an adjacent
plate and there is no slip.
The solution with d/t=1.423 and s/t=0 appearing in Table B
corresponds to the embodiment of FIG. 10 where L has been increased
to approximately twice the thickness of the plate. FIG. 10A shows
the projection of the array of FIG. 10 parallel to the cube
diagonal (approximately 35.54.degree. to the normal to the plane of
the cube apices corresponding to incidence angle I of 60.degree.).
Viewed at 35.54.degree. to the normal, as in FIG. 10A, the
effective aperture of the microcubes of FIG. 10 is 100%. FIG. 10B
shows a projection of the microcubes of FIG. 10 perpendicular to
the plane of the cube apices and illustrates that the effective
aperture at this angle is low. FIG. 10C shows a projection
perpendicular to the sides of the plates wherein alternating plates
are shaded differently for clarity.
The solution with d/t=0.707 and s/t=0.932 appearing in Table D
corresponds to the embodiment illustrated in FIG. 12, for which the
active aperture is 100% at the 60.degree. incidence angle as in
FIG. 12A. FIG. 12B is a projection of FIG. 12 perpendicular to the
sides of the plates, wherein alternating plates have been different
shaded for clarity.
The solution with d/t=0.352 and s/t=0.75 appearing in Table C
corresponds closely to the embodiment whose performance is shown in
the uppermost curve of FIG. 45. Table C shows that this cube is
100% effective at an incidence angle I of 20.degree.. If these
cubes are in paired arrays, as they were for the example of FIG.
45, then when one cube array receives light at I=20.degree. the
other array receives it at I=-20.degree., for which incidence angle
the cube array has low effective aperture. The rising and falling
efficiencies of the two cube arrays add to produce the performance
curve of FIG. 45 which is flat for entrance angle values from
-20.degree. to 20.degree..
When d/t and s/t solve Equation E for a certain value of r the
hexagon cube achieves 100% active aperture for just that one
internal incidence angle. Depending on the refractive index this
corresponds to one external incidence angle I. The percent active
aperture, and more generally the retroreflectance, of this hexagon
cube for all other incidence angles requires addition calculation.
Graphs of retroreflectance and percent active aperture versus
incidence angle from -90.degree. to +90.degree. are shown in FIGS.
38 and 39, respectively, for nine different unpaired hexagonal
microcube arrays. Each of the microcubes has n=1.49, s/t=0 and d/t
chosen, in accordance with Equation E, to make 100% active aperture
at one incidence angle between -80.degree. to +80.degree., in
20.degree. increments.
Graphs of retroreflectance versus incidence angle from -90.degree.
to +90.degree. are shown in FIG. 37 for an unpaired hexagonal
microcube array with d/t=0.707 and s/t=0 and for five different
refractive indices. FIG. 37 illustrates, as is well known in the
industry, that any analysis of retroreflectance must include the
refractive index of the materials used.
When slip is non-zero the cube corners are no longer, strictly
speaking, hexagons. In instances where there is an uninterrupted
face shared by two or more adjacent cube elements, the dividing
lines between elements shall be considered to be the shortest
imaginary lines (15 in FIG. 12A) that can be drawn to complete the
polygon. The shared or continuous face becomes optically
advantageous at certain orientation and entrance angles where a ray
that first reflects off the continuous face within one hexagon
makes its next two reflections, achieving retroreflection, in a
neighboring hexagon.
Slip is a useful parameter for the optical designer. For example,
while the solutions in Tables C and D assure 100% geometric
efficiency at the chosen incidence angles, they entail different
shapes of hexagonal cubes, with different volumes, different
diffraction apertures; different spot "weights", and a different
cube axis cant.
Cube axis cant, measured with respect to the front face of the
array, depends simply on (s+d)/t according to this equation:
.degree.'.times. .times..times. ##EQU00002##
It follows from equation E that for an array of hexagonal cubes
assembled from grooved plates to have 100% active aperture at
0.degree. incidence angle, d, s and t must satisfy the equation:
(2d+s).(d+s).=t.sup.2. Equation G: From this it follows that:
.ltoreq..ltoreq..times. .times..times. ##EQU00003## This
corresponds, according to Equation F, to a range of cants from
0.degree. to -9.74.degree.. While all cants are obtainable with
grooved plate constructions, only those in the range from 0.degree.
to -9.74.degree. can be chosen also to have 100% active aperture at
0.degree. incidence angle.
To further increase entrance angularity, however, the designer may
choose to accept less than 100% efficiency at 0.degree. incidence
angle. As illustrated by the series of retroreflectance graphs in
FIGS. 42a through e, useful performance, including that at
0.degree. entrance angle, can be obtained from grooved plates
having (d+s)/t varying from 0.5 up to 1.2, i.e., far beyond the
bounds of Relation H.
Each of the five families of curves in FIGS. 42a through e
represents a different value of d+s and a resultant axis cant; for
example, in FIG. 42a, d+s for all three curves is equal to 0.5t and
the resulting cant is +8.70.degree. emp, where "emp" means
edge-more-parallel. Each of the three curves within each family
represents different values of d and s, the sum of which is 0.5t in
the 42a family; for one of the three curves within each family, s
is chosen equal to 0 (as exemplified by the d/t=0.5, s/t=0 curve in
FIG. 42a), and for another of the three curves within each family,
d is chosen equal to 0.1t (as exemplified by the d/t=0.1, s/t=0.4
curve in 42a). For comparison purposes, the curve of
retroreflectance versus entrance angle for the Hoopman triangle
discussed in PCT WO95/11463 is the heavier solid line in each
figure. The hexagonal microcube can be designed to provide 40% to
100% greater retroreflectance than Hoopman through 34.degree.
entrance angle as exemplified in FIG. 42b, or to provide a constant
retroreflectance through 40.degree. that exceeds Hoopman by more
than 50% from 10.degree. to 40.degree.0, as shown by the d/t=0.3,
s/t=0.2 curve of FIG. 42a, or exceeds Hoopman from 10.degree. to
70.degree. as in the d/t=0.1, s/t=1.1 curve of FIG. 42e.
Note in FIG. 42 that even for an active aperture of 100% the
retroreflectance never exceeds 0.9 for polycarbonate articles
because of Fresnel losses at the front surface that are included in
the calculation of retroreflectance.
Method of Making Rectangular Microcubes
The method of making a tool with rectangular microcubes in
accordance with the instant invention begins with a stack of plates
110 (shown in partial top plan view in FIG. 14A), the thickness t
of the plate 110 being equal to the desired dimension H (FIG. 26)
of the rectangle. The pates 110 are preferably flat and each has at
least one flat end 112, shown in side view in FIG. 14B that is
cuttable, such as by a diamond cutting tool.
Each plate 110 or a stack of plates 115 is positioned on a ruling
machine with the cuttable end 112 up and with the front faces 124
of the plates angled by a desired amount X, for example
35.26.degree., with respect to a perpendicular to the cutting plane
of the ruling machine, FIG. 15. If a stack of plates is used, the
upper edges 125 of the ends 112 all lie within a single plane and,
to provide clearance for the cutting tool between the plates to be
machined, spacers of cuttable material or spacers 111 retracted
from the plane of the edges 125 are provided between plates, FIG.
15, so that the cutting tool does not contact any material that
might damage it. The cutting edge 119A of the cutting tool 119 as
projected parallel to the direction of cutting, is positioned
perpendicular to the plane of the machine bed, and the lower edge
of the cuttable end 112 is cut away along the length of a plate 110
until the cutting tool reaches the midpoint of end 112, or beyond,
creating bevel face 113, FIG. 15. FIGS. 16A and B show plan and
side views, respectively, of a plate 110 after cutting the bevel
face 113. This step is repeated for each plate 110 in the stack
115.
To prevent the formation of burrs, after the bevel faces 113 have
been cut, the spaces between plates may be filled with a plastic
compound 114, FIG. 17, that will not deteriorate the cutting tool.
Grooves with a desired included angle Y, for example 90.degree.,
are then cut with cutting tool 118 in a direction parallel to each
other and substantially perpendicular to the direction of the bevel
face cut, forming faces 116, FIG. 18. Dotted line 116A indicates a
face 116 yet to be cut. It will be understood and appreciated that
the angle Y can be adjusted by controlled tilting of the cutting
tool 118, in the manner illustrated in FIGS. 7A, 7B, 8A and 8B for
groove angle C+.DELTA.C. In this embodiment, the root of the groove
defined by faces 116 intersects the lower edge of bevel face
113.
FIG. 19 is a section (19--19 of FIG. 18) through a finished plate
taken at the root of a groove and perpendicular to the direction of
the second ruling operation. FIG. 20 is a view taken in the
direction of arrows 20--20, which is parallel to the face of plate
110 and perpendicular to a line through the cube apices, showing
the rectangular outline of the microcube 110 defined by bevel face
100A and faces 100B and 100C from adjacent grooves. It may be seen
that cube face 100A is a portion between grooves of bevel face 113,
and cube faces 100B and 100C are groove faces 116 from adjoining
grooves. The thin ruled plates of FIG. 18 can be stacked together,
with the orientation rotated 180.degree. in alternating plates,
FIG. 21.
Note that the microcubes could be machined in one plate at a time,
but the plates are preferably grouped for machining in order to
minimize cost.
A variation of the process which may be useful to make very small
microcubes is to machine two rows of microcubes on a single plate,
thereby permitting doubling the thickness of the plate and
increasing its rigidity. As shown in FIG. 22, the thicker plates
210 without spacers are positioned on the ruling machine with the
cuttable end 212 up and with the front faces 224 of the plates
angled by a desired amount, X, for example 35.26.degree., with
respect to a perpendicular to the plane of the machine bed, FIG.
22.
With one cutting edge 219A of the cutting tool 219, FIG. 22A, as
viewed parallel to the direction of tool travel, positioned
perpendicular to the plane of the machine bed, a cut is made in the
cuttable end 212 extending from the midpoint of the thickness of
the plate at its lower edge 223 to a point 222 less than 25% of the
width of the plate from the top edge 225 of the plate, FIG. 22,
creating first bevel face 213 and temporary face 213A at an angle Z
(FIG. 22A) to face 213, where angle Z is between 1 and 2 times the
tilt angle X.
The cut may be filled with a plastic compound 114, FIG. 22C, that
will not deteriorate the diamond tool, and V-shaped grooves with a
desired included angle; Y, for example 90.degree., are then cut by
means of diamond tool 118, FIG. 23, in a direction substantially
perpendicular to the direction of cut of first bevel face 213,
forming groove faces 216, with the groove roots 221 passing through
the lower edge 223, FIG. 23A, of the first bevel face 213.
Inclined faces 216 of adjacent grooves, which meet at a top edge
220, form two faces 200B and 200C of microcube 200, and the first
bevel face 213 forms the third face 200A, FIG. 23B; the rectangular
outline of the microcube 200 is readily apparent. The method to
this point forms a first row of microcubes on the end of the
plate.
The plates 210 are then tilted so that front faces 224 are at an
angle X with respect to the perpendicular to the plane of the
machine bed, FIG. 24. It will be understood that the symbol "X" is
used herein generally to designate the angle between the front face
of a plate and the perpendicular to the plane of the machine bed,
so that the angle "X" in FIG. 22 may or may not be equal to the
angle "X" in FIG. 24, depending on the desired performance
characteristics of the retroreflective article. Cutting tool 219 is
again positioned, as viewed parallel to the direction of tool
travel, with a cutting edge being perpendicular to the plane of the
machine bed, and a cut is made in the cuttable end 212 of plate 210
completely removing temporary face 213A, FIG. 24, and creating
second bevel face 313. The grooves may again be filled with a
plastic compound (not illustrated), and additional grooves are cut
perpendicular to the direction of cut of second bevel face 313 by
means of tool 118, FIG. 25, forming groove faces 316.
Inclined faces 316 of adjacent grooves which meet at a top edge 320
form two faces 300B and 300C of microcube 300 and the second
beveled surface 313 forms the third face 300A, FIG. 25B. Thus a
second row of microcubes is formed on the other side of the same
end of the plate where the first row of microcubes was formed. As
is evident from the dotted lines in FIG. 25 representing the
intersections of the faces of the microcubes 200, the lines of
intersection are discontinuous so that it is not possible to rule a
master comprising all-rectangular microcubes with opposing
orientations by ruling straight lines in a single flat surface.
Method of Positioning Plates for Ruling
Methods of fixturing to obtain the cube corner configurations
described herein will be apparent to those skilled in the art.
However, because of the exacting tolerances required for
microcubes, further detail is provided regarding means of
positioning the plates for machining operations. For all shapes of
microcubes, two dowel holes R, FIG. 3A will be ground through the
front face of each plate. For hexagonal microcubes, the dowel holes
R will be used both to assemble the plates for cutting grooves and
to position each plate for grinding another set of two dowel holes
M for assembly of the electroforming master. The dowel holes M will
be in a different position on each plate. Vertically, the dowel
holes M will be displaced from dowel holes R (see FIG. 3A) by an
amount equal to k.sub.1+n(d+s), where k.sub.1 is a constant, n is
the number of the plate in the stack, d is groove depth and s is
slip; horizontally all dowel holes M will be displaced from the
reference holes R by a constant k.sub.2 in all odd numbered plates
and by k.sub.2 plus d in even numbered plates where d is the groove
depth and is equivalent to 1/2 the groove width. For cutting
grooves, dowels will be inserted only in the reference dowel holes
R; for electroforming, dowels will be inserted only in dowel holes
M. The error in locating a groove in one plate relative to a groove
in an adjacent plate is anticipated to be less than 0.0002''
(5.mu.) in any direction. To avoid negative slip, which will
introduce undercut and increases loss, the microcubes will
preferably be designed for positive slip greater than 0.0005''
(12.5.mu.).
To machine rectangular microcubes one plate at a time, the plates
will be positioned on the ruling machine by means of dowels through
the reference dowel holes R and matching dowel holes provided in a
fixture, the surface of which is angled by an amount X from a
perpendicular to the bed of the ruling machine. After the bevel
face and grooves have been machined, the reference dowel holes R
will be used to position the plates of electroforming. The maximum
error in positioning the apex for the microcube with respect to the
center of the plate is anticipated to be less than 0.0001''
(2.5.mu.). If a number of plates are to be ruled at one time,
secondary dowel holes can be provided on each plate in a manner
somewhat similar to the procedure described for hexagonal
microcubes; however, for a stack of 10 plates, the error in
positioning the apex of the microcube is expected to increase
possibly to 0.0005'' (12.5.mu.) in a direction perpendicular to the
side of the plate.
Preferred methods of tooling, microcubes have been described in
great detail; however, it should be understood that alternative
methods of tooling based upon the plate concept will be readily
apparent to a skilled toolmaker, and the descriptions above should
not be considered as limiting.
Retroreflector Performance
Rectangular microcubes of the present invention differ from
hexagonal microcubes of the present invention in two main ways.
First, the rectangular microcubes can be arranged as paired (mirror
image) elements, whereas the hexagonal microcubes produced from
single cut plates are all alike in orientation; pairing of
hexagonal microcubes to produce symmetrical performance requires
pairing small mirror image arrays of hexagonal microcubes into a
larger array. Second, rectangular microcubes offer generally
greater design freedom than hexagonal microcubes produced from
single cut plates; for rectangles, the axis cant, the apex
centration, and the rectangular proportions are each independently
variable (see FIG. 28), whereas for hexagons a change in one of the
variables also requires a change in one of the other two.
Rectangular cubes can have 100% active aperture at 0.degree.
incidence by centering the apex; the cant is then fully adjustable
from -54.74.degree. to +35.26.degree., and the proportions are
still variable. By contrast, prior art direct ruled triangles have
no independent variables; cant, apex centrations and proportions
are inextricably interrelated.
For directly ruled triangular microcubes, cube axis cant is
determined by the shape of the triangle according to the equation:
.times..times..function..times..times. .times..times. ##EQU00004##
where A and B are the tangents of the triangle's two acute angles.
For triangular microcubes tooled by the plate assembly technique of
the instant invention (see FIG. 31), cube axis cant becomes a
combination of the angle calculated above and the angle between the
triangle base and the front surface.
In the recent PCT publications Nos. WO 95/11463, WO 95/11465 and WO
95/11470 of the Minnesota Mining and Manufacturing Co., various
graphs depict comparisons of retroreflectivity according to percent
active aperture, but do not consider total internal reflection
(TIR) limits, regarding the cube faces as if metallized to have
100% reflectance; nor do they consider the front surface specular
losses, which become substantial at high incidence angles.
In the graphs depicted in the present application, unless noted
otherwise, the following parameters were chosen for the
determination of retroreflectance: 1. The prismatic article was
regarded as a single material having a single refractive index. 2.
Internal reflectance was calculated with the Fresnel equations,
assuming (contrary to fact) unpolarized light. 3. The front surface
transmittance was calculated with the Fresnel equations, assuming
unpolarized light. 4. No account was taken of cosine losses due to
incidence angle. 5. The entrance plane was parallel to a symmetry
plane of the cube corners. 6. Diffraction effects were ignored.
The various depicted curves of possible designs are not necessarily
representative of commercially practical articles, but do ably
demonstrate the wide variety of results that can be achieved by
producing tools and microcube retroreflectors in accordance with
various aspects of the present invention.
Most of the graphs are for unmetallized cubes and include the
effect of total internal reflection (TIR). FIGS. 39, 40, 44 and 45
demonstrate what happens when the microcubes are metallized. (The
term "metallized" is used in a general sense to cover any material
applied to the cube faces to provide specular reflection at angles
where TIR breaks down.) The various concepts in the above
identified recent PCT publications in measuring percent active
aperture are material only if the cubes are going to be
metallized.
FIGS. 44 and 45 each compare the performance of some articles of
this invention with certain prior art. These figures include curves
showing the best published geometric efficiencies (measured as
percent active aperture) known to applicants, reproduced from FIG.
12 of WO 95/11470 and FIG. 32 of WO 95/11463, respectively, as well
as corresponding curves for articles of this invention. FIG. 44
compares the efficiency of two very simple uncanted rectangle cube
designs of the instant invention (such as illustrated in FIG. 26),
with the efficiency curves from FIG. 12 of WO 95/11470. Note in
FIG. 44 that at 0.degree. the percent active aperture of the
inventive microcubes is 9% higher than that of the best curve
(curve 153) of FIG. 12 of WO 95/11470 and 50 percent higher than
the curve for Hoopman. At 20.degree., the percent active aperture
of the inventive microcubes is 29 percent higher than that of curve
153 and 19 percent higher than that of Hoopman.
EXAMPLE 1
Retroreflectors For Increased Entrance Angularity
To increase the entrance angularity of the cubes as described in
patents U.S. Pat. Nos. 3,541,606, 3,873,184 and U.S. Pat. No.
3,923,378 issued to the same assignee and incorporated herein by
reference, the s/t=0, d/t=0.707 solution shown in FIG. 6 might be
superseded by an s/t=0.45; d/t=0.55 solution as shown in FIG. 13,
for which the cube axis tilt is -9.74.degree. to the front surface
of the array and the percent active aperture is 72.5% at 0.degree.
incidence angle and 100% at 19.6.degree. incidence angle.
(Throughout this example, the entrance plane is assumed to be
aligned with the symmetry plane of the cube corners, and the
refractive index is assumed to be 1.59.) However, if the hexagon
arrays are paired for each cube favorably oriented for 19.6.degree.
incidence angle, there is also its mirror image having only 45%
effective aperture for that same incident light; the paired array
therefore averages 72.5% for light incident at an angle of
19.6.degree., which is as high as the average at 0.degree.
incidence. The result of this averaging of the active apertures is
the desirable, surprisingly flat curves of percent active aperture
versus entrance angle extending from -20.degree. to +20.degree. for
the paired canted rectangles and paired arrays of canted hexagons
of FIG. 45, which curves, throughout the 20.degree. entrance angle
region, are superior to the active aperture curve for Hoopman by
more than 48% and the active aperture curve for example 460 of
WO95/11463 by more than 16 percent. The curves of the exemplary
rectangles and hexagons of the instant invention continue to be
superior to the curve for Hoopman through 50.degree. entrance angle
and to the curve for example 460 through 70.degree., either of
which entrance angles is beyond any meaningful entrance angle or
specification.
Intimately paired rectangles can be ruled with 1:2 (width:height)
proportions of FIG. 27C with the same -9.74.degree. cant and with
substantially the same 72.5% active aperture at both 0.degree. and
19.6.degree. incidence angles as for the exemplary hexagons by
decentering the cube apex by 13.75% of the rectangle height. As
illustrated by the curves in FIG. 40 and FIG. 45, the average
percent active aperture of paired arrays of hexagons and paired
rectangles can be remarkably similar at all entrance angles for
those cases where the percent active apertures at 0.degree.
entrance are matched.
Since the advantages of cube axis canting are realized primarily
with cubes relying on TIR, it is more appropriate to base these
efficiency considerations on retroreflectance rather than on
percent active aperture. In both the rectangle and hexagon
examples, when the incidence angle is 19.6.degree. TIR is preserved
for that cube (or array) of the pair which gains in effective
aperture and lost for the cube (or array) which loses in effective
aperture. The net result is total retroreflectance of
0.898.times.50.2% for the paired rectangles and 0.898.times.52.3%
for the paired arrays of hexagons. (The 0.898 factor is due to the
front surface losses.) FIG. 40 compares the retroreflectance and
percent active aperture of these rectangle pairs and paired arrays
of hexagons over a wide range of entrance angles for an entrance
plane aligned with the symmetry plane of the cubes. The d/t=0.55
and s/t=0.45 curve of FIG. 42D compares the retroreflectance of the
paired arrays of hexagons (and by association, the retroreflectance
of the rectangle pairs of FIG. 27C) with Hoopman for entrance
angles aligned with the symmetry plane. FIG. 43 shows
retroreflectance versus entrance angle for the same rectangle pairs
and paired arrays of hexagons for an entrance plane perpendicular
to the symmetry plane. In the plane of symmetry the
face-more-parallel paired hexagon arrays of FIG. 13 and rectangle
pairs of FIG. 27C are superior to Hoopman through 47.degree.; in a
plane perpendicular to the symmetry plane, these pairs are superior
to Hoopman through 60.degree..
Percent active aperture and retroreflectance for paired pentagons
(see FIG. 36) are substantially the same as those of the described
hexagons and rectangles for the same axis cant and percent active
aperture at 0.degree. incidence.
For a discussion of the advantages of the "face-more-parallel"
construction with sets of cubes oppositely oriented, see patent
U.S. Pat. No. 3,541,606, at col. 15, line 62 through col. 16 line
47, and FIGS. 18, 19 and 20.
Note that the method outlined in Example 1 is intended to maximize
the range of entrance angles in one or more planes through which a
predetermined minimum retroreflectance can be maintained; the
concept requires cubes (or cube arrays) with canted cube axes
oppositely oriented as previously described in commonly assigned
patents and as used in 3M's "Diamond Grade" sheeting (see also
Hoopman U.S. Pat. No. 4,588,258).
EXAMPLE 2
Retroreflectors For Large Incidence Angles, Such As For Pavement
Markers
Example 2 is quite different. The method of Example 2 is intended
to maximize the retroreflectance through a relatively smaller range
of entrance angles about an axis (the principal incident ray) which
is not normal to the face of the retroreflector. For example, a
raised retroreflective lane marker mounted on a road may have its
front surface tilted back 60.degree. from a plane perpendicular to
the plane of the pavement. A light ray from the headlight of an
approaching vehicle, being substantially parallel to the pavement,
becomes incident on the face of the retroreflector at an angle to
the normal of 60.degree. and is refracted (in acrylic) to an angle
to the normal of 35.5.degree.. For purposes of discussion, the ray
parallel to the pavement surface and to the centerline of the road
will be called the principal incident ray of optical axis and the
ray within the marker after reflection at the front surface will be
called the principal refracted ray.
A retroreflector for which L=t, the plates for which are
illustrated in FIG. 6, will not be preferred for use as a pavement
marker if the plates are stacked with the upper edges of a groove
of one plate aligned with the root of a groove in a neighboring
plate as in example 1, FIG. 6A, primarily because of loss of
effective cube area. A retroreflected ray departs from a cube
corner at a point on the opposite side of the cube apex from the
point of incidence and at the same distance from the cube apex. If
the principal refracted ray is at an angle to the cube axis, some
of the light incident on the cube for which L=t will be lost
because there is no corresponding point on the opposite side of the
cube center. For 100% utilization of the area of each cube in the
direction of the optical axis, the cube diagonal 28, FIG. 12, drawn
from the point of intersection 29 of the three real faces of the
cube corner to the point of intersection 30 of three imaginary
planes parallel respectively to each of the three real faces, must
be parallel to the principal refracted ray.
As stated in equation E, for hexagonal microcubes the relationship
between I', d, s, and t is: .degree.'.times..times. .times..times.
##EQU00005##
For an acrylic pavement marker with front surface tilt of
30.degree. to the road, I'=35.54.degree.. If slippage is chosen to
be zero (s/t=0), then
90.degree.-35.54.degree.-tan.sup.-1(t/d)+tan.sup.-1(t/2d):
from which d/t=1.42.
To produce a tool comprising hexagonal microcubes for the above
pavement marker, the plates will be ruled so that d/t=1.42 and will
be offset from one another by an amount d=1.42t in both the
horizontal and vertical directions as in FIG. 10.
Alternatively, the plates of FIG. 6 may be used (d/t=0.707), and
the plates offset in the horizontal direction by d=0.707t and in
the vertical direction from one another by an amount d=0.707t plus
s=0.932t as in FIG. 12. The irregular hexagons projected along the
cube diagonal 28 are defined in part by dotted lines 15 in FIG.
12A. The microcubes may be metallized to provide better horizontal
entrance angularity.
Pavement markers comprising rectangular microcubes tooled by the
plate method can be made with improved horizontal entrance
angularity compared with the direct-ruled cubes of Nelson U.S. Pat.
No. 4,895,428. To tool .[.9.]. .Iadd.9.degree..Iaddend.
face-more-parallel rectangular cubes for use in an acrylic pavement
marker with a front surface tilt of 55.degree., the plate thickness
is chosen to be equal to H, which is the dimension of the side of
the cube that is parallel to the symmetry plane as projected
parallel to the principal refracted ray as in FIG. 29A; the plates
are positioned on a ruling machine with the plate at an angle to
the vertical, X equal to 35.26.degree. less the cube axis cant
(hereinafter "CAC"), (in this example at an angle X, equal to
35.26.degree.-(-9.degree.), or 44.26.degree.); the bevel face 113
is cut to the midpoint of the plate; and grooves are ruled
perpendicular to the direction of cut of the bevel face 113 to a
depth equal to 0.5W as shown in FIG. 29 where W in FIG. 29A is the
dimension of the side of the rectangle perpendicular to H. The
angle .theta. in FIG. 29 is the angle between the pentagonal face
and the normal to the plane of the cube tips, which angle is equal
to 35.26.degree. minus CAC minus sin.sup.-1 [(sinT)/n], where T is
the front surface tilt. For the direct ruled cubes of Nelson U.S.
Pat. No. 4,875,428, .theta. is necessarily 0.degree. and the
pentagonal face becomes a triangle. FIG. 29 shows the resulting
rectangular cube in section, FIG. 30 shows an array of such cubes
in perspective, and FIG. 41 illustrates the approximately
11.degree. improvement in horizontal entrance angularity compared
with Nelson that is achieved by means of .[.-90.degree..].
.Iadd.-9.degree..Iaddend. face-more-parallel construction in
accordance with the principles taught in Heenan U.S. Pat. No.
3,541,606. The use of face-more-parallel angles greater than
.[.-90.degree..]. .Iadd.-9.degree..Iaddend. for acrylic pavement
markers is questionable because of installation tolerances. Note in
FIG. 41 that the maximum retroreflectance is limited to about 0.87
because of the front surface losses at 55.degree. incidence
angle.
EXAMPLE 3
Retroreflectors With Increased Divergence
The divergence of the retroreflected beam (i.e., the observation
angularity) can be varied in one plane or in multiple planes by
changing the dihedral angles between either two or three faces as
taught in U.S. Pat. No. 3,833,285 also to the same assignee and
incorporated herein by reference and/or by changing the size of the
cube, which affects diffraction.
The dihedral angle can be changed by making the groove angle
greater or less than 90.degree. and/or by tilting the stack of
plates 10 slightly off the perpendicular to the cutting plane, as
illustrated by angle "b" in FIG. 11, before the grooves are cut.
The groove angle can be varied by changing the angle "C" of the
diamond tool (FIG. 7A) or by adjusting the angle "e" of the diamond
tool (FIG. 8B) with respect to the perpendicular to the surface
being ruled, in accordance with Equation A, previously stated.
The tilt angle "e" of the cutting tool can be held constant for all
grooves. Alternatively, the tilt angle "e" of the cutting tool can
be adjusted continuously as each groove is cut as a function of the
distance traveled by the cutting tool along the ruled surface, or
the cutting tool can be held at a constant angle "e" for the entire
length of each groove, but changed for each successive groove cut
into the surface. It is also possible to use a combination of these
techniques; i.e., change the angle "e" of the cutting tool with
respect to the surface both along the length of each groove, and
from groove to groove.
Diffraction is the spreading of a light beam caused by restriction
of the beam size. Diffraction is the main optical difference
between macrocubes and microcubes. For the observation angles
associated with such commercial applications as highway markings,
approximately 0.1.degree. to 1.5.degree., the diffraction effects
for microcubes may be significant while those for macrocubes are
insignificant. For macrocubes observation angularity is completely
determined by the dihedral angles, the flatness of the faces, and
the cube shape, but for microcubes size is an additional
determinant.
FIGS. 46a-c show the effect of diffraction on the pattern of
retroreflected light for d/t=0.707, s/t=0 hexagonal cube corners of
refractive index 1.49 for 0.degree. incidence angle and three
different cube sizes. The circumference of the figures represents
0.5.degree. divergence and each band of grey represents a factor of
two in the retroreflected intensity. All the cube corners have
perfectly flat faces and an error of 0.103.degree. on just one of
the dihedral angles. FIG. 46a is for t=0.866 mm; FIG. 46b is for
t=0.217 mm; FIG. 46c is for t=0.087 mm.
By making the groove angle 90.103.degree. in the plates of FIG. 6,
a prismatic article with index 1.49 accurately reproduced from the
tool should, by geometry alone, have exactly 25.degree. divergence
and with all the retroreflection directed at two points. In fact,
the light pattern depends on the cube size. For the large
microcubes of FIG. 46a, having a cube height of 1 mm, and a width
of 1.22 mm across the flats, the light pattern does approximate the
geometric prediction (FIG. 46a). For the average size microcubes of
FIG. 46b, having a cube height of 0.25 mm and a width of 0.306 mm
across the flats, the light pattern still resembles the geometric
prediction but with considerable broadening (FIG. 46b). For the
small microcubes of FIG. 46c, having a cube height of 0.1 mm and a
width of 0.122 mm across the flats, the light pattern, contrary to
the geometric prediction, has its major peak at 0.degree.
divergence and only weak secondary peaks at 0.3.degree. divergence,
near the two predicted points (FIG. 46c). Diffraction by microcubes
usefully smooths light patterns, but since it may send light in
non-functional directions it must be reckoned in all microcube
designs. Adequate cube corner diffraction theory has been in the
optical literature for at least 35 years.
The plates used in the ruling method of the instant invention may
be formed of any material that is sufficiently strong and rigid to
be ruled when formed into flat plates of the thinness required. The
material must also be capable of being cut and polished with a high
degree of precision. Certain plastics, such as
polymethylmethacrylate, may be suitable if metallized after
machining to provide electrical conductivity for electroforming.
Suitable metals include hardened sterling silver 925 fine, hardened
aluminum 7075T6, and electroless nickel. Electroless nickel is
known to be very hard yet readily cut with a diamond cutting tool.
An electroless nickel overlay on a stainless steel substrate may be
sliced into plates with the electroless nickel on one end, which
plates may be particularly suited for use in the instant invention.
Alternatively, the electroless nickel may be formed as non-adherent
plates on a passivated stainless steel block (or a block of another
material such as aluminum or metallized plastic) to a thickness of
about 0.012 inch and separated from the block to serve as plates
10.
In one form of the invention, the assembly of microcubes defined by
the plates when ruled, assembled, and oriented as described herein
may be used as a master to electroform copies. The copies are then
assembled into a cluster of contiguous elements; the cluster is
replicated to provide a number of copies; and the process is
repeated, eventually to produce flexible strips having an
uninterrupted pattern; the strips are assembled on a cylindrical
mandrel to provide cylindrical segments; the cylindrical segments
are assembled to provide a cylinder of the desired dimensions
corresponding to the width of the web intended to be provided with
retroreflective elements; and the assembled cylinder is replicated
to provide a flexible endless master cylinder having the pattern of
microcubes thereon. The master cylinder may then be replicated to
form a relatively thick mother cylinder, which may in turn be
replicated to form a generally cylindrical metal embossing
tool.
The embossing tool so made may then be used to emboss the
microcubes on a surface of a continuous resinous sheeting material
to manufacture a retroreflective sheeting article, as disclosed in
U.S. Pat. No. 4,486,363. In accordance with the method disclosed
therein, the embossing tool described above is moved along a closed
course through a heating station where it is heated to a
predetermined temperature and then to a cooling station where it is
cooled below that temperature; a resinous sheeting material is
continuously fed onto the embossing tool through a part of the
heating station so that the sheeting is in direct contact with the
pattern of hollow microcubes; the sheeting is pressed against the
embossing tool at one or more points in the heating station until
one surface of the sheeting conforms to the pattern of hexagonal or
rectangular microcubes; the embossing tool and sheeting are passed
to the cooling station such that the sheeting is cooled below its
glass transition temperature; and the embossed sheeting is stripped
from the embossing tool.
Those skilled in the art will recognize that, in addition to the
embossing tools and techniques described above, the hexagonal or
rectangular microcube embossing tool made as described above may
also be used to manufacture retroreflective sheeting by other
methods such as molding, pressing, or casting. For example, the
electroformed strip as described above having the pattern of hollow
hexagonal or rectangular microcubes can be provided with a proper
support and used directly as an embossing or compression molding
tool but in a non-continuous manner, as described in Rowland U.S.
Pat. No. 4,244,683.
The retroreflective sheeting made in accordance with the instant
invention and having a precise optical pattern of microcubes of
various cube shapes is advantageous over sheeting currently being
made with triangular microcubes. For the small entrance angles of
0.degree. to 5.degree., which are of particular interest for
retroreflective highway markers and signs, substantially the entire
area of the hexagonal or rectangular microcubes is effective for
retroreflectance, but only 66 percent of the area of triangular
microcubes is retroreflective. Thus, at these small entrance
angles, the hexagonal or rectangular microcube retroreflective
sheeting represents a 50 percent increase in retroreflective area
compared with prior art triangular microcubes.
Retroreflective articles other than sheeting that are currently
manufactured with macrocubes may also benefit from a change to
hexagonal or rectangular, microcubes. For example, pavement markers
incorporating microcubes of the instant invention will be less
costly because of reduced material cost, may be deteriorated less
by abrasion because the exiting rays are closer to the incident
rays so that the effect of surface irregularities is reduced, and,
for recessed pavement markers or low profile plowable pavement
markers, the loss due to shadowing is minimized.
It is well-known in the reflective sheeting art that different
sheeting materials such as acrylic, polycarbonate, and vinyl, have
different indices of refraction, "n", and will yield different
retroreflective results, even for identical cube shapes (see FIG.
37).
Many variations of cubes are possible by modifications of the
tooling procedure of the instant invention. For example:
(1) Square cubes, as in FIG. 26, can be tooled by reducing the
depth of the intersection at 421 of groove faces 416 and of the
intersection at 521 of groove faces 516, relative to the depth of
the intersection at 423 of the bevel faces 413 and 513, as shown in
FIGS. 27 and 27A. The resulting array of square microcubes is shown
in plan view in FIG. 27B, wherein cube 500 is square and face 500A
with extended imaginary lines 515 is pentagonal; compare 500A of
FIG. 27B with the triangular face 300A of FIG. 25B. Also note that
the quadrilateral faces 500B and 500C of FIG. 27B are elongated
compared with faces 300B and 300C of FIG. 25B. Square cubes or even
cubes elongated beyond square have some advantages regarding the
spot pattern of retroreflected light.
(2) The angle of the cube axis with respect to the normal to the
plane of the cube apices can be varied by selection of the angle X
(FIGS. 15, 22 and 23A) of the front face 124 or 224 of the plate
with respect to the perpendicular to the bed of the machine and/or
by angling the bisector of the included angle of the V grooves in
FIGS. 18, 23, 25 and 27 with respect to the perpendicular to the
bed of the machine; for a discussion of the effect of cube axis
angle on entrance angularity, see patent U.S. Pat. No. 3,541,606 to
the same assignee and subsequent related patents, such as Hoopman
U.S. Pat. No. 4,588,258.
(3) For rectangular or pentagonal microcubes, the dihedral angles
between cube faces can be varied from 90.degree. by setting the
cutting edge 119A of tool 119, FIG. 15, for example, at an angle to
the perpendicular to the machine bed, as viewed in the direction of
tool travel, for machining the bevel face, and/or by increasing or
decreasing from 90.degree. the included angle Y of the V grooves
(FIG. 18); changing the dihedral angle between faces controls
divergence of the retroreflected beam.
(4) The cube aperture size can be varied by changing the plate
thicknesses and groove depth or by machining one row of microcubes
on a double thickness plate larger than the row of microcubes with
which it is paired; combining microcubes of different cube aperture
size minimizes the potential diffraction loss at any one
observation angle.
(5) Because one edge of the rectangular cube is rectilinear, sets
of opposed pairs of rectangular cubes with different
characteristics can be assembled without area loss or slippage
walls between the sets; therefore adjoining sets can have different
cube axes or different divergence, or different cube height with no
inactive surfaces or sharp edges between the sets. For the
transition between plates with different cube heights, the cube
apices of one or both adjoining rows of cubes of different size may
be moved off center; moving the apices of the last row of cubes in
a set of large cubes towards a set of smaller cubes will tend to
equalize the volume of material in the two sets of cubes.
Similarly, sets of opposed pairs of rectangular cubes can be
assembled with plates bearing optic detail other than microcubes,
such as a flat surface, a cylindrical surface, or lenticular
elements. Such sheeting comprising retroreflective portions and
other optical portions is known in the art as transilluminated
sheeting. The rectilinear edge of a flat or cylindrical optic
surface may be set at the same height as the rectilinear edges of
the rectangular microcubes, thereby avoiding any slippage walls
between the two types of plates.
(6) For large angles of incidence, in macrocube technology the
rectangular cubes in a bundle of pins may be assembled oriented all
in one direction as exemplified by the use of hex cubes for
pavement markers, in which use there will be a slippage wall
paralleling the cube axis and corresponding to one exposed side of
the pin. Similarly, for microcube technology, plates on which
rectangular microcubes have been machined can be assembled with
adjacent plates oppositely oriented (or for large incidence angles
optionally oriented in the same direction) and with the cube apices
contacting a reference surface set at an angle of (90.degree.-R) to
the side of the plates, where R is the angle between the principal
refracted ray and the normal.
(7) Square cubes such as illustrated in FIG. 32, in which four
orientation sets are closely grouped, can be produced by making
plates as in FIG. 33. Three sets of grooves are cut as indicated,
although not necessarily in any order. For each of the three
grooves, two faces are shaped, one on each of two different cubes.
Each set of grooves requires a different tilt angle X for the
plates and a different included angle of the cutting tool, both of
which are calculable by trigonometry. Table J below lists plate
tilt angles and the included angle of the cutting tools used to
generate cubes of various cube axis cants. For example, if the cube
axis cant is to be 0.degree., then to make cut #1 the angle X to
which the plate must be tilted will be 45.degree. and the included
angle of the first cutting tool will be 109.47.degree.. To create
the four cube orientations shown in FIG. 32, the finished plates
are assembled with alternate plates oppositely oriented, i.e.,
rotated 180.degree. with respect to each other. When the cube axis
cant is to be other than 0.degree., the values of the tilt angle of
the plate and included angle of the cutting tool, for each of the
three sets of grooves, can be calculated as shown in the following
Table J.
TABLE-US-00004 TABLE J Cube Groove 1 Groove 2 Groove 3 Axis Tilt
Included Tilt Included Tilt Included Cant Angle Angle Angle Angle
Angle Angle -10.degree. 35.02.degree. 120.31.degree. 16.22.degree.
62.44.degree. 59.80.degree. 1- 63.35.degree. -8.degree.
36.92.degree. 138.02.degree. 16.99.degree. 65.15.degree.
58.57.degree. 1- 61.90.degree. -6.degree. 38.87.degree.
135.78.degree. 17.76.degree. 67.85.degree. 57.36.degree. 1-
63.40.degree. -4.degree. 40.84.degree. 133.61.degree. 18.53.degree.
70.54.degree. 56.16.degree. 1- 58.85.degree. -2.degree.
42.90.degree. 111.51.degree. 19.32.degree. 73.21.degree.
54.97.degree. 1- 57.25.degree. 0.degree. 45.degree. 109.47.degree.
20.10.degree. 75.88.degree. 53.79.degree. 155.6- 0.degree.
2.degree. 47.15.degree. 107.51.degree. 20.90.degree. 78.53.degree.
52.63.d- egree. 153.91.degree. 4.degree. 49.35.degree.
105.63.degree. 21.70.degree. 81.16.degree. 51.49.d- egree.
152.17.degree. 6.degree. 51.60.degree. 103.83.degree. 22.51.degree.
83.78.degree. 50.35.d- egree. 150.38.degree. 8.degree.
53.91.degree. 102.11.degree. 23.32.degree. 86.39.degree. 49.23.d-
egree. 148.56.degree. 10.degree. 56.28.degree. 100.50.degree.
24.14.degree. 88.98.degree. 48.13- .degree. 146.69.degree.
The above noted values of the cube axis cant are for illustrative
purposes only, and are not intended to limit the scope of the
invention or the range of cube axis cants obtainable by the method
of the instant invention.
(8) To produce pentagonal microcubes such as illustrated in FIG.
36, plates 710 and 810 are provided, each of which has one side
flat and the other side grooved with V grooves having a width equal
to the desired spacing of the cubes on the plate and an included
angle equal to .times.
.times..times..times..function..function..times..function..times.
.times..times. ##EQU00006## where g is the included angle of the
grooves and u and v are the angles of cant of the cubes formed on
plates 710 and 810, respectively (See FIG. 36A). Plates 710 and 810
are not necessarily the same thickness. Bevel faces 813 and groove
faces 716 are cut into the smooth side and the grooved side
respectively of plate 810 following a procedure similar to that
described in detail for rectangular cubes. Bevel faces 713 and
groove faces 816 are cut into the grooved side and the smooth side
respectively of plate 710. The plates are then assembled as
illustrated in FIG. 36 with two plates 710 paired and oppositely
oriented alternating with two plates 810 paired and oppositely
oriented. The equivalent of the assembly of two paired and
oppositely oriented plates 710 could also be made by cutting two
rows of cubes on one thicker plate as was illustrated for
rectangular cubes in FIGS. 22 through 25A; for this construction
both sides of the plate would be grooved. Note that the bevel faces
713 and 813 are continuous for the length of the plates 710 and
810, respectively; as with hexagonal cubes, in instances where
there is an uninterrupted face shared by two or more adjacent cube
elements, the dividing line between elements shall be considered to
be the shortest line (lines 715 and 815 in FIG. 36) that can be
drawn to complete the polygon. To avoid damage to the edges of the
grooves on the sides of the plates, the plates are assembled for
machining with the grooved sides against a similarly grooved dummy
plate.
(9) To produce triangular microcubes such as illustrated in FIG.
31, for which the cant and active area are not solely dependent
upon cube shape, a plate 110 or a stack of plates is positioned on
a ruling machine with the cuttable end up and with the sides of the
plate angled by a desired amount X with respect to a perpendicular
to the cutting plane of the ruling machine. A pattern of triangular
microcubes is then ruled onto the cuttable ends of the plates in a
manner similar to the ruling of an uninterrupted surface, which is
taught in Stamm, U.S. Pat. No. 3,712,706 or in U.S. Pat. No.
4,478,769 assigned to applicant's assignee. The ruled plates are
then assembled as shown in FIG. 31 with alternate plates oriented
180.degree. to each other. Alternatively, the assembly of FIG. 31
could be made by starting with a double thickness plate 210 and
separately ruling two arrays of triangular microcubes on its end,
which was illustrated for rectangular microcubes in FIGS. 22
through 25. The cant of the triangular microcubes tooled by either
of the methods above will be a combination of the angle X and the
cube axis cant resulting from the selected ruling angles. In most
instances, the paired cubes in the array will be alternately
face-more-parallel and edge-more-parallel.
(10) A retroreflective array comprising hexagonal cubes with
pentagonal faces, FIG. 35, is made from a plurality of plates, each
plate having a plurality of parallel V-grooves on the two opposing
surfaces. To make the plates, first a master is made by plating
adherent electroless nickel onto the surface of a stainless steel
block to a thickness of approximately 0.010''. The electroless
nickel master is ruled to form one set of parallel V-grooves with a
120.degree. included angle and a groove width equal to the desired
dimension across flats of the hexagonal microcube, 0.006'' for
example. The grooved surface is passivated and additional
electroless nickel is deposited on the master to a depth of
approximately 0.010''. Before removing the electroless nickel
deposit from the master, the surface of the deposit is machined
with a like set of parallel 120.degree. V-grooves, aligned with the
first set of V-grooves on the master, and to a depth such that the
greatest thickness of nickel in the deposit is equal to the desired
dimension across flats times 1.155. The deposit is separated as a
grooved plate from the master.
The plate is positioned with the grooves perpendicular to the bed
of the ruling machine. Faces A are machined by a cutting tool
having an included angle of 70.52.degree. (as projected in the
direction of cutting), the bisector of the included angle being
perpendicular to the bed of the machine. The plates then are tilted
so that a grooved side makes an angle X equal to 50.77.degree. with
respect to a perpendicular to the bed of the machine and faces B1
are cut with a cutting tool having an included angle of
131.81.degree. with bisector of the included angle perpendicular to
the bed of the machine. The process is repeated for faces B2.
The finished plates are stacked for electroforming with grooves
interlocking, which results in adjacent plates being displaced half
a cube width laterally. One plate in the assembly is shown in bold
outline.
For each microcube there will be left exposed in the assembly of
plates one small triangular vertical wall where the cube dihedral
edge in one plate abuts the face of a cube in an adjacent plate as
indicated by the circles labeled C in FIG. 35. This exposed wall is
not expected to be a problem in either electroforming or in
assignee's embossing process, but, if necessary, the exposed wall
can be drafted.
Those skilled in the art will recognize alternative methods for
making arrays of hexagonal cubes with pentagonal faces, based on
the invention herein, but the method shown is preferred for ease of
tooling plates.
It will be understood that while machining using diamond tools to
form grooves and edges is the disclosed embodiment, other linear
forming techniques, such as laser cutting, EDM, or ion machining,
or the like may be used. It will further be understood that known
variations of ruling techniques may be employed without departing
from the scope and spirit of the invention. For example, grooves
may be cut wherein the faces are not planar, but have a slight and
known curvature.
* * * * *