Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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LENTICULAR LENS ARRAY AND
TOOL FOR MAKING A LENTICULAR LENS ARRAY
PRIORITY AND RELATED APPLICATIONS
This application claims the benefit of priority to U.S. Provisional Patent
Application Serial Number 60/297,148, entitled "Lenticulax Lens Array
Optimization
for Printed Display," filed June 8, 2001. The complete disclosure of the above-
identified priority application is fully incorporated herein by reference.
1o FIELD OF THE INVENTION
The present invention relates generally to a lenticular lens array for
producing
visual effects from interdigitated or interlaced images. More particularly,
the present
invention relates to a lenticular lens array where a cross section of each
lens element
on the array comprises an elliptical shape. The present invention also relates
to a tool
and a method for creating such a lenticular lens array.
BACKGROUND OF THE INVENTION
A lenticular lens can create visual animated effects for interdigitated or
interlaced (hereinafter "interlaced") printed images. The images can be
printed using
non-impact printing, known as masterless printing, or by conventional printing
processes, known as master printing. Typically, a lenticular lens application
comprises two major components: an extruded, cast, or embossed plastic
lenticular
lens and the interlaced printed image. The front of the lenticular lens
comprises a
plurality of lenticules arranged in a regular array, having cylindrical lens
elements
running parallel to one another. The back of the lenticular lens is flat and
smooth.
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The interlaced images are printed on the flat, smooth backside of the
lenticular lens.
Exemplary methods for printing the images include conventional printing
methods
such as screen, letterpress, flexographic, offset lithography, and gravure;
and non-
impact printing methods such as electro-photography, iconography,
magnetography,
ink jet, thermography, and photographic. Any of the above printing
technologies can
be used in either sheet-fed or roll web-fed forms.
The interlaced images are viewed individually, depending on the angle
through which a viewer observes the images through the lenticular lens
elements. At
a first viewing angle, a first image appears through the lenticular lens
elements. As
to the lenticular lens is rotated, the first image disappears and another
image appears
through the lenticular lens elements. Viewing the images through the
lenticular lens
elements can create the illusion of motion, depth, and other visual effects. A
lenticular lens can create those illusions through different visual effects.
For example,
the visual effects can comprise three-dimensions (3-D), animation or motion,
flip,
morph, zoom, or combinations thereof.
For a 3-D effect, multiple layers of different visual elements are interlaced
together to create the illusion of 3-D, distance, and depth. For example,
background
objects are pictured with foreground objects that appear to protrude when
viewed
through a straight forward, non-angled view. For an animation or motion
effect, a
series of sequential photos can create the illusion of animated images. A
viewer
observes the series of photos as the viewing angle of the lens changes.
Animation is
effective in showing mechanical movement, body movement, or products in use.
For a flip visual effect, two or more images flip back and forth as the
viewing
angle changes. The flip effect can show before-and-after and cause-and-effect
scenarios. It also can show bilingual messages, such as flipping from English
to
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Spanish. For a morph visual effect, two or more unrelated images gradually
transform or morph into one another as the viewing angle of the lenticular
lens
changes. Finally, for a zoom effect, an object moves from the background into
the
foreground as the viewing angle of the lenticular lens changes. The object
also may
travel from side to side, but usually works better in a top to bottom format.
Figure 1 illustrates a partial cross section of a conventional lenticular lens
array 100. The array 100 comprises lenticules 102, 104, 106. Each lenticule
102,
104, 106 comprises a cylindrical lens element 102a, 104a, 106a, respectively.
Each
lens element 102a, 104a, 106a operates to focus light on a back surface 107 of
the
l0 array 100. In operation of the conventional array 100, multiple images can
be printed
on the rear surface 107. An observer can singularly view the images through
the lens
elements 102a, 104a, 106a by rotating the array 100.
Specific characteristics of each lenticule 102, 104, 106 will be described
with
reference to exemplary lenticule 104. Each lens element 102a, 104a, 106a has a
circular cross section of radius R. The circular cross section corresponds to
a desired
circular shape 108 having the radius R. The lens element 104a comprises a
portion of
the circular shape 108. Lenticule 104 also has a distance t from a vertex of
the lens
element 104a to the rear surface 107 of the array 100. The lens element 104a
has a
lens junction depth d where it joins adjacent lens elements 102a, 106a.
Finally, the
2o material forming the lens array 100 determines a refractive index N of the
array 100.
The relationship between the distance t, the radius R, and the refractive
index
N is given by the following equation:
(1) t = ~
N-1
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As shown in equation (1), the thickness t and radius R are a function of the
refractive index N, which is a fraction of wavelength of light. Accordingly,
the
lenticular lens elements can be optimized for a particular wavelength based on
the
wavelength that provides the best overall performance for the desired
application.
Regularity of the array 100 can be defined by the separation or distance S
between the vertex of adjacent lens elements. For the conventional cylindrical
lenticular lens array 100, the maximum separation between the vertex of each
lens
element 102a,104a, 106a is given by the following equation:
(2) Smax = 2R
to A pitch P of the lenticules can be defined as a number of lenticules per
unit
length (lpu). For example, the unit length can comprise an inch or a
millimeter. For
the conventional cylindrical lenticular lens array 100, the minimum pitch is
given by
the following equation:
(3) Pmin - 2R [lpu,
i5 Figure 2 illustrates a light ray trace illustrating several problems
associated
with a conventional lenticular lens array 100. In general, the array 100
operates by
passing light from the rear surface 107 through the lens elements 102a, 104a,
106a to
an observer. Reciprocity allows viewing the light path in reverse as
illustrated in
Figure 2. Ideally, on-axis light LI passes through lens element 104a and 1S
focused to
2o a common point 202 on the rear surface I07 of the array 100. However, the
circular
cross-section of the lens element 104a produces a projected image having
spherical
aberration. For example, the light L1 is projected over a large area 204 on
the rear
surface 107. The large projection area limits resolution and the number of
interlaced
images that can be viewed on the rear surface 107.
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Additionally, off axis light LZ passes through the lens element 104a and is
focused upon the rear surface 107 near point 203. However, the circular cross-
section
of lens element 104a produces coma and an astigmatic aberration 208. Finally,
Figure
2 illustrates that the depth d of the lens surface can approach the radius of
the circular
cross-section at the junction of adjacent lenses. Accordingly, portions of the
light LZ
are blocked by lens 106a and may be redirected to the wrong location 206.
Figure 3 illustrates a light beam projection illustrating another problem
associated with the conventional lenticular lens array 100. Figure 3
illustrates light
beams projected to an observer from different printed areas of the
conventional
to lenticular lens array 100. As shown, the light beams in the central area
302 are not
reasonably matched over the circular angle of the lens.
Furthermore, conventional lenticular sheet-fed printing has been used to
create
promotional printed advertising pieces printed on a lenticular lens array. For
example, the advertising pieces' include limited volumes of thicker gauge
lenticular
material designs such as buttons, signage, hang tags for clothing, point-of
purchase
displays, postcards, greeting cards, telephone cards, trading cards, credit
cards, and
the like. Those thicker gauge lenticular printed products are printed on
cylindrical
lenticular material having a standaxd thickness. For example, standard
thicknesses
include 0.012 mil, 0.014 mil, 0.016 mil, 0.018 mil, and up to 0.0900 mil.
Printed
quality on those thicker lenses are generally acceptable because the lenticule
pitch is
more course (fewer lenticules) and the printing process can place more printed
image
pixels within the lenticule band range. Additionally, lenticular materials at
the thicker
ranges tend to be more optically forgiving then thinner gauges.
Recently, lenticular extruders, lenticular casting/embossers, and print
manufacturers have experimented with decreasing the overall lenticular
material
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thickness using the common cylindrical lens elements discussed above. However,
as
the thickness of the lenticular lens array decreases, the print quality
suffers significant
aberration. As the thickness decreases, lenticule pitch must increase to
provide more
lenticules per unit length, thereby reducing the separation between
lenticules. That
thinner configuration does not allow using as many printed pixel images when
compared to the thicker lenticular material designs. Accordingly, the quality
of the
printed visual effects is degraded with the thinner material.
Another problem with thicker lenticular materials is that the thicker
materials
cannot be used for the majority of the consumer packaging industry. That
problem
to arises because thicker materials of 0.012 mil and thicker cannot be applied
nor
handled properly to cylindrical or truncated package shapes without de-
laminating off
the package due to plastic memory pull. Even when a strong adhesive is used to
bond
the thick lenticular piece to the packaged unit, problems with de-lamination
still occur
over time due to the continual pull of the plastic material, as the plastic
memory pulls
the material to its natural, straight produced shape.
Thicker lenticular materials also experience problems during the label
application process. Automated printed label blow-down or wipe-down packaging
labeling equipment cannot apply the thicker lenticular materials, because of
the plastic
memory issues discussed above. The plastic memory causes the thicker
lenticular die
cut labels to rise off the lenticular label rolls before the application
process.
Therefore, a need in the art exists for a lenticular lens array that can
provide a
more focused or resolved image by mitigating the spherical aberration
associated with
conventional arrays. A need in the art also exists for a tool and a method for
making
such a lenticular lens array. Furthermore, a need exists in the art for a
lenticular lens
array having a lenticular lens element shaped to mitigate the spherical
aberration.
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associated with conventional lenticular lens elements. A need also exists for
a
lenticular lens array having a thin structure to mitigate plastic memory
issues
associated with thicker, conventional arrays.
SUMMARY OF THE INVENTION
The present invention can provide a lenticular lens array that can optimize
printed display quality of animated/three-dimensional images for mass
production.
The present invention can provide a Ienticular lens array that can mitigate
the
to spherical aberration typically produced by a conventional array. For
example, the
present invention can provide a lenticular lens array that can produce a
substantially
focused axial image and can improve the off axis image. Additionally, the
present
invention can provide a lenticular lens array having a reduced lens junction
depth,
which can mitigate off axis light blocking by adjacent lenses.
The lenticular lens array according to the present invention can comprise a
plurality of lenticules disposed adjacent to each other. Each lenticule can
comprise a
lenticular lens element on one side and a substantially flat surface on an
opposite side.
Each Ienticular lens element can have a vertex and a cross section comprising
a
portion of an elliptical shape. Alternatively, the cross section can comprise
an
2o approximated portion of an elliptical shape. The elliptical shape can
comprise a major
axis disposed substantially perpendicular to the substantially flat surface of
each
respective lenticular lens element. The vertex of each respective lenticular
lens
element can lie substantially along the major axis of the elliptical shape.
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These and other aspects, objects, and features of the present invention will
become apparent from the following detailed description of the exemplary
embodiments, read in conjunction with, and reference to, the accompanying
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 illustrates a partial cross section of a conventional lenticular lens
array.
Figure 2 illustrates a light ray trace illustrating problems associated with a
conventional lenticulax lens array.
1o Figure 3 illustrates a light beam projection illustrating another problem
associated with the conventional lenticular lens array.
Figure 4 illustrates a partial cross section of a lenticular lens array
according to
an exemplary embodiment of the present invention.
Figure 5 illustrates a light ray trace illustrating optical characteristics of
a
I5 lenticular lens array according to an exemplary embodiment of the present
invention.
Figure 6 illustrates a light beam projection illustrating additional optical
characteristics of the lenticular lens array according to an exemplary
embodiment of
the present invention.
Figure 7 illustrates a partial cross section of a lenticular lens array
according to
2o an alternative exemplary embodiment of the present invention.
Figure 8A illustrates a cross-section of a cylindrical rod for producing a
tool
for forming elliptically-shaped lens elements according to an exemplary
embodiment
of the present invention.
Figure 8B illustrates a front view of the tool for forming elliptically-shaped
25 lens elements according to an exemplary embodiment of the present
invention.
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Figure 9 illustrates a cross section of a pseudo elliptical lenticule for
approximating an elliptically shaped lens element of a lenticular lens array
according
to an exemplary embodiment of the present invention.
Figure 10 illustrates a pseudo elliptical tool for creating a pseudo
elliptical lens
element according to an exemplary embodiment of the present invention.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
The present invention can reduce spherical aberration associated with
conventional lenticular lens arrays by providing a lenticular lens array
having an
to elliptical cross-sectional shape. The elliptical cross-sectional shape can
provide sharp
focusing of on-axis light and can increase the clarity of off axis light. The
characteristic shape of the elliptical cross section can be determined based
on a
particular application. Many parameters can influence the elliptical shape.
For
example, the parameters include a refractive index N of the array material, a
thickness
t from the vertex of each lens element to a rear surface of the array, a lens
junction
depth d where adjacent lenses join, and other parameters. A pseudo elliptical
lens
element also can provide a lenticular lens array having reduced spherical
aberration.
Figure 4 illustrates a partial cross section of a lenticular lens array 400
according to an exemplary embodiment of the present invention. The array 400
2o comprises lenticules 402, 404, 406. Each lenticule 402, 404, 406 comprises
an
elliptically-shaped lens element 402a, 404a, 406a, respectively. Each lens
element
402a, 404a, 406a operates to focus light on a back surface 407 of the array
400. In
operation of the array 400, multiple images can be printed on the rear surface
407 of
the array 400. An observer can singularly view the images through the lens
elements
402a, 404a, 406a by rotating the array 400.
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Specific characteristics of each lenticule 402, 404, 406 will be described
with
reference to exemplary lenticule 404. Each lens element 402a, 404a, 406a has
an
elliptical cross section corresponding to a portion of a desired elliptical
shape 408.
The lens element 404a comprises a portion of the elliptical shape 408. At a
vertex of
the lens element 404a, the elliptical shape 408 has a radius R. Lenticule 404
also has
a distance t from a vertex of the lens element 404a to the rear surface 407 of
the array
400. The lens element 404a has a lens junction depth d where it joins adjacent
lens
elements 402a, 406a. The material forming the lens array 400 determines a
refractive
index N of the array 400. The relationship between the distance t, the radius
R, and
l0 the refractive index N is given by equation (1) discussed above.
The characteristics of the elliptical shape 408 will now be described. The
elliptical shape 408 comprises an ellipse having a major axis 410 and a minor
axis
412. The ellipse crosses the major axis 410 at points ~ a and the minor axis
412 at
points ~ b. The major axis 410 and the minor axis 412 cross at the origin o.
The
ellipse also comprises foci located at points ~ c on the major axis 410. The
junction
point of adjacent lens elements 402a, 404a, 406a crosses the elliptical shape
408 at a
distance y from the major axis 410. The optical axis of the lenticule 404,
which is the
major axis 410 of the elliptical shape 408, is perpendicular to the rear
surface 407 of
the array 400. The vertex of the lens element 404a is positioned along the
major axis
410 of the elliptical shape 408.
For the lenticular lens array 400, the maximum separation between the vertex
of each lens element 402a, 404a, 406a is given by the following equation:
(4) S",ax = 2b
The maximum separation between the vertex of each lens element 402a, 404a,
406a also is given by the following equation:
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2RN
(5) Sma~ = Nz -1
The array 400 has a pitch defined by the number of lenticules per unit length
(lpu). For example, the unit length can comprise an inch or a millimeter. For
the
lenticular lens array 400, the minimum pitch is given by the following
equation:
(6) Pmin ' 2b [lpuj
Parameters for a particular application of the lenticular lens array 400 can
determine the characteristics of the elliptical shape 408. The characteristics
can be
determined for each application. For example, the characteristics d, t, y, and
R of the
elliptical shape 408 can be determined from the refractive index of the
material
to forming the array 400 and standard geometric equations. For instance, the
major axis
410 can lie along an x-axis and the minor axis 412 can lie along a y-axis of a
rectangular coordinate system. Accordingly, the elliptical shape 408 is given
by the
following equation:
(7) y2 - 2Rx + px2 = 0
The constant p can be determined in terms of a conic constant as shown in the
following equation:
(8) p = K + 1
The conic constant x can define the elliptical shape of the lens 404 and can
be
determined from the following equation:
(9) x = - 1
Nz
The refractive index N is typically in the range of about 1.3 to about 2.0,
and
more commonly in the range of about 1.5 to about 1.6, for plastics used in the
printing
industry. Accordingly, the conic constant x for the bounding refractive index
range
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covers from about -0.25 to about -0.60. Accordingly, those conic constants
indicate
an elliptical shape for the lens element 404a, because a conic constant Iess
than zero
and greater than minus one indicates an elliptical shape.
The eccentricity a of the elliptical shape 408 is given by the following
equations:
(10) a = ~, or
(11) a = ~
a
Other standard geometric relationships for the elliptical shape 408 include
the
following:
(12) a = R
or
P
(13) a=
x+1
( 14) b2 =a2 -c2
An example of determining particular characteristics for the elliptical shape
408 will now be described. A desired material to form the array 400 can be
chosen.
The desired material can have an associated refractive index N. Using the
refractive
index N, a conic constant K for the elliptical shape 408 can be determined
using
equation (9). Additionally, a lenticule thickness t can be chosen for the
particular
application. For example, the lens thickness t can be in the range of about
0.003 to
about 0.100 inches. In an exemplary embodiment, the lenticule thickness t can
be
chosen in the range of about 0.007 to about 0.011 inches. Alternatively, the
lenticule
thickness t can Using the standard geometric equations, the points ~ a and ~ b
that
define the elliptical shape 408 can be determined. For example, the radius R
can be
determined using equation (1) and the conic constant K from equation (9).
Then,
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points ~ a can be determined using equation (12) or (13). Next, the
eccentricity a can
be determined using equation (10). Points ~ c can be determined using equation
(11).
Points ~ b can be determined using equation (14).
The distance y can be chosen based on the particular application for the array
400. The distance y is one half the width of the lens element 404a. The width
of the
lens element 404a can define a field of view for the lens element 404a on the
rear
surface 407. Accordingly, the distance y can be chosen to provide a field of
view
wide enough for a desired number of interlaced images. After choosing the
distance
y, the x coordinate on the major axis 410 for the distance y can be determined
using
i0 equation (7).
The particular characteristics of the elliptical shape 408 can be determined
from many combinations of the parameters that define those characteristics.
Accordingly, the present invention encompasses determining elliptical
characteristics
based on a different set of chosen or given initial parameters than those
described
above.
Figure 5 illustrates a light ray trace illustrating optical characteristics of
the
lenticular lens array 400 according to an exemplary embodiment of the present
invention. The lenticular lens array 400 can mitigate the spherical aberration
typically
produced by a conventional array. For example, the array 400 can provide a
substantially focused axial image and can improve the off axis image. As shown
in
Figure 5, the on-axis light L1 can pass through the lens element 404a of the
array 400
and can be focused at point 502 on the rear surface 407. As shown, the
elliptically-
shaped lens element 404a can mitigate spherical aberration produced around the
focal
point 502. By reducing the base spherical aberration, spherochromatism can
also be
reduced.
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Additionally, the off axis image produced from the off axis light L2 at point
503 is improved over the conventional lens, with coma 508 being the clear
residual
aberration. Also, the elliptically-shaped lens element 404a can reduce the
lens
junction depth d between adjacent lens elements. Accordingly, the array 400
can
mitigate off axis light blocking by adjacent lenses, as shown in Figure 4. For
a given
width 2y, radius R, and index of refraction N, ghosting can be reduced because
off axis light blocking is reduced compared to a conventional circular array
having
the same width, radius, and index of refraction characteristics.
Figure 6 illustrates a Iight beam projection illustrating additional optical
to characteristics of the lenticular lens array 400 according to an exemplary
embodiment
of the present invention. Figure 6 illustrates light beams projected to an
observer
from different printed areas of the lenticular lens array 400. As shown, the
light
beams in the central axea 602 are reasonably matched over the angle of the
elliptically-shaped lens.
Figure 7 illustrates a partial cross section of a lenticular lens array 700
according to an alternative exemplary embodiment of the present invention. The
array 700 can comprise the Ienticular lens array 400 coupled to a substrate
702. In the
exemplary embodiment, the lens elements 402a, 404a, and 406a can focus light
on a
rear surface 704 of the substrate 702. The total distance T from each lens
vertex to
the rear surface 704 of the substrate 702 can comprise the distance tl from
the lens
vertex to the rear surface 407 of the axray 400 plus the distance to from the
rear
surface 407 of the array 400 to the rear surface 704 of the substrate 702. In
practice,
the Ienticular lens array is cast and has a thickness tl typically equal to
about lens
junction depth d or slightly greater than the lens junction depth d. The
characteristics
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of the elliptically-shaped lenses 402a, 404a, 406a can be similar to those
described
above with reference to Figure 4.
The array 400 and the substrate 702 can comprise different materials.
Accordingly, the different materials can have different refractive indexes.
For
example, the array 400 can comprise a material having a refractive index of
N~, and
the substrate 702 can comprise a material having a refractive index of N2. The
different refractive indices of the array and substrate materials can
introduce
additional spherical aberration. For example, for a single additional
substrate of
thickness t2 and refractive index Na, the focal displacement is shifted with
respect to
1o an array comprising a single material of refractive index Nl and having the
same R.
The shift in focal displacement can be either positive or negative depending
upon the
relationship of the materials. To compensate for the different refractive
indices,
equation (1) can be modified to the following equation to determine the radius
R of
each lens element 402a, 404a, 406a when the array 700 comprises two or more
different materials:
(15) R = (N, -1)( t' + t2 +... t-"
Ni Nz N"
The value of the radius R results in the image from a distant source being
formed upon the back surface of the substrate 702. As shown above, equation
(15)
can apply when the lenticular lens array comprises more than one substrate.
The conic constant can be estimated from equation (9) and can be optimized
with an optical computer program to mitigate the additionally induced
spherical
aberration of the substrate(s).
In an alternative exemplary embodiment, the substrate 702 can be bonded to
the array 400 through a bonding layer (not shown) such as a resin. Typically,
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bonding layer will have a finite thickness and an associated index of
refraction. If a
bonding layer is used, it can be treated as an additional substrate.
Accordingly,
equation (15) can be used to compensate for the thickness and index of
refraction of
the bonding layer, as well as for that of the substrate. The associated conic
constant is
determined and optimized in the manner previous described.
In another alternative exemplary embodiment, the substrate 702 can comprise
an adhesive layer.
In another alternative exemplary embodiment, the substrate 702 can comprise
an opaque substrate. For example, the opaque substrate can comprise paper.
to Additionally, the interlaced image can be printed on a front surface 706 of
the opaque
substrate. Then, the opaque substrate can be laminated to the lenticular lens
array
400. In that case, the image is located at the rear surface 407 of the array
400.
Accordingly, the thickness of the substrate does not have to be considered to
determine the proper thickness T. However, if a bonding layer is used to
laminate the
opaque substrate to the array 400, then the thickness of the bonding layer
should be
considered to determine the proper thickness T.
In another alternative exemplary embodiment, the lenticules 402-406 can be
cast onto the substrate 702 such that a discontinuity exists between one or
more pairs
of adjacent lenticules. For example, the lenticules 402-406 can be cast onto
the
substrate 702 such that a discontinuity exists between lenticules 402 and 404
or
between lenticules 404 and 406.
A tool 800 for producing an elliptically-shaped lens element according to an
exemplary embodiment of the present invention will now be described with
reference
to Figures 8A and B. Tool 800 can be constructed from diamond or other
suitable
material. Figure 8A illustrates a cross-section of a base member 802 for
producing
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the tool 800 for forming elliptically-shaped lens elements according to an
exemplary
embodiment of the present invention. Figure 8B illustrates a front view of the
tool
800 for forming elliptically-shaped lens elements according to an exemplary
embodiment of the present invention.
The tool 800 can be is used to produce a regular array of groves in a mandrel
for casting or extruding the lenticular lens array. The tool 800 is not used
to directly
form the lenticular lens array. For example, the mandrel can comprise a drum,
and
the tool 800 can produce a spiral or screw pattern in the drum. Alternatively,
the tool
800 can produce a straight-cut (parallel-grooved) pattern in the drum.
Furthermore,
to the mandrel can be coated with a copper alloy prior to being shaped by the
tool 800.
The copper alloy can be used because it cuts cleanly and holds it shape. After
cutting,
the copper alloy can be plated with another material to improve the mandrel's
durability. For example, the plating material can comprise chrome. If a
coating or
plating material is used after cutting, then the dimensions of the tool 800
can be
I5 adjusted (increased) to compensate for a finite thickness of the coating or
plating
material. The following description details a tool that creates a mandrel
without a
coating or plating. In practice, the size of the tool 800 can account for the
added
thickness of the coating or plating.
As shown in the exemplary embodiments of Figures 8A and 8B, the base
2o member 802 can comprise a cylindrical rod and can have a radius b
corresponding to
the dimensions ~ b of an elliptical shape 806 for the tool 800. The base
member 802
can be cut along a plane 804 at an angle k to a minor axis 808 of the base
member
802. The angle k can be determined from the following equation:
(16) cosine(k) = b
a
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The elements b and a correspond to elliptical characteristics of the
elliptical
shape 806. The elliptical shape 806 corresponds to the desired elliptical
shape of
lenticular lens elements on a lenticular lens array according to an exemplary
embodiment of the present invention. Accordingly, each of the elliptical
characteristics a, b, and c, correspond to the same characteristics for the
elliptically shaped lens elements of the array.
In an alternative exemplary embodiment, the base member 802 can comprise a
cone. The cone can comprise a truncated cone. The cone can comprise diamond or
other suitable material. Standard geometric equations can be used to determine
a
to proper angle to cut the cone to produce the desired elliptical shape for
the tool 800.
Accordingly, the cone can be cut at an angle to produce the desired elliptical
shape for
the tool. Potential advantages of a truncated conical base member 802 include
Less
material being required and the conical apex angle providing a general
reduction in
angular range capability of the fabrication equipment.
The tool 800 comprises a mother tool that can be used to cut a mandrel for
producing elliptically-shaped lens elements of the array. The mandrel then can
be
used to create the elliptically-shaped lens elements in a lenticular lens
array. For
example, the mandrel can be used for casting or extruding the lenticular lens
elements
of the array.
2o Figure 9 illustrates a pseudo elliptical lenticule 900 for approximating an
elliptically shaped lens element of a lenticular lens array according to an
exemplary
embodiment of the present invention. The lenticule 900 can be included in a
lenticular lens array according to an exemplary embodiment of the present
invention.
The lenticule 900 comprises a pseudo elliptical lens element 901. As shown,
the
pseudo elliptical lens element 90I approximates a portion of an elliptical
shape 902.
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The pseudo elliptical lens element 90I comprises a circular portion 905,
corresponding straight portions 906a, 906b, and corresponding straight
portions 908a,
908b.
The circular portion 905 comprises a portion of a circular shape 904 that
approximates the radius R of the elliptical shape 902. Accordingly, the
circular shape
904 can have a radius equal to the radius R of the elliptical shape.
Alternatively, the
circular shape 904 can have a radius different from the radius R of the
elliptical shape,
if the different radius can better approximate the elliptical shape. The
circular portion
905 can comprise that portion of the circular shape 904 that approximates the
to elliptical shape 902 within a specified tolerance. The specified tolerance
can be
determined based on a desired projected image quality for a particular
application.
The maximum residual shape error of the circular and straight regions can be
maintained to be approximately the same.
Corresponding straight portions 906a, 906b can be provided beginning at a
point where the circular shape 904 exceeds the specified tolerance from the
elliptical
shape 902. Accordingly, straight portions 906a, 906b can approximate a portion
of
the desired elliptical shape 902.
Corresponding straight portions 908a, 908b can be provided beginning at a
point where the straight portions 906a, 906b, respectively, exceed the
specified
tolerance from the elliptical shape 902. The straight portions 908a, 908b can
approximate a portion of the desired elliptical shape 902.
Any number of straight portions can be used to approximate the elliptical
shape 902. The number of straight portions can be adjusted to minimize
deviation
from the elliptical shape 902. For example, using more straight portions can
achieve
less deviation from the desired elliptical shape 902. In other words, a
smaller
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tolerance limit can be used when more straight portions are used. Typically,
if more
straight portions are used, then a smaller circular portion 905 can be used to
allow a
smaller tolerance limit.
In an alternative exemplary embodiment, a plurality of facets can be used to
approximate the desired elliptical shape without using a circular portion. In
one
embodiment, corresponding pairs of facets can be used to approximate the
desired
elliptical shape. In that embodiment, the pseudo elliptical lens elements can
have a
point where a facet pair meets at the vertex of the lens element. In an
alternative
embodiment, the vertex can be approximated with a single facet positioned
l0 substantially orthogonal to the major axis of the elliptical shape, and
corresponding
pairs of facets can be used to approximate outer portions of the elliptical
shape.
Accordingly, the pseudo elliptical lens element 901 can approximate an
elliptical shape 902, thereby improving the image characteristics in a similar
manner
as described above for the array 400 of Figure 4.
Figure 10 illustrates a pseudo elliptical tool 1000 for creating a pseudo
elliptical lens element according to an exemplary embodiment of the present
invention. The tool 1000 can be is used to produce a regular array of groves
in a
mandrel for casting or extruding the lenticular lens array. The tool 1000 is
not used to
directly form the lenticular lens array. For example, the mandrel can comprise
a
2o drum, and the tool 1000 can produce a spiral or screw pattern in the drum.
Alternatively, the tool 1000 can produce a straight-cut (parallel grooved)
pattern in
the drum. Furthermore, the mandrel can be coated with a copper alloy prior to
being
shaped by the tool 1000. The copper alloy can be used because it cuts cleanly
and
holds it shape. After cutting, the copper alloy can be plated with another
material to
improve the mandrel's durability. For example, the plating material can
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chrome. If a coating or plating material is used after cutting, then the
dimensions of
the tool 1000 can be adjusted (increased) to compensate for a finite thickness
of the
coating or plating material. The following description details a tool that
creates a
mandrel without a coating or plating. In practice, the size of the tool 1000
can
account for the added thickness of the coating or plating.
In Figure 10, only one side of the elliptical tool 1000 is illustrated. The
other
side of the elliptical tool 1000 comprises a mirror image of the illustrated
side. The
elliptical tool 1000 can be constructed from diamond or other suitable
material. The
elliptical tool 1000 can comprise a tool for cutting a form that can be used
to extrude
l0 or cast pseudo elliptical lens elements of a lenticular lens array
according to an
exemplary embodiment of the present invention.
As shown, the desired elliptical shape comprises an elliptical shape 1002. A
circular shape 1004 having a radius can approximate a portion 1005 of the
elliptical
shape 1002. Point 1007 indicates an intersection of a tangent 1006 to the
ellipse 1004
where the circular shape 1004 exceeds a specified tolerance from the
elliptical shape
1002. A first facet 1008 can be provided beginning at the point 1007 and can
approximate a portion of the elliptical shape 1002. A second facet 1010 can be
provided beginning at a point 1009 where the first facet exceeds the specified
tolerance from the elliptical shape 1002. The second facet 1010 can
approximate a
2o portion of the elliptical shape 1002 until the desired width y is reached.
The tangent 1006, the first facet 1008, and the second facet 1010 can form an
angle I, m, and n, respectively, with the major axis 1003 of the elliptical
shape 1002.
The actual angles 1, m, and n, the radius R, and the length of the first and
second
facets 1008, 1010 can be determined for a particular application based on the
characteristics of the elliptical shape 1002 and the specified tolerance.
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In practice, the radius of the circular shape 1004 can be chosen to
approximate
a radius R of the elliptical shape 1002. Accordingly, the circular shape 1004
can have
a radius equal to the radius R of the elliptical shape. Alternatively, the
circular shape
1004 can have a radius different from the radius R of the elliptical shape, if
the
different radius can better approximate the elliptical shape. The chosen
radius can be
used until it exceeds the specified tolerance from the elliptical shape 1002.
The angle
m of the first facet 1008 can be determined based on the elliptical shape 1002
at the
tangent point 1007. Similarly, the angle n of the second facet 1010 can be
determined
based on the elliptical shape 1002 at the point 1009.
l0 Any number of facets can be used to approximate the elliptical shape 1002.
The number of facets can be adjusted to minimize deviation from the elliptical
shape
1002. For example, using more facets can achieve less deviation from the
desired
elliptical shape 1002. In other words, a smaller tolerance limit can be used
when
more facets are used. Typically, if more facets are used, then a smaller
circular
portion 1005 can be used to allow a smaller tolerance limit.
The mitigation of the spherical aberration afforded by the inclusion of the
elliptically shaped lens, when compared to conventional lenses, allows the
utilization
of thinner lenticular lenses to achieve the same or better performance. A
common
metric used to express the light gathering capability of a lens is know as the
focal ratio
or F-number (F/#). The focal ratio is simply defined at the ratio of the focal
length of
the lens divided by the diameter of the lens (specifically the entrance pupil
of the
lens). The spherical aberration of the conventional lens follows the well-
known
relationship of being directly proportional to 1/(F/#)3. As a conventional
lenticular
lens is thinned (t becoming smaller) while maintaining the pitch, it is
evident that the
image resolution/quality degrades quickly since the F# becomes smaller. For
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example, the resolution decreases by a factor of over 10 as the t changes from
0.020
inch to 0.009 inch. Sheets of thinner lenticular lenses offer significant
advantages
when affixed to cylindrical objects as explained elsewhere in this
specification.
In an alternative exemplary embodiment, a plurality of facets can be used to
approximate the desired elliptical shape without using a circular portion. In
one
embodiment, corresponding pairs of facets can be used to approximate the
desired
elliptical shape. In that embodiment, the pseudo elliptical lens elements can
have a
point where a facet pair meets at the vertex of the lens element. In an
alternative
embodiment, the vertex can be approximated with a single facet positioned
l0 substantially orthogonal to the major axis of the elliptical shape, and
corresponding
pairs of facets can be used to approximate outer portions of the elliptical
shape.
The tool 1000 can be used to carve a mandrel having a pseudo elliptical shape.
The pseudo elliptical mandrel then can be used for casting or extruding lens
elements
having a pseudo elliptical shape for a lenticular lens array.
The elliptical shape of the lenticular lens elements according to the
exemplary
embodiments of the present invention can provide the following benefits over
conventional designs: producing less visible print projected aberrations;
providing
higher printed image contrast; providing thinner gauge lenticular materials
that
maintain the print quality present in thicker gauge materials (for example,
the thinner
lenticular materials can be produced with a thickness less than 0.012 inch,
and more
specifically in the range of about 0.005 inch to about 0.010 inch); providing
print
images with clearer and smaller serif type and point sizes; providing the
thinner
lenticular material gauges that can be flexible enough to affix to cylindrical
or
truncated packaging containers, such as jars, bottles, beverage cups, cartons,
etc.
without de-laminating off the consumer packaging; providing the thinner
lenticular
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material gauges that can be adaptable to the packaging industry's in-line
labeling
applicators for rotary roll fed blow down or wipe-down labeling systems;
providing
the thinner gauge materials that can reduce the thickness and weight per
square inch
of material, thereby reducing cost; providing increased lenticule viewing
width area
for broader animated imaging techniques at a lower material thickness and
finer lens
pitch; or reducing cross-talk and image ghosting.
The elliptical shape lens elements of the lenticulax lens array according to
the
exemplary embodiments of the present invention can be used in the following
printed
product types and markets due to the thinner lenticular material possible with
the
to elliptical design: entire outer lenticular packaging enhancements (box
overwraps);
segmented applied lenticular label coverage to outer packaging; pressure
sensitive,
non-pressure sensitive, self adhesive, and non-self adhesive lenticular label
products;
multi-ply, multi-substrate peel open pressure sensitive and non-pressure
sensitive
lenticular labels; lenticular laminated to paperboard products; packaging in-
packs and
on packs; beverage cups having decorative partial or full lenticular cup
wraps; video,
dvd, or cd disc cover lenticular treatments; direct mail; magazine inserts;
newspaper
inserts; or contest and game sweepstake components that comprise use of
partial or
full lenticular enhancements .
Although specific embodiments of the present invention have been described
2o above in detail, the description is merely for purposes of illustration.
Various
modifications of, and equivalent steps corresponding to, the disclosed aspects
of the
exemplary embodiments, in addition to those described above, can be made by
those
skilled in the art without departing from the spirit and scope of the present
invention
defined in the following claims, the scope of which is to be accorded the
broadest
interpretation so as to encompass such modifications and equivalent
structures.
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