U.S. patent application number 13/360655 was filed with the patent office on 2015-01-15 for perceived image depth for autostereoscopic displays.
This patent application is currently assigned to SOLIDDD CORP.. The applicant listed for this patent is Richard A. Muller. Invention is credited to Richard A. Muller.
Application Number | 20150015946 13/360655 |
Document ID | / |
Family ID | 52276874 |
Filed Date | 2015-01-15 |
United States Patent
Application |
20150015946 |
Kind Code |
A1 |
Muller; Richard A. |
January 15, 2015 |
Perceived Image Depth for Autostereoscopic Displays
Abstract
An autostereoscopic display provides an extremely deep
projection area by observing a relationship between a desired depth
of projection and an autostereoscopic display design that includes
a focal length of lenticles of a lenticular array and a number of
views. The relationship specifies a projected depth at which
lenticular crossover can occur for a given autostereoscopic with
the specific lenticular focal length and number of views.
Approximations can be used to simplify the relationship such that
the projected depth is directly related to a product of the focal
length and the number of views. To reduce optical aberrations,
lenticles of the lenticular array include meniscus-cylinder
lenses.
Inventors: |
Muller; Richard A.;
(Berkeley, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Muller; Richard A. |
Berkeley |
CA |
US |
|
|
Assignee: |
SOLIDDD CORP.
Brooklyn
NY
|
Family ID: |
52276874 |
Appl. No.: |
13/360655 |
Filed: |
January 27, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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12901478 |
Oct 8, 2010 |
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13360655 |
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Current U.S.
Class: |
359/463 |
Current CPC
Class: |
G02B 30/29 20200101;
G02B 30/27 20200101; G02B 27/0075 20130101 |
Class at
Publication: |
359/463 |
International
Class: |
G02B 27/22 20060101
G02B027/22 |
Claims
1-12. (canceled)
13. An electronically controlled dynamic autostereoscopic display
comprising: an image that contains a number of views; and a
lenticular array that includes at least two lenticles and that is
operatively coupled to the image and that makes only one of the
views of the image visible from each viewing angle throughout a
perceived three-dimensional projection area; wherein viewing the
image through the lenticular array from two different viewing
angles simultaneously results in perception of a three-dimensional
image in the perceived three-dimensional projection area; wherein
the autostereoscopic display has a width of from 17 to 35 inches;
and wherein the ratio of (i) four times the product of a focal
length of the lenticles and the number of views to (ii) the width
of the autostereoscopic display is at least 0.25:1.
14. The autostereoscopic display of claim 13 wherein the
autostereoscopic display displays video content having a 1080p
display format.
15-16. (canceled)
17. The autostereoscopic display of claim 13 wherein the
autostereoscopic display displays video content having a WQXGA
display format; and wherein the ratio of (i) four times the product
of a focal length of the lenticles and the number of views to (ii)
the width of the autostereoscopic display is at least 1:1.
18-25. (canceled)
26. A static autostereoscopic display comprising: an image that
contains a number of views; and a lenticular array that includes at
least two lenticles and that is operatively coupled to the image
and that makes only one of the views of the image visible from each
viewing angle throughout a perceived three-dimensional projection
area; wherein viewing the image through the lenticular array from
two different viewing angles simultaneously results in perception
of a three-dimensional image in the perceived three-dimensional
projection area; wherein the autostereoscopic display has a width
of at least 28 inches; and wherein the ratio of (i) four times the
product of a focal length of the lenticles and the number of views
to (ii) the width of the autostereoscopic display is at least
0.6:1.
27-55. (canceled)
56. An autostereoscopic display comprising: an image that contains
a number of views; and a lenticular array that includes at least
two lenticles and that is operatively coupled to the image and that
makes only one of the views of the image visible from each viewing
angle throughout a perceived three-dimensional projection area;
wherein viewing the image through the lenticular array from two
different viewing angles corresponding to an intraocular distance
of 2.4 inches simultaneously results in clear perception of a
three-dimensional image in the perceived three-dimensional
projection area from a viewing distance of at least 48 inches; and
wherein the ratio of (i) four times the product of a focal length
of the lenticles and the number of views to (ii) the width of the
autostereoscopic display is at least 0.1:1.
57. The autostereoscopic display of claim 56 wherein the ratio of
(i) four times the product of a local length of the lenticles and
the number of views to (ii) the width of the autostereoscopic
display is at least 0.2:1.
58-62. (canceled)
63. The autostereoscopic display of claim 56 wherein the
autostereoscopic display is an electrically controlled dynamic
display; and wherein the ratio of (i) four times the product of a
focal length of the lenticles and the number of views to (ii) the
width of the autostereoscopic display is at least 0.25:1.
64. The autostereoscopic display of claim 63 wherein the
autostereoscopic display displays video content having a 1080p
display format.
65. The autostereoscopic display of claim 63 wherein the
autostereoscopic display displays video content having a WQXGA
display format.
66. The autostereoscopic display of claim 63 wherein the ratio of
(i) four times the product of a focal length of the lenticles and
the number of views to (ii) the width of the autostereoscopic
display is at least 0.8:1.
67. The autostereoscopic display of claim 66 wherein the
autostereoscopic display displays video content having a 1080p
display format.
68. The autostereoscopic display of claim 66 wherein the
autostereoscopic display displays video content having a WQXGA
display format.
69. The autostereoscopic display of claim 63 wherein the ratio of
(i) four times the product of a focal length of the lenticles and
the number of views to (ii) the width of the autostereoscopic
display is at least 0.9:1.
70. The autostereoscopic display of claim 63 wherein the ratio of
(i) four times the product of a focal length of the lenticles and
the number of views to (ii) the width of the autostereoscopic
display is at least 1:1.
71. The autostereoscopic display of claim 70 wherein the
autostereoscopic display displays video content having a 1080p
display format.
72. The autostereoscopic display of claim 70 wherein the
autostereoscopic display displays video content having a WQXGA
display format.
73. The autostereoscopic display of claim 57 wherein viewing the
image through the lenticular array from two different viewing
angles corresponding to an intraocular distance of 2.4 inches
simultaneously results in clear perception of a three-dimensional
image in the perceived three-dimensional projection area from a
viewing distance of at least 60 inches.
74. The autostereoscopic display of claim 73 wherein the ratio of
(i) four times the product of a focal length of the lenticles and
the number of views to (ii) the width of the autostereoscopic
display is at least 0.4:1.
75. (canceled)
76. The autostereoscopic display of claim 56 wherein viewing the
image through the lenticular array from two different viewing
angles corresponding to an intraocular distance at 2.4 inches
simultaneously results in clear perception of a three-dimensional
image in the perceived three-dimensional projection area from a
viewing distance of at least 96 inches.
77. The autostereoscopic display of claim 76 wherein the
autostereoscopic display is a static display.
78-84. (canceled)
Description
FIELD OF THE INVENTION
[0001] The present invention relates generally to autostereoscopic
displays, and, more particularly, to a video autostereoscopic
display with significantly improved depth of projection.
BACKGROUND OF THE INVENTION
[0002] Conventional autostereoscopic displays use arrays of lenses
or parallax barriers or other view selectors to make a number of
pixels of the display visible to one eye of a viewing person and to
make a number of other pixels of the display visible to the other
eye of the viewing person. By isolating the pixels of the display
visible to each eye, the two fields of a stereoscopic image can be
presented on the display. The presentation of separate fields to
each eye is often used to cause the viewer to perceive a
three-dimensional image.
[0003] Current stereoscopic displays project a perceived depth of
about a few centimeters. In other words, most autostereoscopic
displays project portions of an image no more than about 1-2
centimeters in front of, and no more than about 1-2 centimeters
behind, the display. Some autostereoscopic displays a purported to
project a perceived depth of up to one foot, i.e., about 30 cm.
However, such displays suffer from optical aberrations such a poor
focus except for items projected near the surface of the
display.
[0004] One of the major difficulties in projecting a greater depth
of perception is that of optical artifacts in the lenticular array
often used to select a different field to be visible to each eye of
the human viewer. One such effect is that a given portion of the
image can be visible in two or more places, such as in two or more
lenticles of a lenticular array. Other effects include optical
aberrations that are typically not noticeable with very short
projected distances, such as just a few centimeters.
[0005] What is needed is an autostereoscopic display in which
significantly greater projected depths of perception can be
achieved without undesirable artifacts.
SUMMARY OF THE INVENTION
[0006] In accordance with the present invention, an
autostereoscopic display provides an extremely deep projection
area, for example appearing to have a depth of a meter or more, by
observing a relationship between a desired depth of projection and
an autostereoscopic display design that includes a focal length of
lenticles of a lenticular array and a number of views. For parallax
barrier autostereoscopic displays, the focal length is the distance
between the parallax barrier and the underlying display having
multiple views.
[0007] The relationship specifies a projected depth at which
lenticular crossover can occur for a given autostereoscopic with
the specific lenticular focal length and number of views. In some
configurations, approximations can be used to simplify the
relationship such that the projected depth is directly related to a
product of the focal length and the number of views.
[0008] The autostereoscopic display configuration often specifies a
view selector (such as a lenticular array) with a focal length much
greater than typical focal lengths seen in conventional
autostereoscopic display view selectors. One of the challenges with
such long focal lengths in lenticles of a lenticular array is that
a number of optical aberrations become noticeable and
problematic.
[0009] To reduce these optical aberrations, lenticles of the
lenticular array include meniscus-cylinder lenses, to provide a
more flat field of view.
[0010] The result is an autostereoscopic display with depths of
projection well beyond what conventional autostereoscopic displays
are capable of, while still avoiding effects such as lenticular
crossover and curved fields of view.
A BRIEF DESCRIPTION OF THE DRAWINGS
[0011] FIG. 1 shows an autostereoscopic display according to the
present invention in conjunction with a human viewer and showing,
in plan view, a three-dimensional area into which the
autostereoscopic display can project elements shown in the
display.
[0012] FIG. 2 shows the autostereoscopic display and viewer of FIG.
1 and shows the projection of a picture element behind the
display.
[0013] FIG. 3 shows the autostereoscopic display and viewer of FIG.
1 and shows the projection of a picture element before the
display.
[0014] FIG. 4 shows the autostereoscopic display and viewer of FIG.
1 and shows the reduced curvature of field achieved in accordance
with the present invention.
[0015] FIGS. 5, 6, and 7 are each a cross-section view of a
lenticle of a respective embodiment of the lenticular array of FIG.
1 in accordance with the present invention.
DETAILED DESCRIPTION OF THE INVENTION
[0016] In accordance with the present invention, a depth 130 (FIG.
1) of a projection area 120 in which parts of an autostereoscopic
display that includes a lenticular array 100 and a display 110 is
dramatically improved--e.g., to a meter or more, 20-30 times what
is seen in conventional autostereoscopic displays--by determining a
relationship between depth 130 and an autostereoscopic display
configuration at which a portion of display 110 can be visible at
multiple locations (lenticular crosstalk). This relationship
establishes a limiting configuration within which lenticular
crosstalk is minimized. Once this relationship is determined for a
desired depth 130, the autostereoscopic display is constructed to
meet or exceed the autostereoscopic display configuration to ensure
that lenticular crosstalk is only possible at depths of projection
beyond depth 130.
[0017] The autostereoscopic includes a focal length of individual
lenticles of lenticular array 100 and a number of views represented
in display 110. Choosing a relatively deep projection area 120
produces a very long focal length for lenticular array 100 and a
large number of views for display 110.
[0018] "A view" is used herein to refer to a subset of an image
presented to a viewer from a particular angle of view. As an
example, it is helpful to consider a simple autostereoscopic
display in which one eye of the human viewer can see every
odd-numbered column of pixels and the other eye of the viewer can
see every even-numbered column of pixels. The odd-numbered columns
of pixels would collectively represent one view, and the
even-numbered columns of pixels would collectively represent
another view. It should be appreciated that most autostereoscopic
displays have many more than just two views and that this very
simple example is merely to illustrate how "view" is used
herein.
[0019] In this illustrative embodiment, lenticular array 100
includes a number of vertical lenticles that makes one of a number
of view elements visible depending upon the angle of perspective of
an eye of viewer 10. In other words, for each of the views that can
be visible through lenticular array 100, each lenticle of
lenticular array 100 covers a portion of that view, sometimes
referred to herein as a view element, and makes that view element
visible from a given angle of perspective. In embodiments in which
display 110 is an electronic display, such as an LCD for example,
view elements are collections of pixels. In embodiments in which
display 110 is a static image such as a poster, view elements can
be tall, thin slivers of one of a number of views printed or
otherwise represented visually in display 110.
[0020] Design of lenticular 100 and display 110 begins with
selecting a designed depth 130 of projection area 120. In this
illustrative embodiment, depth 130 is selected to be one meter,
much, much deeper than any currently available autostereoscopic
displays.
[0021] FIG. 2 illustrates a circumstance to be avoided that
therefore sets a limit on high-quality autostereoscopic display
with a projected area 120 having depth 130. The left eye of viewer
10 sees a portion of display 110 through lenticle 500A and that
portion of display 110 appears to be at point 202 as a result of
the focal length of lenticle 500A. The same portion of display 110
can also be seen through lenticle 500B and every lenticle between
lenticle 500A and lenticle 500B. Light travels from point 202 at an
angle .theta. and is bent by lenticle 500B at an angle .phi. to the
left eye of viewer 100. This phenomenon of a single portion of
display 110 being visible to viewer 10 through multiple lenticles
of lenticular array 100 is sometimes referred to herein as
lenticular crosstalk.
[0022] Lenticular array 100 and display 110 are designed to provide
a projection area 120 of depth 130 with minimum lenticular
crosstalk.
[0023] The angles of FIG. 2 are related to one another as
follows:
.theta.+.alpha.=.phi. (1)
[0024] These angles can be rewritten in terms of dimensions of
lenticular array 100, display 110, and projection area 120.
.theta. = tan - 1 ( NS d ) .apprxeq. NS d ( 2 ) ##EQU00001##
[0025] In equation (2), S is the spacing of lenticles of lenticular
array 100, i.e., the width of a single lenticle. N is the offset of
lenticle 500B from lenticle 500A in terms of a number of lenticles.
Thus, NS is the offset of lenticle 500B from lenticle 500A as a
measured distance. In equation (2), d is projection depth 220, i.e,
the distance from lenticular array 110 that point 202 is projected.
The last portion of equation (2) estimates the arctangent function
using small angle approximation, which is appropriate in most
practical implementations of lenticular array 100 and display
110.
.alpha. = tan - 1 ( NS D ) .apprxeq. NS D ( 3 ) ##EQU00002##
[0026] In equation (3), D is distance 210, i.e, the distance from
lenticular array 110 to the eye of viewer 10. The last portion of
equation (3) estimates the arctangent function using small angle
approximation, which is appropriate in most practical
implementations of lenticular array 100 and display 110.
[0027] Angle .phi. depends on the size (.delta.) of the portion of
display 110 to be shown through a single lenticle as a part of a
single view and on the distance (f) of that portion from lenticle
500B. Equation (4) shows angle .phi. in terms of .delta. and f and
the index of refraction, n.sub.0, of lenticular array 110.
.phi. = .delta. n 0 2 f ( 4 ) ##EQU00003##
[0028] Using equations (2), (3), and (4), equation (1) can be
rewritten as follows:
NS d + NS D = .delta. n 0 2 f ( 5 ) ##EQU00004##
[0029] Small angle approximation of arctangent values should not be
used in equation (5) when such introduces appreciable error.
[0030] The number of views (n.sub.v) represented by display 110
relates to the size (.delta.) of the portion of display 110 and
lenticular size (S) as follows:
n v = NS .delta. ( 6 ) ##EQU00005##
[0031] To minimize lenticular crosstalk, N is chosen to be one (1)
to identify a configuration at which lenticular crosstalk between
adjacent lenticles is possible. Using the relationship of equation
(6), setting N to 1, and applying some algebra yields the following
relationship between configuration of lenticular array 100 and
display 110 and a maximum projection depth d at which lenticular
crosstalk begins between adjacent lenticles for a viewer a
distance, D, away:
2 n v f = ( 1 d + 1 D ) - 1 ( 7 ) ##EQU00006##
[0032] A similar relationship is observed for parts of display 110
projected toward viewer 10 as shown in FIG. 3, and this
relationship is as follows:
2 n v f = ( 1 d - 1 D ) - 1 ( 8 ) ##EQU00007##
[0033] In situations in which D is much greater than d, 1/D can be
approximated by zero. The result is that equations (7) and (8) can
then both be expressed as:
2n.sub.v f=d (9)
[0034] In equation (8), d represents distance 320 (FIG. 3), which
is chosen to be the same as distance 210 (FIG. 2) in this
illustrative embodiment.
[0035] The particular measure of depth 130 of projection area 120
at which lenticular crosstalk can happen between adjacent lenticles
is given by 2d:
2 d=4n.sub.vf (10)
[0036] Equation (10) provides guidance in designing lenticular
array 100 and display 110 to provide a desired depth 130 of
projection area 120 within which lenticular crosstalk is avoided.
In particular, the focal length of the lenticles of lenticular
array 100 and the number of views provided by display 110 are
chosen such that four (4) times their product is at least the
desired depth.
[0037] If more precision is required in designing a depth of a
projection area, the approximations used in equations (1)-(10)
above can be excluded. The resulting, exact version of equation
(10) is as follows:
2 d = 4 n v fD + S 2 D - 2 n v f ( 11 ) ##EQU00008##
[0038] It should be observed that as D gets very large relative to
other values in equation (11), equation (11) is approximated by
equation (10).
[0039] As an illustrative example using equation (10), consider
that depth 130 of projection area 120 is to be one meter. To
achieve this, the product of the number of views of display 110 and
the focal length of lenticles of lenticular array 100 should be at
least one-quarter of a meter, or 25 centimeters. A typical
conventional design would include eight views and a focal length of
1 millimeter, providing a projection area having a maximum depth of
about 3.2 cm while still avoiding lenticular crosstalk. However,
lenticular array 100 and display 110 require dimensions way beyond
those to achieve the desired depth of projection. For example, if
lenticular array 100 is designed to include lenticles whose focal
lengths are one centimeter and display 110 is designed to include
25 views, projection area 120 would have a maximum depth 130 of one
meter with little or no lenticular crosstalk.
[0040] Without the benefit of equations (10) and (11), the trend is
to make autostereoscopic displays, both static images and dynamic
monitors, thinner and to have a greater apparent resolution. Such
is directly contrary to extending the focal length of lenticles of
a lenticular array to dramatically improve the perceived depth of
the autostereoscopic display as suggested by equation (10). In the
example above, increasing the focal length of a conventional
lenticle by 1,000% (from 1 mm to 1 cm) and increasing the number of
views to twenty-five (25) improves the apparent depth by 3,000%
(from 3.2 cm to 1 m).
[0041] At the expense of thinness of the lenticular array,
lenticles with focal lengths significantly greater than the width
of the lenticles can provide very dramatic improvements in the
perceived depth of an autostereoscopic display without introducing
lenticular crosstalk. In the example above, the lenticles have a
focal length that is ten (10) times their width and provide an
apparent depth without lenticular crosstalk that is thirty (30)
times that of a comparable conventional autostereoscopic display.
Lenticles that have a focal length that is merely five (5), or even
just three (3), times their width still provide dramatic
results.
[0042] The following Table provides a number of examples of
crosstalk-free apparent depths of autostereoscopic displays
according to equation (10) above.
TABLE-US-00001 TABLE A Display Type Size (in) Hor. Res. (ppi) S f
n.sub.v 2d f S ##EQU00009## Bookmark 1200 0.01'' 0.05'' 12 1.6'' 5
1'' .times. 6'' 1200 0.02'' 0.1'' 24 6.4'' 5 2400 0.02'' 0.1'' 48
12.8'' 5 Business card 1200 0.01'' 0.05'' 12 1.6'' 5 2.5'' .times.
2'' 1200 0.015'' 0.05'' 18 2.4'' 3.33 2400 0.02'' 0.05'' 48 6.4''
2.5 Postcard 1200 0.01'' 0.04'' 12 1.28'' 4 5'' .times. 3'' 1200
0.015'' 0.05'' 18 2.4'' 3.33 2400 0.02'' 0.05'' 48 6.4'' 2.5
Digital Picture Frame 240 0.025'' 0.1'' 6 1.6'' 4 6'' .times. 4''
1440 (.times.6) 0.019'' 0.1'' 28 7.47'' 5.14 Smart Phone 326
0.012'' 0.05'' 4 0.53'' 4.08 4'' .times. 2'' 3912 (.times.12)
0.01'' 0.05'' 40 5.33'' 4.89 Tablet Computer 1584 (.times.12)
0.015'' 0.1'' 24 6.4'' 6.6 7.75'' .times. 5.8'' 3912 (.times.12)
0.009'' 0.05'' 36 4.8'' 5.43 46'' HDTV 48 0.125'' 0.5'' 6 12'' 4
40'' .times. 22.5'' 576 (.times.12) 0.042'' 0.4'' 24 38.4'' 9.6
46'' UDTV 1152 (.times.12) 0.042'' 0.4'' 48 76.8'' 9.6 40'' .times.
22.5'' 85'' HDTV 25.95 0.0231'' 0.75'' 6 12'' 2.16 74'' .times.
41.5'' 311.35 (.times.12) 0.077'' 0.4'' 24 38.4 5.19 85'' UDTV
622.7 (.times.12) 0.077'' 0.4'' 48 76.8'' 5.19 74'' .times. 41.5''
20'' WQXGA Monitor 1755.43 (.times.12) 0.036'' 0.2'' 64 51.2'' 5.49
17.5'' .times. 10'' Display Wall of 40'' 144 (.times.3) 0.083''
1.0'' 12 48'' 12 HDTVs tiled 4 .times. 4 160'' .times. 90''
Single-Sheet Poster 600 0.04'' 0.4'' 24 38.4'' 10 28'' .times. 42''
10' .times. 5' Static Sign 200 0.04'' 0.4'' 24 38.4'' 10 120''
.times. 60'' 600 0.12'' 0.4'' 24 38.4'' 3.33 48' .times. 14'
Billboard 100 0.48'' 2.0'' 48 256'' (21.33') 4.17 576'' .times.
168'' 300 0.16'' 2.0'' 48 256'' (21.33') 12.5 600 0.08'' 2.0'' 48
256'' (21.33') 25 48' .times. 14' Billboard with 50.4 (.times.8)
0.476'' 6.0'' 24 576'' (48') 12.6 4 mm pitch LEDs 576'' .times.
168'' 48' .times. 14' Billboard with 68 (.times.8) 0.353'' 6.0'' 24
576'' (48') 17 3 mm pitch LEDs 576'' .times. 168''
[0043] As used herein, the "(.times.3)", "(.times.6)",
"(.times.8)", and "(.times.12)" notes in the horizontal resolution
(ppi) column above indicate application of one or more of the
following technologies: (i) the subpixel remapping described in
U.S. patent application Ser. No. 12/868,038 filed Aug. 25, 2010 by
Dr. Richard A. Muller for "Improved Resolution for Autostereoscopic
Video Displays" (hereinafter the '038 Application) and (ii) the
pixel time multiplexing described in U.S. patent application Ser.
No. 12/969,552 filed Dec. 15, 2010 by Dr. Richard A. Muller for
"Improved Resolution For Autostereoscopic Video Displays"
(hereinafter the '552 Application). Both of those descriptions are
incorporated herein by reference.
[0044] The subpixel remapping taught by the '083 Application
teaches how to triple the horizontal resolution of a video display.
The "(.times.3)" note indicates use of this technology alone. The
time multiplexing taught by the '552 Application teaches how to
double the apparent horizontal resolution of a video display one or
more times, thereby scaling the apparent horizontal resolution by
an integer power of two. The "(.times.8)" indicates use of three
(3) doubling layers to produce an eight-fold increase in the
apparent horizontal resolution of the display. The "(.times.6)" and
"(.times.12)" notes indicate a combination of the tripling of
apparent horizontal resolution described in the '083 Application
with a single-layer doubling and a double-layer quadrupling,
respectively, of the apparent horizontal resolution described in
the '552 Application.
[0045] It should also be appreciated that the horizontal
resolutions specified in Table A are in pixels per inch (ppi), not
dots per inch (dpi). In addition, resolutions for smart phones and
tablet computers take into consideration resolutions of iPhone and
iPad products using Retina displays available from Apple Inc. of
Cupertino, Calif., which are purported to provide 326 pixels per
inch.
[0046] Traditionally, and without the benefit of equations (10) and
(11), the trends in autostereoscopic displays has been to minimize
thickness. There has generally been a perceived trade-off in
autostereoscopic display quality between greater apparent
horizontal resolution and the number of views. To avoid loss of
views, lenticles have generally been kept relatively shallow (short
focal lengths) and broad. Shallowness of lenticles maintains the
thinness of the autostereoscopic display but limits the focal
length of the lenticles. Lenticle breadth allows more views behind
each lenticle. Accordingly, the ratio of lenticle focal length (f)
to lenticle width (S) is low in conventional autostereoscopic
displays--typically no greater than about 1:1.
[0047] However, equations (10) and (11) illustrate the value of
dramatically increasing the focal length of the lenticles.
Accordingly, the ratio of lenticle focal length (f) to lenticle
width (S) in autostereoscopic displays designed according to the
present invention are significantly greater. This ratio is
sometimes referred to herein as a lenticular aspect ratio. As shown
in Table A above, lenticular aspect ratios are generally at least
2.5:1, more commonly 3:1, 4:1, 5:1, 6:1, and even greater than 10:1
in some displays. The result is that a one-inch-wide bookmark can
have an error-free perceived depth of about 12.8 inches. Similarly,
a 46'' HDTV can have an error-free perceived depth of about one
meter. Autostereoscopic smart phones displays can have an
error-free perceived depth of over five (5) inches, and
autostereoscopic tablet computer displays can have an error-free
perceived depth of over six (6) inches. Large, billboard-sized
displays can have error-free perceived depth of over 20 feet, even
as much 48 feet.
[0048] These maximum error-free perceived depths are far beyond
what any prior autostereoscopic displays have been able to achieve.
Exemplary minimum ratios of maximum error-free perceived depths to
display widths are summarized in Table C below.
TABLE-US-00002 TABLE B Exemplary Minimum Ratios Minimum of Maximum
Viewing Display Projection Depth Display Type Distance Width
(4n.sub.vf) to Width Business cards, Postcards, Digital Picture 12
inches 2.5 to 18 inches 0.4:1, 0.6:1, 0.9:1 Frames, Smart Phones,
Tablet Computers Digital Picture Frames, Smart Phones, 12 inches
>4 inches 0.5:1, 1:1, 1.2:1 Tablet Computers, and Televisions
Digital Picture Frames, Smart Phones, 12 inches 5-18 inches 0.25:1,
0.4:1, 1:1 Tablet Computers, and Small to Medium Prints Small to
Medium Televisions (1080p and 48 inches 17-35 inches 0.25:1, 0.4:1,
WQXGA, for example) 0.8:1, 1:1 Larger Televisions 48 inches >40
inches 0.8:1, 0.9:1, 1:1 Very Large Televisions and Large Video 60
inches >74 inches 0.2:1, 0.4:1, 06:1 Displays Medium-Large
Printed Posters 48 inches >28 inches 0.6:1, 0.8:1, 1:1 Large
Printed Posters 48 inches >56 inches 0.3:1, 0.5:1, 0.8:1 Very
Large Printed Posters 48 inches >120 inches 0.1:1, 0.2:1, 0.3:1
Billboards 96 inches >576 inches 0.1:1, 0.25:1, 0.4:1 Large
Dynamic and Static Displays 96 inches >100 inches 0.15:1, 0.2:1,
0.3:1
[0049] There is a practical limit to how great the lenticular
aspect ratio can be in autostereoscopic displays. FIG. 10 is
illustrative.
[0050] Given a lenticle 1002 having a focal length 1004 (f) and a
width 1006 (S), the width 1010 of a viewing "sweet spot" at viewing
distance 1008 is given by the following equation:
W = SD f ( 12 ) ##EQU00010##
[0051] In equation (12), W is width 1010 of the viewing sweet spot,
and D is viewing distance 1008. The sweet spot is defined as a
position in which both eyes of viewer 10 see a view corresponding
to the same lenticle, e.g., lenticle 1002. If width 1010 is not at
least the intraocular distance 1012 of viewer 10, viewer 10 will
not be able to see both left and right views through the same
lenticle and the autostereoscopic image will not be clearly
visible. In addition, the amount by which viewer 10 can move his
head side-to-side and still see the autostereographic image
properly is given by the following equation:
W ss = SD f - E ( 13 ) ##EQU00011##
[0052] In equation (13), W.sub.SS is the amount by which viewer 10
can move his head side-to-side and still see the autostereographic
image properly, and E is the intraocular distance 1012 of viewer
10. A typical intraocular distance for adult viewers is about 2.4
inches. Herein, the amount by which viewer 10 can move his head
side-to-side and still see the autostereographic image properly is
sometimes referred to as a practical viewing sweet spot.
[0053] The practical viewing sweet spots W.sub.SS for the various
types of displays in Table A above at various viewing distances are
shown in Table C below.
TABLE-US-00003 TABLE C Display Type f S ##EQU00012## D W.sub.ss
Bookmark, Business card, Postcard, 2.5 2' 7.2'' Smart Phone,
Digital Picture Frame, 3.33 2' 4.8'' Tablet Computer 4 2' 3.6'' 5
2' 2.4'' 6.6 2' 1.24'' 46'' HDTV/UDTV, 85'' HDTV/UDTV, 4 8' 21.6''
Display Wall of 40'' HDTVs tiled 4 .times. 4, 5 8' 16.8'' 20''
WQXGA Monitor, Single- 6.6 8' 12.15'' Sheet Poster, 10' .times. 5'
Static Sign, 9.6 8' 7.6'' Digital Picture Frame, Tablet Computer
46'' HDTV/UDTV, 85'' HDTV/UDTV, 2.16 20' 108.6'' Display Wall of
40'' HDTVs 5 20' 45.6'' tiled 4 .times. 4, 20'' WQXGA Monitor,
Single- 10 20' 21.6'' Sheet Poster, 10' .times. 5' Static Sign 12
20' 17.6'' 10' .times. 5' Static Sign, 48' .times. 14' Billboard
3.33 100' 357.6'' 10 100' 117.6'' 12.5 100' 93.6'' 17 100' 68.19''
25 100' 45.6''
[0054] As can be seen in Table B, hand-held devices that are
typically viewed from about two (2) feet away have lenticular
aspect ratios of about 2.5 to 6.6 and corresponding practical
viewing sweet spots of about 7.2 down to 1.24 inches. Hand-held
displays can be easily tilted by viewer 10 to find the practical
sweet spot, so a practical sweet spot of only 1.24 inches isn't
particularly worrisome for a hand-held display. Generally, the
largest hand-held device display measures about 17 inches
diagonally. Thus, as long as the lenticular aspect ratio of such a
display is below 7, viewer 10 should be able to properly perceive
the autostereoscopic display.
[0055] Larger displays, such as televisions and posters and
sometimes digital picture frames and tablet computers (when used as
a digital picture frame), are more typically viewed from up to
about eight (8) feet away. These types of display have lenticular
aspect ratios of about 4 to 9.6 and corresponding practical viewing
sweet spots of about 21.6 down to 7.6 inches, providing ample room
for viewer 10 to move his head to view the autostereoscopic display
properly.
[0056] While a practical viewing sweet spot of only 7.6 inches may
sound like at most a single viewer can see the autostereoscopic
display properly or perhaps two viewers with their heads pressed
uncomfortably close together, it should be appreciated that there
are many 7.6-inch-wide practical viewing sweet spots. In
particular, the viewing sweet spot (10 inches in this example),
repeat contiguously through the range of visibility of an
autostereoscopic display. Only when the eyes of viewer 10 straddle
a boundary between adjacent viewing sweet spots that the eyes see
views behind two distinct lenticles and the autostereoscopic view
is improper. In such a situation, viewer 10 needs only to move his
head up to 1.2 inches in either direction to position both eyes in
a single viewing sweet spot. Within that viewing sweet spot, viewer
10 can move his head within a space that is 7.6 inches wide.
[0057] Televisions and other large displays are commonly viewed
from up to about twenty (20) feet away, ie., from across a large
room. These types of display have lenticular aspect ratios of about
2.16 to 12 and corresponding practical viewing sweet spots of about
108.6 down to 17.6 inches, providing ample room for viewer 10 to
move his head to view the autostereoscopic display properly.
[0058] As viewing distances become large, width of the practical
viewing sweet spot becomes much less of a limitation. In very large
displays, such as billboards and large posters, it is common for
the display to be viewed from 100 feet away. These types of display
have lenticular aspect ratios of about 3.33 to 25 and corresponding
practical viewing sweet spots of about 357.6 down to 45.6
inches--roughly 30 down to four (4) feet, providing ample room for
viewer 10 to move his head to view the autostereoscopic display
properly.
[0059] One of the challenges in making a lenticular array with such
a long focal length is that optical aberrations become significant
and detrimental to the viewer's three-dimensional viewing
experience. One such aberration is illustrated in FIG. 4 and is
generally known as curvature of field. Lenticles of conventional
lenticular arrays focus along a curved field of view 404. However,
at such small focal lengths used in conventional lenticular lenses
render this aberration hardly noticeable to viewers at most angles
of view. Simply modifying conventional lenticular arrays to have
ten (10) times the focal length as described above would render
this aberration very noticeable at most angles of view. Lenticular
array 100 is designed to provide a much more flat field of view
than conventional lenticular arrays. Such flattening is analogous
to flattening that is accomplished in spherical lenses by applying
the "Petzval condition", a known equation that is typically applied
to spherical lenses rather than the cylindrical, lenticular lenses
described here.
[0060] FIG. 5 shows a single lenticle 500 of lenticular array 100
(FIG. 1) in cross section. Lenticle 500 (FIG. 5) includes a
meniscus-cylinder lens 502. As used herein, a "cylinder" is not
limited to cylinders with circular cross-sections.
Meniscus-cylinder lens 502 includes a proximal surface 502P and a
distal surface 502D, a width 508, and a thickness 514. Proximal
surface 502P is convex, and distal surface 502D is concave. In this
illustrative embodiment, width 508 and thickness 514 are one (1)
millimeter (mm) each. In one embodiment, the radius of curvatures
of proximal surface 502P and distal surface 502D are 1.29 mm. In
addition, meniscus-cylinder lens 502 is separated from display 110
by a transparent layer 506 of glass or plastic whose thickness 510
is 9 mm.
[0061] In an alternative embodiment, transparent layer 506 is
ordinary air, nitrogen, or some other gas. FIG. 8 shows a
lenticular array 800 in which transparent layer 806 is air. To
prevent moisture or anything that might fog or otherwise reduce
transparency of transparent layer 806, transparent layer 806 is
sealed from ambient air. To prevent warping of lenticular array 800
by changes in ambient air pressure, transparent layer 806 is
connected to a bladder 804 such that air of transparent layer 806
can freely move into and out of bladder 804. As a result, air
pressure within transparent layer 806 is therefore in equilibrium
with air pressure outside of transparent layer 806, avoiding any
warping of lenticular array 800. Bladder 804 is shown significantly
enlarged for illustration purposes. In general, bladder 804 should
be designed to be as small and unobtrusive as possible while still
accepting and releasing an amount of air to accommodate the
greatest and least expected ambient air pressures without
appreciably affecting the air pressure or restricting air flow.
[0062] One of the advantages of a transparent layer of air between
a lenticular array and a multi-view display such as display 110 is
that convex surfaces of the lenticular array can be positioned
toward display 110 as shown in FIG. 9. Such allows a flat surface
of lenticular array 900 to be easily cleaned while the convex
surfaces of lenticles of lenticular array 900 simply fit into the
air space of a transparent layer 906.
[0063] Returning to FIG. 5, a meniscus-cylinder lens dramatically
flattens the field of view of lenticle 500 having such a long focal
length, ten (10) times thickness 514 in this illustrative
embodiment.
[0064] Other designs of lenticle 500 also reduce other aberrations,
such as coma and circular aberration. Coma is well-known and is not
described further herein. Lenticles which have a
circular-cylindrical proximal surfaces have aberrations (sometimes
referred to herein as "circular aberrations") that are
two-dimensional analogs to spherical aberrations, which are also
well-known and are not described further herein.
[0065] One embodiment that further flattens the field of view from
even more extreme angles and reduces other aberrations has a radius
of curvature of 1.894 mm on proximal surface 502P and a radius of
curvature of 2.131 mm on distal surface 502D. In addition, proximal
surface 502P and distal surface 502D can reduce circular
aberrations by being made non-circular, e.g., parabolic, in
cross-section.
[0066] An alternative embodiment of lenticle 500 is shown in
cross-section as lenticle 600 (FIG. 6). In addition to a
meniscus-cylinder lens 602 having a proximal surface 602P with a
radius of curvature of 1.894 mm and a distal surface 602D with a
radius of curvature of 2.131 mm and a thickness 614 of 0.5 mm. In
addition, lenticle 600 includes a plano-convex lens 604 with a
proximal surface 604P having a radius of curvature of 9.302 mm.
Lenticle 600 includes the same transparent layer as does lenticle
500 (FIG. 5).
[0067] Another alternative to lenticles 500 and 600 is lenticle 700
(FIG. 7). Lenticle 700 includes a proximal meniscus-cylinder lens
702 and a distal meniscus-cylinder lens 704. Proximal
meniscus-cylinder lens 702 is directly analogous to
meniscus-cylinder lens 502 (FIG. 5). Distal meniscus-cylinder lens
704 is reversed, having a proximal surface 704P that is concave and
a distal surface that is convex. In this illustrative embodiment,
distal meniscus-cylinder lens 704 is of the same dimensions as
proximal meniscus-cylinder lens 702, aside from having convex and
concave surfaces reversed.
[0068] In some embodiments, optical aberrations resulting from
lenticles with unusually long focal lengths are reduced in a manner
described in U.S. patent application Ser. No. 12/969,552 filed Dec.
15, 2010 by Dr. Richard A. Muller for "Improved Resolution For
Autostereoscopic Video Displays" at FIGS. 5-7 and accompanying text
in the Application. That description is incorporated herein by
reference.
[0069] The above description is illustrative only and is not
limiting. The present invention is defined solely by the claims
which follow and their full range of equivalents. It is intended
that the following appended claims be interpreted as including all
such alterations, modifications, permutations, and substitute
equivalents as fall within the true spirit and scope of the present
invention.
* * * * *