JP2005189864A - Three-dimensional image display device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To realize a three-dimensional image display device that does not deteriorate in imaging performance against environmental changes of temperature etc., and can display a sharp three-dimensional aerial image in an easy-to-observe state. <P>SOLUTION: Disclosed is the three-dimensional display device which forms the aerial image in accordance with an original image by using a lens array having a plurality of lens elements arranged in two dimensions and the original image which is a finely inverted or Fourier-transformed image of a reproduced image, the finely inverted image or Fourier-transformed image being recorded or displayed in accordance with individual lens elements constituting the lens array. This three-dimensional image display device is characterized in that the lens array and the main material constituting the original image are nearly equal in coefficient of heat-ray expansion. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a three-dimensional image display device capable of displaying a three-dimensional image having parallax in the vertical and horizontal directions as an aerial image.

  Images that give a three-dimensional effect can be broadly classified into the following three types depending on the visual effect that gives a three-dimensional effect. This is described on page 40 of “Three-dimensional display” (author: Chihiro Masuda) published by Sangyo Tosho.

ここで、(1)の心理効果については、透視図法や照明効果などから得られる。また、(2)の両眼視差は、色や偏光の眼鏡を用いる方式やレンチキュラーレンズ等を用いて表示面を工夫した方式などから得られる。(3)については、ホログラフィ等が一般に良く知られている。

Here, the psychological effect of (1) can be obtained from a perspective projection method or a lighting effect. In addition, the binocular parallax (2) can be obtained from a system using color or polarized glasses, a system using a lenticular lens, etc. As for (3), holography and the like are generally well known.

  Of these, only the three-dimensional image of (3) reproduces the same visual effect as when actually viewing a three-dimensional object. This is superior to (1) and (2) in that a natural stereoscopic effect can be obtained, and an image aimed by the present invention described below also belongs to this three-dimensional image.

  As one of methods for obtaining this three-dimensional image, a method called integral photography is known. This was invented in 1908 by Lippmann in France, and in principle, is an excellent one that can reproduce a complete three-dimensional aerial image.

The most basic recording / reproduction flow of this method is shown below.
(1) Record:
As shown in FIG. 7, a dry plate 200 is placed at a conjugate position of a subject in a two-dimensional lens array (generally called a fly's eye lens) 100 in which a plurality of spherical convex lenses are arranged in a two-dimensional plane. Shoot and record a minute inverted image. FIG. 8 shows this state, and representatively shows points A and B of the subject. The light path is schematically shown in a simplified manner.

(2) Preparation for playback:
A positive image 200 ′ baked to the same size as the dry plate 200 is produced. If a reversal film is used instead of the dry plate 200, it may be developed only.

(3) Playback:
When the positive image 200 ′ is accurately placed at the position of the original dry plate 200 and illuminated from the back side of the positive image 200 ′ and observed through the fly-eye lens 100 as shown in FIG. Is played back. Therefore, the aerial images A and B of the subject are reproduced at the same position as when shooting. In FIG. 9, the light path is schematically shown in a simplified manner.

In this state, a reverse image with reverse concavities and convexities can be seen. For this reason, in order to return the unevenness to normal, it is necessary to devise such as re-taking the aerial image once reproduced by this method.
In the above description, as an example, a spherical two-dimensional lens array 100 is shown as a fly-eye lens.

General integral photography is also described in Patent Document 1 below.
JP-A-8-262371 (first page, FIG. 1)

  However, the integral photography has not been put into practical use until now, though it is an excellent method. This is largely due to the fact that there is no fly-eye lens that simultaneously satisfies the following conditions, as well as the problem of reverse vision.

Condition 1: imaging performance is good,
Condition 2: Whether an image with sufficient brightness and contrast is obtained,
Under these conditions, the integral type fly-eye lens that has been reported to date has the following problems.

  (1) First, the aerial image was adversely affected by the aberration of each lens element. In particular, when chromatic aberration occurs, blur and color blur due to chromatic aberration extend not only in the two-dimensional plane but also in the depth direction, and there is a problem that the resolving power is remarkably lowered. Another problem is that the aerial image cannot be seen clearly due to other aberrations.

  (2) When an aerial image is observed from the observation position, there is a light source that illuminates the positive image behind the aerial image. Here, when both the lens array and the aerial image are in focus, the aerial image may have a lowered contrast or difficult to observe.

  (3) Since the lens array as described above is a plane, the light beam from the peripheral portion to the aerial image has a large angle with respect to the normal of the array plane. For this reason, problems such as a decrease in the amount of light and an increase in aberrations have been caused, thereby preventing the formation of a clear aerial image.

  (4) Although the 3D image display device is used in various environments, no consideration has been given to prevent the imaging performance from deteriorating against environmental changes, particularly temperature changes. There wasn't.

  The present invention has been made to solve the above-mentioned problems, and its object is to propose a new method that simultaneously satisfies each condition required for a fly-eye lens, and is easy to manufacture. An object of the present invention is to realize a three-dimensional image display device capable of displaying a clear three-dimensional aerial image in an easily observable state without deterioration of imaging performance due to environmental changes such as temperature.

  The inventor of the present application has conducted extensive research to improve various problems in the previously proposed integral method, and as a result, has selected a material suitable for the lens element, and has a clear three-dimensional air. Devise the position of the lens array and aerial image suitable for forming an image, and the shape of the lens array suitable for forming a clear three-dimensional aerial image, and respond to changes in the environment. The present inventors have newly found that various problems can be solved by devising so as to maintain the imaging performance, and the present invention described below has been completed.

Therefore, the invention for solving the problem is specifically as shown below.
(1) The invention according to claim 1 is a lens array in which a plurality of lens elements are two-dimensionally arranged, and a minute inverted image or Fourier transform of a reproduced image corresponding to each lens element constituting the lens array. A three-dimensional image display device for forming an aerial image corresponding to an original image from an original image on which an image is recorded or displayed, wherein a thermal linear expansion coefficient of a lens array and a thermal linear expansion coefficient of a main material constituting the original image are approximately The three-dimensional image display device is characterized by being configured to be equal.

  According to such a three-dimensional image display device, the linear thermal expansion caused by the environmental temperature change is substantially equal between the lens array and the original image, so that the correspondence between the individual lens elements of the lens array and the original image is maintained. The state can be maintained. Therefore, the blur amount of the aerial image can be kept small, and a clear three-dimensional aerial image can be displayed.

(2) The invention according to claim 2 is a lens array in which a plurality of lens elements are two-dimensionally arranged, and a minute inverted image or Fourier transform of a reproduced image corresponding to each lens element constituting the lens array. A three-dimensional image display device for forming an aerial image corresponding to an original image from an original image on which an image is recorded or displayed, wherein a thermal linear expansion coefficient aL of a lens array and a thermal linear expansion coefficient aF of a main material constituting the original image Is | aL−aF | <δx / (10L)
However, δx = (f (1 + 1 / M) · d · tan α) / t where f is the focal length of each lens element of the lens array, t is aerial from the aerial image side main plane of each lens element of the lens array The distance to the image, M is the imaging magnification at the time of reproduction (M> 0), L is the maximum length of the lens array, d is the distance from the viewpoint to the aerial image, and α is a resolution that allows the eye to recognize blur. The three-dimensional image display device is characterized by being configured to satisfy the following condition.

  According to such a three-dimensional image display device, the linear thermal expansion caused by the environmental temperature change is substantially equal between the lens array and the original image, so that the correspondence between the individual lens elements of the lens array and the original image is maintained. The state can be maintained.

  Then, the blur amount δx caused by the temperature change is smaller than the resolution angle α at which the observer's eyes can recognize the blur in the entire maximum length L of the lens array, so that the blur amount of the aerial image is kept smaller than the allowable range. And a clear three-dimensional aerial image can be displayed.

(3) The invention according to claim 3 is a lens array in which a plurality of lens elements are two-dimensionally arranged, and a minute inverted image or Fourier transform of a reproduced image corresponding to each lens element constituting the lens array. A three-dimensional image display device for forming an aerial image corresponding to an original image from an original image on which an image is recorded or displayed, wherein a thermal linear expansion coefficient aL of a lens array and a thermal linear expansion coefficient aF of a main material constituting the original image Is | aL−aF | <δx / (10Lc)
However, δx = (f (1 + 1 / M) · d · tan α) / t where f is a focal length of each lens element of the lens array, M is an imaging magnification at the time of reproduction (M> 0), Lc is 1/3 of the maximum length of the lens array, d is the distance from the viewpoint to the aerial image, and α is a resolution angle at which the eye can recognize blur. Is a three-dimensional image display device.

  According to such a three-dimensional image display device, the linear thermal expansion caused by the environmental temperature change is substantially equal between the lens array and the original image, so that the correspondence between the individual lens elements of the lens array and the original image is maintained. The state can be maintained.

  Then, in the range of at least 1/3 of the maximum length L of the lens array (for example, near the center), the blur amount δx caused by the temperature change is smaller than the resolution angle α at which the observer's eyes can recognize the blur. Therefore, the blur amount of the aerial image can be kept smaller than the allowable range, and a clear three-dimensional aerial image can be displayed.

According to each invention described in this specification, the following effects can be obtained.
(1) In the invention described in claim 1, since the linear thermal expansion caused by the environmental temperature change is made substantially equal between the lens array and the original image, the correspondence between the individual lens elements of the lens array and the original image is The maintained state can be maintained, the blur amount of the aerial image can be kept small, and a clear three-dimensional aerial image can be displayed.

  (2) In the invention described in claim 2, over the entire maximum length L of the lens array, the blur amount δx caused by the temperature change is made smaller than the resolution angle α at which the observer's eyes can recognize the blur. Therefore, it is possible to keep the amount of blur of the aerial image smaller than the allowable range, maintain the correspondence between the individual lens elements of the lens array and the original image, and display a clear three-dimensional aerial image. It becomes possible to do.

  (3) In the invention according to claim 3, in the range of at least 1/3 of the maximum length L of the lens array (for example, near the center), the blur amount δx caused by the temperature change is recognized by the observer's eyes. Because the resolution angle α is smaller than the possible resolution angle, it is possible to keep the amount of blur of the aerial image smaller than the allowable range, and the correspondence between the individual lens elements of the lens array and the original image is maintained. And a clear three-dimensional aerial image can be displayed.

The present invention is a fly-eye lens used in integral photography.
(1) selecting a material suitable for the lens element;
(2) Arrangement of lens array and aerial image suitable for forming a clear three-dimensional aerial image,
(3) The shape of a lens array suitable for forming a clear three-dimensional aerial image,
(4) Selection of a material having a coefficient of thermal expansion suitable for forming a clear three-dimensional aerial image,
It is characterized by determining the optimum conditions and relations for.

Hereinafter, each feature will be described according to each embodiment.
<First Embodiment>
FIG. 1 is an explanatory diagram schematically showing a cross section of the lens array, an aerial image, and the viewpoint of the observer.

  In FIG. 1, a lens array 10 consisting of seven lens elements is shown in the vertical direction for the sake of simplicity. However, in the actual lens array, a larger number of lens elements are two-dimensional, including the direction perpendicular to the paper surface. Arranged.

  In addition, an original image 20 is arranged on the back surface of the lens array 10 (opposite the viewpoint 50). The original image 20 includes a reproduced image (aerial image to be reproduced) corresponding to each lens element constituting the lens array. ) Is recorded or displayed.

  A light source 30 is disposed on the back of the original image 20, and the original image 20 is uniformly irradiated from the back as viewed from the viewpoint 50, thereby forming a three-dimensional aerial image 40 at a predetermined position on the viewpoint 50 side.

  In the example of FIG. 1, the convex surface of the lens array 10 is directed to the viewpoint side, but it can be reversed by correcting the aberration using an aspherical surface or the like. Here, FIG. 1A shows a case where an aerial image without chromatic aberration is formed according to this embodiment, and FIG. 1B shows a case where an aerial image is formed using a lens array having chromatic aberration. Show.

  As shown in FIG. 1B, when a lens material having an Abbe number νd of less than 28 is used, a large chromatic aberration occurs, so that the aerial image becomes unclear. In this case, unlike a camera or a projector that forms a two-dimensional image, a three-dimensional aerial image is formed, so blurring and color blur due to chromatic aberration extend not only in the two-dimensional plane but also in the depth direction. The inventor of the present application has found that a problem peculiar to a three-dimensional image display device that the resolving power is significantly reduced occurs.

  In a normal photographic lens, it is known that chromatic aberration can be reduced by reducing the aperture diameter. In this case, even if the aperture is reduced, the image size does not change. That is, the aperture position is set so that the image size does not change.

  However, in the case of integral photography fly-eye lenses, it is difficult to place a stop at the above positions. Even if the aperture can be set at an appropriate position using an array element, the image becomes dark, which is not preferable.

  Further, in order to limit the luminous flux without using the diaphragm and maintain the brightness, it is only necessary to reduce the distance between adjacent lenses. However, this is not preferable because the size of the original image is limited.

  For the reasons described above, it is difficult to reduce chromatic aberration by a diaphragm with a fly-eye lens made of a convex lens made of a homogeneous material. In such a case, the inventors' research has found that the reduction of chromatic aberration by the definition of the Abbe number is particularly effective.

  Therefore, in this embodiment, a lens element having a uniform refractive index is configured by using a lens material having an Abbe number νd of a predetermined value or more. By configuring the lens with such a material, chromatic aberration can be substantially suppressed. Therefore, it is possible to display a clear three-dimensional aerial image that does not shift.

  The inventors of the present application have found that an Abbe number νd of 28 or more is sufficient to solve such a problem. Examples of the lens material that satisfies this condition include polycarbonate (PC: νd = 30), polymethyl methacrylate (PMMA: νd = 58), ARTON (νd = 57, trade name of optical resin of Nippon Synthetic Rubber Co., Ltd.), etc. It has been known.

  As described above, the lens array of the three-dimensional image display device is configured using a lens material having an Abbe number νd of 28 or more, so that a clear three-dimensional aerial image faithful to the original image can be displayed. become.

  In this embodiment, an optical resin is used as the lens material of the three-dimensional image display device. The optical resin is a colorless and transparent synthetic resin. Thus, by forming the lens array 10 with the optical resin, there is an advantage that the lens array 10 can be mass-produced by molding and can be easily manufactured.

  As described above, a lens array of a three-dimensional image display device is configured using a lens material having an Abbe number νd of 28 or more made of an optical resin, so that a three-dimensional aerial image that is easy to manufacture, is faithful to the original image, and is clear. Can be displayed.

  In addition, as a material having an Abbe number νd of 28 or more shown in the above embodiments, a material that satisfies the condition of the Abbe number νd can be used other than the above-described materials. For example, diethylene glycol bisallyl carbonate (CR-39: trade name, νd = 58), diallyl isophthalate (DAI: abbreviation of chemical name, νd = 35), sialyl terephthalate (DAT: abbreviation of chemical name, νd = 35), etc. Is mentioned.

  In this embodiment, when at least one lens surface of the lens array 10 of the three-dimensional image display device is aspherical, various aberrations including spherical aberration can be corrected satisfactorily. A clear three-dimensional aerial image could be formed.

  In particular, when various aberrations remain, a new problem has been found that the three-dimensional aerial image is not clear, and such a problem can be avoided by using an aspherical surface. I found it.

  As described above, by forming an aspheric lens array using a lens material having an Abbe number νd of 28 or more, it becomes possible to display a clear three-dimensional aerial image that is faithful to the original image.

<Second Embodiment>
FIG. 2 is an explanatory diagram schematically showing the positional relationship between the cross section of the lens array, the aerial image, and the viewpoint of the observer.

  In FIG. 2, a lens array 10 consisting of seven lens elements is shown in the vertical direction for the sake of simplicity. However, in the actual lens array, a larger number of lens elements are two-dimensional, including the direction perpendicular to the paper surface. Arranged.

  In addition, an original image 20 is arranged on the back surface of the lens array 10 (opposite the viewpoint 50). The original image 20 includes a reproduced image (aerial image to be reproduced) corresponding to each lens element constituting the lens array. ) Is recorded or displayed.

  A light source 30 is disposed on the back of the original image 20, and the original image 20 is uniformly irradiated from the back as viewed from the viewpoint 50, thereby forming a three-dimensional aerial image 40 at a predetermined position on the viewpoint 50 side.

  In the example of FIG. 2, the convex surface of the lens array 10 is directed to the viewpoint side, but it can be reversed by correcting the aberration using an aspherical surface or the like. Here, the distance from the original image 20 to the aerial image 40 is a [m], and the distance from the aerial image 40 to the viewpoint 50 is b [m]. In this case, the diopter DL of the lens array can be expressed as DL = −1 / (a + b), and the diopter DI of the aerial image can be expressed as DI = −1 / b.

  In the three-dimensional image display apparatus having such an arrangement, the observer sees the original image 20 and the lens array 10 irradiated by the light source 30 in the back (in the same direction) of the aerial image 40. In this case, depending on the positional relationship between the viewpoint 50, the aerial image 40, the original image 20, and the lens array 10, a problem peculiar to the three-dimensional image display device that it is difficult to visually recognize the aerial image 40 occurs. Found.

  And the optimal positional relationship for solving the problem which becomes difficult to visually recognize was newly found. That is, by satisfying the condition of | DL−DI |> 0.6 for the diopter difference | DL−DI | in the relationship between the diopter DL of the lens array and the diopter DI of the aerial image, Even if a light-emitting object (the original image 20 and the lens array 10 irradiated by the light source 30) is present behind 40, it is possible to maintain an environment that does not impair visibility.

  Here, this diopter difference will be described. The depth of focus ΔD [diopter] of the observer is ΔD = (ε / r) D, where the pupil diameter is r [mm], the resolving power on the retina is ε [mm], and the refractive power of the eye is D [diopter]. Given in.

This is described on page 214 of “Physiological Optics” edited by Optical Society of Applied Physics (1975, published by Asakura Shoten Co., Ltd.). Here, D = 60 [diopter], r = 1.5 to 8.0 [mm], ε = 0.015 [mm]
It is. That is, when r = 1.5 [mm], ΔD has a maximum value of 0.6.

  Regarding D, r, and ε, the 40th and 55th pages of “Physiological Optics” (published by Asakura Shoten Co., Ltd., 1975) edited by the Optical Society of Applied Physics, “Looking Mechanism” by Toyohiko Hatada (MEDICAL IMAGING TECHNOLOGY, Vol.12, No.4, July, 1994).

  Therefore, the inventor newly found that if the diopter difference | DL−DI | of the aerial image is set to be larger than 0.6, the eyes of the observer can be focused only on the aerial image. As a result, when an aerial image is being observed, it is impossible to grasp the detailed state of the background lens array, and there is no inconvenience and a clear three-dimensional aerial image is obtained.

  As described above, by satisfying the condition that the diopter difference | DL−DI | is larger than 0.6, the diopter difference becomes larger than 0.6 of the depth of focus of the observer, and an aerial image is obtained. As a result, the three-dimensional aerial image can be displayed in an easily observable state.

  That is, it is possible to maintain an environment that does not impair the visibility of the aerial image even when the background of the light emitting object (the original image 20 and the lens array 10 illuminated by the light source) exists behind the aerial image. It becomes possible to display a three-dimensional aerial image in an easily observable state.

  For example, in the case of a three-dimensional image display device designed for a = 1 [m], this condition is satisfied by setting the distance b from the aerial image 40 to the viewpoint 50 to be less than 0.88 [m]. It is possible to maintain an environment that does not impair visibility. That is, by determining the distance a for forming the aerial image 40 and the appropriate observation position that is less than the distance b from the aerial image 40, a good aerial image of a good three-dimensional image can be observed in a clear state. become.

<Third Embodiment>
FIG. 3 is an explanatory view schematically showing the positional relationship between the cross section of the lens array, the aerial image, and the viewpoint of the observer, and the state of the refraction angle θ of the light beam contributing to the formation of the aerial image at the periphery of the lens array. .

  In FIG. 3, a lens array 10 consisting of seven lens elements is shown in the vertical direction for the sake of simplicity of explanation, but an actual lens array has a two-dimensional structure including a large number of lens elements including the direction perpendicular to the paper surface. Arranged.

  In addition, an original image 20 is arranged on the back surface of the lens array 10 (opposite the viewpoint 50). The original image 20 includes a reproduced image (aerial image to be reproduced) corresponding to each lens element constituting the lens array. ) Is recorded or displayed.

  A light source 30 is disposed on the back of the original image 20, and the original image 20 is uniformly irradiated from the back as viewed from the viewpoint 50, thereby forming a three-dimensional aerial image 40 at a predetermined position on the viewpoint 50 side.

  In the example of FIG. 3, the convex surface of the lens array 10 is directed to the viewpoint side, but it can be reversed by correcting the aberration using an aspherical surface or the like. In the three-dimensional image display device having such an arrangement, the refraction angle of the light beam contributing to the formation of the aerial image 40 at the periphery of the lens array becomes large, so that the influence of coma and astigmatism cannot be ignored and the imaging performance. The inventor of the present application has found that a problem peculiar to a three-dimensional image display device that the image quality deteriorates occurs.

  Furthermore, even when the F number of the lens elements constituting the lens array is small, if there are residual aberrations of the lens elements, the effect of those aberrations on the formation of the aerial image cannot be ignored. The inventors of the present application have found that this problem occurs.

  In addition to the existence of such problems, the present inventors have newly found an optimum light ray relationship for solving these problems. That is, by satisfying the condition of θ <30 ° with respect to the refraction angle θ of the light beam that contributes to the formation of the aerial image 40 at the periphery of the lens array 10, the refraction angle can be kept small even in the lens elements at the periphery of the lens array. It is possible to maintain an environment in which the influence of astigmatism and coma is eliminated and the imaging performance is not deteriorated.

  That is, with respect to the refraction angle θ of the light beam that contributes to the formation of the aerial image 40 at the periphery of the lens array, it is configured to satisfy the condition of θ <30 °, thereby suppressing the deterioration of the imaging performance at the periphery of the lens array. Will be able to.

  By satisfying the condition of F> 4 with respect to the F number of the lens elements constituting the lens array, even when there are residual aberrations in the lens elements, the influence of those aberrations can be ignored in forming an aerial image. It becomes possible to keep the environment.

  That is, by setting the F number of the lens elements constituting the lens array to satisfy the condition of F> 4, it is possible to suppress various aberrations including spherical aberration.

Thereby, it is possible to prevent the imaging performance of the lens array from deteriorating and display a clear three-dimensional aerial image.
<Fourth embodiment>
FIG. 4 is an explanatory diagram schematically showing the positional relationship between the cross section of the lens array, the aerial image, and the viewpoint of the observer.

  In FIG. 4, a lens array 10 consisting of seven lens elements is shown in the vertical direction for the sake of simplicity. However, in the actual lens array, a larger number of lens elements are two-dimensional including the direction perpendicular to the paper surface. Arranged.

  In addition, an original image 20 is arranged on the back surface of the lens array 10 (opposite the viewpoint 50). The original image 20 includes a reproduced image (aerial image to be reproduced) corresponding to each lens element constituting the lens array. ) Is recorded or displayed.

  A light source 30 is disposed on the back of the original image 20, and the original image 20 is uniformly irradiated from the back as viewed from the viewpoint 50, thereby forming a three-dimensional aerial image 40 at a predetermined position on the viewpoint 50 side.

  In the example of FIG. 4, the convex surface of the lens array 10 is directed toward the viewpoint, but it can be reversed by correcting the aberration using an aspherical surface or the like. In the three-dimensional image display device having such an arrangement, the refraction angle of the light beam contributing to the formation of the aerial image 40 at the periphery of the lens array becomes large, so that the influence of coma and astigmatism cannot be ignored and the imaging performance. The inventor of the present application has found that a problem peculiar to a three-dimensional image display device that the image quality deteriorates occurs.

  Furthermore, even when the F number of the lens elements constituting the lens array is small, if there are residual aberrations of the lens elements, the effect of those aberrations on the formation of the aerial image cannot be ignored. The inventors of the present application have found that this problem occurs.

  In addition to the existence of such problems, the present inventors have newly found an optimum light ray relationship for solving these problems. That is, with respect to the refraction angle θ1 of the light beam that contributes to the formation of the aerial image 40 at the periphery of the lens array, when the refraction angle when the lens array is a plane is θ0, the condition that θ1 <θ0 is satisfied. The lens element at the peripheral edge of the array can keep the refraction angle small, eliminate the influence of astigmatism and coma, and maintain an environment that does not deteriorate the imaging performance.

  Thereby, it is possible to prevent the imaging performance of the lens array from deteriorating and display a clear three-dimensional aerial image. In the case of realizing such a configuration, the lens array 10, the original image 20, and the light source 30 may be configured by curved surfaces. The curved surface may be a part of a paraboloid, a part of a cylindrical surface, or a part of a spherical surface. However, it is preferable to use a part of a cylindrical surface or a part of a spherical surface because it can be easily manufactured.

<Fifth embodiment>
FIG. 5 is an explanatory diagram schematically showing the positional relationship between the cross section of the lens array, the aerial image, and the viewpoint of the observer.

  In FIG. 5, a lens array 10 consisting of seven lens elements is shown in the vertical direction for the sake of simplicity. However, in the actual lens array, a larger number of lens elements are two-dimensional, including the direction perpendicular to the paper surface. Arranged.

  In addition, an original image 20 is arranged on the back surface of the lens array 10 (opposite the viewpoint 50). The original image 20 includes a reproduced image (aerial image to be reproduced) corresponding to each lens element constituting the lens array. ) Is recorded or displayed.

  A light source 30 is disposed on the back of the original image 20, and the original image 20 is uniformly irradiated from the back as viewed from the viewpoint 50, thereby forming a three-dimensional aerial image 40 at a predetermined position on the viewpoint 50 side.

  In the example of FIG. 5, the convex surface of the lens array 10 is directed to the viewpoint side, but it can be reversed by correcting the aberration using an aspherical surface or the like. In the three-dimensional image display device having such an arrangement, the refraction angle of the light beam contributing to the formation of the aerial image 40 at the periphery of the lens array becomes large, so that the influence of coma and astigmatism cannot be ignored and the imaging performance. The inventor of the present application has found that a problem peculiar to a three-dimensional image display device that the image quality deteriorates occurs.

  In addition to the existence of such problems, the present inventors have newly found an optimum light ray relationship for solving these problems. That is, the lens array 10, the original image 20, and the light source 30 are configured by curved surfaces (part of a paraboloid, part of a cylindrical surface, part of a spherical surface) and contribute to the formation of the aerial image 40 at the periphery of the lens array. With respect to the refraction angle θ1 of the light beam, the condition of R ≧ a is satisfied, where R is the radius of curvature of the lens array composed of a cylindrical surface or spherical surface, and a is the distance from the center of the lens array to the aerial image. Configure as follows.

  With this configuration, it is possible to keep the refraction angle small even in the lens elements at the periphery of the lens array, and it is possible to maintain an environment that does not deteriorate the imaging performance without being affected by astigmatism and coma. .

  Then, by setting the radius of curvature R of the lens array to be equal to or greater than the distance a from the center of the lens array to the aerial image, there is no significant difference between the lens element at the periphery of the lens array and the lens element at the center. A light beam can be emitted from the aerial image in a state. That is, since the radius of curvature R of the lens array is set to be equal to or greater than the distance a from the lens array to the aerial image, the curved surface of the lens array is in a state suitable for forming an aerial image.

  Thereby, it is possible to prevent the imaging performance of the lens array from deteriorating and display a clear three-dimensional aerial image. In this case, when R = a, θ1 = 0 as described above, so that the refraction angle can be kept at 0 even in the lens element at the periphery of the lens array. A light beam can be emitted with respect to the aerial image in a state where there is no difference in refraction angle with the element, and the maximum effect can be obtained. Further, when R <a, the direction of the refraction angle θ1 is reversed, which is not preferable because it has an adverse effect.

  In such a configuration, the lens array 10, the original image 20, and the light source 30 may be part of a paraboloid, part of a cylindrical surface, and part of a spherical surface. However, in manufacturing, a part of a cylindrical surface or a part of a spherical surface is preferable.

<Sixth embodiment>
FIG. 6 schematically shows the amount of blur of the aerial image 40 generated when the lens array 10 and the original image 20 are displaced due to the difference between the thermal linear expansion coefficient aL of the lens array 10 and the thermal linear expansion coefficient aF of the original image 20. It is explanatory drawing shown in.

  In this figure, a case where a difference in elongation amount of δx occurs at the peripheral edge due to a difference | aL−aF | between both the thermal linear expansion coefficients. Due to this δx, the correspondence between the individual lens elements of the lens array 10 and the original image 20 is broken, and ΔX blur is generated in the aerial image 40.

  Here, f is the focal length [mm] of the lens array, t is the distance from the lens array to the aerial image side main plane to the aerial image [mm], M is the imaging magnification during reproduction (M> 0), L is defined as the maximum length of the lens array (for example, in the diagonal direction) [mm], d is the distance from the viewpoint to the aerial image [mm], and α is the resolution angle [′] at which the observer's eyes can recognize blur. To do.

In this case, the blur amount ΔX of the aerial image 40 when the difference in the expansion amount of δx occurs is ΔX≈t · (δx / (f (1+ (1 / M)))) (1),
However, in the case of a Fourier transform image, it can be expressed as M → 0.

In general, it is known that α = 3 ′. Therefore, the blur amount ΔX that is allowable (not noticeable) at the distance d [mm] is ΔX = d · tan α = d · tan 3 ′ (2),
It can be expressed as.

Therefore, from the above (1) and (2), the maximum allowable δx is t · (δx / (f (1+ (1 / M)))) = d · tan 3 ′ Therefore, δx = (f ( 1+ (1 / M)) · d · tan 3 ′ / t (3),
Here, when the thermal linear expansion coefficient is obtained so that the above condition is satisfied even when the environmental temperature changes by ± 10 ° C. from the set value, L · | aL −aF | · 10 <δx.

That is, | aL−aF | <δx / (10L) (4),
It becomes.
In this way, the thermal linear expansion coefficient is brought close, that is, the material having the thermal linear expansion coefficient satisfying the above expression (4) is selected for the lens array 10 and the original image 20, so that the imaging performance is deteriorated due to the change of the environmental temperature. It is possible to realize a three-dimensional image display device that does not cause the problem.

  In the description of the above formulas (1) to (4), the maximum length of the diagonal line of the lens array 10 is L. However, the above-mentioned conditions are focused on only the central portion of the lens array 10 instead of the entire lens array 10. You may comprise so that it may satisfy | fill.

  That is, in view of the fact that the central portion of the lens array 10 (for example, a region of about 1/3 of the entire area) is particularly important for the formation of an aerial image, this portion Lc (Lc = L / 3) causes the above (4). It is also possible to configure to satisfy the equation.

Here, the above formula (1) will be described using a specific example.
When f = 20 [mm], t = 400 [mm], M = 21, L = 300 [mm], and d = 300 [mm] with respect to the right side of the equation (1), | aL−aF | = δx / (10L)
Therefore, the above equation (3) is substituted for this,
δx / (10L)
= (F (1+ (1 / M)). D.tan 3 '/ (10 L.t)
= 4.6 × 10 ⁻⁶ (5),
Therefore, in the case of the above conditions, by selecting the material so that | aL−aF | becomes smaller than the value of (5), it is possible to form a clear aerial image satisfying the allowable range of the blur amount. become.

For example, polymethylmethacrylate (PMMA: aL = 7.0 × 10 ⁻⁵ ) is used as the material of the lens array 10, and polyethylene terephthalate (PET: aL = 7.0 × 10 ⁻⁵ ) is used as the base material of the original image 20 film. Thus, the above conditions (1) and (5) can be satisfied.

  As described above, according to the three-dimensional image display apparatus as in this embodiment, the linear thermal expansion caused by the environmental temperature change is substantially equal between the lens array 10 and the original image 40. It is possible to maintain a state in which the correspondence between the lens element and the original image is maintained.

  Then, the blur amount δx caused by the temperature change is smaller than the resolution angle α at which the observer's eyes can recognize the blur in the entire maximum length L of the lens array, so that the blur amount of the aerial image is kept smaller than the allowable range. And a clear three-dimensional aerial image can be displayed.

FIG. 6 is an explanatory diagram showing a comparison between a three-dimensional image display device using a lens material having an Abbe number νd of 28 or more and a three-dimensional image display device using a lens material having an Abbe number νd of less than 28 in the embodiment of the present invention. is there. It is explanatory drawing which shows typically the mode of the positional relationship of the cross section of the lens array of an embodiment of this invention, an aerial image, and an observer's viewpoint. Schematic representation of the cross-section of the lens array and the aerial image of the embodiment of the present invention, the position of the observer's viewpoint, and the refraction angle θ of the light beam contributing to the formation of the aerial image at the periphery of the lens array It is explanatory drawing shown. It is explanatory drawing which shows typically the mode of the positional relationship of the cross section of the lens array of an embodiment of this invention, an aerial image, and an observer's viewpoint. It is explanatory drawing which shows typically the mode of the positional relationship of the cross section of the lens array of an embodiment of this invention, an aerial image, and an observer's viewpoint. It is explanatory drawing which shows the mode of the embodiment which considered the thermal linear expansion coefficient of this invention. It is a perspective view which shows the external appearance structure of the two-dimensional lens array which uses the conventional convex lens. FIG. 4 is a schematic diagram schematically illustrating recording of integral photography by a state of image formation by a two-dimensional lens array using a conventional convex lens. FIG. 6 is a schematic diagram schematically illustrating the reproduction of integral photography according to a state of image formation by a two-dimensional lens array using a conventional convex lens.

Explanation of symbols

10 Lens array 20 Original image 30 Light source 40 Aerial image 50 Viewpoint

Claims (3)

  A lens array in which a plurality of lens elements are two-dimensionally arranged, and an original image on which a minute inverted image or Fourier transform image of a reproduced image is recorded or displayed corresponding to each lens element constituting the lens array A three-dimensional image display device for forming an aerial image corresponding to an original image, wherein the thermal linear expansion coefficient of the lens array and the thermal linear expansion coefficient of the main material constituting the original image are substantially equal. 3D image display device. A lens array in which a plurality of lens elements are two-dimensionally arranged, and an original image on which a minute inverted image or Fourier transform image of a reproduced image is recorded or displayed corresponding to each lens element constituting the lens array A three-dimensional image display device for forming an aerial image corresponding to the original image, wherein the thermal linear expansion coefficient aL of the lens array and the thermal linear expansion coefficient aF of the main material constituting the original image are:
| AL -aF | <δx / (10L)
However,
δx = (f (1 + 1 / M) · d · tan α) / t
here,
f is the focal length of each lens element of the lens array,
t is the distance from the aerial image side principal plane of each lens element of the lens array to the aerial image,
M is the imaging magnification at the time of reproduction (M> 0),
L is the maximum length of the lens array,
d is the distance from the viewpoint to the aerial image,
α is the resolution angle at which blur can be recognized,
A three-dimensional image display device characterized by satisfying the following conditions. A lens array in which a plurality of lens elements are two-dimensionally arranged, and an original image on which a minute inverted image or Fourier transform image of a reproduced image is recorded or displayed corresponding to each lens element constituting the lens array A three-dimensional image display device for forming an aerial image corresponding to an original image, wherein the thermal linear expansion coefficient aL of the lens array and the thermal linear expansion coefficient aF of the main material constituting the original image are | aL−aF | <δx / ( 10Lc)
Where δx = f (1 + 1 / M) · d · tan α / t where f is the focal length of each lens element of the lens array, and t is the aerial image side main plane of each lens element of the lens array to the aerial image. , M is the imaging magnification during reproduction (M> 0), Lc is 1/3 of the maximum length of the lens array, d is the distance from the viewpoint to the aerial image, and α can recognize blur A three-dimensional image display device characterized by satisfying the following conditions:

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