JP4804877B2 - 3D image display system and 3D image display method - Google Patents

Description

  The present invention relates to a three-dimensional image display system and a three-dimensional image display method for displaying a three-dimensional image by presenting a hologram on a spatial light modulation element and irradiating illumination light to generate reproduction light.

  In a 3D image display system or 3D image display method for displaying a 3D image using a spatial light modulator, a hologram is presented by adjusting the transmittance or phase change amount of each pixel of the spatial light modulator. The spatial light modulator is irradiated with illumination light to generate reproduction light, and this reproduction light is imaged to form a three-dimensional reproduction image. The three-dimensional image display system described in Patent Literature 1 uses the fact that the spatial light modulation element has a discrete pixel structure, and expands the viewing area when the observer observes the reproduced image. Is intended.

  Similarly to the case where the 0th-order diffracted wave, ± 1st-order diffracted wave, and higher-order diffracted wave are separated and emitted when parallel light is incident on the diffraction grating, the spatial light modulator has a discrete pixel structure. When the illumination light is incident on the spatial light modulation element on which the hologram is presented, the 0th-order diffracted wave, the ± 1st-order diffracted wave, and the higher-order diffracted wave are separated from each other and emitted. The

  When a computer generated hologram is displayed with the hologram display range limited to a range where the phase of the combined wavefront of the object light and the reference light of adjacent pixels does not exceed π (the range without the aliasing component), reproduction caused by illumination light irradiation The higher-order diffracted wave of light has the same wavefront as that of the 0th-order diffracted wave, but the exit angles from the spatial light modulator are different, so the rear focal plane of the lens placed behind the spatial light modulator The images are individually formed after separation at intervals of λf / P for each order. Here, P is the pixel pitch of the spatial light modulator, f is the focal length of the lens, and λ is the wavelength of the illumination light. Therefore, by providing a mask having an aperture of “λf / P” at the position where the 0th-order diffracted wave passes on the focal plane after the lens, other high-order diffracted waves are shielded to obtain an assumed reproduced image. be able to.

  On the other hand, when a computer generated hologram is displayed with the hologram display range limited to a range in which the phase of the combined wavefront of the object light and the reference light of adjacent pixels is from π to 2π (a range including a first-order aliasing component) The high-order diffracted wave of the reproduction light generated by the light irradiation has the same wavefront as that of the zero-order object light, and all the diffracted waves including the zero-order light are all composed of only the first-order folded component generated by calculation. Reproduction light. Among these diffracted waves, in order to extract only the first order diffracted wave having a required emission angle, the size is at a position where the first order diffracted wave passes through the back focal plane of the lens placed behind the spatial light modulator. A mask having an opening of “λf / P” is provided to shield the 0th-order diffracted wave and other high-order diffracted waves, and to pass only the necessary 1st-order diffracted waves.

That is, the three-dimensional image display system described in Patent Document 1 limits a computer generated hologram including a specific-order folding component and a display range thereof, and selects only a corresponding aperture, so that necessary reproduction light is obtained. Take out. With this method, the display of the hologram corresponding to the aliasing component and the selection of the aperture are performed by time division or space synthesis, thereby expanding the exit angle range, that is, the viewing zone, of the imaged reproduced image by the lens.
JP 2000-250387 A

  In the three-dimensional image display system and the three-dimensional image display method using the spatial light modulator including those described in Patent Document 1, the viewing area when observing the three-dimensional reproduced image with binocular vision of the observer is set. Ensuring is an issue.

  However, in the technique described in Patent Document 1, the 0th-order diffracted light and the higher-order diffracted light of the reproduction light emitted from the spatial light modulator are imaged by the lens, and the position where the 0th-order diffracted light and the high-order diffracted light intersect. A reconstructed image is formed. For this purpose, the computer generated hologram is displayed by limiting the display range of the computer generated hologram to a range where the phase of the combined wavefront of the object light and the reference light of adjacent pixels is from π to 2π (a range including the first-order aliasing component). Therefore, there is a problem that the calculation of the computer generated hologram is complicated. In addition, the reproduced image cannot be brought close to the focal point behind the lens, and the reproduced image is formed at a position away from the focal point behind the lens, so that the observation position is further away from the focal point. There is also a problem that the whole system becomes large.

  The present invention has been made to solve the above problems, and an object of the present invention is to provide a three-dimensional image display system and a three-dimensional image display method capable of securing a viewing zone and miniaturizing the system. And

The three-dimensional image display system according to the present invention includes: (1) a first spatial light modulation element that presents a first hologram and generates first reproduction light by vertical incidence of first illumination light; and the first spatial light modulation element A first display device including a first afocal optical system that inputs the first reproduction light generated in step 1 to form a first reproduction image; and (2) second illumination light presented by the second hologram. A second spatial light modulation element that generates the second reproduction light by vertical incidence of the light, and a second reproduction light that forms a second reproduction image by inputting the second reproduction light generated by the second spatial light modulation element and forming an image. And a second display device including a focal optical system. Further, the three-dimensional image display system according to the present invention includes: (3) an optical path between the front-stage optical system and the rear-stage optical system of the first afocal optical system, and a front-stage optical system and a rear-stage optical system of the second afocal optical system. Mirrors are inserted in both or any one of the optical paths between the first afocal optical system and the second afocal optical system. (4) the first afocal optical system and the second afocal optical system are common to each other, and (5) the first afocal optical system. And the second afocal optical system form the first reproduced image and the second reproduced image in the same spatial region, and (6) in the second display device, on a plane perpendicular to the optical axis of the second afocal optical system. On the other hand, the second spatial light modulator (7) In the first display device, the pixel pitch of the first spatial light modulator is P, the focal length of the front optical system of the first afocal optical system is f, and the first illumination A first mask having an aperture of a size “λf / P” or less when the wavelength of light is λ is provided on the rear focal plane of the front optical system of the first afocal optical system. (8) Second display In the apparatus, when the pixel pitch of the second spatial light modulator is P, the focal length of the front optical system of the second afocal optical system is f, and the wavelength of the second illumination light is λ, the size “λf” The second mask having an opening of “/ P” or less is provided on the rear focal plane of the front optical system of the second afocal optical system.

  In the three-dimensional image display system according to the present invention, when the first illumination light is vertically incident on the first spatial light modulation element on which the first hologram is presented in the first display device, the first spatial light modulation element First reproduction light is generated, and the first reproduction light is imaged by the first afocal optical system to form a first reproduction image. Similarly, in the second display device, when the second illumination light is perpendicularly incident on the second spatial light modulation element on which the second hologram is presented, second reproduction light is generated from the second spatial light modulation element, The second reproduction light is imaged by the second afocal optical system to form a second reproduction image. Here, the first afocal optical system and the second afocal optical system are common to the subsequent optical systems, and form the first reproduced image and the second reproduced image in the same spatial region. At least in the second display device, the surface of the second spatial light modulator is inclined with respect to the surface perpendicular to the optical axis of the second afocal optical system. In the first display device, the first mask provided on the back focal plane of the front stage optical system of the first afocal optical system has an opening having a size of “λf / P” or less. The second mask provided on the rear focal plane of the front optical system of the two-afocal optical system has an opening having a size of “λf / P” or less. As described above, in the three-dimensional image display system according to the present invention, by using a plurality of display devices, the viewing zone can be secured and the system can be miniaturized.

  In addition to the first display device and the second display device, the 3D image display system according to the present invention may include another display device having the same configuration. In addition to the fact that the surface of the second spatial light modulator is inclined with respect to the surface perpendicular to the optical axis of the second afocal optical system in the second display device, the first display device also has the first a The surface of the first spatial light modulator may be inclined with respect to a surface perpendicular to the optical axis of the focal optical system.

  In the three-dimensional image display system according to the present invention, (8) in the first display device, the 0th-order light included in the first reproduction light generated by the first spatial light modulator is the first stage of the first afocal optical system. The center of the opening of the first mask is located at a point condensed by the optical system. (9) In the second display device, the 0th-order light included in the second reproduction light generated by the second spatial light modulation element is It is preferable that the center of the opening of the second mask is positioned at a point where light is collected by the preceding optical system of the second afocal optical system. In this case, a reproduced image is formed by the 0th-order light, so that a bright image can be obtained and the illumination light can be used efficiently.

In the 3D image display system according to the present invention, in the second display device, the inclination angle of the surface of the second spatial light modulator with respect to the surface perpendicular to the optical axis of the second afocal optical system is an integer other than zero. It is preferable that “sin ⁻¹ (nλ / P)” when n is n. In this case as well, the viewing zone can be secured and the system can be downsized.

  A three-dimensional image display method according to the present invention is a method for displaying a three-dimensional image using the above-described three-dimensional image display system according to the present invention, and in the second display device, the light of the second afocal optical system. The inclination angle of the surface of the second spatial light modulator with respect to the surface perpendicular to the axis is set according to the position of the observer who observes the three-dimensional image and the distance between both eyes, and the first display image is displayed by the first display device. And forming a second reproduced image by the second display device. The 3D image display method according to the present invention provides a second display device in the second display device included in the 3D image display system according to the present invention, according to the position of the observer who observes the 3D reproduced image and the distance between both eyes. The inclination angle of the surface of the two spatial light modulator is set. Therefore, it is possible to set an optimal reproduced image display condition for each observer, and to secure an optimal viewing area for each observer.

  According to the present invention, a viewing zone can be secured, and the system can be downsized.

  The best mode for carrying out the present invention will be described below in detail with reference to the accompanying drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted.

(First embodiment)
When a hologram is presented on a spatial light modulation element having a discrete pixel structure and illumination light is incident on this spatial light modulation element to generate reproduction light, the maximum diffraction angle θ of the reproduction light, the wavelength of the illumination light The following equation (1) is established between λ and the pixel pitch P of the spatial light modulator. Therefore, the maximum diffraction angle θ of the reproduction light is expressed by the following equation (2).

  Many spatial light modulators have a pixel pitch P of several tens of μm, and the wavelength of illumination light is in the visible range, so the diffraction angle θ is only a few degrees. Therefore, when a three-dimensional image is reproduced and displayed in the vicinity of the spatial light modulation element, the observer needs to observe at a distance of 1 m or more in order for the reproduction light generated in the entire area to enter the observer's pupil. . Furthermore, it is necessary to secure a longer distance for observation with both eyes. In the conventional three-dimensional image display technology, such a narrow viewing zone has been a problem.

  In contrast, in the three-dimensional image display system according to the present embodiment, a right-eye display device that forms a reproduced image to be observed with the observer's right eye, and a reproduced image to be observed with the observer's left eye. A display device for the left eye to be formed is provided separately, and each reproduced image is spatially overlapped by a mirror, a half mirror, or the like, so that the observer can observe the reproduced image with both eyes. In each of the right-eye display device and the left-eye display device, an optical system that forms a reproduction image by forming an image of the reproduction light generated by the spatial light modulator is configured as an afocal optical system. The latter stage optical system of the optical system is shared.

  The role of the rear optical system of the afocal optical system is to draw the position where the 0th-order diffracted wave and the higher-order diffracted wave cross to the front optical system side, and to determine the distance between the real image of the spatial light modulator and the three-dimensional reconstructed image. It is to shorten it. As a result, the calculation range of the propagation function is reduced, the amount of hologram calculation per bright spot can be reduced, and the overlap of hologram patterns per bright spot is reduced, so that limited spatial light There is an advantage that the gradation of the modulation element can be used effectively.

FIG. 1 is a plan view of a 3D image display system 1 according to the first embodiment. The three-dimensional image display system 1 shown in this figure includes a spatial light modulation element 11, a lens 12, a mask 13, a spatial light modulation element 21, a lens 22, a mask 23, a mirror 25, and a lens 31. The spatial light modulation element 11 and the spatial light modulation element 21 have the same configuration. Lens 12 and the lens 22 are of equal construction to each other, it has a focal length f _1. Lens 31 has a focal length _{f 2.} A mirror 25 is inserted in the optical path between the mask 23 and the lens 31, and the virtual image of the lens 22 by the mirror 25 overlaps the lens 12.

The distance between the spatial light modulator 11 and the lens 12 is f _1, the distance between the lens 12 and the mask 13 is f _1, the distance between the mask 13 and the lens 31 is a f ₂ . The lens 12 and the lens 31 constitute an afocal optical system, and form the image 14 of the spatial light modulation element 11 on the rear focal plane of the lens 31. Spatial light modulation element 11, a lens 12, a mask 13 and the lens 31 constitute a right eye display device for forming a right-eye reproduced image to be viewed by the observer's right eye E _R. In this right-eye display device, the spatial light modulator 11 presents a hologram, and generates reproduction light L _R1 by vertical incidence of illumination light L _I1 that is a plane wave. Afocal optical system (lens 12, 31) is imaged by entering the reproduction light L _R1 generated in the spatial light modulator 11, forming a right-eye reproduced image to be viewed by the observer's right eye E _R To do.

The distance between the spatial light modulator 21 and the lens 22 is f _1, the distance between the lens 22 and the mask 23 is f _1, the distance between the mask 23 and the lens 31 is f ₂ It is. The lens 22 and the lens 31 constitute an afocal optical system, and form an image 24 of the spatial light modulator 21 on the rear focal plane of the lens 31. Spatial light modulator 21, a lens 22, a mask 23 and the lens 31 constitute a display device for the left eye to form a left-eye reproduced image to be viewed by the observer's left eye E _L. In this left-eye display device, the spatial light modulation element 21 presents a hologram and generates reproduction light L _R2 by vertical incidence of illumination light L _I2 that is a plane wave. Afocal optical system (lens 22 and 31) is imaged by entering the reproduction light L _R2 generated in the spatial light modulator 21, forming a left-eye reproduced image to be viewed by the observer's left eye E _L To do.

  The afocal optical system (lenses 12 and 31) included in the right-eye display device and the afocal optical system (lenses 22 and 31) included in the left-eye display device are respectively used as subsequent optical systems. The lens 31 is shared, and the image 14 of the spatial light modulation element 11 and the image 24 of the spatial light modulation element 21 are formed in the same spatial region, and a reproduction image for the right eye and a reproduction image for the left eye Are formed in the same spatial region (a spatial region in the vicinity of the images 14 and 24).

In the display device for the right eye, the surface of the spatial light modulator 11 is perpendicular to the optical axis of the afocal optical system (lenses 12 and 31). On the other hand, in the display device for the left eye, the surface of the spatial light modulator 21 is inclined by an angle θ _{1 with} respect to the surface perpendicular to the optical axis of the afocal optical system (lenses 22 and 31).

In the display device for the right eye, the mask 13 provided on the rear focal plane of the lens 12 that is the front stage optical system of the afocal optical system has an opening having a size of “λf ₁ / P” or less, and spatial light modulation. High-order diffraction images such as ± 1st order and ± 2nd order are removed from the reproduced light generated by the element 11, and only the 0th-order reproduced light is allowed to pass through. In the left-eye display device, the mask 23 provided on the rear focal plane of the lens 22 which is the front stage optical system of the afocal optical system has an opening having a size of “λf ₁ / P” or less, and is a space. High-order diffraction images such as ± 1st order and ± 2nd order are removed from the reproduction light generated by the light modulation element 21, and only the 0th-order reproduction light is passed. Here, P is the pixel pitch of the spatial light modulators 11 and 21, and λ is the wavelength of the illumination light L _I1 and L _I2 .

Next, a method for removing high-order diffracted waves from the reproduction light generated by the spatial light modulator will be described. FIG. 2 is a plan view showing how the reproduction light is generated in the spatial light modulator 11. Since the spatial light modulator 11 has a discrete pixel structure, when illumination light that is a plane wave is perpendicularly incident on the spatial light modulator 11, reproduction is generated in the spatial light modulator 11 as shown in FIG. n next Oriha of the light is focused at a position a _n on the focal plane of the lens 12. Incidentally, the figure have represents a plan view, but focusing point A _n in the horizontal direction are discretely shown, two-dimensionally converging point at the focal plane of the lens 12 are present discretely .

When the diffraction angle of the n next Oriha of reproduction light generated at the spatial light modulator 11 and theta _o, the diffraction angle theta _o, the diffraction order n, the following between the illumination light wavelength λ and a pixel pitch P (3 ) Formula holds. Therefore, the diffraction angle of the n-order Oriha theta _o is expressed by the following equation (4).

The n-th order diffracted light beam that passes through the center of the convex lens 12 travels straight, and the n-th order diffracted wave generated at another position of the spatial light modulator 11 is also parallel to the light beam that passes through the center of the convex lens 12. since there, n next Oriha is focused on a point a _n of the back focal plane of the convex lens 12. In the figure, the spatial light modulation element 11 is located at the front focal plane of the lens 12, but regardless of this position, the diffraction angle is the same even if the spatial light modulation element 11 is arranged at the front and back, and the parallel light It will be condensed by a _n points on the focal plane of the lens 12. Distance from the optical axis to the focusing point A _n in the focal plane of the lens 12 is expressed by the following equation (5).

  When the order n is small, since the denominator of the rightmost side of the above equation (5) is approximately 1, the above equation (5) is approximated by the following equation (6). As can be seen from this equation, the condensing points of the diffracted waves of the respective orders are arranged at equal intervals on the rear focal plane of the lens 12.

FIG. 3 is a diagram illustrating how the diffracted waves of the respective orders are collected on the rear focal plane of the lens 12. Diffracted waves of each order of the reproduction light illumination light to the spatial light modulator 11 in which a hologram is presented occurs when the incident is passed through a square area centered on the focal point A _n at the focal plane of the lens 12 To do. The diffracted waves of the respective orders have the same wavefront but different amounts of light. Since the wavefronts of these orders of diffracted waves travel at different angles, the reconstructed images formed by them are shifted and overlapped with each other. Therefore, in order to take out only the 0th-order diffracted light and block other high-order diffracted light to remove the image overlap, a square aperture of one side size “λf ₁ / P” or less is formed on the rear focal plane of the lens 12. Is disposed, and a light shielding plate for shielding the condensing point of the 0th-order transmitted light is disposed at the center of the opening. If the spatial light modulator 11 can modulate both the amplitude and phase of light, a light shielding plate that shields the condensing point of the zeroth order transmitted light is unnecessary.

FIG. 4 is a plan view showing a left-eye display device (an optical system from the spatial light modulation element 21 to the image 24) in the three-dimensional image display system 1 according to the first embodiment. Here, it is assumed that the mirror 25 in FIG. 1 is omitted and the optical axes of the afocal optical systems (lenses 22 and 31) are on a straight line. In the left-eye display device, the surface of the spatial light modulation element 21 is inclined by an angle θ _{1 with} respect to a surface perpendicular to the optical axis of the afocal optical system (lenses 22 and 31), and is an illumination that is a plane wave. The light L _I2 is perpendicularly incident on the inclined spatial light modulator 21.

The diffracted waves of the respective orders of the reproduction light generated by the spatial light modulator 21 are emitted from the spatial light modulator 21 at the same diffraction angle as that of the spatial light modulator 11. The nth-order diffracted wave of the reproduction light generated by the spatial light modulator 21 is collected at a position _Bn on the rear focal plane of the lens 22. The diffracted waves of the respective orders of the reproduction light generated by the spatial light modulator 21 are diffracted waves having the same angle as that shown in FIG. 2, and the diffracted lights having the same order are parallel to each other. The interval between the condensing points for condensing light at the focal plane is the same as the above equation (6). Here, the light having a large amount of light is 0th-order light, and a mask 23 having a square opening having a side size “λf ₁ / P” or less around the condensing point B ₀ is formed on the rear focal plane of the lens 22. It is arranged to take out only the 0th-order diffracted light and block other high-order diffracted light. Since the intensity of the 0th-order diffracted light is usually more than an order of magnitude higher than that of the higher-order diffracted light, the light source can be used effectively as the reproduction light quantity.

FIG. 5 shows a display device for the right eye (an optical system from the spatial light modulation element 11 to the image 14) and a display device for the left eye (from the spatial light modulation element 21) in the three-dimensional image display system 1 according to the first embodiment. FIG. 6 is a plan view showing the optical system reaching the image 24) superimposed on each other. Also here, the mirror 25 in FIG. 1 is omitted, and the optical axes of the afocal optical system (lenses 12 and 31) and the afocal optical system (lenses 22 and 31) are assumed to coincide with each other. Further, in this figure, holograms for reproducing two bright spots are presented to the spatial light modulation element 11 and the spatial light modulation element 21 respectively, and the real image point C ₁ and the reproduction light generated by the spatial light modulation elements 11 and 12 are displayed. for the case of forming the image points D _1, shown superimposed these light beams.

The real image point C ₁ is converted into a virtual image point C ₂ by the lenses 12 and 22, and further converted into a real image point C ₃ by the lens 31. Further, the virtual image point D ₁ is converted into a virtual image point D ₂ by the lenses 12, 22, and 31 to be a real image point D ₃ .

When the spatial light modulator 11 has no inclination with respect to the optical axis, the light beam of the reproduction light has at least a size “λf ₁ ” centered on the condensing point A ₀ of the 0th order transmitted light on the rear focal plane of the lens 12. / P "passes through the area inside the square, is collected at the real image points C ₃ and D ₃ , and then diverges as a light beam having a central axis parallel to the optical axis.

The light beam of the reproduction light when the illumination plane wave is perpendicularly incident on the spatial light modulator 21 inclined by the angle θ _{1 with} respect to the optical axis is the condensing point B ₀ of the 0th order transmitted light on the rear focal plane of the lens 22. A center that passes through at least a region inside a square having a size of “λf ₁ / P” and is focused at the real image points C ₃ and D ₃ and then has an angle θ ₂ with respect to the optical axis. Diverges as a luminous flux with an axis.

By tilting angle theta ₂ with respect to the optical axis line of sight of the left eye E _L of the observer with the line of sight of the observer's right eye E _R and parallel to the optical axis, i.e., the spatial light modulator 21 By setting the center of the image 24 as the line-of-sight intersection, the observer can observe the real image points C ₃ and D ₃ with both eyes. In this case, parallax, it is possible to naturally observed to satisfy the focusing function of the congestion and eye, three-dimensional reconstructed image of the observation at close range by a large angle theta ₂ is possible. The viewing angle θe that can be observed with a single eye is expressed by the following formula (7) or (8), where M is the magnification of the afocal optical system. A magnification M at which the entire spatial light modulators 11 and 21 are imaged in this angular range is selected.

Next, the case where the spatial light modulator 21 is tilted by the angle theta ₁ around the Y1 axis, the position of the bright point to be reproduced on the spatial light modulation element 21 from the reproduction position of the bright spot to be observed by the eye of the observer The conversion to will be described. If the distance between the eyes of the observer is E and the distance from the center of both eyes to the centers of the images 14 and 24 of the spatial light modulators 11 and 21 (that is, the observation distance) is L, the angle θ ₂ is 9) It is represented by the formula or the formula (10).

FIG. 6 is a plan view showing the spatial light modulator 21 and its image 24. In this figure, the afocal optical system between the spatial light modulation element 21 and the image 24 is not shown, and the virtual image point D ₁ by the reproduction light generated in the spatial light modulation element 21 and the virtual image point D A real image point D ₃ corresponding to ₁ is shown.

  As shown in this figure, an X2-Y2-Z2 coordinate system is set with the rear focal position of the rear lens 31 of the afocal optical system (lenses 22 and 31) as the origin. The Y2 axis is the vertical direction, and the Z2 axis coincides with the optical axis of the afocal optical system. An X1-Y1-Z1 coordinate system with the center position of the spatial light modulator 21 as the origin is set. The Y1 axis is the vertical direction, and the Z1 axis coincides with the optical axis of the afocal optical system. In addition, an Xs-Ys-Zs coordinate system with the center position of the spatial light modulator 21 as the origin is set. The Ys axis is the vertical direction, and the Zs axis is the vertical direction with respect to the plane of the spatial light modulator 21.

The position of the virtual image point D ₁ formed by the spatial light modulation element 2 by the illumination light incidence is expressed as (x ₁ , y ₁ , z ₁ ) in the X1-Y1-Z1 coordinate system, and the observed position of the real image point D ₃ is It is expressed as (x ₂ , y ₂ , z ₂ ) in the X2-Y2-Z2 coordinate system. Between these image points D ₁ and object point D ₃ each coordinate value, relationship expressed by the following equation (11) or (12). Here, M is the magnification of the afocal optical system.

In addition, there is a relationship represented by the following formula (13) or (14) between the tilt angle θ ₁ of the spatial light modulator 21 and the tilt angle θ ₂ of the image 24 of the spatial light modulator 21.

A rotation matrix Tθ ₁ for converting a coordinate value in the X1-Y1-Z1 coordinate system into a coordinate value in the Xs-Ys-Zs coordinate system is expressed by the following equation (15). Then, the position (x ₁ , y ₁ , z ₁ ) of the virtual image point D ₁ expressed in the X1-Y1-Z1 coordinate system is the virtual image point D expressed in the Xs-Ys-Zs coordinate system according to the following equation (16). Is converted to a position of ₁ (x _s , y _s , z _s ).

When inserting a mirror between the spatial light modulation element 21 and the image 24, paying attention to the number of mirrors, the equations (11a) and (11b) and the above (12a) and (12b) It is necessary to give a sign to the formula as appropriate. This concludes the description of the coordinate transformation of the bright point to be presented to the left eye E _L. The coordinate conversion of the bright point to be presented to the right eye E _R, (11) uses a formula and (12), conversion of the rotation is not required.

  Next, a method for calculating a hologram to be presented to the spatial light modulation elements 11 and 21 will be described. In this calculation method, the spatial light modulation element spatially modulates both the amplitude and phase of light, and the spatial light modulation element spatially modulates only one of the amplitude and phase of light. It depends on what you want to do. As the calculation method, there are a spherical wave method and a Fresnel transform method using FFT (Fast Fourier Transform). Hereinafter, the calculation method will be described in four cases.

  First, a method for calculating a hologram by the spherical wave method when the spatial light modulation element modulates both the amplitude and phase of light will be described.

It is assumed that the three-dimensional reproduced image to be displayed is composed of q bright spots, and the h-th bright spot among the q bright spots is the amplitude I at the position of (x _s , y _s , z _s ). _h , the number of pixels of the spatial light modulator is N × N, and the complex amplitude distribution O _h (m, n) of the wavefront at the pixel in the m-th row and n-th column of the spatial light modulator is (17) It is expressed by an expression. At this time, it is important to calculate only when the phase between adjacent pixels does not exceed π (that is, the range in which the difference in distance between the bright spot and the pixel position does not exceed λ / 2).

  When the coordinate value zh is negative (that is, when the bright spot is located on the afocal optical system side with respect to the spatial light modulator), it is necessary to take a complex conjugate to correct the direction of light. Then, by accumulating the wavefronts from all the bright spots, the local component O (m, n) of the wavefront is expressed by the following equation (18).

  As described above, when the spatial light modulation element modulates both the amplitude and phase of light, the hologram to be presented to the spatial light modulation element is calculated by the spherical wave method.

  Next, a method for calculating a hologram by the Fresnel transformation method when the spatial light modulation element modulates both the amplitude and phase of light will be described.

  The wavefront O (i, j) on the spatial light modulator is obtained by inverse Fresnel transformation or Fresnel transformation from the wavefront o (i, j) of the bright spot. Further, instead of using the inverse Fresnel transform, a complex conjugate may be taken to reverse the direction of the wave front after the Fresnel transform from the bright spot to the spatial light modulator.

  In order to calculate the Fresnel transformation at high speed, since the Fresnel transformation is a convolution integral of the wavefront of the bright spot and the propagation function, the real image wavefront o (i, j) is expressed as shown in the following equation (19). This is equivalent to calculating the inverse Fourier transform of the product of the Fourier transform and the propagation function ((1 / r) exp (jkr)).

Here, F represents a Fourier transform, and k is a wave number. Further, if the z-direction distance from the bright spot to the hologram is z _s , r is expressed by the following equation (20).

  Since actual calculations are performed discretely, it is always necessary to examine the Nyquist interval. For this reason, instead of mechanically transforming the propagation function, the following approximate expression (21) obtained by analytically solving the Fourier transform of the propagation function may be used. Here, μ is a spatial frequency.

The above calculation is expressed discretely as follows. The propagation distance is z _s , the pitch of the hologram is P, the wavefront distribution at the bright spot is o (Pm, Pn), the wavefront on the hologram surface is O (Pm, Pn), and the propagation function is f (Pm, Pn). Pn), the wavefront O (Pm, Pn) on the hologram surface is expressed by the following equation (22). From this equation, the wavefront on the spatial light modulator is obtained. At this time, it is important to calculate only when the phase between adjacent pixels does not exceed π (that is, the range in which the difference in distance between the bright spot and the pixel position does not exceed λ / 2).

Depending on the Fresnel propagation distance z _s , it is preferable to use the following equation (23). Also at this time, it is important to calculate only when the phase between adjacent pixels does not exceed π (that is, the range in which the difference in distance between the bright spot and the pixel position does not exceed λ / 2).

  The above Fresnel conversion is repeated for the number of bright spots having different distances from the spatial light modulation element, and the obtained wavefronts are cumulatively added to obtain a hologram to be written in the spatial light modulation element. As described above, when the spatial light modulation element modulates both the amplitude and phase of light, the hologram to be presented to the spatial light modulation element is calculated by the Fresnel conversion method.

  Next, a method for calculating a hologram by the spherical wave method when the spatial light modulation element modulates only one of the amplitude and phase of light will be described. When using a spatial light modulator that modulates only one of the amplitude and phase of light as compared to the case of using a spatial light modulator that modulates both the amplitude and phase of light as described above, the wavefront It is important to note the following two points in the calculation.

As a first point of attention, the wavefront is calculated only for half of the wavefront propagating from the bright spot onto the spatial light modulator, and 0 is given as data for the remaining half. That is, in the hologram display region centered on the normal line from the spatial light modulation element that passes through the bright spot, the line segment assumed to be parallel to the normal line and the Xs axis is used as the axis of symmetry of the Ys axis. A region (hereinafter referred to as “Ys ⁺ region”) and a region in the negative direction of the Ys axis (hereinafter referred to as “Ys ⁻ region”) are divided into two. Then, a case of calculating the transfer function only Ys ⁺ region Ys ^- performed in the case of calculating only the propagation function region, two types of.

As a second point of attention, each of the apertures of the masks 13 and 23 placed on the back focal planes of the front lenses 12 and 22 of the afocal optical system passes through the condensing point of the 0th-order transmitted light and is parallel to the Xs axis. The opening is limited to a half opening with line segments symmetrical. That is, the mask 13 of the right-eye display device includes a case leaving an opening on closing the opening below the A _0-point, two kinds of the case to leave an opening at the bottom closes the opening above the A ₀ points carry out. Also, the mask 23 of the left-eye display device, and when leaving an opening on closing the opening below the ₀ point B, two kinds of the case to leave an opening at the bottom closes the opening above the _zero point B carry out.

It is assumed that the three-dimensional reproduced image to be displayed is composed of q bright spots, and the h-th bright spot among the q bright spots is the amplitude I at the position of (x _s , y _s , z _s ). _h and the number of pixels of the spatial light modulator is N × N. When calculating the propagation function only in the Ys ⁻ region, the complex amplitude distribution O _h (m, n) of the wavefront in the pixel in the m-th row and the n-th column of the spatial light modulator is expressed by the following equation (24) and ( 25). On the other hand, when calculating the propagation function only in the Ys ⁺ region, the complex amplitude distribution O _h (m, n) of the wavefront in the pixel in the m-th row and the n-th column of the spatial light modulator is given by the following equation (26): And (27). At this time, it is important to calculate only when the phase between adjacent pixels does not exceed π (that is, the range in which the difference in distance between the bright spot and the pixel position does not exceed λ / 2).

  When the coordinate value zh is negative (that is, when the bright spot is located on the afocal optical system side with respect to the spatial light modulator), it is necessary to take a complex conjugate to correct the direction of light. Then, by accumulating the wavefronts from all the bright spots, the local component O (m, n) of the wavefront is expressed by the following equation (28).

  Further, by extracting the real number component of the equation (28) by the following equation (29), the hologram distribution ON (i, j) to be presented to the spatial light modulation element that modulates only one of the amplitude and the phase of light. ) Further, as another method for extracting only the real number component, the above equation (24) and after may be calculated using only the real number.

  As described above, when the spatial light modulation element modulates only one of the amplitude and phase of light, the hologram to be presented to the spatial light modulation element is calculated by the spherical wave method.

  Next, a method for calculating a hologram by the Fresnel transformation method when the spatial light modulation element modulates only one of the amplitude and phase of light will be described. Also in this case, it is important to pay attention to the first and second points to be noted.

  The wavefront O (i, j) on the spatial light modulator is obtained by inverse Fresnel transformation or Fresnel transformation from the wavefront o (i, j) of the bright spot. Further, instead of using the inverse Fresnel transform, a complex conjugate may be taken to reverse the direction of the wave front after the Fresnel transform from the bright spot to the spatial light modulator.

  In order to calculate the Fresnel transform at high speed, since the Fresnel transform is a convolution integral of the wavefront of the bright spot and the propagation function, the real image wavefront o (i, j) can be expressed by the following equation (30). This is equivalent to calculating the inverse Fourier transform of the product of the Fourier transform and the propagation function ((1 / r) exp (jkr)).

Here, F represents a Fourier transform, and k is a wave number. Further, when the z-direction distance from the bright spot to the hologram is z _s , r is expressed by the following equation (31).

Whether to use any of a virtual image reproduced image and real reproduced image formed by the spatial light modulation element, in order to switch the light-shielding portion of the opening to be described later, by utilizing the two case analysis, the case of Ys ⁺ or In the case of Ys ⁻ , the value of the propagation function is set to 0 as represented by the following equation (32).

  Instead of mechanically Fourier transforming the propagation function, the following approximate expression (33) obtained by analytically solving the Fourier transform of the propagation function may be used. Here, μ is a spatial frequency.

The above calculation is expressed discretely as follows. The propagation distance is z _s , the pitch of the hologram is P, the wavefront distribution at the bright spot is o (Pm, Pn), the wavefront on the hologram surface is O (Pm, Pn), and the propagation function is f (Pm, Pn). Pn), the wavefront O (Pm, Pn) on the hologram surface is expressed by the following equation (34). From this equation, the wavefront on the spatial light modulator is obtained. However, the transfer function f (Pm, Pn) for, when the Ys ⁺ is the following equation (35), Ys ^- the following equation (36) in the case of. At this time, it is important to calculate only when the phase between adjacent pixels does not exceed π (that is, the range in which the difference in distance between the bright spot and the pixel position does not exceed λ / 2).

Depending on the Fresnel propagation distance z _s , it is preferable to use the following equation (37). However, when the propagation function and the half-plane, and because the even Fourier transform becomes half plane, propagation function f (Pm, Pn) for the Fourier transform of the case of Ys ⁺ The following equation (38), Ys ^- the case of Is the following equation (39). Also at this time, it is important to calculate only when the phase between adjacent pixels does not exceed π (that is, the range in which the difference in distance between the bright spot and the pixel position does not exceed λ / 2).

  The above Fresnel conversion is repeated for the number of bright spots having different distances from the spatial light modulation element, and the obtained wavefronts are cumulatively added to obtain a hologram to be written in the spatial light modulation element. As described above, when the spatial light modulation element modulates only one of the amplitude and phase of light, the hologram to be presented to the spatial light modulation element is calculated by the Fresnel transform method.

  Next, a description will be given of light shielding by the masks 13 and 23 when a spatial light modulation element that modulates only one of the amplitude and phase of light is used and the propagation function is used only in the half plane as described above. To do.

FIG. 7 is a perspective view showing a right-eye display device (an optical system from the spatial light modulation element 11 to the image 14) in the three-dimensional image display system 1 according to the first embodiment. The figure (a) shows the perspective view. FIG. 2B shows a front view of the mask 13. In this figure, a hologram, which is a calculation result obtained by convolving a Ys ⁻ half-plane propagation function with respect to one bright spot, is presented to the spatial light modulator 11, and the illumination plane wave incident perpendicularly to the spatial light modulator 11 is used. A reconstructed image is shown. The calculation result obtained by convolving the half-plane propagation function with respect to one bright spot is obtained by halving the cosine wave zone plate in a central symmetry.

When the illuminated part of the cosine wave zone plate is enlarged, it can be considered that the diffraction grating is recorded. When a beam-like plane wave is incident on this diffraction grating, not only 0th order transmitted light (0th order light) is generated but also ± 1st order light that is diffracted with an angle is generated. Order diffracted light to generate a real image point C _1, -1 order diffracted light generates the image points D _1. Since the entire hologram is illuminated, such ± first-order diffracted light is generated in each minute portion, and a real image point C ₁ and a virtual image point D ₁ are formed. The real image point C ₁ and the virtual image point D ₁ are transmitted by the afocal optical system including the lenses 12 and 31 to form real image points C ₃ and D ₃ .

On the cosine wave zone plate of FIG. 7, at the incident position far from the bright point (real image point C ₁ , virtual image point D ₁ ) (ie, away from the center), the distance between the cosine wave zone plates is small, Therefore, the diffraction angle becomes large. On the other hand, at the incident position close to the luminescent spot (real image point C ₁ , virtual image point D ₁ ) (that is, close to the center), the distance between the cosine wave zone plates is large, so the distance as the diffraction grating is also large. The corner becomes smaller.

The + 1 since order diffracted light and -1-order diffracted light each diffraction angles are equal to each other, the distance from the hologram surface to object point C _1, and the distance from the hologram plane to the virtual image point D _1, equal to each other. Therefore, the real image point C ₁ and the virtual image point D ₁ are reproduced at positions symmetrical with respect to each other with the hologram plane as a symmetry plane. The aperture of the mask 13 transmits the 0th-order diffracted wave, but the spatial light modulator 11 described below reproduces by further adding a light-shielding plate that divides the aperture into two above and below the condensing point and shields one of them. having any function of selecting one of the real image points C ₁ and image points D ₁ to.

8 and 9 show the Ys ⁻ half-plane propagation function in the right-eye display device (the optical system from the spatial light modulator 11 to the image 14) in the three-dimensional image display system 1 according to the first embodiment. It is a side view which shows the light beam at the time of utilizing. Figure 8 shows a light beam of image points D _1, FIG. 9 shows a light beam of the real image point C _1. In the case of reproduction by the Ys ⁻ half-plane propagation function, the light beam from the virtual image reproduction image D ₁ is downward with respect to the optical axis, and the light beam from the real image reproduction image C ₁ is upward with respect to the optical axis. Therefore, when the light beam above the optical axis is shielded on the rear focal plane of the lens 12, a real image obtained by forming the virtual image reproduction image of the hologram by the lens is obtained (FIG. 8), and below the optical axis on the rear focal plane of the lens 12. When the light beam is blocked, a real image reproduction image of the hologram is obtained as a virtual image by the lens (FIG. 9).

10 and 11 show Ys ⁺ half-plane propagation functions in the right-eye display device (optical system from the spatial light modulator 11 to the image 14) in the three-dimensional image display system 1 according to the first embodiment. It is a side view which shows the light beam at the time of utilizing. Figure 10 shows a light beam of image points D _1, Figure 11 shows the luminous flux of object point C _1. In the case of reproduction by half-plane propagation function ys ⁺ is light from the virtual image reproduced image D ₁ is the upward relative to the optical axis, light rays from the real image reproduced image C ₁ is downward with respect to the optical axis. Therefore, if light rays below the optical axis are shielded on the rear focal plane of the lens 12, a real image in which a virtual image reproduction image of the hologram is formed by the lens is obtained (FIG. 10), and above the optical axis on the rear focal plane of the lens 12. When the light beam is blocked, a real image reproduction image of the hologram is obtained as a virtual image by the lens (FIG. 11).

  Even if the reconstructed object is composed of a plurality of bright spots, on the hologram surface, due to the nature of convolution integral, a plurality of one-point half-plane propagation functions are superimposed, so that the state of reproduction is also one-half Similar to a hologram with a plane propagation function.

  As described above, in the 3D image display system and the 3D display method using the system according to the first embodiment, the viewing area is secured by using the right eye display device and the left eye display device. And miniaturization of the system. In addition, since the 0th-order diffracted wave is used in the reproduction light generated by the spatial light modulator, a bright image can be obtained and the use efficiency of the illumination light is good.

(Second Embodiment)
Next, a second embodiment of the three-dimensional image display system according to the present invention will be described. Also in the second embodiment, when the viewing zone is expanded by using a plurality of 0th-order diffracted waves, the latter lens of the afocal optical system composed of at least two lenses is shared to reduce the number of parts.

  FIG. 12 is a plan view of the 3D image display system 2 according to the second embodiment. The three-dimensional image display system 2 includes three sets of display devices. In this figure, illustration of a mirror, a half mirror, etc. is abbreviate | omitted, and the afocal optical system contained in each of 3 sets of display apparatuses is mutually superimposed and displayed.

  Of the three sets of display devices, the first display device includes an optical system from the spatial light modulation element 51 to the image 54, and includes a lens 52 and a lens 81 as an afocal optical system. The second display device includes an optical system from the spatial light modulator 61 to the image 64, and includes a lens 62 and a lens 81 as an afocal optical system. The third display device includes an optical system from the spatial light modulator 71 to the image 74, and includes a lens 72 and a lens 81 as an afocal optical system. Images 54, 64, and 74 are images of the spatial light modulation elements 51, 61, and 71 using an afocal optical system.

The three spatial light modulators 51, 61, 71 are arranged to be inclined with respect to each other with a specific angle with respect to the afocal optical system. In addition, illumination light that is a plane wave is vertically incident on each of the three spatial light modulation elements 51, 61, and 71. Here, the specific angle of the spatial light modulator is such that the traveling direction of the nth-order diffracted wave can coincide with the optical axis of the afocal optical system, and the arrangement angle θ _{n of the nth} spatial light modulator Is represented by the following equation (40).

  Even if the spatial light modulator has an angle with respect to the optical axis, the illumination plane wave is incident perpendicularly to the spatial light modulator to generate a diffracted wave. The angle of the diffracted wave follows the equation (40), and therefore the lens 52 , 62, 72 are parallel to each other, and exhibit the same behavior as the above expressions (5) and (6) on the rear focal planes of the lenses 52, 62, 72.

In FIG. 12, when an illumination plane wave is incident perpendicularly to a spatial light modulator arranged at an angle θ _n with respect to a plane perpendicular to the optical axis, the 0th-order diffracted light generated by the spatial light modulator is shown in FIG. focusing point a as the _n, focused on the n next Oriha the focal point when a is incident illumination plane wave vertically arranged spatial light modulator at angles 0.

For example, when an illumination plane wave is vertically incident on a spatial light modulator having an angle θ ₁ , the 0th-order diffracted light is condensed at the condensing point A ₁ and the −1st-order diffracted light is condensed at the condensing point A ₀ . and, + 1-order diffracted light is focused at the focal point a _2. At this time, the −1st order diffracted light follows the same light beam as the 0th order diffracted light when the illumination plane wave is vertically incident on the spatial light modulator arranged without giving an angle.

Further, for example, when an illumination plane wave is vertically incident on a spatial light modulator having an angle θ ₂ , the 0th-order diffracted light is collected at the condensing point A ₂ and the −1st-order diffracted light is collected at the condensing point A ₁ . light and -2-order diffracted light is focused on the focal point a _0. At this time, the −2nd order diffracted light follows the same luminous flux as the 0th order diffracted light when the illumination plane wave is vertically incident on the spatial light modulator arranged without giving an angle.

As described above, when the illumination plane wave perpendicular to the spatial light modulation element arranged with the angle θ _n represented by the above equation (40) is incident, the zeroth-order diffraction generated in the spatial light modulation element. The waves follow a different path by the afocal optical system and are re-imaged. The different paths pass through positions indicated by the above formula (5) or (6). The wavefront generated by the hologram is equally contained in the nth-order diffracted wave, but the intensity of the 0th-order diffracted wave is maximized. Therefore, it is effective to reproduce the three-dimensional object using this 0th-order diffracted wave. It becomes use.

  Here, as in FIG. 4, the X2-Y2-Z2 coordinate system is set with the rear focal position of the rear lens 81 of the afocal optical system as the origin. The Y2 axis is the vertical direction, and the Z2 axis coincides with the optical axis of the afocal optical system. An X1-Y1-Z1 coordinate system having the origin at the center position of the spatial light modulator is set. The Y1 axis is the vertical direction, and the Z1 axis coincides with the optical axis of the afocal optical system. Also, an Xs-Ys-Zs coordinate system with the center position of the spatial light modulator as the origin is set. The Ys axis is the vertical direction, and the Zs axis is the vertical direction with respect to the plane of the spatial light modulator.

The position of the virtual image point D ₁ formed by the spatial light modulation element by the illumination light incidence is expressed as (x ₁ , y ₁ , z ₁ ) in the X1-Y1-Z1 coordinate system, and the observed position of the real image point D ₃ is X2 It is expressed as (x ₂ , y ₂ , z ₂ ) in the -Y2-Z2 coordinate system. Between the coordinate values of the virtual image point D ₁ and the real image point D _3, there is a relationship represented by the above expression (11) or (12).

The rotation matrix Tθ _n for converting the coordinate value in the X1-Y1-Z1 coordinate system into the coordinate value in the Xs-Ys-Zs coordinate system is expressed by the following equation (41). The position (x ₁ , y ₁ , z ₁ ) of the virtual image point D ₁ expressed in the X1-Y1-Z1 coordinate system is expressed by the virtual image point D expressed in the Xs-Ys-Zs coordinate system according to the following equation (42). Is converted to a position of ₁ (x _s , y _s , z _s ).

Further, the inclination θ _on of the image of the spatial light modulation element has a relationship represented by the following expression (43) or (44) with respect to the inclination θn of the spatial light modulation element. Further, when the above equation (40) is substituted into this equation (44) and approximated, the following equation (45) is obtained.

  The method for calculating the hologram is the same as in the first embodiment.

Next, it will be described with reference to FIG. 13 that the divergence angle of the reproduction bright spot is increased and the viewing zone is enlarged. FIG. 13 is a plan view showing a state of reproduction light generation in the three-dimensional image display system 2 according to the second embodiment. Also in this figure, illustration of a mirror, a half mirror, etc. is abbreviate | omitted, and the afocal optical system contained in each of three sets of display apparatuses is mutually superimposed and displayed. Further, in this figure, holograms for reproducing two bright spots are presented to the spatial light modulation elements 51, 61, 71, respectively, and the real image point C ₁ and the reproduction light generated by the spatial light modulation elements 51, 61, 71 are displayed. for the case of forming the image points D _1, shown superimposed these light beams.

The real image point C ₁ is converted into a virtual image point C ₂ by the lenses 52, 62, and 72, and further converted into a real image point C ₃ by the lens 81. Further, the virtual image point D ₁ is converted into a virtual image point D ₂ by the lenses 52, 62, 72, and ₃₁ to be a real image point D ₃ .

When the spatial light modulator 51 is not inclined with respect to the optical axis, the light beam of the reproduction light has at least a size “λf ₁ ” centered on the condensing point A ₀ of the 0th order transmitted light on the rear focal plane of the lens 52. / P "passes through the area inside the square, is collected at the real image points C ₃ and D ₃ , and then diverges as a light beam having a central axis parallel to the optical axis.

The light beam of the reproduction light when the illumination plane wave is perpendicularly incident on the spatial light modulation element 61 inclined by the angle θ _{1 with} respect to the optical axis is the condensing point A ₊₁ of the 0th order transmitted light on the rear focal plane of the lens 62. A center that passes through at least a region inside a square having a size of “λf ₁ / P” and is focused at the real image points C ₃ and D ₃ and then has an angle θ _o1 with respect to the optical axis. Diverges as a luminous flux with an axis.

When the illumination plane wave is perpendicularly incident on the spatial light modulator 71 tilted by an angle (−θ ₁ ) with respect to the optical axis, the light beam of the reproduction light is collected by the zero-order transmitted light on the rear focal plane of the lens 72. The light passes through at least a region inside a square having a size of “λf ₁ / P” centered on the point A− ₁ , is condensed at the real image points C ₃ and D ₃ , and then has an angle θ _{o− with} respect to the optical axis. Diverges as a light beam having a central axis with an inclination of ₁ .

Since the apertures of the size “λf ₁ / P” on the rear focal planes of the lenses 52, 62, and 72 are continuously arranged, the divergent light beams from the real image points C ₃ and D ₃ are continuous, The continuous viewing zone is expanded. Therefore, it is not necessary to fix the viewpoint as in the first embodiment.

  12 and 13, the spatial light modulation elements 51, 61 and 71 are displayed as if they exist in the same spatial region. Only one set of the spatial light modulation element and the illumination light source is provided, and these directions are changed in time series, and the hologram is presented to the spatial light modulation element according to the direction, and the afocal optical system The position of the opening on the rear focal plane of the front lens may be changed by, for example, an electromagnetic shutter. However, a configuration as shown in FIG. 14 may be used more suitably and simply.

FIG. 14 is a plan view of the 3D image display system 2 according to the second embodiment. The three-dimensional image display system 2 shown in this figure includes a spatial light modulator 51, a lens 52, a mask 53, a spatial light modulator 61, a lens 62, a mask 63, a mirror 65, a spatial light modulator 71, a lens 72, and a mask. 73, a mirror 75 and a lens 81. The spatial light modulators 51, 61, 71 have the same configuration. Lens 52, 62, 72 is of comparable construction to each other, has a focal length _{f 1.} Lens 81 has a focal length _{f 2.} A mirror 65 is inserted in the optical path between the mask 63 and the lens 81, and the virtual image of the lens 62 by the mirror 65 overlaps the lens 52. A mirror 75 is inserted in the optical path between the mask 73 and the lens 81, and the virtual image of the lens 72 by the mirror 75 overlaps the lens 52.

The distance between the spatial light modulator 51 and the lens 52 is f _1, the distance between the lens 52 and the mask 53 is f _1, the distance between the mask 53 and the lens 81 is f ₂ . The lens 52 and the lens 81 constitute an afocal optical system, and form an image 54 of the spatial light modulation element 51 on the rear focal plane of the lens 81. The spatial light modulation element 51, the lens 52, the mask 53, and the lens 81 constitute one display device. In this display device, the spatial light modulation element 51 presents a hologram and generates reproduction light by vertical incidence of illumination light that is a plane wave. The afocal optical system (lenses 52 and 81) inputs the reproduction light generated by the spatial light modulation element 51 and forms an image by forming an image.

The distance between the spatial light modulator 61 and the lens 62 is f _1, the distance between the lens 62 and the mask 63 is f _1, the distance between the mask 63 and the lens 81 is f ₂ . The lens 62 and the lens 81 constitute an afocal optical system, and form an image 64 of the spatial light modulator 61 on the rear focal plane of the lens 81. The spatial light modulator 61, the lens 62, the mask 63, and the lens 81 constitute one display device. In this display device, the spatial light modulation element 61 presents a hologram and generates reproduction light by vertical incidence of illumination light that is a plane wave. The afocal optical system (lenses 62 and 81) inputs the reproduction light generated by the spatial light modulation element 61 and forms an image by forming an image.

The distance between the spatial light modulator 71 and the lens 72 is f _1, the distance between the lens 72 and the mask 73 is f _1, the distance between the mask 73 and the lens 81 is f ₂ It is. The lens 72 and the lens 81 constitute an afocal optical system, and form an image 74 of the spatial light modulator 71 on the rear focal plane of the lens 81. The spatial light modulator 71, the lens 72, the mask 73, and the lens 81 constitute one display device. In this display device, the spatial light modulator 71 presents a hologram and generates reproduction light by vertical incidence of illumination light that is a plane wave. The afocal optical system (lenses 72 and 81) inputs the reproduction light generated by the spatial light modulation element 71 and forms an image by forming an image.

  The afocal optical system (lenses 52 and 81), the afocal optical system (lenses 62 and 81), and the afocal optical system (lenses 72 and 81) share the lens 81 as the subsequent optical system. The images 54, 64, 74 of the spatial light modulators 51, 61, 71 are formed in the same spatial region, and the reproduced images are formed in the same spatial region (near the images 54, 64, 74). Space region).

The surface of the spatial light modulator 61 is inclined by an angle (−θ ₁ ) with respect to a surface perpendicular to the optical axis of the afocal optical system (lenses 62 and 81). Further, the surface of the spatial light modulator 71 is inclined by an angle θ _{1 with} respect to a surface perpendicular to the optical axis of the afocal optical system (lenses 72 and 81). Here, the angle θ ₁ is expressed by the above equation (40).

The mask 53 provided on the rear focal plane of the lens 52 has an opening having a size of “λf ₁ / P” or less, and ± 1st order, ± 2nd order, etc. of the reproduction light generated by the spatial light modulator 51. Are removed, and only the 0th order reproduction light is allowed to pass through. The mask 63 provided on the rear focal plane of the lens 62 has an opening having a size of “λf ₁ / P” or less, and ± 1st order, ± 2nd order, etc. of the reproduction light generated by the spatial light modulator 61. Are removed, and only the 0th order reproduction light is allowed to pass through. The mask 73 provided on the rear focal plane of the lens 72 has an opening having a size of “λf ₁ / P” or less, and ± 1st order and ± 2 of the reproduction light generated by the spatial light modulator 71. The next-order higher-order diffraction image is removed, and only the 0th-order reproduction light is allowed to pass. Here, P is the pixel pitch of the spatial light modulators 51, 61, 71, and λ is the wavelength of the illumination light.

  Even in the three-dimensional image display system according to the second embodiment configured as described above, by using a plurality of display devices, a viewing zone can be secured and the system can be downsized. In addition, since the 0th-order diffracted wave is used in the reproduction light generated by the spatial light modulator, a bright image can be obtained and the use efficiency of the illumination light is good.

1 is a plan view of a 3D image display system 1 according to a first embodiment. 3 is a plan view showing a state of reproduction light generation in the spatial light modulation element 11. FIG. It is a figure which shows the mode of condensing of the diffraction wave of each order in the back focal plane of the lens. It is a top view which shows the display apparatus for left eyes (the optical system from the spatial light modulation element 21 to the image 24) in the three-dimensional image display system 1 which concerns on 1st Embodiment. In the three-dimensional image display system 1 according to the first embodiment, a display device for the right eye (an optical system from the spatial light modulator 11 to the image 14) and a display device for the left eye (from the spatial light modulator 21 to the image 24). FIG. 2 is a plan view showing a spatial light modulation element 21 and an image 24 thereof. FIG. It is a perspective view which shows the display apparatus for right eyes (the optical system from the spatial light modulation element 11 to the image 14) in the three-dimensional image display system 1 which concerns on 1st Embodiment. FIG. 6 shows a light beam when a Ys ⁻ half-plane propagation function is used in a right-eye display device (an optical system from the spatial light modulator 11 to the image 14) in the three-dimensional image display system 1 according to the first embodiment. It is a side view. FIG. 6 shows a light beam when a Ys ⁻ half-plane propagation function is used in a right-eye display device (an optical system from the spatial light modulator 11 to the image 14) in the three-dimensional image display system 1 according to the first embodiment. It is a side view. FIG. 6 shows a light beam when a Ys ⁺ half-plane propagation function is used in the right-eye display device (an optical system from the spatial light modulator 11 to the image 14) in the three-dimensional image display system 1 according to the first embodiment. It is a side view. FIG. 6 shows a light beam when a Ys ⁺ half-plane propagation function is used in the right-eye display device (an optical system from the spatial light modulator 11 to the image 14) in the three-dimensional image display system 1 according to the first embodiment. It is a side view. It is a top view of the three-dimensional image display system 2 which concerns on 2nd Embodiment. It is a top view which shows the mode of the generation | occurrence | production of the reproduction | regeneration light in the three-dimensional image display system 2 which concerns on 2nd Embodiment. It is a top view of the three-dimensional image display system 2 which concerns on 2nd Embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1, 2 ... Three-dimensional image display system, 11 ... Spatial light modulation element, 12 ... Lens, 13 ... Mask, 14 ... Image, 21 ... Spatial light modulation element, 22 ... Lens, 23 ... Mask, 24 ... Image, 25 ... Mirror, 31 ... lens, 51 ... spatial light modulator, 52 ... lens, 53 ... mask, 54 ... image, 61 ... spatial light modulator, 62 ... lens, 63 ... mask, 64 ... image, 65 ... mirror, 71 ... Spatial light modulation element, 72 ... lens, 73 ... mask, 74 ... image, 75 ... mirror, 81 ... lens.

Claims (4)

A first spatial light modulation element that presents a first hologram and generates first reproduction light by vertical incidence of the first illumination light, and inputs and images the first reproduction light generated by the first spatial light modulation element A first display device including a first afocal optical system for forming a first reproduced image;
A second spatial light modulation element that presents a second hologram and generates second reproduction light by vertical incidence of second illumination light, and inputs and images the second reproduction light generated by the second spatial light modulation element A second display device including a second afocal optical system for forming a second reproduced image;
With
Mirrors are provided on either or either of the optical path between the front optical system and the rear optical system of the first afocal optical system and the optical path between the front optical system and the rear optical system of the second afocal optical system. The virtual image by the mirror of one preceding optical system of the first afocal optical system and the second afocal optical system is overlapped with the virtual image by the other preceding optical system or the mirror of the preceding optical system. ,
The latter optical system of each of the first afocal optical system and the second afocal optical system is common,
The first afocal optical system and the second afocal optical system form the first reproduced image and the second reproduced image in the same spatial region;
In the second display device, a surface of the second spatial light modulator is inclined with respect to a surface perpendicular to the optical axis of the second afocal optical system,
In the first display device, the pixel pitch of the first spatial light modulator is P, the focal length of the front optical system of the first afocal optical system is f, and the wavelength of the first illumination light is λ. Sometimes, a first mask having an opening of a size “λf / P” or less is provided on the back focal plane of the front stage optical system of the first afocal optical system,
In the second display device, the pixel pitch of the second spatial light modulator is P, the focal length of the front optical system of the second afocal optical system is f, and the wavelength of the second illumination light is λ. Sometimes, a second mask having an opening of a size “λf / P” or less is provided on the rear focal plane of the front stage optical system of the second afocal optical system,
A three-dimensional image display system characterized by this. In the first display device, the first-order light included in the first reproduction light generated by the first spatial light modulation element is condensed by a first stage optical system of the first afocal optical system. The center of the mask opening is located,
In the second display device, the second-order light included in the second reproduction light generated by the second spatial light modulation element is condensed by the front optical system of the second afocal optical system. The center of the mask opening is located,
The three-dimensional image display system according to claim 1. In the second display device, when the inclination angle of the surface of the second spatial light modulator with respect to the surface perpendicular to the optical axis of the second afocal optical system is an integer other than 0 , “sin ⁻¹ The three-dimensional image display system according to claim 1, wherein (nλ / P) ”. A method for displaying a three-dimensional image using the three-dimensional image display system according to claim 1, comprising:
In the second display device, the angle of inclination of the surface of the second spatial light modulator with respect to the surface perpendicular to the optical axis of the second afocal optical system, the position of the observer observing the three-dimensional image, and both eyes Set according to the interval,
Forming a first reproduced image by the first display device and forming a second reproduced image by the second display device;
A three-dimensional image display method characterized by the above.

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