LG Patent | Image display element and device

Description

TECHNICAL FIELD

The present invention relates to an image display element and a device that are small and lightweight and capable of performing augmented reality display by combining a light guide plate and a diffraction element.

BACKGROUND ART

In an augmented reality image display device, a user can view not only an image to be projected but also surroundings at the same time. The projected image may overlap the real-world perceived by the user. Other uses for these displays include video games and wearable devices such as glasses. The user can visually recognize the image supplied from the projector while superimposing the image on the real world by wearing glasses or a goggle-like image display device in which a translucent light guide plate and the projector are integrated.

One of such image display devices is described in “PTL 1” to “PTL 3”. In these patent documents, the light guide plate includes a plurality of diffraction gratings having an uneven shape formed on a glass substrate. The light beam emitted from the projector is coupled to the light guide plate by the diffraction grating for incidence and propagates inside the light guide plate while being totally reflected. The light beam is totally reflected and propagated in the light guide plate while being converted into a plurality of light beams replicated by another diffraction grating, and finally emitted from the light guide plate. A part of the emitted light beam is imaged on the retina through the pupil of the user, and is recognized as an augmented reality image superimposed on an image of the real world.

In the light guide plate using such a concavo-convex diffraction grating, the wave number vector K of the light beam emitted from the projector is refracted in the light guide plate, and the wave number vector becomes K0 by Snell's law. Further, the diffraction grating for incidence converts the wave number vector into a wave number vector K1 capable of total reflection propagation inside the light guide plate. A diffraction action is received by another one or a plurality of diffraction gratings provided in the light guide plate, and the wave number vector changes each time diffraction is repeated as in K2, K3,

Assuming that a wave number vector of a light beam finally emitted from the light guide plate is K′, |K′|=|K|, and in a case where the projector is on the opposite side of the eye via the light guide plate, K′=K is satisfied. On the other hand, in a case where the projector is on the opposite side of the eye via the light guide plate, the light guide plate has the same action as the reflection mirror with respect to the wave number vector, and when the normal vector of the light guide plate is in the z direction and x, y, and z components of the wave number vector are compared, Kx′=Kx, Ky′=Ky, and Kz′=−Kz can be expressed.

The function of the light guide plate is to guide a plurality of light beams emitted from the projector while duplicating the light beams, and the plurality of emitted light beams are recognized by the user as image information equivalent to the original image. At this time, the duplicated light beam group has a wave number vector equivalent to the light beam having the video information emitted from the projector, and has a spatial extent. A part of the duplicated light beam group enters the pupil and is visually recognized by being imaged on the retina together with information of the outside world, and it is possible to provide the user with augmented reality information added to the information of the outside world.

A light beam having video information has a wave number vector whose magnitude varies depending on its wavelength. Since the concavo-convex diffraction grating has a constant wave number vector, the diffracted wave number vector K1 varies depending on the wavelength of the incident light beam, and propagates in the light guide plate at different angles. The refractive index of the glass substrate constituting the light guide plate is substantially constant with respect to the wavelength, and the range of the condition for guiding light while totally reflecting light varies depending on the wavelength of the incident light beam. Therefore, in order to make the user recognize an image with a wide viewing angle, it is necessary to stack a plurality of light guide plates different for each wavelength. In general, it is considered that the number of light guide plates is appropriately about 2 to 4, which is the number corresponding to each of R, G, and B or ±1.

The image display device described in “PTL 1” is an image display device for expanding input light in two dimensions, and includes three linear diffraction gratings. One is a diffraction grating for incidence, and the other two diffraction gratings for emission are typically disposed to overlap with each other on the front surface and the back surface of the light guide plate, and function as a diffraction grating for duplication and emission. In addition, “PTL 1” describes an example in which a diffraction grating for emission is formed on one surface by a periodic structure of a columnar photonic crystal.

In order to solve the problem that the image projected by the photonic crystal in “PTL 1” has high luminance in the central portion of the visual field, the image display device described in “PTL 2” discloses a technique of configuring the shape of the optical structure with a plurality of linear side surfaces.

In the image display devices described in “PTL 3” and “PTL 4”, three diffraction gratings also serving as an incident diffraction grating, a deflection diffraction grating, and an emission diffraction grating are disposed without overlapping regions in a light guide plate. “PTL 3” discloses an overhung triangular diffraction grating in order to increase diffraction efficiency of the incident diffraction grating.

“PTL 5” and “PTL 6” disclose techniques using two reflection-type volume holograms for incidence and emission as diffraction gratings formed on a light guide plate. In these, a reflection-type volume hologram is formed by multiplexing diffraction gratings corresponding to a plurality of wavelengths in a space, and diffracts light beams of a plurality of wavelengths at the same angle, unlike the concavo-convex diffraction gratings in “PTL 1” to “PTL 3”. Therefore, the user can recognize the RGB image with one light guide plate. On the other hand, in the above concavo-convex diffraction grating, a wide viewing angle can be realized because the light beam is replicated in a two-dimensional direction in the light guide plate, whereas the reflection-type volume hologram has a feature that the viewing angle is relatively narrow because only a one-dimensional replication function is provided.

CITATION LISTPatent Literature

PTL 1: JP 2017-528739 A

PTL 2: WO 2018/178626 A1

PTL 3: WO 2016/130342 A1

PTL 4: WO 99/52002 A1

PTL 5: JP 2007-94175 A

PTL 6: JP 2013-200467 A

SUMMARY OF INVENTIONTechnical Problem

Hereinafter, a light guide plate having a concavo-convex diffraction grating as the light guide plate will be described. In addition, in order to facilitate understanding, the inversion of the image by the lens action of the eye and the effect of processing the image projected on the retina with the brain and further inverting and recognizing the image are omitted, and the relationship between the pixel position and the luminance will be discussed for the projection image projected on the front screen from the video light source disposed on the same side as the eye with respect to the light guide plate. The actually visually recognized image is vertically inverted with respect to this.

“PTL 1” relates to a substrate material of a light guide plate, and discloses a technique using a glass material as illustrated in FIG. 15A. Regarding the diffraction grating, as described in paragraph 0017 thereof, a technique of forming a waveguide (=glass plate) surface by etching is disclosed. In addition, as described in paragraph 0039, “PTL 1” discloses a technique of forming two emission diffraction gratings on one surface using a photonic crystal. In a case where a cylindrical structure similar to the photonic crystal of “PTL 1” is to be formed by an injection molding method, as described later, the refractive index of the cylinder is equal to that of the waveguide (or the substrate). In this case, if the aspect ratio that is the ratio of the diameter to the height of the cylinder is not about 2 or more, the luminance of the projection image becomes insufficient.

In the photonic crystal in which the central portion of the projection image is improved to have high luminance described in “PTL 2”, the optical structure is configured by a plurality of linear side surfaces in order to solve the problem that the image projected by the linear photonic crystal rather than the cylindrical photonic crystal has high luminance at the central portion of the visual field. In “PTL 2”, as described line 34 on page 1, the high luminance portion in the stripe shape in the central portion is improved. Note that WO 2016/020643 cited in “PTL 2” is the same as “PTL 1”. In “PTL 2”, the stripe-shaped high luminance portion in the central portion, which is a problem, is not explicitly disclosed in the drawings and the like.

The cross-sectional shape of the incident diffraction grating disclosed in FIG. 5C of “PTL 3” has an overhanging triangular cross section, and it is possible to efficiently couple the video light beam incident from the upper direction (air side) in the drawing to the inside of the hatched light guide plate.

In general, in an image display element, a light beam having video information is coupled by an incident diffraction grating provided in a light guide plate so as to have a wave number capable of total reflection light guide in the light guide plate, and propagates in the light guide plate. A part of the light beam intersecting the emission diffraction grating is diffracted, and emitted from the light guide plate with a wave number equivalent to the original video light beam. The video information provided to the user has travel angle information corresponding to a pixel position of the original video information, that is, a wave number. In order for the video information of one pixel to be emitted from the light guide plate and reach the pupil of the user, it is necessary to be emitted from a specific position in the light guide plate that is determined by the traveling angle, the distance between the light guide plate and the pupil of the user, and the size of the pupil of the user. As described above, in the light guide plate, the light beam is replicated and spatially spread and emitted, so that the light beam visually recognized by the user decreases as the spatial spread increases, and the luminance visually recognized decreases. On the other hand, since the emission position visually recognized by the user changes depending on the pixel position of the original video information, it is inevitable that the luminance changes depending on the pixel position in the image display device using the light guide plate.

In the above-described prior art, it has been suitable to use a method of directly etching a glass substrate for producing a light guide plate, a nanoimprint method suitable for forming a pattern having a high aspect ratio, or the like. When the structures of the photonic crystals of “PTL 1” and “PTL 2” based on the “PTL 1” are obtained by injection molding of plastic, it is necessary to set, in the photonic crystal, an aspect ratio, which is a ratio between a representative length such as a diameter of a bottom surface and a height thereof, to about 2 or more.

Here, in a case where glass is used for the light guide plate as disclosed in “PTL 1” or the like, there are problems in processing cost and weight at the time of mounting by the user. Therefore, this problem can be solved by using plastic for the light guide plate. In the present specification and the like, the terms “resin” and “plastic” are used synonymously. The plastic means a material made of a polymer compound, does not contain glass, and is a concept including a resin, polycarbonate, an acrylic resin, and a photocurable resin.

When plastic is used for the light guide plate, the diffraction grating can be formed by an injection molding technique or the like that has been used as a manufacturing method of the optical disk medium. Since the aspect ratio of the surface-uneven pattern formed by an injection molding technique or the like does not exceed 1, the accuracy of pattern transfer decreases at an aspect ratio of 2 or more, and it is difficult to apply the pattern transfer. This is a problem caused by the principle of the essential manufacturing method in which molten polycarbonate resin, acrylic resin, polyolefin resin, and the like have high viscosity, and the resin does not accurately enter unevenness having a high aspect ratio formed with a nanometer period. In addition, since the incident diffraction grating of “PTL 3” uses an overhung triangular diffraction grating, it cannot be applied because the mother plate (stamper) and the light guide plate cannot be peeled off by the injection molding technique or the like.

The plastic light guide plate has smaller mechanical strength (Young's modulus) than the conventional glass light guide plate, and thus deformation due to environmental temperature or atmospheric pressure becomes large. Although details will be described later, it is effective to adopt a transmission-type optical configuration in which the image source and the user are located on the opposite side with the light guide plate interposed therebetween. Therefore, a configuration capable of avoiding a decrease in luminance of image information visually recognized by the user even in the transmission-type optical configuration is desirable.

As described above, in order to apply the plastic light guide plate to the image display element, it is necessary to have a configuration in consideration of a manufacturing method and luminance of image information. Therefore, an object of the present invention is to improve luminance of image information visually recognized by a user while using plastic for a light guide plate.

Solution to Problem

A preferred aspect of the present invention is an image display element including: a plastic substrate; an incident diffraction grating integrally formed on a surface of the plastic substrate and configured to diffract incident video light; an emission diffraction grating integrally formed on a surface of the plastic substrate and configured to emit the video light; and a coating layer formed on the emission diffraction grating and having a thickness of 10 nm or more and 1000 nm or less and a refractive index of 1.64 or more and 2.42 or less.

A preferred aspect of the present invention is an image display element including: a plastic substrate; an incident diffraction grating integrally formed on a surface of the plastic substrate and configured to diffract incident video light; an emission diffraction grating integrally formed on a surface of the plastic substrate and configured to emit the video light; and a coating layer in which two types of dielectric materials are alternately stacked for N (N is a natural number) periods, d1 and d2 are film thicknesses of these dielectric materials, d1+d2 is substantially equal to H, and (d1+d2)×N is 1000 nm or less, where H is a period height of an uneven pattern of the incident diffraction grating.

Another preferred aspect of the present invention is an image display device on which the image display element is mounted, in which the incident diffraction grating and the emission diffraction grating are formed on a first surface of a plastic substrate, and video light is incident from a second surface side opposite to the first surface of the plastic substrate so that the video light can be visually recognized from the first surface side of the plastic substrate.

Advantageous Effects of Invention

According to the present invention, it is possible to improve the luminance of the image information visually recognized by the user while using plastic for the light guide plate.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is a schematic cross-sectional view illustrating a light guide plate of an embodiment.

FIG. 1B is a schematic cross-sectional view illustrating the light guide plate of the embodiment.

FIG. 2 is an image diagram illustrating an example of a phase function of an emission diffraction grating.

FIG. 3 is a perspective view of a mesh-type diffraction grating of an embodiment.

FIG. 4 is a conceptual diagram illustrating a definition of an emission circle as a basis of simulation.

FIG. 5 is an image diagram illustrating a simulation result of an intensity distribution of a light beam propagating inside the light guide plate.

FIG. 6 is a schematic cross-sectional view illustrating a configuration of an image display element of an embodiment.

FIG. 7 is a schematic plan view illustrating a relationship between a diffraction grating of a light guide plate and a wave number vector.

FIG. 8 is an image diagram illustrating a simulation result of a projection image.

FIG. 9 is an image diagram of a simulation result showing a diffracted light beam of an incident diffraction grating.

FIG. 10A is a schematic view of an example of an image display element in which incident light and emitted light are on the same side of the light guide plate.

FIG. 10B is a schematic view of an example of an image display element in which incident light and emitted light are on opposite sides of the light guide plate.

FIG. 11 is a graph illustrating simulation results of a film thickness, diffraction efficiency, and transmittance of a dielectric thin film.

FIG. 12 is a schematic view of a simulation model of an emission diffraction grating of an embodiment.

FIG. 13 is an image diagram of a visually recognized image of a user.

FIG. 14A is a graph of a simulation result of a visually recognized image of the user.

FIG. 14B is a graph of a simulation result of a visually recognized image of the user.

FIG. 14C is a graph of a simulation result of a visually recognized image of the user.

FIG. 15A is a graph illustrating a range of refractive indexes of dielectric materials.

FIG. 15B is an enlarged graph illustrating a range of refractive indexes of dielectric materials.

FIG. 16A is a graph illustrating characteristics of an emission diffraction grating with respect to a dielectric film thickness.

FIG. 16B is a graph illustrating characteristics of an emission diffraction grating with respect to a dielectric film thickness.

FIG. 16C is an enlarged graph illustrating characteristics of an emission diffraction grating with respect to a dielectric film thickness.

FIG. 17 is a table of simulation results showing RGB display images of the light guide plate of an embodiment.

FIG. 18 is a schematic cross-sectional view illustrating a configuration of an image display element of an embodiment.

FIG. 19 is a schematic view illustrating a relationship between the incident diffraction grating and diffracted light.

FIG. 20 is a schematic view illustrating a relationship between the incident diffraction grating and diffracted light.

FIG. 21 is a table illustrating a relationship between a cross-sectional shape and a period height of the incident diffraction grating.

FIG. 22A is a schematic view illustrating a simulation model of the incident diffraction grating.

FIG. 22B is a schematic view illustrating a simulation model of the incident diffraction grating.

FIG. 23A is a schematic view illustrating a simulation model of the incident diffraction grating.

FIG. 23B is a schematic view illustrating a simulation model of the incident diffraction grating.

FIG. 24A is a graph illustrating wavelength dependency of performance of the incident diffraction grating.

FIG. 24B is a graph illustrating wavelength dependency of performance of the incident diffraction grating.

FIG. 24C is a graph illustrating wavelength dependency of performance of the incident diffraction grating.

FIG. 25 is a graph illustrating a relationship between a thickness and a period height of a dielectric coating formed on the incident diffraction grating.

FIG. 26 is a schematic cross-sectional view illustrating a film shape when 13 dielectric thin films of the embodiment are stacked.

FIG. 27 is a schematic view illustrating another example of the image display element.

FIG. 28 is a schematic cross-sectional view illustrating a method for forming a light guide plate of an embodiment.

FIG. 29 is a schematic view illustrating a configuration of an image display device according to an embodiment.

DESCRIPTION OF EMBODIMENTS

Hereinafter, embodiments of the invention will be described with reference to the drawings. However, the invention is not interpreted in a limited way to the following embodiments. A person skilled in the art can easily understand that the specific configurations may be changed within a scope not departing from the ideas and the spirit of the invention.

In the configuration of the invention described below, the same reference numerals are commonly used for the same portions or portions having similar functions in different drawings, and redundant description may be omitted.

When there are a plurality of elements having the same or similar functions, different subscripts may be given for the same reference numerals for explanation. However, when there is no need to distinguish between a plurality of elements, the description may be omitted with subscripts omitted.

The notations of “first”, “second”, and “third” in this specification are attached in order to identify the components, but not necessarily used to indicate the number, the order, or the contents. In addition, a number for identifying a component is used for each context, and a number used in one context does not necessarily indicate the same configuration in another context. In addition, it does not prevent a component identified by a certain number from also functioning as a component identified by another number.

The position, size, shape, range, and the like of each element illustrated in the drawings and the like may not necessarily represent the actual position, size, shape, range, and the like, in order to facilitate understanding of the invention. For this reason, the invention is not necessarily limited to the position, size, shape, range, and the like disclosed in the drawings and the like.

The publications, patents, and patent applications cited herein constitute a part of the description of this specification as such.

Components expressed in the singular herein are intended to include the plural unless the context clearly dictates otherwise.

In the present embodiment, a thin film coating layer is formed on an emission diffraction grating by a sputtering method or the like to improve diffraction efficiency in a direction of a user's eye. Thus, the luminance of the image information is improved while the plastic light guide plate is applied. The upper limit of the diffraction efficiency due to the uneven pattern formed on the surface of the plastic light guide plate is mainly determined by the wavelength and pattern height of the light source and the refractive index of the plastic material, and is about 4% at the maximum as described later. By forming a thin film coating layer of a dielectric material on the emission diffraction grating, it is possible to improve the thin film coating layer about twice. Details will be described in the following embodiments.

FIGS. 1A and 1B are schematic views illustrating improvement of diffraction efficiency of a transmission-type emission diffraction grating by thin film coating. FIG. 1A is a schematic view of a cross section of a plastic light guide plate. A light guide plate 100 is formed of a plastic material, and the emission diffraction grating 102 is formed as an uneven pattern on the surface. When a plastic molding technique such as an injection molding method is used, these are integrally molded and formed of the same material. However, in a plastic molding technique such as an injection molding method, the aspect ratio (height/width) of the uneven pattern of the emission diffraction grating is preferably approximately 1 or less. The phase modulation amount of the emission diffraction grating with respect to the incident light is governed by a difference between the refractive index of the plastic material of the convex portion and the refractive index of the air of the concave portion.

FIG. 1B is a schematic view in a case where a coating layer 103 is formed of a dielectric film on the surface of the emission diffraction grating 102 by a sputtering method or the like. An uneven pattern of the dielectric material is formed on the surface by reflecting the unevenness of the original diffraction grating pattern. At this time, by making the refractive index of the dielectric material to be used higher than the refractive index of the plastic material, the phase modulation amount becomes large so as to reflect the refractive index difference between the dielectric material and air. This makes it possible to obtain high diffraction efficiency even when the aspect ratio of the uneven pattern is 1 or less. Specifically, it is necessary to determine the film thickness of the dielectric material so that predetermined diffraction efficiency can be obtained by performing electromagnetic field analysis by a finite differential time domain (FDTD) method or the like. As described later, when the film thickness of the dielectric material to be formed is about from 10 nm to 200 nm, the effect of increasing the diffraction efficiency can be obtained.

In a plastic molding technique having a track record such as an injection molding method, it is easier to form the uneven pattern when the aspect ratio of the uneven pattern transferred to the surface of the light guide plate is small. As a method for reducing the aspect ratio of the uneven pattern, it is desirable to employ a diffraction grating of a two-dimensional mesh-like pattern as the emission diffraction grating 102. As a result, the aspect ratio of the uneven pattern transferred to the surface of the light guide plate easily becomes 1 or less, and it is possible to easily provide a light guide plate using a plastic molding technique having a track record such as an injection molding method.

The photonic crystal or the diffraction grating spatially applies phase modulation to incident light due to surface unevenness. The magnitude of the phase modulation increases in proportion to the difference in refractive index between the surface structure and the air and the height of the surface unevenness.

FIG. 2 schematically illustrates the wave number of the emission diffraction grating 102. The phase functions of the diffraction gratings having wave numbers K1 and K2 having an azimuth angle of ±60 degrees with respect to the Y axis are illustrated in FIGS. 2(a) and 2(b), respectively, and each has a sinusoidal phase distribution. The phase modulation amount is normalized to 1. FIG. 2(c) is obtained by synthesizing these, and it can be said that the photonic crystal described in PTL 1 or the like is formed on the surface of the light guide plate with a material having a high refractive index by approximating the photonic crystal to a pillar or the like. As can be seen from the drawing, the maximum value of the phase modulation amount of K1+K2 is 2, and when this is approximated by an isolated cylinder or the like, it is found that a height (aspect ratio) that is twice as large as that of the single sinusoidal diffraction grating of FIGS. 2(a) and 2(b) is required.

FIG. 3 is a perspective view of an embodiment in which the emission diffraction grating 102 is a mesh-like emission diffraction grating. Compared with FIG. 2(c), since the light guide plate does not have a sinusoidal structure, the light guide plate has a higher-order wave number component when subjected to Fourier transform. However, when the light guide plate is used as a light guide plate, the wave number component of the second or higher order can be made incapable of being diffracted with respect to incident light (wave number is an imaginary number) by appropriately selecting a period. In addition, the mesh-like diffraction grating is obtained by overlapping rectangular diffraction gratings of ±60 degrees, and does not have a wave number component other than the directions of the fundamental waves K1 and K2 as compared with a cylinder or the like, so that diffraction efficiency can be increased.

As a result, a two-dimensional emission diffraction grating having a small aspect ratio can be provided, and a light guide plate that is safe, lightweight, and high in image luminance can be provided by a plastic molding technique such as an injection molding method.

As will be described later, with respect to the incident diffraction grating of the present embodiment, it is desirable to achieve a low aspect ratio by using reflection having a large deflection effect on refraction by using a reflection-type diffraction grating instead of the transmission-type diffraction grating of “PTL 3”.

In the present specification, the description will proceed with a coordinate system in which the optical axis direction is the Z axis and the XY plane is taken on the surface of the light guide plate. In addition, when the pupil of the user is approximated to a circle, the emission position in the light guide plate visually recognized by the user also becomes a circle according to the pixel position. Hereinafter, this will be referred to as an emission circle.

FIG. 4 is a schematic view for explaining an emission circle. Here, a case where a projector 300 which is a light source for forming an image and the user's pupil 400 are arranged on the opposite side of the light guide plate 100 is illustrated. Assuming that the wave number vector of an incident diffraction grating 101 faces the y direction, the arrow in FIG. 4 represents a light beam in the x-z plane. Here, it is assumed that the incident diffraction grating 101 does not have a wave number vector component in the x direction.

Among the video light beams visually recognized by the user, a light beam 301 at the center of the display image corresponding to the center of the visual field goes straight in the x-z plane and is reached to the user's pupil 400 as illustrated in the drawing. Diffraction in the y direction, which is an action of the light guide plate 100, is not explicitly expressed, but occurs at least once by the incident diffraction grating 101 and the emission diffraction grating 102.

On the other hand, among the video light beams visually recognized by the user, a light beam 302 around the display image corresponding to the periphery of the visual field advances in the right direction in the drawing when there is no diffraction in the x direction. On the other hand, in order for the user to recognize this light beam as a projection image, it is necessary for light beams having the same angle to reach the user's pupil 400 through a path indicated as the light beam 304 visually recognized in the drawing. An emission circle 303 is a virtual circle on the emission diffraction grating 102 and obtained by translating the user's pupil 400 in the direction of the visually recognized light beam. Only the light beam 304 emitted from the emission circle 303 on the emission diffraction grating 102 is recognized as the projection image by the user, and the other light beams are not recognized. As described above, the diffraction action in the x direction is required for the emission diffraction grating 102.

FIG. 5 is an intensity distribution of light beams propagating inside the light guide plate calculated using a simulation method to be described later. Here, it should be noted that the intensity distribution is shown in the in-plane x-y plane including the diffraction grating of the light guide plate. In the drawing, the incident diffraction grating 101 is disposed on an upper side, and a pupil corresponding to a user's eye is disposed below the incident diffraction grating.

FIG. 5(a) illustrates an intensity distribution of light toward the center of the image when the pixel position is at the center of the image to be projected. The emission circle in the drawing indicates a region where the light beam reaching the pupil is finally diffracted on the emission diffraction grating 102. A high-luminance region on a straight line extending from the incident diffraction grating 101 in the y direction indicates a main light beam group (hereinafter, main light beam group) diffracted by the incident diffraction grating 101 and propagating inside the light guide plate. As can be seen in the drawing, it has a characteristic that the intensity gradually attenuates due to the propagation of the main light beam group. The light beam group with low luminance spreading around the main light beam group is a light beam group diffracted by the emission diffraction grating 102 and whose traveling direction is deflected in the x-y plane. Under this condition, since the projected light beam is in the z-axis direction, it is found that the emission circle and the pupil coincide with each other in the x-y plane. Therefore, a part of the main light beam group with high intensity is reached to the pupil and recognized as an image.

FIG. 5(b) illustrates the intensity distribution of the light to the periphery of the image in the case of the pixel position at the upper right corner of the projection image. As can be seen in the drawing, the main light beam group travels from the incident diffraction grating 101 toward the lower right direction. Although the position of the pupil is constant, the emission circle is the emission position of the light beam group traveling to the upper right toward the pupil. Therefore, the emission circle is shifted to the lower left with respect to the pupil in the x-y plane. In this case, since the emission circle is located away from the main light beam group, the light beam group that reaches the pupil and is recognized as an image has lower luminance than the above case. The above is the main reason why luminance unevenness occurs when an image is projected using the light guide plate 100.

When the grating pitch is P, the magnitude of the wave number vector of the diffraction grating is expressed by K=2π/P. When expressed in a coordinate system in which the optical axis direction is taken as the z axis, a wave number vector of the incident diffraction grating 101 is K₁=(0, −K, 0). The emission diffraction grating 102 has two wave number vectors with an angle of 120 degrees, which are K₂=(+K/√3, K/2, 0) and K3=(−K/√3, K/2, 0). When the wave number vector of the light beam incident on the light guide plate 100 is kⁱ=(kⁱ_x, kⁱ_y, kⁱ_z), the wave number vector of the light beam to be emitted is k^o=(k^o_x, k^o_y, k^o_z), and K₁, K₂, and K₃ are sequentially applied to kⁱ, k^o=kⁱ is obtained as follows, and it can be seen that the light beam having the same wave number vector as the incident light beam, that is, the light beam having the same video information is emitted.

k^o=kⁱ