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BACKGROUND OF THE INVENTION
The basic cube-corner retroreflective element used in cube-corner
retroreflective articles has a notoriously low angularity, i.e., the
element will only brightly retroreflect light that impinges on it within a
narrow angular range centering approximately on its optical axis. Low
angularity arises by the inherent nature of these elements, which are
trihedral structures having three mutually perpendicular lateral faces,
such as occur at the corner of a cube. In use, the elements are arranged
so that light to be retroreflected impinges into the internal space
defined by the faces, and retroreflection of the impinging light occurs by
internal reflection of the light from face to face of the element.
Impinging light that is inclined substantially away from the optical axis
of the element (which is the trisector of the internal space defined by
the faces of the element) strikes a face at an angle less than its
critical angle, thereby passing through the face rather than being
reflected.
Some workers have addressed this problem by coating the trihedral faces of
the cube-corner element with specularly reflective metal, e.g.,
vapor-deposited aluminum, to cause even highly inclined light to be
reflected by the faces. But such coatings reduce overall reflection from
the faces (because a percentage of light impinging on the faces is
absorbed by the coating), and introduce a gray color to the element which
is often objectionable. Also the coatings could be susceptible to
corrosion problems that would limit the useful life of an article having
such elements.
Others have addressed the problem by arranging a second retroreflective
plate or sheet in back of a first retroreflective plate or sheet (see
Weber, U.S. Pat. No. 3,140,340, McGrath, U.S. Pat. No.4,025,159, or Jones,
U.S. Pat. No. 4,303, 305), but such an approach is expensive and provides
a thick and generally rigid construction not suited for many uses.
Others have addressed the problem by attempting to change the configuration
of the cube-corner retroreflective elements, but none of these efforts has
provided a practically manufactured sheeting suitable for the most common
uses of retroreflective sheeting (e.g., on traffic signs, license plates,
advertising signs, etc.). For example, White, U.S. Pat. No. 4,349,598
teaches a limited-use broader-angularity retroreflective sheeting obtained
by tilting the central axes of the cube-corner elements to an
approximately 35-degree angle and joining two adjacent elements into a
right triangle prism or "pup-tent"-like configuration. Such cube-corner
retroreflective elements achieve retroreflection of light having incidence
angles (the angle between the incident light and a line perpendicular to
the sheeting) approaching 90.degree., which makes them useful particularly
for pavement markings or the like. But 0.degree.-incidence angle light
(light that is perpendicular to the sheeting) is not reflected, and
accordingly the sheeting is not useful for conventional traffic signs.
The desire for a thin pliable cube-corner retroreflective sheeting that
would reflect inclined light is recognized in Haggerty, U.S. Pat. No.
3,450,459, but the patent teaches no practical method for achieving such a
result. Thin pliable sheeting requires that the cube-corner elements be of
very small "microsizes," which so far as known, have only been
accomplished by grooving techniques for which the elements taught in
Haggerty are not adapted.
Prior efforts have also been made to increase the angular range of
reflector plates that use larger cube-corner retroreflective elements,
such as the reflector plates mounted on vehicles. The molds for such
reflector plates are generally made by bundling together individual mold
parts, typically pins which each have an end portion shaped like a
cube-corner, retroreflective element. Heenan et al, U.S. Pat. No.
3,541,606, teaches reflector plates for vehicles containing cube-corner
retroreflective elements arranged into discrete, rather large groups. The
optical axes of the cube-corner elements in each group are inclined at
angles different from the angles of the elements of a different group so
as to increase the angular range of reflection in a horizontal plane
around a vehicle. Heenan, U.S. Pat No. 3,923,378 and Heenan, U.S. Pat. No.
Re: 29,396 teach an improvement in which the cube-corner retroreflective
elements are arranged in rows, and the optical axes of the cube-corner
elements of one row are inclined towards the elements of the other row,
for example, in an amount between about 6.degree. and 13.degree. (see
column 5, line 45 et seq. of U.S. Pat. No. 3,923,378). Such tilting is
intended to increase the angularity of the reflector plate in a
predetermined plane (see column 5, lines 64 and 65), which is typically
the horizontal plane around a vehicle in other embodiments (see FIGS. 19
and 31 of either U.S. Pat. No. Re. 29,396 or U.S. Pat. No. 3,923,378),
increased angularity is obtained in two planes by mixing two different
sets of cube-corner retroreflective elements, one set comprising
cube-corner elements inclined towards one another in one of the planes of
desired increased angularity, and the other set comprising cube-corner
elements that are inclined towards one another in the other of the planes
of desired increased angularity. Lindner, U.S. Pat. No. 4,066,331, has a
similar objective with cube-corner retroreflective elements arranged in
rows.
The noted improvement as to the angularity of reflector plates in one
plane, such as the horizontal plane around a vehicle, has less value for
other kinds of retroreflective articles. Retroreflective sheeting, in
particular, is generally intended for use on large-area surfaces that are
viewed over their whole surface and from many angles. For reflective
sheeting used on sign faces it is important to maintain a uniform
brightness over the whole surface of the sheeting irrespective of the
viewing angle, so that the whole sign has uniform brightness, and so that
the legends or symbols on the sign are legible. Legibility requires
control of the contrast between the graphic images and background area of
the sign and such control of contrast requires uniformity in reflective
brightness over the whole viewing surface.
DISCLOSURE OF THE INVENTION
The present invention provides a new cube-corner retroreflective article
which exhibits wide retroreflective angularity in multiple viewing planes,
and which is based on cube-corner retroreflective elements that can be
adapted for manufacture in microsizes such as needed in thin flexible
retroreflective sheeting.
In brief summary, a new retroreflective article of the invention comprises
at least one pair of cube-corner retroreflective elements which are
rotated 180.degree. with respect to one another, which have three mutually
perpendicular lateral faces defined at their bases by linear edges that
lie in a common plane, and which have optical axes tilted towards one edge
of the element (when considered from the front surface of the article, on
which light to be retroreflected impinges). It has been found that such a
"matched" pair of tilted cube-corner elements produces a wide
retroreflective angularity not only in a plane that is perpendicular both
to the common plane and the edge toward which the optical axis of an
element is tilted, but also in a plane that is perpendicular to that plane
and the common plane. Further, such a pair has good angularity in planes
intermediate those two planes, i.e., throughout a full 360.degree.-range
of viewing planes.
In thin sheeting form, a new retroreflective article of the invention
typically comprises a dense array of micro-sized cube-corner
retroreflective elements arranged in matched pairs with the axes of the
elements in each pair being tilted toward one another (i.e., the edge
toward which the optical axis of each pair or elements are tilted is
typically a common edge between the elements). Preferably, for sheeting
made from polymeric material having indices of refraction of about 1.5,
the axes of the elements are tilted to an angle between about 7 and
slightly less than 10 degrees from a position perpendicular to the common
plane in which the base edges of the lateral faces lie.
The new retroreflective article is adapted to manufacture in sheeting form
because the base edges of the lateral faces of the cube-corner elements
lie in a common plane. As noted above, tooling for molding thin flexible
cube-corner retroreflective sheeting has previously been made by grooving
techniques. In these techniques a master plate is grooved with three sets
of parallel V-shaped grooves that intersect to form cube-corner elements
(see Erban, U.S. Pat. No. 3,057,256 and Stamm, U.S. Pat No. 3,712,706).
Since the present invention uses cube-corner elements having full
triangular lateral faces, with base edges in a common plane, they may be
formed by such grooving techniques, with the stated common plane being
established by the bottom edges of the grooves.
DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective view showing a cube-corner retroreflective element
used in a retroreflective article of the invention;
FIGS. 2a, 2b, and 2c are side elevational views of the lateral faces of the
cube-corner element shown in FIG. 1;
FIG. 3 is a plan view of a representative retroreflective sheeting of the
invention with a dense array of cube-corner elements as pictured in FIGS.
1 and 2;
FIGS. 4A and 4B are sectional views taken along the lines 4A--4A and 4B--4B
of FIG. 3 showing particularly two representative matched pairs of
cube-corner elements in retroreflective sheeting of the invention;
FIG. 5 is a sectional view taken along the lines 5--5 of FIG. 4A;
FIG. 6 is a graph of isobrightness curves for a representative matched pair
of cube-corner elements, showing the percentage of the maximum
retroreflection from such a pair of cube-corner elements that is retained
when the light being retroreflected impinges on the elements at increasing
incidence angles, i.e., at angles displaced from a line perpendicular to
the base plane of the elements; the magnitude of the incidence angle is
represented by the radial distance of a point on the curve from the origin
of the graph and the rotational plane of the incidence angle is
represented by the angular position of a point on the curve; and
FIG. 7 is a graph of isobrightness curves measured for a representative
retroreflective sheeting of the invention.
DETAILED DESCRIPTION
A cube-corner retroreflective element useful in a retroreflective article
of the invention is shown in perspective view in FIGS. 1 and in side
elevation views in FIGS. 2a, 2b, and 2c. As shown, the element 10 has
three mutually perpendicular lateral faces 11, 12, and 13 which meet at
the apex 14. The base edges 15 of the lateral faces 11, 12, and 13 are
linear and lie in a single plane, i.e., the base plane 16 of the element.
The element 10 also has a central or optical axis 17, which is a trisector
of the internal angle defined by the lateral faces 11, 12, and 13 and
which is tilted with respect to a line 18 perpendicular to the base plane
16. Retroreflection will occur when light incident on the base plane 16 of
the element is internally reflected by one of the three lateral faces to a
second face, then to a third face, and then back through the base toward
the source of light.
In retroreflective articles of the invention, a cube-corner element as
shown in FIGS. 1 and 2 is generally used with at least one other
cube-corner element as part of a matched pair, and commonly is used with
an array of such elements. The other cube-corner elements as they might
appear in such an array of elements are shown in plan view in FIG. 3,
which pictures the back of a representative retroreflective article of the
invention 20. The elements are joined together, e.g., by being formed as a
part of a single integral sheet material or by being attached at their
base plane 16 to a carrier film. FIG. 4 shows in section view a portion of
the article pictured in FIG. 3, and shows a thickness 21 of material, such
as a polymeric film, connecting the elements together. Because the base
edges 15 of the element 10 are linear and in a common plane, an array of
such elements is defined by intersecting sets of grooves. Element 10.sub.1
in FIG. 3 is defined by three V-shaped grooves 22, 23, and 24, which are
each one member of three sets of grooves which cross the array in an
intersecting pattern.
As seen from FIGS. 3, 4A, 4B, and 5, the cube-corner elements in the
illustrated representative retroreflective article of the invention can be
considered as being arranged in pairs, with the optical axes of the
elements in each pair being tilted or canted toward one edge of the
elements, when considered from the front surface 25 of the article 20 on
which light to be retroreflected impinges. FIG. 4A shows one such pair,
10.sub.3 and 10.sub.4, in which the edge toward which the optical axes 17
of the elements have been tilted or canted, i.e., in the direction of the
arrows 26 in FIG. 4A, is a common edge. The cube-corner elements of the
pair are identical, but they face in opposite directions, i.e., one is
rotated 180.degree. about the line 18 from the orientation of the other.
Other elements in the array pictured in FIG. 3 can be considered a pair
besides the pair of FIG. 4A which abut at a common edge. Thus, elements
10.sub.5 and 10.sub.6 shown in FIG. 4B are also a matched pair, even
though they abut at a point rather than an edge. They are such a pair,
since they are identical except for being rotated 180.degree. from one
another. The optical axes of the elements 10.sub.5 and 10.sub.6 are tilted
toward one edge, which is a matching edge in each element (i.e., upon
rotation of one of the elements 10.sub.5 and 10.sub.6 in an amount of
180.degree., the edges toward which the optical axes are tilted would
coincide).
The optical axes of the pairs of elements 10.sub.3 and 10.sub.4, and of
10.sub.5 and 10.sub.6, are in a single plane, but it should be noted that
a pair of elements could have their axes in different planes. For example,
the elements 10.sub.7 and 10.sub.8 in FIG. 3 can be considered as a pair.
Whichever pair in FIG. 3 is considered, however, the tilting of the
optical axes of the elements in the pair occurs in the same plane or in
parallel planes, identified as the X-axis planes in FIG. 3.
The angular range of retroreflection from the tilted cube-corner elements
of a pair combine to provide a broad angularity of reflection. The tilting
of the elements in the X-axis plane shown in FIG. 3 shifts the angular
range of reflection in that plane from being centered on a line
perpendicular to the front surface of the article 20 to being centered on
paths represented by the light rays 27 and 28 in FIGS. 4A and 4B. Each
tilted cube-corner element 10 retroreflects with maximum brightness light
that is incident on the article 20 on a path represented by light rays 27
and 28; and each element retroreflects with gradually reduced brightness
light that is incident on the article 20 on paths further displaced from
the paths 27 and 28. The angular ranges of reflection are arbitrarily
represented by the ranges .beta..sub.3X, .beta..sub.4X, .beta..sub.5X, and
.beta..sub.6X in the drawings (actually, there is no sharp delineation of
a range, but instead a gradual reduction in the brightness of
retroreflection). As shown, one end of each of these ranges is more
inclined than the other end of the range, indicating that more highly
inclined light is reflected at that end of the range than at the other
end. The more inclined ends of the range represent the ends of the
combined ranges of reflection from a pair of elements, and the combined
range is represented by .sub.TX. The tilted elements combine to provide a
broad angular range of retroreflection .beta..sub.TX in the X-axis plane,
which is substantially larger than the representative ranges .beta..sub.3X
and .beta..sub.4X or .beta..sub.5X and .beta..sub.6X provided by the
individual elements.
More than achieving a broadened angular range in the X-axis plane, however,
it has now been found that the tilted elements also achieve a substantial
increase in angular range in a Y-axis plane that is perpendicular to the
X-axis plane (and to the base plane of the elements). Also, there is a
substantial increase in angular range in planes intermediate the two
perpendicular X and Y planes. As shown in FIG. 5, the angular range
.beta..sub.TY of retroreflection in the Y-axis plane perpendicular to the
X-axis plane is increased to a surprisingly large amount by the tilting of
the elements, even though that tilting occurs in the X-axis plane.
This result is further illustrated in FIG. 6 which is a set of
isobrightness curves plotting the magnitude of retroreflection obtained
from cube-corner elements as used in retroreflective articles of the
invention (as described in Example 1 herein). The magnitude of
retroreflection is plotted versus the magnitude of the incidence angle of
the light being reflected (the angle between the incident light and a line
perpendicular to the front face of the sheeting). Values plotted on the
X-axis in FIG. 6 represent the magnitude of reflection for light incident
on the elements in X-axis planes parallel to the planes defined by the
optical axes of the elements; values plotted on the Y-axis are for light
incident on the sheet in Y-axis planes perpendicular to the X-axis planes
defined by the optical axes of the elements; and values plotted at points
between the X and Y axes are for light incident on the elements in planes
intermediate the perpendicular X and Y planes.
As may be seen, for the particular measurements reported in FIG. 6, the
cube-corner elements reflect at 50% of maximum retroreflective brightness
light that impinges on the elements in the X-axis plane at about
40.degree. (the "half-brightness angle"), and reflect at 50% brightness
light that impinges on the elements in the Y-axis plane at about
35.degree.. Such an angular range in retroreflective brightness along two
perpendicular planes is far beyond any range previously known to be
obtained in a cube-corner retroreflective sheeting. As is also seen from
FIG. 6, good retroreflective brightness is also obtained in planes
intermediate the perpendicular planes.
Computer simulations of cube-corner designs based on designs of the
invention indicate that, for best results, the optical axes of each pair
of cube-corner elements abutting at a common edge lie in a single plane
perpendicular to the edge and to the base plane. However, in other
embodiments, the optical axes may be tilted in two directions, e.g.,
toward one edge as well as out of a plane that is perpendicular to the
edge and the base plane.
The greatest improvement in angular range along the X-axis plane is
obtained with the greatest amount of tilting of the optical axes, but at
some degree of tilting, which varies with index of refraction of the
materials of the retroreflective article or sheeting, the retroreflection
of light that is perpendicular to the article (i.e,
0.degree.-incidence-angle light) begins to decline rapidly. The degree of
tilting which provides optimum angularity is generally an angle just short
of the angle at which perpendicular retroreflection begins to decline
rapidly. For materials having an index of refraction of 1.5 this angle is
about 12.degree.-13.degree., and it varies with the index of refraction
(.eta..sub.D) according to the following formula:
##EQU1##
The optimum angle of tilting is also affected by the desired manufacturing
technique, as well as by related questions as to desired areal density of
cube-corner elements, and desired efficiency of reflection. For
manufacturing techniques using a grooved master, the degree of tilting is
limited by the fact that if the groove between matched pairs of elements
abutting at a common edge (e.g., the groove 24 in FIG. 3) is of too large
an angle, the grooving tool will remove portions of edges of adjacent
elements that abut the groove on either side of the matched pair of
elements. This fact can be illustrated in FIG. 3 by reference to
cube-corner element 10.sub.9, which abuts groove 24 and is adjacent to a
matched pair of elements. If the degree of tilting of the elements
pictured in FIG. 3 is increased beyond a certain angle, which is found to
be 9.736.degree. for an array as shown in FIG. 3 in which the optical axes
of a matched pair of elements lie in a common plane, the angle of the
groove 24 increases to such an extent that the edge 29 of element 10.sub.9
would penetrate into the groove. Thus the grooving tool forming the groove
24 removes a portion of the element 10.sub.9 (and similar elements
abutting groove 24) at the edge 29.
Removal of a portion of the elements abutting groove 24 can be avoided by
separating cube-corner elements, e.g., by forming the bottom of grooves 22
and/or 23 with a flat area or trough. Such a separation reduces the
magnitude of retroreflection, since there are then fewer cube-corner
elements per unit area of sheeting, but the separation has other
advantages such as allowing an underlying substrate (which may have a
desired color, for example) to be viewed through the flat area of the
bottom of the groove, or allowing transmission of light through the flat
area (as when a sheeting of the invention is used as the front plate of an
internally illuminated sign).
Also, removal of a portion of an adjacent element, and the accompanying
loss of retroreflection, can be acceptable under some circumstances when
the total magnitude of retroreflection is otherwise sufficient.
Somewhat greater retroreflection of 0.degree.-incident light can be
obtained with a degree of tilting less than the optimum for Y-axis angular
range, but generally, for materials having an index of refraction of 1.5,
the degree of tilting will be at least 7.degree., and will vary with index
of refraction according to the above-stated formula. For 1.6-index
materials, the degree of tilting will generally lie within the range of
9.degree.-15.degree., preferably 10.degree.-13.degree. for articles having
flat-bottomed grooves between elements, and otherwise preferably less than
9,736.degree..
Articles of the invention may be made as one integral material, e.g., by
embossing a preformed sheet with a described array of cube-corner
elements, or casting a fluid material into a mold; or they may be made as
a layered product, e.g., by casting the elements against a preformed film
as taught in U.S. Pat. No. 3,684,348, or by laminating a preformed film
over the front face of individual molded elements.
Acrylics, which generally have an index of refraction of about 1.5, are one
useful material for an integral sheet material, or they are useful as a
facing adhered over the cube-corner retroreflective elements in a layered
product to obtain good outdoor weathering properties. Other useful
materials include polycarbonates, which have an index of refraction of
about 1.6, reactive materials such as taught in United Kingdom Pat. No.
2,027,441; polyethylene-based ionomers (marketed under the name of
"SURLYN"), polyesters, and cellulose acetate butyrates. Generally any
transparent material that is formable typically under heat and pressure
may be used.
Retroreflective articles of the invention may incorporate cube-corner
elements in a wide range of sizes. For flexible sheeting of the invention
(for example, rollable around a three-inch-diameter core), the elements
preferably have a size (i.e., spacing between the center lines of grooves)
less than about 0.025 inch. The most common rigid cube-corner
retroreflective articles use cube-corner elements of a size of about 0.060
to 0.100 inch. However, the beneficial increased angularity offered by the
invention will also occur with larger sizes. For example, the effects
achieved by the invention are illustrated in the examples below by using
macro-sized glass cube-corner retroreflective elements.
Since sheeting of the invention is typically used by adhering it to a
substrate, and since it is desired to maintain an air interface at the
three lateral mutually perpendicular surfaces of the cube-corner elements,
the sheeting is preferably sealed to a back film in a cellular pattern
such as taught in U.S. Pat. No. 4,025,159. A variety of heat-activated,
solvent-activated, pressure-sensitive or other adhesives may then be
coated on or laminated to the back surface of the sealing film for use in
adhering the sheeting to a substrate. Other structure may also be added to
a retroreflective article of the invention, such as specularly reflective
coatings over the mutually perpendicular lateral faces of the elements,
and protective films over the front face of a retroreflective article,
e.g., to improve weathering properties.
The invention will be further illustrated by the following examples.
EXAMPLE 1
A series of large cube-corner retroreflective elements were machined from
glass. These glass bodies were tetrahedrons, having three mutually
perpendicular lateral faces and a bottom or base face. The latter face was
at a different angle in each element of the series so as to place the
optical axes of the different elements at different angles. The base edges
of the lateral faces of the elements were between about 11/2 and 2 inches
(3.8 to 5 centimeters) in length. Some elements or bodies in the series
were machined from glass having an index of refraction of 1.5 and some
from glass having an index of refraction of 1.6. Four different elements
of each index of refraction were prepared. The optical axes of the
different 1.5-index elements were tilted toward one edge in a plane
perpendicular to that edge respectively 7.2.degree.,9.2.degree.,
11.3.degree., and 13.6.degree.. The different 1.6-index elements were
tilted respectively 9.2.degree., 11.3.degree., 13.6.degree. and
18.1.degree.. Total light return in a 2-degree-radius cone was then
measured for each of the elements by conventional darkroom photometry
techniques. To determine the amount of light that would be returned by a
matched pair of the elements, the measured data for an element was
mathematically summed with the data that such an element would provide if
rotated 180.degree.. Isobrightness curves were drawn using such a
summation of data for the 1.5-index 9.2.degree.-tilt elements and are
shown in FIG. 6. The results for the other elements are shown in Table I.
TABLE I
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Mathematical sum of retroreflection
from matched pairs of macro-sized
cube-corner elements which differ as to
index of refraction and angle of tilt
1.5-index 1.6-index
Tilt angle Tilt angle
Incidence
7.2.degree.
9.2.degree.
11.3.degree.
13.6.degree.
9.2.degree.
11.3.degree.
13.6.degree.
18.1.degree.
angle (normalized percent of brightest retroreflection)
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X-axis
0 100 100 100 54 100 100 100 56
5 97 98 64 67 100 98 72 52
10 73 69 64 72 99 72 70 56
20 60 67 72 87 68 75 82 68
30 52 62 69 93 62 74 87 79
40 39 50 59 83 51 63 80 77
50 24 33 41 63 35 46 62 64
Y-axis
0 100 100 100 54 100 100 100 56
5 97 99 98 56 99 99 99 62
10 94 96 95 85 96 95 95 100
20 82 82 81 90 84 82 81 85
30 63 62 60 64 65 61 58 59
40 7 24 31 32 42 36 31 29
50 1 2 2 2 8 13 7 5
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EXAMPLE 2
A diamond-shaped flat acrylic plate having a 6-inch axial length was cut
with three intersecting sets of parallel V-shaped grooves using a
diamond-tipped tool. Two sets of the grooves intersected at an angle of
70.degree.. These grooves were cut with a tool haivng an included angle of
60.degree., 36 minutes, and were spaced on 0.012-inch (0.205 millimeter)
centers. The third set of grooves intersected the first two sets of
grooves at an angle of 55.degree.. Individual grooves of the third set
were in line with the points of intersection of the grooves of the first
two sets. The grooves in the third set were cut using a tool having an
included angle of 88.degree., 51 minutes at a spacing of 0.0105-inch
(0.254 millimeter).
The described grooving provided an array of cube-corner elements arranged
in pairs with the optical axes of each element of a pair being tilted
towards one another through an angle of 9.2.degree., i.e., 9.2.degree.
from a line perpendicular to the face of the acrylic plate.
An electroform was made from the grooved plate by electrolytic deposition
of nickel onto the plate, and the electroform was used as a stamper to
emboss the pattern of the electroform into a preformed 0.030-inch-thick
(750 micrometers) acrylic film having an index of refraction of about
1.49. The electroform was placed in a platen press and the pressing was
done at a temperature of 350.degree. to 400.degree. F.
The total light retroreflected in a 2-degree-radius cone by the stamped
retroreflective sheeting was then measured for light impinging on the
sheeting at various incidence angles by darkroom photometry techniques.
The results are shown in FIG. 7 as a set of isobrightness curves
presenting retroreflective brightness as a percentage of maximum
brightness and as a function of the magnitude and rotational plane of the
incidence angle. FIG. 7 is seen to correlate well with the results
presented in FIG. 6.
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