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Description  |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a display in which small diffraction
gratings are arranged in units of dots on a surface of a flat substrate
and, more particularly, to an inexpensive display having diffraction
grating patterns which can be easily manufactured and can express a
stereoscopic (three-dimensional) image having no image omissions.
2. Description of the Related Art
A display having a diffraction grating pattern by arranging a plurality of
small dots each consisting of a diffraction grating on a surface of a flat
substrate has been frequently used. A method disclosed in, e.g., Published
Unexamined Japanese Patent Application No. 60-156004 is used as a method
of manufacturing a display having a diffraction grating pattern of this
type. According to this method, small interference fringes (to be referred
to as diffraction gratings hereinafter) obtained by two-beam interference
are changed in pitch, direction, and light intensity, and the resultant
images are sequentially exposed on a photosensitive film.
In recent years, the present inventor has proposed a method of
manufacturing a display having a diffraction grating pattern of a given
graphic image in such a manner that an X-Y stage on which a flat substrate
is placed is moved under the control of a computer using, e.g., an
electron beam exposure apparatus, and a plurality of small dots consisting
of diffraction gratings are arranged on the surface of the flat substrate.
This method is disclosed in U.S. Pat. No. 5,058,992.
In a display manufactured by this method, however, an image input from an
image scanner or the like or a two-dimensional image formed by computer
graphics is used as an image for the display having the diffraction
grating patterns. For this reason, a graphic image expressed by the
diffraction grating pattern are located on the surface of the flat
substrate on which the diffraction gratings are arranged, so that only a
flat (two-dimensional) graphic image can be expressed. As a result, a
stereoscopic (three-dimensional) image cannot be expressed, resulting in
inconvenience.
SUMMARY OF THE INVENTION
It is the first object of the present invention to provide a display having
diffraction grating patterns capable of expressing a stereoscopic
(three-dimensional) image without any image omissions.
It is the second object of the present invention to provide an inexpensive
display having diffraction grating patterns which can be easily
manufactured.
In order to achieve the above objects of the present invention, there is
provided a display having a diffraction grating pattern, comprising:
(a) a flat substrate; and
(b) at least one dot formed on a surface of the flat substrate, the dot
being formed by a diffraction grating pattern as an aggregate of a
plurality of curves obtained by translating a curve.
In particular, the dot is constituted by an aggregate of a plurality of
curves obtained by translating a curve at a predetermined pitch.
Changes in gradient .OMEGA. where .OMEGA. changes from .OMEGA..sub.1 to
.OMEGA..sub.2 when a pitch d is used are preferably defined as follows:
tan(.OMEGA..sub.1)=sin(.alpha..sub.1)/sin(.theta.)
tan(.OMEGA..sub.2)=sin(.alpha..sub.2)/sin(.theta.)
d=.lambda./sin(.theta.)
where .theta. is the incident angle of illumination light, .alpha..sub.1
and .alpha..sub.2 are angles (directions of first-order diffracted light)
from which the diffraction gratings are observed, and .lambda. is the
wavelength of the first-order diffracted light.
The dot is constituted by an aggregate of a plurality of curves obtained by
translating a curve upon arbitrary changes in pitch of the curves.
If wavelengths of diffracted light components are defined as
.lambda..sub.1, .lambda..sub.2, . . . , .lambda..sub.m, . . . ,
.lambda..sub.n, and intensities of the light components at the respective
wavelengths are defined as A.sub.1, A.sub.2, . . . , A.sub.m, . . . ,
A.sub.n, spatial frequencies (reciprocals of the pitches) of the
diffraction gratings required to diffract the light components having the
respective wavelengths are defined as follows:
f.sub.1 =sin(.theta.)/.lambda..sub.1
f.sub.2 =sin(.theta.)/.lambda..sub.2
f.sub.m =sin(.theta.)/.lambda..sub.m
f.sub.n =sin(.theta.)/.lambda..sub.n
A delta function is defined as .delta.(x), a spatial frequency distribution
of F(fx) represented by the following equation is given to the diffraction
gratings, and a function obtained by transforming F(fx) in accordance with
an inverse Fourier transform is defined as f(x), and the curve is
translated to have an f(x) distribution in the translation direction:
##EQU1##
On the other hand, the dot has a region in which no diffraction grating is
present. This region in which no diffraction grating is present is divided
by parallel curves in the translation direction of the curve.
In a display having diffraction grating patterns according to the present
invention, when the display is observed, a flat image to be displayed upon
observation from the right direction can be observed from the right
direction. A flat image to be displayed upon observation from the front
can be observed from the front direction, and a flat image to be displayed
upon observation from the left direction is observed from the left
direction. For this reason, an observer can observe images having
parallaxes in the left, front, and right directions, thereby observing a
stereoscopic (three-dimensional) image.
Since diffraction gratings are formed in the form of dots, no diffraction
grating is formed at a position where no data is present. For this reason,
unnecessary diffraction gratings need not be formed, and noise can be much
reduced as compared with a hologram.
In addition, an ideal diffraction grating can be digitally formed, so that
a bright image can be reproduced as compared with a conventional hologram.
Since the diffraction gratings are constituted by an aggregate of curves
obtained by translating a curve with arbitrary changes in pitch of
diffracted light components in units of dots, colors of the diffracted
light components in units of dots are not limited to colors of single
wavelengths but can be set to be arbitrary colors. For this reason, the
observer can observe a more natural stereoscopic image.
In order to achieve the above objects of the present invention, there is
also provided a display having a diffraction grating pattern having
another arrangement. That is, there is provided a display having a
diffraction grating pattern, comprising:
(a) a flat substrate;
(b) at least one dot formed on a surface of the flat substrate, the dot
being formed by a diffraction grating pattern as an aggregate of a
plurality of curves obtained by translating a curve; and
(c) light-shielding means having a predetermined shape and arranged on an
illumination light incident side of the diffraction gratings, or
light-shielding means having a predetermined pattern and arranged on a
diffracted light emerging side of the diffraction gratings.
The light-shielding means is formed by a printing ink or by using a spatial
modulation element.
In the display having the diffraction pattern having the above arrangement
according to the present invention, since the light-shielding means is
arranged on the illumination light incident side of the diffraction
gratings, a portion irradiated with the illumination light and a portion
not irradiated with the illumination light are formed on the display.
Alternatively, a portion through which diffracted light is transmitted and
a portion through which diffracted light is not transmitted are formed on
the display on the diffracted light emerging side of the diffraction
gratings. Therefore, when the observer observes the display, he observes
images having parallaxes in the left, front, and right directions, thereby
observing a stereoscopic (three-dimensional) image.
Even if the number of types of diffraction gratings is one, the shielding
means is interchanged with one another to change the shape, thereby freely
expressing the shapes of the stereoscopic (three-dimensional) images.
In addition, even if a graphic image is changed, the diffraction grating is
constant independently of the graphic image. The diffraction grating need
not be formed by an electron beam drawing apparatus every time the shape
of the graphic image is changed. For this reason, efficiency can be
greatly improved in terms of time and cost.
Additional objects and advantages of the invention will be set forth in the
description which follows, and in part will be obvious from the
description, or may be learned by practice of the invention. The objects
and advantages of the invention may be realized and obtained by means of
the instrumentalities and combinations particularly pointed out in the
appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part
of the specification, illustrate presently preferred embodiments of the
invention, and together with the general description given above and the
detailed description of the preferred embodiments given below, serve to
explain the principles of the invention.
FIG. 1 is a view for explaining a method of photographing an original image
according to the present invention;
FIG. 2 is a view for explaining a method of observing a dot formed
according to the present invention;
FIG. 3 is an enlarged view of the dot according to the present invention;
FIG. 4 is an enlarged view of a basic dot of a diffraction grating image
according to the present invention;
FIG. 5 is a view for explaining a method of dividing one dot according to
the present invention;
FIG. 6 is a view for explaining a method of manufacturing a display
according to the first embodiment of the present invention;
FIG. 7 is a view for explaining a method of observing the display formed in
the first embodiment of the present invention;
FIG. 8 is a schematic view of an electron beam exposure apparatus used in
the manufacture of the display having a diffraction grating pattern
according to the first embodiment of the present invention;
FIG. 9 is a view showing an EB resist dry plate placed on an X-Y stage;
FIG. 10 is a flow chart for explaining a method of manufacturing the
display according to the first embodiment of the present invention;
FIG. 11 is a view for explaining a method of manufacturing a display
according to the second embodiment of the present invention;
FIG. 12 is a schematic view showing an arrangement of the display according
to the second embodiment of the present invention;
FIG. 13 is a schematic view showing another arrangement of the display
according to the second embodiment of the present invention;
FIG. 14 is a schematic view showing sill another arrangement of the display
according to the second embodiment of the present invention;
FIG. 15 is a schematic view showing a detailed arrangement of the display
according to the second embodiment of the present invention; and
FIG. 16 is a schematic view showing another detailed arrangement of the
display according to the second embodiment of the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
A display having diffraction grating patterns according to the present
invention will be described with reference to FIGS. 1 to 10. The display
is formed by using an electron beam in this embodiment.
A method of inputting a plurality of flat images will be described with
reference to FIG. 1. A flat image 80 of an object 85 to be
stereoscopically displayed is photographed using a television camera 81.
One television camera 81 is located at each of a plurality of positions
defined at an interval p and photographs the plurality of flat images 80
of the object 85 at the respective positions. These data of the flat
images 85 are input to a computer 82 through a digitizer 83 and are stored
as image data. In order to input the data of the flat images 85 to the
computer 82, data recorded on a video tape may be used, or data of a
photograph or movie may be used. The object 85 to be stereoscopically
displayed is not limited to an existing object, but may be a computer
graphic object.
A method of determining a direction .OMEGA. and a pitch d of a diffraction
grating will be described with reference to FIGS. 2 and 3.
As shown in FIG. 2, assume that an observer observes a display 15 having a
dot 16. As shown in FIG. 2, an incident angle of illumination light 91 is
defined as .theta., a direction of first-order diffracted light 92
diffracted by a diffraction grating 18 is defined as .alpha., and a
wavelength of the first-order diffracted light 92 is defined as .lambda..
As shown in FIG. 3, the direction .OMEGA. and the pitch d (i.e., a
reciprocal of a spatial frequency) of the diffraction grating 18 can be
obtained by the following equations. Note that the illumination light 91
passes through the Y-Z plane, and diffracted light passes through the X-Z
plane:
tan(.OMEGA.)=sin(.alpha.)/sin(.theta.)
d=.lambda./{sin.sup.2 (.theta.)+sin.sup.2 (.alpha.)}.sup.1/2
By using the above equations, the direction .OMEGA. and the pitch d of the
diffraction grating can be obtained to diffract the illumination light 91
in an arbitrary direction. That is, by giving the incident angle .theta.
of the illumination light 91, the direction .alpha. of the first-order
diffracted light 92, and the wavelength .lambda. of the first-order
diffracted light 92, the direction .OMEGA. and the pitch d of the
diffraction grating 18 can be obtained.
A pitch d' of a diffraction grating for diffracting incident light to the
front direction (.alpha.=0) is obtained as follows:
d'=.lambda./sin(.theta.)
therefore,
##EQU2##
As shown in FIG. 4, in an arrangement in which a curve is translated at a
predetermined pitch, the above equation is always satisfied. For this
reason, the diffraction grating is so constructed that the observer can
always observe the diffracted light having a wavelength of the same color
even if viewpoints are moved in the horizontal direction. In the dot shown
in FIG. 4, the gradients of the curves constituting the dot are changed
from .OMEGA..sub.1 to .OMEGA..sub.2, and the resultant curves are aligned
at the pitch d'. That is, in order to obtain a grating dot such that the
diffraction range in the horizontal direction covers a region ranging from
an angle .alpha..sub.1 to .alpha..sub.2 with respect to the normal to the
surface on which the grating is present, the following equations are
established:
tan(.OMEGA..sub.1)=sin(.alpha..sub.1)/sin(.theta.)
tan(.OMEGA..sub.2)=sin(.alpha..sub.2)/sin(.theta.)
d=.lambda./sin(.theta.)
Therefore, a grating obtained by translating a curve having a gradient
.OMEGA. which changes from .OMEGA..sub.1 to .OMEGA..sub.2 when the pitch
d' is used.
A basic dot of the diffraction image according to the present invention has
an arrangement shown in FIG. 4.
This dot is divided into three regions in the vertical direction, as shown
in FIG. 5. These three regions are defined as r.sub.1, r.sub.2, and
r.sub.3 from the left. Light incident on the region r.sub.1 is diffracted
in the left direction, light incident on the region r.sub.2 is diffracted
in the front direction, and light incident on the region r.sub.3 is
diffracted in the right direction.
In order to observe this dot from only the left direction, a diffraction
grating portion for only the region r.sub.1 is drawn, and no patterns are
drawn for the regions r.sub.2 and r.sub.3. In this case, the observer can
observe this dot bright only when the viewpoint falls within a range
e.sub.1. In the arrangement of FIG. 5, the dot of the diffraction grating
is vertically divided into the three regions but can be divided into four
or more regions. That is, the dot of the diffraction grating is divided by
the number corresponding to the number of desired input parallax images.
For the sake of descriptive convenience, assume that three parallax images
of a given object are photographed. Assume that the object image is
observed to be "T" from the left direction, that the object image is
observed to be "O" from the front direction, and that the object image is
observed to be "P" from the right direction (although such an object does
not actually exist). Since the number of parallax images is three, the dot
is vertically divided into three regions. As shown in FIG. 6, a
diffraction grating pattern of a diffraction pattern image is obtained by
drawing a diffraction grating corresponding to the left dot portion
representing "T", a diffraction grating corresponding to the central dot
portion representing "O", and a diffraction grating corresponding to the
right dot portion representing to "P".
The diffraction grating image thus obtained is reconstructed, as shown in
FIG. 7. "T" can be observed from the left direction, "O" can be observed
from the front direction, and "P" can be observed from the right
direction. In this case, the number of input images is three. However,
four or more parallax images are used to reconstruct different images
observed with the right and left eyes of the observer. That is, the
observer observes images having parallaxes at the right and left eyes and
thus can observe a stereoscopic (three-dimensional) image. When the
observation position of the observer is moved in the horizontal direction,
a parallax image observed from another direction can be obtained.
Therefore, a natural stereoscopic image can be obtained.
Drawing of a diffraction grating by an electron beam exposure apparatus
will be described with reference to FIGS. 8 and 9.
As shown in FIG. 8, the electron beam exposure apparatus comprises an
electron gun 50, alignment elements 52, a blanker 54, condenser lenses 56,
a stigmeter 58, a deflector 60, an objective lens 62, and an X-Y stage 20.
A dry plate 14 coated with an EB resist is placed on the X-Y stage 2. The
blanker 54, the deflector 60, and the X-Y stage 20 are connected to a
computer 66 through a control interface 64. An electron beam emitted from
the electron gun 50 is controlled by the computer 66 and scans the dry
plate 14.
FIG. 9 shows the dry plate 14 placed on the X-Y stage 20. An electron beam
70 emitted from the electron gun 50 draws a diffraction grating pattern 18
in units of dots 16. When the X-Y stage 20 is moved, the diffraction
grating patterns 18 are sequentially drawn in the dots 18, respectively.
An operation for forming a diffraction grating pattern for actually
displaying a three-dimensional image from a plurality of original images
having parallaxes with reference to FIG. 10.
In step a1, various parameters for drawing a diffraction grating pattern
are input. In steps a2 and a3, calculations are performed to obtain other
parameters on the basis of the input parameters. The number of original
images is defined as L, the number of drawing areas in the X direction is
defined as n, the number of drawing areas in the Y direction is defined as
m, the number of dots within one drawing area in the X direction is
defined as 0, and the number of dots within one drawing area in the Y
direction is defined as P. The drawing areas must be assigned to draw a
graphic image having a size larger than an electron beam drawing area used
for the electron beam exposure apparatus because this electron beam
drawing area is a square area having a side of several mm. This electron
beam drawing area is called the drawing area.
In step a4, one-dot data is generated. The one-dot data is basically
pattern data shown in FIG. 4. This data is vertically divided into
portions having the number corresponding to the number of original images,
and the divided data are stored.
A diffraction grating pattern is generated for each drawing area. Data
corresponding to the drawing area of the original image is checked in
units of dots. If data is present in each dot, an original image portion
(one of the divided dot portions) of the calculated one-dot data is copied
to a position of the corresponding dot within the data area (i.e., an
array space representing the diffraction grating patterns). This operation
is repeated for all the drawing areas, all the original images, and all
dots, thereby obtaining diffraction grating patterns. The obtained
diffraction grating patterns are saved in units of drawing areas.
A dry plate having the diffraction grating patterns thus formed is used as
an original plate for copy. A well-known emboss method is used to copy the
diffraction grating patterns on the original plate
In the above diffraction grating patterns, the diffraction grating is
constituted by an aggregate of a plurality of curves obtained by
translating a curve at arbitrary pitches, so that diffracted light can
have a plurality of wavelengths. For this reason, the color of diffracted
light observed by the observer can be arbitrarily determined.
For example, wavelengths and their intensities of diffracted light
components observed by the observer are respectively defined as
.lambda..sub.1, .lambda..sub.2, . . . , .lambda..sub.m, . . . ,
.lambda..sub.n, and A.sub.1, A.sub.2, . . . , A.sub.m, . . . , A.sub.n. At
this time, spatial frequencies (reciprocals of the pitches) f.sub.1,
f.sub.2, . . . , f.sub.m, . . . , f.sub.n required for diffracting light
components having the respective wavelengths are defined as follows:
f.sub.1 =sin(.theta.)/.lambda..sub.1
f.sub.2 =sin(.theta.)/.lambda..sub.2
f.sub.m =sin(.theta.)/.lambda..sub.m
f.sub.n =sin(.theta.)/.lambda..sub.n
A delta function is defined as .delta.(x), a spatial frequency distribution
of F(fx) represented by the following equation is given to the diffraction
gratings, and a function obtained by transforming F(fx) in accordance with
an inverse Fourier transform is defined as f(x), and the curve is
translated to have an f(x) distribution in the translation direction:
##EQU3##
As described above, when the moving direction of the curves constituting
the diffracted light components is changed, the colors of the diffracted
light components in units of dots are not limited to colors having single
wavelengths, but can be arbitrary colors. Therefore, the observer can
observe a stereoscopic image more naturally.
The second embodiment of the present invention will be described with
reference to FIGS. 11 to 16.
In this embodiment, as shown in FIG. 4, one basic dot of the diffraction
grating image is constituted by an aggregate of a plurality of curves
obtained by translating a curve, and a light-shielding means having a
shape shown in FIG. 11 is arranged in front of or behind the diffraction
grating constituting this dot. The illumination or diffracted light is
shielded by this light-shielding means. A portion irradiated with the
illumination light and a portion not irradiated with the illumination
light are formed on the display. Alternatively, a portion through which
the diffracted light is transmitted and a portion through which the
diffracted light is not transmitted are formed on the display.
A detailed arrangement of the display having diffraction grating patterns
according to this embodiment will be described below.
Light shielded by the light-shielding means may be illumination or
diffracted light. More specifically, as shown in FIG. 12, a
light-shielding means 102 is arranged on the diffracted light emerging
side of a transparent diffraction grating 100. Alternatively, a
light-shielding means 102 is arranged on the illumination light incident
side of the transparent diffraction grating 100, as shown in FIG. 13, or a
light-shielding means 102 is arranged on the diffracted light emerging
side, i.e., the illumination light incident side of a reflection
diffraction grating 104.
In this case, as shown in FIG. 15, the light-shielding means can be printed
using a printing ink 106 on the diffraction grating to provide a
light-shielding effect, thereby further simplifying the manufacturing
process and hence obtaining a three-dimensional image. Alternatively,
graphic images may overlap each other by printing, so that an effect for
overlapping a stereoscopic image and a flat image by printing can be
obtained.
As shown in FIG. 16, the light-shielding means may be constituted by a
spatial modulation element (e.g., a liquid crystal display panel) 108, so
that the shape of the spatial modulation element 108 can be changed by a
liquid crystal drive unit 110 within a short period of time, thereby
obtaining a three-dimensional dynamic image.
Additional advantages and modifications will readily occur to those skilled
in the art. Therefore, the invention in its broader aspects is not limited
to the specific details, and representative devices, shown and described
herein. Accordingly, various modifications may be made without departing
from the spirit or scope of the general inventive concept as defined by
the appended claims and their equivalents.
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