JPH11109119A - Diffraction grating display - Google Patents

Abstract

PROBLEM TO BE SOLVED: To avoid the crosstalk between cells, and to stably and visually sensed a display by changing the ratio of the grating width to the grating period at each position in a diffraction grating cell so as to realize the intensity distribution in which the primary diffracted light from a cell comprising a binary diffraction grating becomes weaker from a center part of the cell to the peripheral part in one direction of a cell surface. SOLUTION: The intensity of the outgoing light in a main lobe is uniformized, while the intensity of the noise light outside the main lobe is reduced by changing 'the ratio of the grating width to the grating period' of a diffraction grating in a diffraction grating cell which is a pixel from a center part to a peripheral part at least in one direction. When the amplitude distribution of the primary diffracted light immediately behind the cell is changed by the ratio modulation of the diffraction grating in the cell, the intensity at the peripheral part can be reduced even when the primary diffracted light immediately behind the cell has the phase distribution of spherical wave shape. In such a cell, the intensity distribution of the primary diffracted light tends to be uniformized.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a display having pixels (cells) as constituent units. In particular, the diffraction grating serving as a pixel (cell) is a binary diffraction grating (a diffraction grating expressed by the binary value of the amplitude or phase of the diffracted light).
The present invention relates to a diffraction grating display having a diffraction grating cell in which the “ratio of the grating width to the grating period” at each position in the diffraction grating changes from the center to the periphery in at least one direction of the diffraction grating surface.

[0002]

2. Description of the Related Art There are various types of displays constituted by a group of cells which are pixels. Of these, a cell is formed of a diffraction grating, and as a display of a type that displays an image using diffracted light (particularly, first-order diffracted light) from the diffraction grating cell, Japanese Patent Laid-Open Publication No.
No. 320 is known.

In a conventional diffraction grating display, a simple diffraction grating whose "ratio of grating width to grating period" does not change in the cell as shown in FIG. 1 is used as a cell. The intensity distribution of the first-order diffracted light is
In the cell plane, it is represented by a rectangle function graph shown in FIG.

That is, the intensity distribution of the first-order diffracted light is constant in the cell plane within the cell range (the intensity distribution does not change depending on the position of the cell), and the intensity distribution of the first-order diffracted light is It is represented by a rectangular function as shown in FIG.

The above-described intensity distribution is a description that is applied within the range of the cell on the cell surface (from -d to + d in FIG. 2). Depending on the relationship between the display observation distance and the cell size, the following is given. The situation will change.

[0006] Fresnel number (N) defined as:
The observation state under the condition of N << 1 corresponds to the Fraunhofer region. The observation state under other conditions corresponds to the Fresnel region. “N << 1” means “N is much smaller than 1”. Generally, a difference of several times or more is sufficient. In any region, the intensity distribution of the first-order diffracted light from a simple diffraction grating cell (in which the distribution of the phase modulation amount does not change) is uniquely determined with respect to the Fresnel number.

[0007]

(Equation 1)

In the above equation, when the light emitted from the cell has the phase of a spherical wave, it is necessary to consider the distance between the convergence point and the divergence point of the spherical wave in the value of the observation distance.

When the observation state corresponds to the Fraunhofer region (generally, when the size of the cell is small), the first-order diffracted light spreads due to the effect of diffraction at the cell. In other words, the light intensity distribution in each cell is accompanied by a noise component in the peripheral portion, resulting in crosstalk between cells.

[0010] Even when the observation state corresponds to the Fresnel region, similarly to the above, the first-order diffracted light from the cell is accompanied by noise components in each peripheral portion, and the light intensity changes drastically in each central portion.

In the cell, "ratio of grating width to grating period"
FIG. 3 shows an example of the light intensity distribution (waveform) of the first-order diffracted light that has a noise component in the peripheral portion in the above two types of observation states. In the drawing, the left-hand diagram conceptually shows a state in which light is incident on the diffraction grating cell and the first-order diffracted light is emitted, and the right-hand diagram (three types vertically) shows the light intensity distribution of the first-order diffracted light ( Waveforms). The prior art with a noise component at the periphery is shown by the middle waveform.

When the size of the cell is large to some extent, the range in which an image displayed by the first-order diffracted light can be observed is extremely limited. At this time, if the first-order diffracted light emitted from the display has scattering properties, observation can be performed from a wide range, but it is difficult to freely set the viewing zone.

In the existing display as shown in FIG. 4, the illumination light to be incident on the cell is the illumination light from the backlight from the side opposite to the observer via the display. As a result, a phenomenon in which the first-order diffracted light spreads may be observed, but no proposal has been made so far that the light emitted intentionally is made to be divergent light.

The present invention is not limited to the above-described embodiment in which the illumination light is incident from the side opposite to the observer via the diffraction grating cell, and the display light (first-order diffracted light) is transmitted and diffracted toward the observer and emitted. ,
The present invention also includes a mode in which the illumination light enters the diffraction grating cell from the observer side, and is reflected and diffracted toward the observer side and emitted.

As described above, when the display is observed due to the non-uniformity of the first-order diffracted light from the conventional cell, the brightness of the display changes depending on the viewpoint position of the observer, or bright and dark stripes appear on the display surface. Is observed.

On a display using pixels as described above with a simple diffraction grating cell as a pixel, different two-dimensional images having parallax according to the viewing direction are visually recognized, so that a three-dimensional image is displayed. Was proposed by the present applicant in Japanese Patent Application Laid-Open Nos. Hei 3-206401 and Hei 4-
Although it is reported in, for example, Japanese Patent No. 31916, a proposal for solving “crosstalk between cells” due to the fact that the first-order diffracted light has a noise component in each peripheral portion has not been reported so far. .

In the above-described display (see FIG. 4), the pupil is positioned in the main lobe from the corresponding cell (the pupil is located in the area where the first-order diffracted light from the specific cell reaches). , The first-order diffracted light in a state where the cell is viewed) cannot be clearly seen due to crosstalk. In addition, the pixels due to the first-order diffracted light from the adjacent cells are mixed and viewed, which is a fatal problem in displaying a three-dimensional image.

[0018]

According to the present invention, the first-order diffracted light from the cell is not accompanied by a noise component in each peripheral portion, and the observation state corresponds to either the Fraunhofer region or the Fresnel region. Also avoids cross-talk between cells and stabilizes the display (so that the brightness does not change depending on the viewpoint position, so that bright and dark stripes are not observed)
Its main purpose is to make it visible.

[0019]

According to the present invention, a diffraction grating (binary diffraction grating) serving as a pixel constituting a display is provided.
At each position in the diffraction grating cell so that the first-order diffracted light from the cell having the intensity distribution in at least one direction of the cell surface decreases from the center of the cell toward the periphery. The ratio of the grating width to the period (hereinafter, referred to as the ratio) is changed.

According to a second aspect of the present invention, the ratio at each position in the diffraction grating cell changes from the center to the periphery in one direction of the diffraction grating surface, and in a direction orthogonal thereto, It is characterized by being constant from the center to the periphery.

The direction in which the ratio changes at each position in the diffraction grating cell can be horizontal (or vertical) to the observer, depending on the display to be made.

According to a fifth aspect of the present invention, the ratio at each position in the diffraction grating cell is in the direction of the diffraction grating surface changing from the center to the periphery, and the ratio is from the center to the periphery. It is characterized by a gradual decrease toward it.

According to a sixth aspect of the present invention, the ratio at each position in the diffraction grating cell is in the direction of the diffraction grating surface changing from the central portion to the peripheral portion, and the ratio is constant near the central portion. And decreases from a position away from the center toward the periphery.

The invention of claim 7 is characterized in that the diffraction grating cell emits first-order diffracted light having a spherical wave-like phase distribution. The spherical wave phase distribution is appropriately selected depending on the display to be manufactured, such as a convergent spherical wave or a divergent spherical wave.

In order to provide a three-dimensional display on the display, the invention according to claim 13 is directed to a cell-like diffraction grating which emits a first-order diffracted light having a spherical wave-like phase distribution. Each sub-cell is divided into a plurality of regions according to the number of pixels, and each cell is a sub-cell which is a pixel unit. It changes toward the periphery, and each subcell displays a stereoscopic image by using pixels constituting a plurality of two-dimensional images having parallax.

<Effect> The diffraction efficiency of the first-order diffracted light from the binary diffraction grating depends on the ratio of the grating width to the grating period. In the case where the binary diffraction grating is a “phase diffraction grating”, the length of the optical path length (the length of optically advanced light) from the time when light enters the diffraction grating to the time when the light comes out is divided into a long portion and a short portion. A grating is formed. When the width ratio of each part is 1: 1, that is, when the width of each part is に 対 し て with respect to the grating period, the diffraction efficiency of the first-order diffracted light is increased. Will be the largest.

As the ratio decreases (or increases), the diffraction efficiency of the first-order diffracted light from the diffraction grating decreases. For example, in a surface relief type diffraction grating, the diffraction efficiency of the first-order diffracted light from the diffraction grating changes depending on the width of the valley or the peak of the diffraction grating with respect to the period of the diffraction grating. Considering that the optical path length changes due to the refractive index, the diffraction grating based on the refractive index modulation can be handled in exactly the same way as the surface relief type.

The binary diffraction grating is an "amplitude diffraction grating".
In the case of (1), a grating is formed by a light-shielding portion and a portion that transmits (or reflects) light. Similarly, in this case, when the width ratio of each portion is 1: 1, that is, the grating is formed. When each width is 周期 of the period, the diffraction efficiency of the first-order diffracted light becomes maximum. As the ratio decreases (or increases), the diffraction efficiency of the first-order diffracted light from this diffraction grating decreases.

Therefore, when the ratio is 2: 1 at the center of the diffraction grating cell, the first-order diffracted light is increased whether the ratio decreases or increases from the center to the periphery of the cell. (Ie, the intensity of the first-order diffracted light) decreases from the center to the periphery of the cell. As a result, the first-order diffracted light from the cell is at least 1
It is also possible to control the direction to have an intensity distribution that decreases from the center of the cell toward the periphery. FIG. 9 shows the phase distribution at the center and the periphery of the diffraction grating cell (in the case of a binary phase diffraction grating) according to the present invention. The upper part of the figure is the central part (grating period: lattice width = 2: 1), and the lower part of the figure is the peripheral part (when the ratio deviates from 2: 1).
It is.

From the above, in the direction in which the ratio in the diffraction grating cell decreases so as to decrease from the center to the periphery, the periphery of the first-order diffracted light from each cell (particularly, the cell) (The portion outside the geometrical optical image of the image) can be reduced, and noise light in the peripheral portion that causes crosstalk can be suppressed.

Further, the uniformity of the distribution of the first-order diffracted light in the main lobe (particularly, the portion inside the geometrical image of the cell) is improved. Here, two directions (X direction,
When the ratio is changed with respect to (Y direction), the distribution of the first-order diffracted light can be made uniform in the above two directions. The uniformity in the inside is improved. (Claim 1)

The ratio is changed only in one direction (either the X direction or the Y direction) of the cell surface, and in the direction perpendicular thereto, the ratio is changed in two directions when the ratio is made uniform. As compared with the case, the ratio of the first-order diffracted light emitted from the cell becomes higher and the light use efficiency is increased, so that the brightness of the display is improved. (Claim 2)

In general, the direction of movement of the viewpoint of the observer is mostly horizontal, and if the ratio is changed in this direction (to decrease from the center to the periphery), the observer moves. In contrast, a display with little change in brightness is obtained. (Claim 3)

When the ratio of the diffraction grating is changed so as to decrease from the center to the periphery, the ratio is set to gradually decrease from the center to the periphery (a waveform as shown in FIG. 7). (Claim 5) The cell has a constant maximum value in the vicinity of the center, and becomes lower from a position somewhat away from the center toward the periphery (trapezoidal waveform shown in FIG. 8). Incident light can be highly efficiently contributed as first-order diffracted light, and the brightness of the display is improved. (Claim 6)

By making the first-order diffracted light emitted from the cell have a spherical wave phase distribution, the emitted first-order diffracted light can be expanded to an arbitrary range regardless of the size of the cell. (Claim 7)

When limiting the viewing area (angle range in which a displayed image can be observed) in a specific direction of the display, one (1)
It is effective to impart a spherical wave phase distribution to the second-order diffracted light, but the distribution of the first-order diffracted light within the above range tends to be non-uniform in that direction. However, when the transmittance or the reflectance of each cell is changed in a direction coinciding with the above-mentioned direction, the intensity of the first-order diffracted light in the above-mentioned direction is made uniform, and unnecessary light out of the above-mentioned range is made unnecessary. (Noise light) can be reduced. Even in this case, since the direction of movement of the viewpoint of the observer is often horizontal, the horizontal direction is more effective as the specific direction. (Claim 8)

The phase distribution of the spherical wave shape may be such that the first-order diffracted light from the cell diverges from a specific position. It may be a “divergent spherical wave shape”. (Claims 9 and 10)

When the present invention is applied to a display for displaying a three-dimensional image, a fatal effect that pixels having parallax due to first-order diffracted light from an adjacent cell are mixed and viewed due to crosstalk. The problem is avoided and a clear stereoscopic image can be viewed. (Claim 13)

[0039]

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a "ratio of a grating width to a grating period" of a diffraction grating in a diffraction grating cell which is a pixel.
Is changed in at least one direction from the central portion to the peripheral portion, thereby making the intensity of the emitted light in the main lobe uniform and reducing the noise light outside the main lobe.

As described above, the diffraction efficiency changes depending on the modulation of the ratio, but the intensity distribution of the diffracted light is related to the amplitude distribution which is the square root thereof. Mathematical expressions for the amplitude distribution of the first-order diffracted light generated depending on the change in the ratio in the diffraction grating cell of the present invention include a sinc function, Bartle
Examples include a tt window function and a generalized Hamming window function.

[0041]

(Equation 2)

[0042]

(Equation 3)

[0043]

(Equation 4)

In the above formula, when the diffraction grating cell is circular, x is the distance from the center of the cell. When the diffraction grating cell is rectangular, x takes an axis perpendicular to any side of the rectangle and sets the center of the opening as the center. These coordinates are 0. Here, T is the size of the cell (diameter in the case of a circular cell, length of one side in the case of a rectangular cell), and takes a value in the range of -T / 2 ≦ x ≦ T / 2.

In the generalized Hamming window function, the form of the function can be optimized by α, but α = 0.5 or 0.54 is general.

Immediately after the cell, the case where the amplitude distribution at the center of the cell is made constant and decreases from a position away from the center to the periphery (the waveform is trapezoidal) corresponds to a trapezoidal function. . However, in the present invention, it is assumed that the oblique side is not necessarily a straight line as a trapezoidal function. (That is, a function that takes a constant value near the center and decreases gently on both sides is called a trapezoidal function.)

Here, some typical functions are given as amplitude functions of the first-order diffracted light from the cell, but the present invention is not limited to these.

It is known that the Fourier transform of the above function has a significantly smaller amplitude value at the periphery than the Fourier transform of a rectangular function. In the optical system, the Fourier transform is equivalent to calculation of a diffracted light distribution in a Fraunhofer region (sufficiently distant) for an arbitrary amplitude distribution having a parallel light phase. That is, the distribution in the Fraunhofer region of the first-order diffracted light having these functions as the amplitude distribution has an extremely small intensity at the peripheral portion.

When the first-order diffracted light from the cell has a spherical wave-like phase distribution, the distribution of the first-order diffracted light does not increase even under normal observation conditions (the distance between the observer and the display is about 30 cm to 1 m). This differs from the Fourier transform of the amplitude distribution immediately after, and tends to be more non-uniform.
At this time, if the amplitude ratio of the cell changes, the distribution of the first-order diffracted light can be made uniform, and the intensity distribution of the first-order diffracted light can be reduced in the peripheral portion.

As described above, when the amplitude distribution of the first-order diffracted light immediately after the cell is changed by modulating the ratio of the diffraction grating in the cell, the first-order diffracted light immediately after the cell has a spherical wave-like phase distribution. However, the strength at the peripheral portion can be reduced. However, in the case where the cell has a spherical wave phase distribution, in the cell represented by the rectangular function, the non-uniformity of the first-order diffracted light distribution in the main lobe tends to be remarkable. In the cell, the intensity distribution of the first-order diffracted light tends to be uniform. FIG. 6 shows an example of a diffraction grating cell according to the present invention. 7 and 8 show examples of the intensity distribution of the first-order diffracted light on the cell plane from the diffraction grating cell according to the present invention. FIG. 7 shows a waveform in which the intensity gradually decreases from the center to the periphery of the cell, and FIG. 8 shows a trapezoidal waveform.

Means for imparting a spherical wave phase distribution to the first-order diffracted light are as follows: (1) The diffraction grating is constituted by a curve. (For example, a part of the zone plate is used as a diffraction grating.) (2) The illumination light for generating the first-order diffracted light is not parallel light but light having a spherical wave phase distribution (for example, divergent light from a point light source). ). and so on.

In the case where the amplitude distribution of the first-order diffracted light immediately after the cell is a trapezoidal function, the intensity at the center can be increased while the intensity distribution of the first-order diffracted light is reduced at the peripheral portion, and the utilization efficiency of incident light is improved. Is more effective. However, if the oblique side of the trapezoid is too small (closer to a rectangle), the intensity distribution of the first-order diffracted light from the cell increases in the peripheral portion, and the effect is reduced. Specifically, for example, when the size of the cell is 50 μm, a sufficient effect is obtained if the oblique side of the trapezoid is about 10 μm (the trapezoid whose upper side is 30 μm).

In displaying an image on a display having a diffraction grating cell as a pixel as described above, the intensity and wavelength of light (illumination light) incident on each pixel (cell) can be changed in the same manner as in a conventional display. Alternatively, the image may be displayed by changing the cell size or the maximum value of the phase modulation amount for each pixel.

The direction of changing the ratio in the cell can be horizontal and / or vertical to the observer.

Normally, when viewing the display,
The observer's viewpoint position can be limited to a relatively narrow range in the vertical direction. (Because there is less displacement due to physique difference and observation posture compared to the movement of the observer in the horizontal direction.) Therefore, if the first-order diffracted light is given a spherical wave-like phase distribution in the vertical direction, Light utilization efficiency can be increased. However, the distribution of the first-order diffracted light tends to be non-uniform, so that the distribution of the first-order diffracted light can be made uniform by changing the ratio in the cell in a direction perpendicular to the observer. The same is true for the horizontal direction.

By making the spherical wave phase distribution a convergent spherical wave shape, the first-order diffracted light from the cell can be made incident on another element (for example, a filter for wavelength selection) arranged near the converging position. It will be easier. In particular, it is very effective when the elements have the same arrangement as the pixels of the display.

By making the spherical wave phase distribution a divergent spherical wave, if the incident light from the illumination light source has a location corresponding to the convergent point of the incident light before passing through the pixel (cell), At this position (a position corresponding to the convergence point), another element as described above can be arranged.

In order to perform a display with a stereoscopic effect due to binocular parallax on such a display, a cell that emits light having a spherical wave-like phase distribution is placed horizontally with respect to the observer (the left and right eyes are lined up). Direction), and each is divided into sub-cells. The number of areas to be divided depends on the number of two-dimensional images having parallax. The display is conceptually shown in FIG. In the figure, there are four types of subcells (two-dimensional images having parallax).

By making each sub-cell a pixel constituting a different two-dimensional image having parallax according to the viewing direction,
The details of the display for displaying a three-dimensional image are described in the above-mentioned Japanese Patent Application Laid-Open No. 3-206.
No. 401, Japanese Unexamined Patent Publication No. 4-31916, and the like.

In each of the subcells, in at least one direction (at least in the horizontal direction in which the left and right eyes are arranged with respect to the observer), the ratio changes from the center to the periphery in a low direction. It is a pixel unit constituting the above two-dimensional image.

By appropriately arranging the subcells and forming a display, different two-dimensional images having parallax can be visually recognized according to the viewing direction, and an image with a three-dimensional effect can be displayed. Become.

At this time, in the display of the present invention, the intensity distribution of the first-order diffracted light becomes uniform within the viewing zone for each parallax image (corresponding to the above-mentioned main lobe). Further, when the ratio is changed in the horizontal direction with respect to the observer, a parallax image to be observed from another viewing zone is overlapped and observed. ) Can be displayed, so that a higher-quality stereoscopic image can be displayed.

[0063]

As described above, in the display according to the present invention, the intensity of the first-order diffracted light, which is the light emitted from each pixel (diffraction grating cell), can be reduced in the peripheral portion. Therefore, it is possible to display a uniform image with little change in the brightness of the display depending on the viewpoint position of the observer and without showing bright and dark stripes on the display surface.
In particular, in the case where the intensity of light emitted from each pixel is reduced in the peripheral portion with respect to the observer in the left-right direction (both eyes are lined up) and the phase of spherical waves is given to the emitted light, Crosstalk due to light emitted from each pixel is avoided, and the uniformity of the distribution of each emitted light in the main lobe is improved, which is effective in displaying a three-dimensional image.

[0064]

[Brief description of the drawings]

FIG. 1 is an explanatory view showing a conventional diffraction grating cell.

FIG. 2 is a graph showing the intensity distribution (in the cell plane) of first-order diffracted light from a conventional diffraction grating cell.

FIG. 3 is a graph showing an example of a light intensity distribution (waveform) of a first-order diffracted light having a noise component in a peripheral portion from a conventional diffraction grating cell.

FIG. 4 is an explanatory view conceptually showing an example of a diffraction grating display.

FIG. 5 is an explanatory view showing a diffraction grating display capable of three-dimensional display.

FIG. 6 is an explanatory view showing an example of the diffraction grating cell of the present invention.

FIG. 7 is a graph showing an example of the intensity distribution (in the cell plane) of the first-order diffracted light from the diffraction grating cell of the present invention.

FIG. 8 is a graph showing an example of the intensity distribution (in the cell plane) of the first-order diffracted light from the diffraction grating cell of the present invention.

FIG. 9 is an explanatory diagram showing a change in a ratio between a grating period and a grating width in a central portion and a peripheral portion of the diffraction grating cell of the present invention.

Claims (13)

[Claims] 1. A display comprising a diffraction grating as pixels, wherein the diffraction grating is a binary diffraction grating, and a ratio of a grating width to a grating period at each position in the diffraction grating is determined in at least one direction of a diffraction grating plane. A diffraction grating display characterized by changing from the center to the periphery. 2. A display comprising a diffraction grating as pixels, wherein the diffraction grating is a binary diffraction grating, and a ratio of a grating width to a grating period at each position in the diffraction grating is one direction of a diffraction grating plane. A diffraction grating display characterized by changing from a central portion to a peripheral portion and being constant in a direction perpendicular to the central portion from the central portion to the peripheral portion. 3. The diffraction grating display according to claim 2, wherein the direction in which the ratio of the grating width to the grating period at each position in the diffraction grating changes is horizontal to an observer. 4. The diffraction grating display according to claim 2, wherein the direction in which the ratio of the grating width to the grating period at each position in the diffraction grating changes is perpendicular to the observer. 5. The ratio of the grating width to the grating period at each position in the diffraction grating varies in the direction of the diffraction grating surface from the center to the periphery, wherein the ratio is from the center to the periphery. 5. The diffraction grating display according to claim 1, wherein the diffraction grating display gradually decreases. 6. The ratio of the grating width to the grating period at each position in the diffraction grating is in the direction of the diffraction grating surface changing from the center to the periphery, and the ratio is constant near the center. 5. The diffraction grating display according to claim 1, wherein the distance decreases from a position distant from the center to the periphery. 7. The diffraction grating display according to claim 1, wherein the diffraction grating emits first-order diffracted light having a spherical wave phase distribution. 8. The diffraction grating has a spherical wave phase distribution only in the direction of the diffraction grating surface where the ratio of the grating width to the grating period at each position in the diffraction grating changes from the center to the periphery. The diffraction grating display according to any one of claims 1 to 6, which emits first-order diffracted light. 9. The diffraction grating display according to claim 7, wherein the spherical wave phase distribution is a convergent spherical wave shape. 10. The diffraction grating display according to claim 7, wherein the spherical wave phase distribution is a divergent spherical wave. 11. The diffraction grating display according to claim 7, wherein the binary diffraction grating is an amplitude type diffraction grating. 12. The diffraction grating display according to claim 7, wherein the binary diffraction grating is a phase type diffraction grating. 13. A cell-like diffraction grating that emits first-order diffracted light having a spherical wave-like phase distribution is divided into a plurality of regions in accordance with the number of two-dimensional images described later, and each of them is a sub-cell that is a pixel unit. For at least the horizontal direction of the subcell surface, the ratio of the grating width to the grating period at each position in the diffraction grating changes from the center to the periphery, and each subcell has parallax. The display according to claim 7 or 8, wherein a stereoscopic image is displayed by using pixels constituting a plurality of two-dimensional images.