JP2989115B2 - Stereoscopic display method and stereoscopic display device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a stereoscopic display method for stereoscopic display of a virtual object or an actual object, and
The present invention relates to a three-dimensional display device that performs three-dimensional display using the three-dimensional display method.

[0002]

2. Description of the Related Art In stereoscopic display technology, two images are given to each eye, images are formed on the retinas of both eyes while being shifted, and only a binocular parallax function for generating binocular parallax is used. Conventionally, stereoscopic display has been implemented. However, the above-mentioned binocular parallax function, which is a factor that constitutes a sense of distance in human vision, an adjustment function for changing the focal length of the crystalline lens, and a certain point due to both eyes. There is an advantage of having all of the convergence function felt when observing from the angle of the line of sight when gazing at the eyes, for light wavefront control for images of virtual objects and real objects Attention has been focused on a technique for displaying a hologram or kinoform three-dimensionally based on the hologram or kinoform created after the hologram or kinoform is created.

Such a three-dimensional display makes it easy to visually understand the structure of a three-dimensional object and gives a sense of power. Therefore, it is possible to display mechanical objects calculated by a computer (computer system) or the like, display medical images, It can also be applied to entertainment displays such as amusement facilities and movies, and excellent effects are expected.

Conventionally, as a typical example of a stereoscopic display device capable of updating a stereoscopic image by light wavefront control, the one disclosed in the following document is known. (Reference 1) "Sunthetic aperture holography: a novel
approach to three-dimenshional displays "Piere St.
Hilaire, Stephen A. Benton, and Mark Lucente J. Opt.S
oc.Am.A vol.9, No.11, p1969 (1992) (Reference 2) "Konoform using an electrically controll
ed birefringent liquied-crystal spatial light m od
ulator "Jun Amako and Tomio Sonehara APPLIEDOPTICS
vol.30, No.32, p4622 (1991) (Reference 3) "Wave-front control using liquid-crystal
devices "APPLIED OPTICS vol.32, No.23, p4323 (1993) Any of the devices disclosed in these documents employs a wavefront-controlled readout light and modulation of either amplitude modulation or phase modulation or both. At the same time, a spatial light modulator for controlling the wavefront and a calculation means for creating data for wavefront control called a hologram or kinoform to be applied to the spatial light modulator are provided.

[0005]

However, since the spatial resolution of the rewritable spatial light modulator is limited, its diffraction angle is reduced, and a sufficiently large spatial light modulator capable of modulating over a wide area. It is difficult to realize the device. Therefore, it is technically difficult to obtain a large stereoscopic display image.

In addition, since light is emitted at a large angle for the purpose of expanding the field of view, a plurality of spatial light modulators having low spatial resolution are arranged along a virtual display surface (for example, a cylindrical surface or a spherical surface). (Japanese Patent Laid-Open No. 6-102813)
However, in this technology, the size of the stereoscopic image itself is still limited to the spatial resolution of one spatial light modulator, and a plurality of spatial light There is a problem that a complicated configuration is required due to the necessity of using an element.

An attempt to read a spatial light modulator having a low spatial resolution with a reduced confocal lens system and convert the spatial light modulator to a high spatial resolution is disclosed in Japanese Patent Application Laid-Open No. HEI 3-110592 and the following document.

(Reference 4) "Real-Time Display of 3-DC
omputer Data Using Computer Generated Holograms ",
Hamid Farhoosh, Yashaiahu Fainman, Kristopher Urqu
hart, and Sing H. Lee SPIE vol.1052 Holographic Opti
cs: Optically and ComputerGenerated (1989) 172-176 However, according to the techniques described in these documents, the optical image forming the stereoscopic image is generated from the image of the reduced spatial light modulator. The field of view that can be observed by the observer is limited to the angle between the observer's eyes and the spatial light modulator. Therefore, the field of view becomes small in exchange for the improvement of the spatial resolution.

A method of observing a plane image by enlarging it with a lens is general and has no novelty. However, a method utilizing stereoscopic vision is disclosed in Japanese Patent Application Laid-Open No. Hei 6-27410. . Since this aims at enlarging only a specific planar image, there is no technical disclosure about a method of correcting an enlargement magnification based on a distance between a three-dimensional image and a lens and a method of correcting aberration of a lens.

The present invention has been made in view of such problems of the prior art, and it is difficult to enlarge an image due to distortion of an image due to lens aberration and a characteristic limit of a spatial light modulator. It is an object of the present invention to provide a three-dimensional display method capable of realizing a clear and large three-dimensional image by eliminating the problem and a three-dimensional display device that performs three-dimensional display using the three-dimensional display method.

[0011]

According to the present invention, there is provided a stereoscopic display method comprising the steps of: displaying a second three-dimensional image in a second three-dimensional coordinate system based on information of the first three-dimensional image in the first three-dimensional coordinate system; A stereoscopic display method of forming, enlarging a second stereoscopic image with an enlargement optical system, and providing the enlarged stereoscopic image to the naked eye. In forming the second stereoscopic image, each part of the second stereoscopic image and the magnifying optical system are formed. A first correction is performed so that a three-dimensional image visually recognized by the naked eye is substantially similar to the first three-dimensional image according to a change in a magnification that occurs according to a relative distance in the optical axis direction. I do.

Here, the three-dimensional image which is visually recognized by the naked eye is made substantially distortion-free with respect to the first three-dimensional image in accordance with the aberration relating to the second three-dimensional image generated after the magnification by the magnifying optical system. 2
The correction may be made.

The magnifying optical system may be configured to execute the enlargement of the second image by a convex lens or to execute the enlargement of the second image by a concave mirror.

Further, when the second three-dimensional image is a monochromatic image, the second correction may be a correction relating to field curvature and distortion.

In the case where the second three-dimensional image is a composite image of images of the three primary colors of light and a convex lens is used for enlarging the second three-dimensional image, the second correction is performed by using It may be characterized in that the correction is for the field curvature, distortion, and chromatic aberration between the images of the three primary colors of light for each of the three primary color images.

The second three-dimensional image is a composite image of images of the three primary colors of light, and when a concave mirror is used for enlarging the second three-dimensional image, the second correction is performed by using the three-dimensional image of light. It may be characterized in that the correction is related to field curvature and distortion for each of the primary color images.

The second three-dimensional image is a right-viewing image and a left-viewing image, and the magnifying optical system includes a right-viewing magnifying optical system and a left-viewing magnifying optical system. Is a three-dimensional image that can be visually recognized by the naked eye according to a change in magnification that occurs according to the relative distance in the optical axis direction between each part of the right-view image and the right-view magnifying optical system. With the naked eye, in accordance with a change in the magnification that occurs according to the relative distance in the optical axis direction between each part of the image for the left eye and the optical system for the left eye, May be a left-view enlargement correction that is substantially similar to the left-view image.

The second correction is performed according to an aberration relating to a right-view image generated after magnification by the right-view magnification optical system.
The right-eye aberration correction that makes the three-dimensional image visually recognized by the naked eye substantially distortion-free with respect to the first three-dimensional image, and the left-eye visual aberration generated after magnification by the left-eye magnifying optical system, May be characterized in that the three-dimensional image visually recognized in step (1) is left-eye aberration correction that makes the first three-dimensional image substantially distortion-free.

The three-dimensional display device of the present invention forms a second three-dimensional image in a second three-dimensional coordinate system based on information of the first three-dimensional image in the first three-dimensional coordinate system, and then forms a second three-dimensional image in the second three-dimensional coordinate system. What is claimed is: 1. A stereoscopic display device for enlarging a stereoscopic image and providing it to the naked eye, wherein: (a) a change in an enlarging ratio that occurs in accordance with a relative distance in the optical axis direction between each part of the second stereoscopic image and an optical system An image forming unit that performs a first correction so that a three-dimensional image visually recognized by the naked eye is substantially similar to the first three-dimensional image to form a second three-dimensional image,
(B) an enlargement optical system for enlarging the second stereoscopic image and providing it to the naked eye.

Here, the image forming unit further converts the three-dimensional image visually recognized by the naked eye with respect to the first three-dimensional image in accordance with the aberration relating to the second three-dimensional image generated after the magnification by the magnifying optical system. A second stereoscopic image may be formed by performing a second correction to eliminate distortion.

The image forming section includes a storage unit for storing information of the first three-dimensional image, and a first unit read from the storage unit.
Image correction means for performing a first correction operation in accordance with the first correction on the information of the three-dimensional image of the second three-dimensional image to calculate information of the second three-dimensional image, and an image correction means of the second three-dimensional image calculated by the image correction means. Image display means for displaying a two-dimensional image based on the information;
An image forming optical system for forming a second three-dimensional image in a second three-dimensional coordinate system from a two-dimensional image displayed on the image display means. Here, the image correction means may further perform a correction operation according to the second correction.

Further, the image forming section may further include a receiving means for receiving the information of the notified first three-dimensional image and storing the information in the storage means.

It is practical that the magnifying optical system includes a convex lens or a concave mirror for magnifying the second stereoscopic image.

Further, when the second stereoscopic image is a monochromatic image, the second correction may be a correction relating to field curvature and distortion.

Further, when the second three-dimensional image is a composite image of images of the three primary colors of light and a convex lens is used for enlarging the second three-dimensional image, the second correction is performed using the light It may be characterized in that the correction is for the field curvature, distortion, and chromatic aberration between the images of the three primary colors of light for each of the three primary color images.

The second three-dimensional image is a composite image of images of the three primary colors of light, and when a concave mirror is used for enlarging the second three-dimensional image, the second correction is performed on the three-dimensional image of light. It may be characterized in that the correction is related to field curvature and distortion for each of the primary color images.

The second stereoscopic image is a right-viewing image and a left-viewing image, and the magnifying optical system includes a right-viewing magnifying optical system and a left-viewing magnifying optical system. Is a three-dimensional image that can be visually recognized by the naked eye according to a change in magnification that occurs according to the relative distance in the optical axis direction between each part of the right-view image and the right-view magnifying optical system. With the naked eye, in accordance with a change in the magnification that occurs according to the relative distance in the optical axis direction between each part of the image for the left eye and the optical system for the left eye, May be a left-view enlargement correction that is substantially similar to the left-view image.

The second correction is performed according to an aberration relating to a right-view image generated after the enlargement by the right-view magnification optical system.
The right-eye aberration correction that makes the three-dimensional image visually recognized by the naked eye substantially distortion-free with respect to the first three-dimensional image, and the left-eye visual aberration generated after magnification by the left-eye magnifying optical system, May be characterized in that the three-dimensional image visually recognized in step (1) is left-eye aberration correction that makes the first three-dimensional image substantially distortion-free.

[0029]

According to the stereoscopic display method of the present invention, first, based on the information of the first stereoscopic image, it is generated in accordance with the relative distance in the optical axis direction between each part of the second stereoscopic image and the magnifying optical system. In accordance with the change in the magnification, the first correction is performed so that the three-dimensional image visually recognized by the naked eye is substantially similar to the first three-dimensional image, and the information of the second three-dimensional image is calculated. Here, a second correction is performed such that the three-dimensional image visually recognized by the naked eye is substantially distortion-free with respect to the first three-dimensional image in accordance with an aberration related to the second three-dimensional image generated after the magnification by the magnifying optical system. It is also possible to do. In this case,
A higher quality stereoscopic image is provided to the naked eye.

When a stereoscopic image viewed with the naked eye is a monochromatic image, a correction relating to field curvature and distortion is performed as a second correction, and the second stereoscopic image is formed as a monochromatic image.

On the other hand, when the image viewed with the naked eye is a multicolor image, correction for curvature of field, distortion and, if necessary, chromatic aberration is performed as a second correction, and the second stereoscopic image is converted to light. Each of the three primary colors is formed as a composite image.

When the binocular vision is adopted, the second stereoscopic image is used for the right-viewing image and the left-viewing image, and the above-described first and second corrections are performed on each of them.

Next, based on the information of the second three-dimensional image, a second
Is formed. This second image stereoscopic image is enlarged by an enlargement optical system and provided to the naked eye.

The three-dimensional display device according to the present invention is characterized in that: (a) the naked eye changes the magnification that occurs according to the relative distance in the optical axis direction between each part of the second stereoscopic image and the magnifying optical system. An image forming unit that performs a first correction to form a second three-dimensional image by making a three-dimensional image visually recognized to be substantially similar to the first three-dimensional image;
And a magnifying optical system for enlarging the stereoscopic image and providing it to the naked eye. Therefore, the stereoscopic display method of the present invention is suitably implemented.

Here, the image forming section further converts the three-dimensional image visually recognized by the naked eye with respect to the first three-dimensional image in accordance with the aberration related to the second three-dimensional image generated after the magnification by the magnifying optical system. It is possible to form a second three-dimensional image by performing a second correction of no distortion.

Further, the image forming section is provided with a storage means for storing information of the first three-dimensional image, and a first read-out means for reading out the information from the storage means.
Image correction means for performing a first correction operation in accordance with the first correction on the information of the three-dimensional image of the second three-dimensional image to calculate information of the second three-dimensional image, and an image correction means of the second three-dimensional image calculated by the image correction means. Image display means for displaying a two-dimensional image based on the information;
An image forming optical system that forms a second three-dimensional image in a second three-dimensional coordinate system from a two-dimensional image displayed on the image display means can be provided. Here, the image correction unit may further perform a correction operation according to the second correction.

In this case, first, the image correction means performs the first or first and second corrections on the information of the first three-dimensional image read from the storage means to obtain the information of the second three-dimensional image. obtain. Next, a two-dimensional image based on the information of the second stereoscopic image is displayed on the image display means. Next, the image forming optical system forms a second three-dimensional image in a second three-dimensional coordinate system from the two-dimensional image displayed on the image display means.

If the image forming unit further includes a receiving means for receiving the information of the three-dimensional form by data communication or the measurement result information of the three-dimensional measuring apparatus by the three-dimensional scanner and storing the information in the storage means, the three-dimensional display is performed. It is possible to easily increase the types of stereoscopic images.

As a magnifying optical component of the magnifying optical system, a convex lens or a concave mirror can be suitably used. When a convex lens is used as an optical component for enlargement, chromatic aberration correction is generally required as the second correction.

If the image forming unit is formed by the right-eye image forming unit and the left-eye image forming unit, the stereoscopic display method of the present invention can be executed to provide a stereoscopic display full of stereoscopic effect by binocular vision. Becomes

[0041]

Embodiments of the present invention will be described below with reference to the accompanying drawings. In the description of the drawings, the same elements will be denoted by the same reference symbols, without redundant description.

FIG. 1 is a basic configuration diagram of a stereoscopic display device of the present invention for executing the stereoscopic display method of the present invention. As shown in FIG. 1, the apparatus includes (a) a magnifying optical system 300 that magnifies the stereoscopic image IM2 and provides it to the naked eye, and (b) a stereoscopic image IM2.
The three-dimensional image visually recognized by the naked eye is substantially similar to the three-dimensional image IM1 according to a change in the magnification that occurs in accordance with the relative distance between each part of the optical system 300 and the magnifying optical system 300 in the optical axis direction z. And a second correction is performed so that the three-dimensional image visually recognized by the naked eye is substantially distortion-free with respect to the three-dimensional image IM1 according to the aberration of the three-dimensional image IM2 generated after the enlargement by the magnifying optical system. , An image processing unit 100 that outputs information about the three-dimensional image IM2, and (c) an image forming optical system 200 that forms a second three-dimensional image based on the information about the three-dimensional image IM2 output from the image processing unit 100. .

The image processing unit 100 stores the information of the three-dimensional image IM1 in the storage unit 110 and the information of the three-dimensional image IM1 read out from the storage unit 110 into the correction operation according to the first correction and the second correction. An image correction unit 120 that performs information processing of the stereoscopic image IM2 by performing a correction operation in accordance with the image processing unit, and an image that displays two-dimensional image information based on the information of the stereoscopic image IM2 calculated by the image correction unit 120. Display means 130
And

The image forming optical system 200 includes the image display unit 13
Image information output from 0 can be written,
Spatial light modulator 21 capable of reading written image information
0 is provided.

The magnifying optical system 300 has a convex lens 310 as a magnifying optical component. In addition, it is also possible to use a concave mirror as an optical component for magnification.

The apparatus shown in FIG. 1 executes the stereoscopic display method of the present invention as follows.

First, the image correction unit 120 reads information on the stereoscopic image IM1 from the storage unit 110. This information is coordinate information relating to the form of the stereoscopic image IM1, and in some cases, color information is added to each coordinate information.

The image correction unit 120 performs the first correction and the second correction on the information of the three-dimensional image IM1, and converts the corrected information into the coordinate system xyz as a result through the image forming optics.
Of the stereoscopic image IM2 forming the stereoscopic image IM2 at the desired position of the image. In the calculation of the image correction 120, after performing a correction calculation according to a change in magnification due to a relative distance between each part of the three-dimensional image IM2 and the convex lens 310 and a correction calculation according to an aberration generated in the convex lens 310, the stereoscopic correction is performed at a desired position. Computation of stereoscopic image information in the form of image information written to spatial light modulator 210 to form image IM2. Hereinafter, each operation will be described in order.

1. Image magnification based on distance between convex lens 310 and stereoscopic image IM2 FIG. 2 is an explanatory diagram of an operation of enlarging stereoscopic image IM2 by convex lens 310. In order to enlarge the three-dimensional image IM2, the position of the three-dimensional image IM2 to be enlarged is arranged inside the focal length of the convex lens.

The position of one section of the three-dimensional image IM2 is represented by z _a (distance from the origin O = a), the position of the enlarged image IM3 is represented by z _b (distance from the origin O = b), and the convex lens 310 (arranged position z ₁ ).
If the focal length of f is f, then from the Gaussian imaging formula, 1 / a + 1 / b = 1 / f (1) where a: positive from origin O in the -z direction b: positive relationship from origin O in the z direction Holds. On the other hand, the _{a = z l + f-z} a ... (2) b = z b -z l -f ... (3).

[0051] from equation (1), b = fa / (a- f) ... (4) so, (2), (3) than _{z b = z 1 + f +} f (z 1 + f-z a) / (z 1 −z _a ) (5) Magnification m = b / a in this case is _{m (z a) = f /} (a-f) = f / (z 1 + f-z a -f) = f / (z 1 -z a) ... (6) Becomes

That is, even if a plurality of tomographic images of a three-dimensional image having the same magnification are arranged within the focal length of the lens, the magnification by the magnifying lens is not constant. Further, even if a plurality of tomograms are arranged at equal intervals, the tomographic intervals of the enlarged image do not become equal. FIG.
FIG. 4 is an explanatory diagram of a difference in magnification m due to _a difference in z _a . As shown in FIG. 3, since the enlarged image IM3 can be observed only as a three-dimensional image distorted with respect to the three-dimensional image IM2, if the three-dimensional image IM2 is similar to the original three-dimensional image IM1, the enlarged image IM3 Can be observed only as a three-dimensional image distorted with respect to the three-dimensional image IM2.

A method for correcting the position distortion and the magnification distortion will be described.

First, when the position z _a and the reduction magnification m (z _b ) = a / b are obtained from the position z _b of the enlarged image IM3, z _a = z ₁ + f−f (z _b −z ₁ −f) a _{/ (z b -z 1 -2f)} ... (7) m (z b) = a / b = f / (z b -z 1 -2f) ... (8).

An enlarged tomographic image i separated by-△ from the position z _b
The position z _a ′ of the input three-dimensional sectional image is given by z _a ′ = z ₁ + f−f (z _b −i · △ −z ₁ −f) / (z _b −i · △ −z ₁ − 2f) (9) position distortion is corrected.

Further, the magnification m (z _b -i · △) at this time.
M (z _b -i · △) is _{= f / (z b -i ·} △ -z 1 -2f) ... (10) so the correction factor _{m '(z b -i · △} ) as m' (z _b −i · △) = m (z _b −i · △) / m (z _b ) (11), and if the correction magnification is multiplied in advance by the input three-dimensional sectional image, an enlarged image at the position of zb is obtained. Thus, an enlarged cross-sectional image having the same magnification as that described above can be obtained. FIG. 4 is an explanatory diagram of the corrected stereoscopic image IM2 and the enlarged image IM3.

The above is the case where the enlarged tomographic images are arranged at equal intervals. However, in order to satisfy the sense of distance between eyes, the tomographic images need not be equal intervals. It is desirable to arrange them densely. Also in this case (9)
The input position and the magnification correction according to the equations (10) and (10) may be considered. Further, these correction formulas are established whether the stereoscopic image IM2 is a virtual image or a real image. However, the sampling interval of the input stereoscopic image must follow the description given below.

2. Lens aberration correction A lens that enlarges a real image or a virtual image with respect to the eye is called an eyepiece in a telescope or a microscope, and is characterized by an asymmetric lens in which an exit pupil is away from the lens. As the complicated aberration correction in the design of the asymmetric eyepiece, 1) field curvature, 2) distortion, and 3) correction of chromatic aberration are well known. For this reason, a lens in which these aberrations are corrected has a complicated design and configuration, and requires precision processing.

In the three-dimensional display method of the present invention, aberrations are corrected by arranging each cross-sectional image of a real image or a virtual image at an arbitrary position and an arbitrary magnification, so that an inexpensive lens that is easily available can be used. Hereinafter, each correction method will be described in order.

(1) Method of Correcting Field Curvature and Distortion The gap between the sagittal image plane and the meridional image plane is called astigmatism, and the middle is the practical image plane. The average image plane is not necessarily a plane, but usually an image plane curved in a bay shape. This is the field curvature. This field curvature assumes that the input of parallel light, that is, the input image is at infinity, but the meaning of field curvature is interpreted widely, and the input plane placed near the lens forms an image on the plane The main consideration is to bend over the bay without.

Further, the aberration representing a defect in the reproducibility of the shape of the image is distorted, and the square on the object plane does not become a square on the image plane but becomes a barrel type or a pincushion type.

Even when the image is formed under the above-mentioned aberration, it can be regarded as an image formed from one object to one point. By applying a moderate field curvature or distortion having a reverse tendency to the three-dimensional image IM2, image distortion of the enlarged image IM3 with respect to the original three-dimensional image IM1 can be eliminated.

FIG. 5 is an explanatory diagram of a method of correcting field curvature and distortion. In this method, first, for an assumed eyepiece, an enlarged image is used as an input image and data of curvature of field or distortion at the image forming position is collected, or data at the time of design is collected, and the coordinate system of the input stereoscopic image is collected. A plurality of reference points are obtained using (x, y, z) and the coordinate system (x ′, y ′, z ′) after correction to be output.

Next, an enlarged image having a necessary reference point is converted into an input image by calculation without distortion. Further, a magnified image is obtained in which an evaluation experiment for forming an image with an actual lens is performed using the magnified image as an input.

Next, a correction conversion formula is obtained from the correspondence between the reduced image obtained by the calculation and the reduced image obtained by the lens evaluation experiment and the reference point.

When the correction is calculated using the correction conversion formula obtained for the input image of the magnifying lens and is arranged on the input surface of the magnifying lens, a magnified image with corrected distortion can be obtained.

In the case of distortion, there is no need to correct in the z direction. Therefore, a coordinate conversion formula is used in the coordinate system (x, y) of the input stereoscopic image and in the coordinate system (x ′, y ′) after correction. Become.

The correction based on the obtained correction conversion formula is applied to the information of the original three-dimensional image IM1, and the bright spots forming the three-dimensional image IM2 are arranged according to the curve and the distortion.
By enlarging the corrected stereoscopic image IM2 with the magnifying lens 130, an enlarged image IM3 having no distortion with respect to the original stereoscopic image IM1 is obtained.

Since these distortions and the like differ for each lens, it is difficult to describe them by a general formula.

There are a number of candidates for the coordinate transformation formula relating to distortion as described below, and selection is made according to the characteristics of an actual magnifying lens.

For a simple radial distortion, r = a ₁ r ′ + a ₃ r ′ ³ + a ₅ r ′ ⁵ where r = (x ² + y ² ) ^(1/2) r ′ = (x ′ ² + y ^'2) the use of ^(1/2).

When it is considered that the Hermitian transform is used, x = ax '+ by' + cy = -bx '+ ay' + d is used.

If it is regarded as an affine transformation, use x = ax '+ by' + cy = dx '+ ey' + f.

If it is considered as a pseudo-affine transformation, x = a ₁ x'y '+ a ₂ x' + a ₃ y '+ a ₄ y = b ₁ x'y' + b ₂ x '+ b ₃ y' + b ₄ use.

If it is regarded as a second-order conformal transformation, x = ax ′ + by′c (x ′ ² −y ′ ² ) + 2dx′y ′ + ey = −bx ′ + ay′−d (x ′ ² − y ′ ² ) + 2cx′y ′ + f When considered as a two-dimensional perspective projection transformation, x = (a ₁ x ′ + a ₂ y ′ + a ₃ ) / (a ₇ x ′ + a ₈ y ′ + 1) y = ( _{a 4 x '+ a 5 y} ' + a 6) using a _{/ (a 7 x '+ a} 8 y' + 1).

In the case of a polynomial expression,

[0077]

(Equation 1)

Is used.

Each coefficient of these coordinate conversion equations is obtained by the least squares method using the coordinates of reference points equal to or more than the number required for determination. A residual equation is examined for coordinates other than the reference point, and a conversion formula that satisfies the accuracy is used.

Using a satisfactory coordinate conversion formula, a distortion-corrected image is obtained by converting the coordinate values of the input stereoscopic image into the coordinate values to be corrected. When the distortion-corrected image is an input image of the magnifying lens, the enlarged image has no distortion. The calculation of the wavefront on the spatial light modulator is performed on the distortion corrected image.

Incidentally, a lens which is easily available as an enlarging lens usually has a spherically symmetric distortion characteristic, so that an ordinary coordinate conversion formula can be applied.

Further, in the case of field curvature, it is considered to be an extension in the z direction in the case of distortion correction. Coordinate system (x, y, z) of input stereoscopic image, coordinate system (x ', y', z ') after correction
Use the coordinate transformation formula.

The coordinate conversion formula is similarly extended in the z direction, and an example is shown below.

In the case of a simple radial curvature of field, z = z ′ + a ₁ r ′ + a ₃ r ′ ³ + a ₅ r ′ ⁵ where r ′ = (x ′ ² + y ′ ² ) ^{(1 / 2)} If it is regarded as an affine transformation, use x = ax ′ + by ′ + cz ′ + by = ex ′ + fy ′ + gz ′ + hz = ix ′ + ji ′ + kz ′ + 1.

In the case of being regarded as a pseudo-affine transformation, x = a ₁ x′y ′ + a ₂ y′z ′ + a ₃ z′x ′ + a ₄ x ′ + a ₅ y ′ + a
_{6 z '+ a 4 y =} b 1 x'y' + b 2 y'z + b 3 z'x '+ b 4 x' + b 5 y '+ b 6 z'
_{+ B 4 z = c 1 x'y} '+ c 2 y'z' + c 3 z'x '+ c 4 x' + c 5 y '+ c
Using the ₆ z '+ _{c 4.}

When considered as a three-dimensional perspective projection, x = (a ₁ x '+ a ₂ y' + a ₃ z '+ a ₄ ) / (a ₁₃ x' + a ₁₄ y '+ a ₁₅
z ′ + 1) y = (a ₅ x ′ + a ₆ y ′ + a ₇ z ′ + a ₈ ) / (a ₁₃ x ′ + a ₁₄ y ′ + a
₁₅ z ′ + 1) z = (a ₉ x ′ + a ₁₀ y ′ + a ₁₁ z ′ + a ₁₂ ) / (a ₁₃ x ′ + a ₁₄ y ′ + a
_{15 Use} z '+ 1).

In the case of a polynomial expression,

[0088]

(Equation 2)

Is used.

Each coefficient of these coordinate conversion equations is obtained by the least squares method using the coordinates of reference points equal to or more than the number required for determination. A residual equation is examined for coordinates other than the reference point, and a conversion formula that satisfies the accuracy is used.

Using a satisfactory coordinate conversion equation, a field curvature corrected image is obtained by converting the coordinate values of the input stereoscopic image into the coordinate values to be corrected. When the image curvature corrected image is used as an input image of the magnifying lens, the enlarged image has no field curvature. The calculation of the wavefront on the spatial light modulator is performed on the image curvature corrected image.

A lens which is easily available as an enlarging lens usually has a spherically symmetric field curvature characteristic.
Normal coordinate conversion formulas can be applied.

(2) Method of Correcting Chromatic Aberration In order to enable color display, a real image or a virtual image for each color is created with multicolor coherent light, and is enlarged by one lens. For this reason, in the eyepiece lens, a color shift occurs unless the enlarged images have the same size for multiple colors.

FIG. 6 is an explanatory diagram of the color shift when a lens having a different focal length depending on the wavelength, that is, a lens having vertical chromatic aberration, is used as the enlarging lens. In addition,
In FIG. 6, the color shift between red and blue is shown as a representative.

[0095] As shown in FIG. 6, if the stereoscopic image IM2 has a red component and a blue component, because different and the focal length f _b of the magnifying lens to the focal length f _r and blue magnifying lens for red , The red component of the enlarged image is the position z
_{At br} , the blue component of the enlarged image is formed at a position z _bb with a different size.

FIG. 7 is an explanatory diagram of the correction according to the chromatic aberration of the magnifying lens which causes the color shift shown in FIG. The position z _b (= z _br =
z _bb ) The position z _ar of the red input image and the magnification _mr (z _b )
_{Is, z ar = z 1 + f} r -f r (z b -z 1 -f r) / (z b -z 1 -2f r) ... (12) m r (z b) = f r / (z b -z ₁ -2f _r) ... it is (13).

[0097] Placing the displacement of △ b with respect to the focal about red focus position f _b about blue, the position z _ab blue input image, the z ₁ in (12) z ₁ + △ b, the f _r f _b Z _ab = z ₁ + △ b + f _b -f _b ｛z _b- (z ₁ + △ b) -f _b } / ｛z _b- (z ₁ + △ b) -2f _b } ... (14), and the magnification _{m b (z b) m b} (z b) = f b / {z b - a _{(z 1 + △ b) -2f} b} ... (15).

Therefore, assuming that the correction magnification is m ′ _b (z _b ), m ′ _b (z _b ) = m _b (z _b ) / m _r (z _b ) (16) In this case, the correction of the enlargement magnification caused by the difference between the focal length and the position for the color is executed.

In the above description, the correction for blue based on red is shown. However, the correction for green based on red can be executed in the same manner. Thus, the chromatic aberration of each of the three primary colors of light is corrected.

3. Calculation of stereoscopic image information written to spatial light modulator 210 Stereoscopic image IM2 calculates the phase amplitude on spatial light modulator 210 as a wavefront derived from the stereoscopic image IM2 by the Fresnel diffraction theory, The calculated value is written to the spatial light modulator 210, and further, the written image information is read, thereby obtaining the phase and amplitude of the light propagating from the three-dimensional image IM2. As a method of reproducing such an image,
There are a hologram method and a kinoform method. The difference in calculation between the case where the hologram method is adopted and the case where the kinoform method is adopted is whether or not reference light is added on the spatial light modulator. That is, there is a difference between taking the complex sum with the reference light and calculating the light intensity by the hologram method and not calculating by the kinoform method, and using the kinoform method with a constant amplitude and using only the phase term. In the following description, the kinoform method is assumed and the contribution of the reference light is not considered. To calculate a hologram, the complex sum with the reference light at the position of the spatial light modulator may be calculated and the light intensity (square of the complex amplitude) may be calculated.

There are two methods for calculating the wavefront of a stereoscopic image, and the method is selected according to the advantages and disadvantages of the method and the actual use mode.

(1) Spherical Wave Method In the first method, a stereoscopic image is regarded as a plurality of point light sources, and a spherical wave is calculated assuming that the spherical waves from these point light sources are all superimposed on one point of the spatial light modulator. Is the law.

Assuming that one section of the three-dimensional image is a light source image and its light source side coordinate system (ε, η), the light source image is “(ε _i ,
_{η i); i = 0~n-} 1 "to n point source present (light source luminance _{= u i (ε i, η} i), the point light source u _i (epsilon in the subsequent
_i , η _i )), the light source image u (ε, η) becomes

[0104]

(Equation 3)

Are represented as follows.

Further, when the coordinate system of the diffraction image plane on which the diffraction image is formed is (x, y), the diffraction image plane and the point light source u _i (ε
_i , η _i ), the diffraction image U
(X, y) is

[0107]

(Equation 4)

R _i = ((ε _i −x) ² + (η _i −y) ² + z _i ² ) ^1/2 (18)

In the spherical wave method, (1) including the equation (18) is used.
Expression 7) is calculated over the entire area of the diffraction image plane to obtain a diffraction image U (x, y). In addition, even if it says the whole area of the diffraction image plane, for the area sufficiently far from all point light sources,
Since the diffraction image U (x, y) ≒ 0, it is practical to omit the calculation.

Since U (x, y) means a complex amplitude distribution, in the case of forming a kinoform, only its phase is extracted.

In the case of a hologram, a complex sum with the reference light is calculated to calculate the light intensity (square of the amplitude),
The amount of calculation can be reduced by calculating only the cosine component of the phase difference between the reference light and the object light.

To further improve the quality of the image, the amplitude component of the complex amplitude distribution is modulated by the amplitude modulation type spatial light modulator, and the phase component is modulated by the phase modulation type spatial light modulator.

Since the above calculation method is a calculation method along the light propagation direction, it is a calculation method for generating a virtual image. On the other hand, in order to generate a real image, the calculation is performed by regarding the real image side on which light converges as the light source side and calculating the complex amplitude distribution on the spatial light modulation element when the light is propagated from the light source image to the spatial light modulation element. A method may be adopted.

In the kinoform, a real wave is obtained by taking the complex conjugate of the complex amplitude distribution and calculating the phase component since the kinoform is read out by a plane wave. At the time of reproduction, a plane wave is applied to the spatial light modulator from the space opposite to the space where the real image is generated.

In the case of a hologram, the process is the same as that of the kinoform up to the point where the real image side is regarded as the light source image and the complex amplitude distribution on the spatial light modulator is calculated. The complex sum and its light intensity are calculated on the spatial light modulator assuming that the light has been irradiated. When reproducing, the reference light used in the calculation and the conjugate reference light
For example, if the reference light is a plane wave, irradiation is performed from a space opposite to the space where the real image is generated, that is, using a plane wave in the direction opposite to the reference light used in the calculation.

The disadvantage of the spherical wave method is that the calculations of the equations (17) and (18) are enormous, and because of this, the calculation when an optical element such as a lens or a prism is inserted into the reproduction optical system. Is extremely complicated because the process of calculating the complex amplitude distribution immediately before the optical element and multiplying by the transfer function of the optical element to calculate the complex amplitude distribution immediately after the optical element is repeated.

Furthermore, it is a disadvantage of the spherical wave method that it is difficult to calculate the inverse transform for calculating the wavefront on the spatial light modulator by assuming that the wavefront of the real image is known.

Also, the advantages are that the sampling pitch is independent of the image and the spatial light modulator, that the calculation of an arbitrary range can be executed, and that a three-dimensional stereoscopic image is calculated naturally. There is no need to prepare a cross section.

As described above, an arbitrary virtual image or real image can be displayed at an arbitrary position in an arbitrary size under the restriction of the spatial resolution of the spatial light modulator.

(2) Fast Fourier Transform Method The second method is a fast Fourier transform method in which the Fresnel transform is calculated using the fast Fourier transform.

This method uses the fast Fourier transform that requires a relatively small amount of calculation, and executes the calculation of the Fresnel diffraction field.

In this method, the number of samples, the wavelength, the sampling pitch, and the propagation distance are involved in the calculation as important parameters. Therefore, the sampling pitch on the diffraction side depends on the light source side, or the sampling pitch on the diffraction side depends on the diffraction side. Has a drawback that the sampling pitch of the sample is fixed.

However, even if an optical element such as a lens or a prism is inserted into the reproducing optical system, the wavefront immediately after the optical element is multiplied by the complex amplitude distribution of the optical element, thereby facilitating the wavefront immediately after the optical element. There is an advantage that it is easy to calculate the inverse Fresnel transform for calculating the input wavefront including the insertion optical element from the known output wavefront using the property that can be calculated.

First, a method of calculating a wavefront propagating from a light source image onto a spatial light modulator will be described.

With one section of the three-dimensional image as a light source image, the light source side coordinate system is (ε, η), the light source image is u (ε, η), and the diffraction image side coordinate system of the diffraction image plane separated by z from the light source image. To (x, y),
Assuming that the diffraction image is U (x, y), (a) the diffraction distance r is sufficiently longer than the wavelength, (b) cosγ = 1 γ: incidence angle (with respect to u (ε, η)), and cosθ = 1θ: An approximate condition of an emission angle (with respect to U (x, y)) is set. Under these conditions, the diffraction image U
(X, y) is

[0126]

(Equation 5)

Where r = ((x−ε) ² + (y−η)
² + z ²⁾ is ^1/2. In equation (19), exp (jkr) is used as a diverging wave, but this sign needs to be consistent with the lens function later. For example, the convex lens function in the above setting needs to be given a negative sign. If the diverging wave is determined as exp (-jkr), the convex lens function needs to be given a positive sign.

Under the above assumption, the propagation distance r is roughly classified into two methods depending on whether approximation is used or not.

[Method not approximating propagation distance r] In this method, equation (19) is regarded as a convolution type, and
Perform two Fourier transforms. That is, the convolution can be regarded as the product of the respective Fourier transforms,
The convolution type,

[0130]

(Equation 6)

By applying the equation (19), A = j / λ u1 (ε, η) = u (ε, η) u2 (x−ε, y−η) = (1 / r) exp [jkr ] = (1 / ((x−ε) ² + (y−η) ² + z ² ) ^1/2 ) × exp [jk ((x−ε) ² + (y−η) ² + z ² ) ^1/2 ].

Therefore, U (x, y, z) = (j / γ) × F ^-1 [F [u (x, y)] × F [(1 / (x ² + y ² + z ² ) ^1/2 ) × exp [jk (x ² + y ² + z ² ) ^1/2 ]]] is calculated mechanically.

When the fast Fourier transform is used, the sampling pitch p on the diffraction image side matches the sampling pitch on the light source image side.

Also, F [(1 / (x ² + y ² + z ² ) ^1/2 ) × exp [jk
(X ² + y ² + z ² ) ^1/2 ]] is analytically solved, and a method of calculating using a Fourier transform type of a transfer function discretely represented is more preferable.

Sampling pitch p, sampling number N
If

[0136]

(Equation 7)

Is obtained.

[Method of Approximating Propagation Distance r] In this method, in addition to the conditions (a) and (b), (c) each light source is in a paraxial region because of the approximation of the transmission distance r. Is assumed. Generally, an application mode in which the approximation can be adopted to maintain the image reproduction accuracy is narrow.

Under these conditions, r ² = z ² + (x−
From ε) ² + (y−η) ² , r ≒ z + (1 / (2z)) ｛(x−ε) ² + (y−η) ² ｝ +.

[0140]

(Equation 8)

Expression (21) may be viewed as a convolution type or a Fourier transform type. Both are mathematically equivalent and either of them may be used. However, when processing the data discretely, both of them are required on condition that the phase change of the phase term does not exceed π at the maximum at one sampling interval. Must be used properly.

Considering the convolution type Considering the convolution type, considering equation (21) in the form of equation (20), assuming that the phase function is pf, pf = (j / (λz)) exp [j2zπ / λ U1 (ε, η) = u (ε, η), u2 (x−ε, y−η) = exp [(jπ / (λz)) ｛(x−ε) ² + (x−η) ² } ].

Therefore, if the propagation function f (ε, η) is expressed as f (ε, η) = F [exp [(jπ / (λz)) ｛x ² + y ² ｝]], U (x, y, z) = pf · F ⁻¹ {F [u (ε, η)] · f (ε, η)} (22)

By the way, when the propagation function f (ε, η) is solved analytically, f (ε, η) = F [u2 (x, y)] = jλzexp [−jπλz (ε ² + η ² )] . That is, the Fourier transform of the light source image u (ε, η) may be multiplied by the Fourier transform f (ε, η) of the propagation function, and the inverse Fourier transform may be further multiplied by the phase function pf.
Of the phase function pf, exp [j2zπ / λ] is regarded as an offset by z and can be ignored.

Here, since a discrete Fourier transform is used, an expression is discretely expressed in consideration of a sampling interval.

The Fourier transform f (ε, η) of the propagation function is
Assuming that the sampling number (m, n), the light source image side sampling pitch p, and the sampling number N are, the diffraction side sampling pitch op becomes: op = 1 / (pN), and f (ε = op · m, η = op · n) Is expressed as f (ε = op · m, η = op · n) = (jλz) exp [− (jπλz) × ((op · m) ² + (op · n) ² )] (23)

The light source image u (ε, η) is defined as a light source side sampling pitch p, and the light source image u (ε = pm, η = pn)
Will be treated as Since the phase function pf is twice Fourier transformed, its sampling interval is equal to the sampling interval on the light source image side.

Here, the application range of the Fourier transform equation (7) of the discretely expressed propagation function is confirmed. The condition is that the phase of equation (7) does not exceed π at one sampling interval. That is, from πλz {(op · (N / 2)) ² − (op · (N / 2-1)) ² } <π, z <p · p · N · N / (λN) = p · p · N / λ (24) is a condition.

When the Fourier Transform Type is Viewed By transforming equation (19), the following equation is obtained.

[0150]

(Equation 9)

The equation of the Fourier transform is

[0152]

(Equation 10)

Therefore, if a phase function pf (x, y) and a propagation function f (ε, η) are set, pf (x, y) = (j / (λz)) exp [j2zπ / λ] × exp [(jπ / (Λz)) (x ² + y ² )] f (ε, η) = exp [(jπ / (λz)) (ε ² + η ² )],

[0154]

[Equation 11]

Is obtained.

When X = x / (λz) and Y = y / (λz) are performed as variable conversion, U (X, Y, z) = pf (X, Y) · F [u (ε, η) · F (ε, η)]. That is, the light source image may be multiplied by the propagation function, Fourier-transformed, and further multiplied by the phase function.

In the phase function pf, exp [j2zπ /
λ] can be regarded as an offset by z and ignored.

In terms of the discrete Fourier transform, u (ε = pk, η = p ・) is used as the sampling number (k, l), the light source image side sampling pitch p, and the sampling number N.
Using 1),

[0159]

(Equation 12)

Is as follows. Here, the pitch of U (X, Y) is the reciprocal of pN, and the discrete expression is U (X, Y) = U (X = n / (pN), Y = m / (pN)). From the function of X = x / (λz) and Y = y / (λz), n / (pN) = x / (λz) and m / (pN) = y / (λz), so that x = λzn / (PN), y = λzm / (pN)
Where op = λz / (pN) where op is the sampling pitch on the diffraction side. Therefore,

[0161]

(Equation 13)

Is obtained.

This is a form suitable for using the fast Fourier transform. It should be noted that the part for performing the fast Fourier transform may be mechanically executed, and its pitch, coefficient, and the like need not be interpreted.

The light source image and the propagation function may be multiplied by the sampling pitch p on the light source image side, and then subjected to fast Fourier transform, and then multiplied by the phase function at the sampling pitch op on the diffraction image side.

Propagation function f (ε, η) = f (pk, pl)
Becomes the following equation.

F (ε = pk, η = p · l) = exp [(jπ / (λz)) (ε ² + η ² )] = exp [(jπ / (λz)) ｛(pk) ² + (Pl) ² }] (25) The applicable range of the discretely expressed propagating function (25) is as follows:
The condition is that the phase of equation (25) does not exceed π at one sampling interval. Therefore, z> p · p · N / λ (26) is a condition.

From the light source images shown above, the spatial light modulator 21
The calculation of the wavefront of a three-dimensional image will be specifically described based on the method of calculating the wavefront propagating on zero.

Calculation Method for Reconstructing Virtual Image Since a virtual image forms a divergent wave from an object on the retina by a lens of the eye lens and observes a three-dimensional image, the divergent wave from the object, that is, Fresnel transformation is executed. .

However, the sampling pitch p on the stereoscopic image side,
If the sampling pitch on the Fresnel conversion side is p ',
When the object is close to the spatial light modulator 210, two Fourier transforms are performed with p = p 'as shown in FIG. If it is far, p '= λz / (pN) or p = λz / (p'N) as shown in FIG. However, a method of repeating the Fourier transform twice to extend the propagation distance is practical.

Assuming that the phase function is pf, pf = (j / (λz)) exp [j2zπ / λ], the object is u (ε, η), and the propagation function is u2 (x−ε, y−η) = exp [ jπ / (λz)) {(x−ε) ² + (y−η) ² }] Fourier transform of the propagation function is expressed as f (ε, η) = F [exp [(jπ / (λz))} x ² + y ² ｝]], the complex amplitude distribution U on the spatial light modulator 210
(X, y, z) is given by U (x, y, z) = pf · F ⁻¹ {F [u (ε, η)] · f (ε, η)}, which may be calculated.

The sampling pitch of f (ε, η) is
Treated as 1 / P · N as in equation (22).

Since U (x, y, z) means a complex amplitude distribution, in the case of a kinoform, only the phase is extracted. In the case of a hologram, a method of calculating the light intensity (square of the amplitude) by taking the complex sum with the reference light or calculating the real component or the imaginary component only in a special case to reduce the calculation amount There is also.

Calculation Method for Reconstructing Real Image As in the case of the spherical wave method, the real image side on which light is condensed is regarded as the light source side, and the complex light on the spatial light modulator 210 that has propagated from this light source image to the spatial light modulator is considered. Calculate the amplitude distribution.

In the case of a kinoform, since it is read out by a plane wave, a real image can be obtained by taking the complex conjugate of the complex amplitude distribution and calculating its phase component. Upon reproduction, the spatial light modulator is irradiated with a plane wave from a space opposite to a space where a real image is generated.

In the case of a hologram, the process is the same up to the point where the real image side is regarded as the light source image and the complex amplitude distribution on the spatial light modulator 210 is calculated. As a result, the complex sum and its light intensity are calculated on the spatial light modulator 210. In the reproduction, the reference light used in the calculation is a reference light conjugate to the reference light.For example, if the reference light is a plane wave, the plane light is in the space opposite to the space where the real image is generated. Irradiation is performed using

In the case of the Fourier transform type, since the Fresnel inverse transform can be performed more directly than the above method, it is easy to use the following method.

In the case of reproducing a real image, the image resulting from the Fresnel transform is known, which corresponds to solving what kind of object is subjected to the Fresnel transform to obtain a known wavefront.

For that purpose, an inverse Fresnel transformation is executed.

A) When the distance between the spatial light modulator and the reproduced image is short: Two Fourier transforms are used. That is, in the arrangement shown in FIG. 10, the complex amplitude distribution on the spatial light modulator 210 is u (ε, η), and the complex amplitude distribution of the reproduced image is U (x, y,
z), and the phase function pf = (j / (λz)) exp [j
2zπ / λ], u (ε, η) = F ⁻¹ {F {U (x, y, z) / pf} ·
f ^* (ε, η)｝ where ^* : denotes complex conjugate.

Assuming that the sampling pitch of u (ε, η) is P, the reproduced image side has the same pitch, and f ^* (ε, η)
η) is 1 / P as shown in equation (22).
N is a fast Fourier transform.

A) When the distance between the spatial light modulator and the reproduced image is long If the phase function pf (x, y) and the propagation function f (ε, η) are set in the arrangement shown in FIG. 11, pf (x, y) = (J / (λz)) exp [j2zπ / λ] × exp [(jπ / (λz)) (x ² + y ² )] f (ε, η) = exp [(jπ / (λz)) (ε ² + Η ² )]

[0182]

[Equation 14]

Is obtained. Variable conversion = X = x / (λz), Y
= Y / (λz), U (X, Y, z) = pf (X, Y) · F [u (ε, η) · f (ε, η)], so u (ε, η) = F ⁻¹ {U (X, Y, z) / pf (X, Y)} × f ^* (ε, η). Therefore, assuming that the sampling pitch of u (ε, η) is P, the pitch on the reproduction image side is λZ / (PN), and the fast Fourier transform is used with the sampling pitch of f ^* (ε, η) being P.

In the case of a kinoform, since it is read out by a plane wave, a real image can be obtained by calculating the phase component of the complex amplitude distribution subjected to the inverse Fresnel transform. Upon reproduction, the spatial light modulator 210 is irradiated with a plane wave from a space opposite to a space where a real image is generated.

In the case of a hologram, the complex light and its light intensity are calculated on the spatial light modulator 210, assuming that the reference light is irradiated from the space opposite to the space on the real image side. At the time of reproduction, irradiation is performed with actual reference light corresponding to the reference light used in the calculation.

The Fresnel diffraction image obtained by the above calculation is
In order to calculate a three-dimensional image including many cross-sections because it is one cross-section of the assumed three-dimensional image, it is necessary to observe deep cross-sections such as a translucent body. I will take the sum. In addition, when assuming an opaque object, the Fresnel diffraction field from the far section to the next section of the assumed stereo image is calculated, and the luminescent spot constituting the solid at that section in the complex amplitude distribution is calculated. Some parts are replaced by the complex amplitude of the bright spot. Also, the shaded part constitutes a new complex amplitude distribution with the wavefront replaced with zero,
The Fresnel propagation to the next cross section is repeated, and after obtaining the complex amplitude distribution in the last cross section, the Fresnel transform or the inverse Fresnel transform to the spatial light modulator is calculated.

As described above, an arbitrary virtual image or real image is displayed at an arbitrary position in an arbitrary size under the restrictions of the spatial resolution of the spatial light modulator 210 and the sampling pitch.

Hereinafter, specific examples will be described.

(First Embodiment) In this embodiment, both eyes are enlarged by an eyepiece.
Performs stereoscopic display that satisfies the binocular parallax, convergence, and eye focusing functions. FIG. 12 is a configuration diagram of a first embodiment of the stereoscopic display device of the present invention used in the first embodiment of the stereoscopic display method of the present invention.

The in-line holograms are displayed on the CRTs 131 and 132 having a long afterglow time,
The data is written to the reflection-type phase modulation type spatial light modulation elements 211 ₁ and 211 ₂ (for example, X-5641, PAL-SLM manufactured by Hamamatsu Photonics KK) via O ₁ and 220 ₂ . The written image is an inline hologram composed of 512 × 512 images, and the length per pixel is 24 μm when converted from the imaging magnification.

The reading light is He at a wavelength of 632.8 nm.
After the -Ne laser 231 is converted into parallel light by the collimator lens 232, the reflected light from the half mirrors 233 ₁ and 233 ₂ is used.

The confocal lens system 240 ₁ (convex lens 241)
₁ (focal length 20 cm) and convex lens 242 ₁ (focal length 20 cm)) and confocal lens system 240 ₂ (convex lens 241 ₂ (focal length 20 cm) and convex lens 24
2 ₂ (focal length 20 cm)) spatial light modulator 211 ₁ ,
The real images 212 ₁ and 212 ₂ of 211 ₂ are formed. In addition,
Convex lens 241 ₁ and a convex lens 242 ₁ and the convex lens 241 ₂ and by selecting the focal length of the convex lens 242 _2, the spatial light modulator 211 _1, 211 ₂ of the real image 2
It is possible to control the 12 _1, 212 ₂ magnification, becomes possible to finely control the spatial resolution of the display. The zero-order cut filters 243 ₁ and 243 ₂ are for removing light generated as background light due to imperfect phase modulation, and are unnecessary when complete phase modulation is achieved. Real images 212 ₁ , 212 of these spatial light modulators 211 ₁ , 211 ₂
Real image I formed from inline hologram from ₂
M2 _1, IM2 ₂ an eyepiece 310 ₁ (focal distance 10
2.3 mm), eyepiece 310 ₂ (focal length 102.
3 mm) and magnify 5 times. This enlarged image is I
M3 ₁ and IM3 ₂ .

In this embodiment, the eyepiece 310 ₁ ,
Measured beforehand expansion characteristics of 310 _2, previously obtained correction conversion expression field curvature and distortion. Thereafter, first, the image correction unit 120 calculates a magnification correction parameter. FIG.
9 is a flowchart of magnification correction. The distance between the spatial light modulator 211 ₁ of the real image 212 ₁ and the eyepiece 310 _first distance and the real image 212 ₂ of the spatial light modulator 211 ₂ and the eyepiece 310 ₂ are both a 20.23Cm, spatial light modulator 211 _1, The distance between the real images 212 ₁ , 212 ₂ of the eyepiece 211 ₂ and the front focal points of the eyepieces 310 ₁ , 310 ₂ is 0.
1 m.

[0194] First, enlarged image IM3 ₁ of cross section (i = 0) as the length 5 cm, 20c from spatial light modulator 211 ₁
The image is displayed on the m light source side, that is, z _b0 = −20 cm, and the image correction unit 120 first calculates the reference magnification m (z _b0 ) based on the equation (8). In the optical arrangement according to the present embodiment, m (z _b0 ) = − 0.20273.

[0195] Next, calculated on the basis of the position z _a0 of the real image IM2 ₁ to (7). In the optical arrangement of this embodiment, z _a0 = 12.07 cm. At this time, the real image IM
2 ₁ of _{magnitude, 5cm × | m (z b0} ) | = 1.014
cm. Since the sampling pitch here uses two Fourier transforms, the spatial light modulator 211
_Since it is equal to the sampling pitch on ₁ and is 24 μm, 423 pixels corresponding to 1.014 cm are set.

Next, from the enlarged cross section at the above-mentioned i = 0, Δ
(= 20 cm) closer to the light source, ie, z _b = −40c
enlarged image IM3 ₁ of cross section (i = 1) as the length 5cm to m, the correction factor m 'a (z _b - [delta) from equation (11), is calculated from the image forming position z _a1 (7) below. In the optical arrangement relationship of the present embodiment, m ′ (z _b −Δ) = 0.7162, z
_a1 = 11.49 cm. At this time, the size of the real image IM2 _{1 is, 1.014cm × m '(z b} -Δ) = 0.7
262 cm. The sampling pitch here is 2
Is equal to the sampling pitch on the spatial light modulator 211 ₁ , 24 μm
Therefore, 309 pixels corresponding to 0.7262 cm were set.

[0197] Subsequently, to calculate the real image IM2 ₁ correction factor _{m '(z b -i · Δ} ) and the image forming position z _ai for each cross section of the enlarged image IM3 _1, further real image for each section of the enlarged image IM3 ₂ IM2 ₂ for the reference position magnification m (z _b0),
The correction magnification m ′ (z _b −i · Δ) and the image forming position z _ai are calculated.

Subsequent to the calculation of the magnification correction parameter, the image correction unit 120 reads the information of the original stereoscopic image IM1 from the storage unit 110, and then corrects the real image IM2.

[0199] That is, with respect to the real image IM2, the lens is aberration correction for application and previously obtained curvature of the magnifying lens 310 ₁ and distortion correction parameters calculated above.

Next, calculation of the written images of the corrected real images IM2 ₁ and IM2 ₂ on the spatial light modulators 211 ₁ and 211 ₂ , that is, the inverse Fresnel transform is performed.

FIG. 14 is a flowchart of the inverse Fresnel transform in this embodiment. As shown in FIG. 14, first, i
= 0th tomographic real image position z _a = 12.07 cm,
Compute the complex conjugate of the Fourier transform of the propagator. In this case, according to the magnitude of z _a , it is selected whether to use an equation solved analytically or to use the one obtained by directly performing the Fourier transform of the propagation function and taking its complex conjugate. Note that z _a
It is possible to store the calculated value according to the above and use this value.

Next, a two-dimensional Fourier transform is applied to the i = 0th tomographic image of the three-dimensional image IM1.

Next, the product of the two-dimensional Fourier transform of the tomographic image and the complex conjugate of the two-dimensional Fourier transform of the propagation function is calculated as follows.
A dimensional inverse Fourier transform is calculated, and the complex value of the calculation result is added to the calculation result of the hologram area.

Thereafter, the same calculation is performed for all the cross-sectional images of the three-dimensional image IM1, and the calculation result is added to the calculation result of the hologram area each time. The real component of the finally obtained complex sum is used as an in-line hologram.

The hologram obtained in this way is
1, 132 and the spatial light modulators 211 ₁ , 211 ₂
After writing to, via a confocal lens system 240 _1, 240 ₂ to form a real image IM2 _1, IM2 _2. By enlarging this with eyepieces 310 ₁ and 310 ₂ ,
An image having a three-dimensional effect faithful to the original three-dimensional image IM1 is provided to the naked eye.

In this embodiment, the image is of a single color. However, in the case of a multicolor image, the same calculation as described above is performed for the right and left eyes for each of the three primary colors of light. The correction may be performed to form the real image IM2.

(Second Embodiment) FIG. 15 is a block diagram of a second embodiment of the stereoscopic display device of the present invention used in the first embodiment of the stereoscopic display method of the present invention. This embodiment is different from the first embodiment in that virtual images are generated by the spatial light modulators 211 ₁ and 211 ₂ . As a result, as shown in FIG. 15, the confocal optical systems 240 ₁ , 24
0 ₂ and the eyepiece 310 _1, 310 optical system between the ₂ different.

In this embodiment, as in the first embodiment, the enlargement characteristics of the eyepieces 310 ₁ and 310 ₂ are measured in advance, and the correction conversion equations for the field curvature and distortion are obtained. Thereafter, first, the image correction unit 12 is executed in the same flow as in FIG.
0 calculates a magnification correction parameter. The distance between the spatial light modulator 211 ₁ of the real image 212 ₁ and the eyepiece 310 _first distance and the real image 212 ₂ of the spatial light modulator 211 ₂ and the eyepiece 310 ₂ are both a 0.0523M, spatial light modulator 211 _1, The distance between the real images 212 ₁ , 212 ₂ of the eyepiece 211 ₂ and the front focal points of the eyepieces 310 ₁ , 310 ₂ is 0.
05 m.

[0209] First, enlarged image IM3 ₁ of cross section (i = 0) as the length 5 cm, 20c from spatial light modulator 211 ₁
The image is displayed on the m light source side, that is, z _b0 = −35 cm, and first, the image correction unit 120 calculates the reference magnification m (z _b0 ) based on the equation (8). In the optical arrangement according to the present embodiment, m (z _b0 ) = − 0.2250.

[0210] Next, calculated on the basis of the position z _a0 of the virtual image IM2 ₁ to (7). In the optical arrangement relation of the present embodiment, z _a0 = 2.70 cm. At this time, the virtual image IM2
The size of ₁ is 5 cm × | m (z _b0 ) | = 1.125c
m. Since the sampling pitch here uses two Fourier transforms, the spatial light modulator 211 ₁
Since it is equal to the above sampling pitch and 24 μm, a virtual image having a size of 450 pixels corresponding to 1.125 cm was obtained.

Next, from the enlarged cross section at the above-mentioned i = 0, Δ
(= 20 cm) closer to the light source, ie, z _b = −55c
enlarged image IM3 ₁ of cross section (i = 1) as the length 5cm to m, the correction factor m 'a (z _b - [delta) from equation (11), is calculated from the image forming position z _a1 (7) below. In the optical arrangement according to the present embodiment, m ′ (z _b −Δ) = 0.69447;
z _a1 = −3.40 cm. At this time, the virtual image IM2 ₁
Is 1.125 cm × m ′ (z _b −Δ) = 0.
78123 cm. The sampling pitch here is equal to the sampling pitch on the spatial light modulator 211 ₁ because two Fourier transforms are used.
4 μm, which corresponds to 0.78123 cm 32
A virtual image having a size of 6 pixels was obtained.

[0212] Subsequently, to calculate the virtual image IM2 ₁ correction factor _{m '(z b -i · Δ} ) and the image forming position z _ai for each cross section of the enlarged image IM3 _1, further, the virtual image of each cross section of the enlarged image IM3 ₂ IM2 ₂ for the reference position magnification m (z _b0),
The correction magnification m ′ (z _b −i · Δ) and the image forming position z _ai are calculated.

[0213] Subsequent to the calculation of the magnification correction parameter, the image correction unit 120 reads the information of the original stereoscopic image IM1 from the storage unit 110, and then corrects the virtual image IM2.

[0214] That is, with respect to the virtual image IM2, the lens is aberration correction on the application and pre-determined in advance magnifying lens 310 ₁ of field curvature and distortion was the correction parameters calculated above.

[0215] Next, calculation of the virtual image IM2 _1, IM2 ₂ spatial light modulator 211 ₁ relates, 211 writes image to ₂ after correction, that is, performs inverse Fresnel transformation.

FIG. 16 is a flowchart of the inverse Fresnel transform in this embodiment. As shown in FIG. 14, first, i
The complex conjugate of the Fourier transform of the propagation function is calculated assuming the 0th tomographic virtual image position z _a = 2.70 cm. In this case, according to the magnitude of z _a , it is selected whether to use an equation solved analytically or to use the one obtained by directly performing the Fourier transform of the propagation function and taking its complex conjugate. Note that z _a
It is possible to store the calculated value according to the above and use this value.

Next, a two-dimensional Fourier transform is applied to the i = 0th tomographic image of the three-dimensional image IM1.

Next, the product of the two-dimensional Fourier transform of the tomographic image and the complex conjugate of the two-dimensional Fourier transform of the propagation function is calculated as follows.
A dimensional inverse Fourier transform is calculated, and the complex value of the calculation result is added to the calculation result of the hologram area.

Thereafter, the same calculation is performed for all the cross-sectional images of the three-dimensional image IM1, and the calculation result is added to the calculation result of the hologram area each time. The real component of the finally obtained complex sum is used as an in-line hologram.

The hologram obtained in this way is
1, 132 and the spatial light modulators 211 ₁ , 211 ₂
After writing to, via a confocal lens system 240 _1, 240 ₂ to form a virtual image IM2 _1, IM2 _2. By enlarging this with eyepieces 310 ₁ and 310 ₂ ,
An image having a three-dimensional effect faithful to the original three-dimensional image IM1 is provided to the naked eye.

In this embodiment, the image is of a single color.
As in the case of the embodiment, in the case of a multicolor image, for the right eye and the left eye, in addition to the above-described calculation for each of the three primary colors of light, the above-described chromatic aberration is corrected to form the virtual image IM2. Good.

[0222]

As described in detail above, according to the three-dimensional display method and three-dimensional display device of the present invention, a hologram or the like is manufactured by performing correction in accordance with image distortion or the like generated in an enlargement system. , And a clear and large stereoscopic image can be displayed.

[Brief description of the drawings]

FIG. 1 is a basic configuration diagram of a stereoscopic display device of the present invention that executes a stereoscopic display method of the present invention.

FIG. 2 is an explanatory diagram of an operation of enlarging a three-dimensional image IM2 by a convex lens 310.

FIG. 3 is an explanatory diagram of a difference in magnification m due to _a difference in z _a ;

FIG. 4 is an explanatory diagram of a corrected stereoscopic image IM2 and an enlarged image IM3.

FIG. 5 is an explanatory diagram of a method of correcting curvature of field and distortion.

FIG. 6 is an explanatory diagram of color shift when a lens having a different focal length depending on wavelength, that is, a lens having longitudinal chromatic aberration, is used as an enlarging lens.

FIG. 7 is an explanatory diagram of correction according to chromatic aberration of a magnifying lens that causes color shift.

FIG. 8 is an explanatory diagram of a virtual image when the object and the spatial light modulator 210 are close to each other.

FIG. 9 is an explanatory diagram of a virtual image when the object and the spatial light modulator 210 are far from each other.

FIG. 10 is an explanatory diagram of a real image in a case where an object is close to a spatial light modulator 210.

FIG. 11 is an explanatory diagram of a real image when the object and the spatial light modulator 210 are far from each other.

FIG. 12 is a configuration diagram of a stereoscopic display device according to a first embodiment of the present invention.

FIG. 13 is a flowchart of magnification correction of the first embodiment.

FIG. 14 is a flowchart of the inverse Fresnel transform of the first embodiment.

FIG. 15 is a configuration diagram of a stereoscopic display device according to a second embodiment of the present invention.

FIG. 16 is a flowchart of the inverse Fresnel transform of the second embodiment.

[Explanation of symbols]

100 image processing unit, 110 storage unit, 120 image correction unit, 130, 131, 132 image display means (CR
T), 200: image forming optical system, 210, 211: spatial light modulator, 300: magnifying optical system, 310: magnifying lens.

Claims (21)

(57) [Claims] 1. A second three-dimensional image in a second three-dimensional coordinate system is formed based on information of a first three-dimensional image in a first three-dimensional coordinate system, and the second three-dimensional image is magnified. A stereoscopic display method of providing the image to the naked eye by enlarging with a system, wherein in forming the second stereoscopic image, a relative distance in the optical axis direction between each part of the second stereoscopic image and the magnifying optical system is determined. A first correction is performed so that a three-dimensional image visually recognized by the naked eye is substantially similar to the first three-dimensional image in accordance with a change in the magnification that occurs accordingly. 2. The method according to claim 1, further comprising: forming a stereoscopic image visually recognized by the naked eye in accordance with an aberration of the second stereoscopic image generated after the enlargement by the magnifying optical system. 2. The stereoscopic display method according to claim 1, wherein a second correction is performed on the three-dimensional image to be substantially distortion-free. 3. 3. The stereoscopic display method according to claim 1, wherein the magnifying optical system executes the magnification of the second image by using a convex lens. 4. The stereoscopic display method according to claim 1, wherein said magnifying optical system executes magnifying the second image with a concave mirror. 5. The method according to claim 1, wherein the second stereoscopic image is a monochromatic image, and the second correction is a correction relating to a field curvature and a distortion.
The stereoscopic display method according to claim 2, wherein: 6. The magnifying optical system executes magnification of the second image with a convex lens, the second stereoscopic image is a composite image of images of three primary colors of light, and the second correction is Field curvature, distortion, and the image quality of each of the three primary color images;
3. The stereoscopic display method according to claim 2, wherein the correction is for chromatic aberration between the images of the primary colors. 7. The magnifying optical system executes magnification of the second image with a concave mirror, the second stereoscopic image is a composite image of images of three primary colors of light, and the second correction is The stereoscopic display method according to claim 4, wherein the correction is for correction of curvature of field and distortion of each of the three primary color images. 8. The second stereoscopic image is a right-viewing image and a left-viewing image, and the magnifying optical system includes a right-viewing magnifying optical system and a left-viewing magnifying optical system; The correction of 1 is performed by a three-dimensional object visually recognized by the naked eye in accordance with a change in an enlargement ratio generated according to a relative distance in the optical axis direction between each part of the right-view image and the right-view magnifying optical system. Right-eye magnification correction for making the image substantially similar to the right-eye image, and an enlargement ratio generated according to the relative distance in the optical axis direction between each part of the left-eye image and the left-eye magnification optical system. The stereoscopic display method according to claim 1, wherein a stereoscopic image visually recognized by the naked eye is a left-view enlargement correction that is substantially similar to the left-eye view image in accordance with the change of the image. 9. The second stereoscopic image is a right-viewing image and a left-viewing image, and the magnifying optical system includes a right-viewing magnifying optical system and a left-viewing magnifying optical system; The correction of 2 is such that the three-dimensional image visually recognized by the naked eye is substantially distortion-free with respect to the first three-dimensional image in accordance with the aberration related to the right-view image generated after the enlargement by the right-view magnifying optical system. Correction for right-view aberration, according to the aberration for the left-view image generated after magnification in the left-view magnifying optical system,
The stereoscopic display method according to claim 2, wherein the stereoscopic image visually recognized by the naked eye is left-eye aberration correction that makes the first stereoscopic image substantially distortion-free. 10. After forming a second three-dimensional image in a second three-dimensional coordinate system based on information of the first three-dimensional image in the first three-dimensional coordinate system, expand the second three-dimensional image. A stereoscopic display device provided to the naked eye according to a change in a magnification that occurs according to a relative distance in the optical axis direction between each part of the second stereoscopic image and the magnifying optical system. An image forming unit that forms the second three-dimensional image by performing a first correction to make the three-dimensional image visually recognized to be substantially similar to the first three-dimensional image; And a magnifying optical system provided for the stereoscopic display device. 11. The image forming unit further includes: a stereoscopic image visually recognized by the naked eye in the first stereoscopic image according to an aberration related to the second stereoscopic image generated after the magnification by the magnifying optical system. The stereoscopic display device according to claim 10, wherein the second stereoscopic image is formed by performing a second correction to make the image substantially distortion-free. 12. The image forming unit according to claim 1, further comprising: a storage unit configured to store the information of the first three-dimensional image; and a first unit corresponding to the first correction based on the information of the first three-dimensional image read from the storage unit. The correction operation of
Image correction means for calculating information on the three-dimensional image of the above, image display means for displaying a two-dimensional image based on the information on the second three-dimensional image calculated by the image correction means, and the image display means The three-dimensional display device according to claim 10, further comprising: an image forming optical system that forms the second three-dimensional image in the second three-dimensional coordinate system from the two-dimensional image displayed on the three-dimensional image. . 13. The image correcting means according to claim 2, further comprising:
13. The stereoscopic display device according to claim 12, wherein a correction operation according to the correction is performed to calculate the information of the second stereoscopic image. 14. The image forming unit according to claim 1, wherein
13. The three-dimensional display device according to claim 12, further comprising a receiving unit that receives the information of the three-dimensional image and stores the information in the storage unit. 15. The magnifying optical system according to claim 1, wherein the magnifying optical system includes a convex lens for magnifying the second stereoscopic image.
0. The stereoscopic display device according to item 0. 16. The optical system according to claim 10, wherein the magnifying optical system includes a concave mirror for magnifying the second stereoscopic image.
The stereoscopic display device as described in the above. 17. The three-dimensional display device according to claim 11, wherein the second three-dimensional image is a monochromatic image, and the second correction is correction relating to field curvature and distortion. 18. The magnifying optical system includes a convex lens that magnifies the second stereoscopic image, the second stereoscopic image is a composite image of images of three primary colors of light, and the second correction is 3 above
12. The three-dimensional display device according to claim 11, wherein the correction is for correction of curvature of field, distortion of each image of the primary colors, and chromatic aberration between the images of the three primary colors. 19. The magnifying optical system includes a concave mirror that magnifies the second three-dimensional image, the second three-dimensional image is a composite image of images of three primary colors of light, and the second correction is 13. The three-dimensional display device according to claim 12, wherein the correction is related to field curvature and distortion for each of the three primary color images. 20. The second stereoscopic image is a right-viewing image and a left-viewing image, and the magnifying optical system includes a right-viewing magnifying optical system and a left-viewing magnifying optical system; The correction of 1 is performed by a three-dimensional object visually recognized by the naked eye in accordance with a change in an enlargement ratio generated according to a relative distance in the optical axis direction between each part of the right-view image and the right-view magnifying optical system. Right-eye magnification correction for making the image substantially similar to the right-eye image, and an enlargement ratio generated according to the relative distance in the optical axis direction between each part of the left-eye image and the left-eye magnification optical system. The three-dimensional display device according to claim 10, wherein a three-dimensional image visually recognized by the naked eye according to the change of (i) is a left-view enlargement correction that is substantially similar to the left-eye view image. 21. The second stereoscopic image is a right-viewing image and a left-viewing image, and the magnifying optical system includes a right-viewing magnifying optical system and a left-viewing magnifying optical system; The correction of 2 is such that the three-dimensional image visually recognized by the naked eye is substantially distortion-free with respect to the first three-dimensional image in accordance with the aberration related to the right-view image generated after the enlargement by the right-view magnifying optical system. Correction for right-view aberration, according to the aberration for the left-view image generated after magnification in the left-view magnifying optical system,
The stereoscopic display device according to claim 11, wherein a stereoscopic image visually recognized by the naked eye is left-eye aberration correction that makes the first stereoscopic image substantially distortion-free.