Patent Application
20090244665
The present invention relates to a computer-generated hologram. In particular, the invention relates to a computer-generated holographic stereogram with high resolution and with many numbers of parallaxes.
A stereogram is known as a medium, which can be observed by an observer by changing over a plurality of images depending on the direction of observation. The stereogram widely used at present has a lens array such as lenticular lens, fly-eye lens, etc. arranged on a printing medium.
When this type of stereogram is used, by changing the direction of observation, a plurality of entirely different images can be changed over for observation of an observer. Also, when the stereogram is used, by changing the direction of observation, an image of a 3-dimensional object can be observed from a direction to match the direction of observation. In this case, the observer can observe the 3-dimensional object with stereoscopic effect. Further, when the stereogram is used, by changing the direction of observation, a plurality of images gradually changing can be observed by an observer. In this case, the observer can observe the plurality of changing images as a series of animated images. The display of the changeover of a plurality of images, the display of images with stereoscopic effect, and the display of images with animation effect as described above can be combined together and used at the same time.
In addition to the stereogram, in the Patent Reference 1, a screen is proposed, which comprises a group of pixels, and each pixel is divided to a plurality of regions. Then, different diffraction grating is assigned to each region so that, when it is seen from different directions, different images can be observed as an assembly of diffraction grating regions to project diffracted light in the direction.
[Patent Reference]
[Patent Reference 2]
[Non-Patent Reference 1]
The stereogram comprising a printed matter with a lens array such as lenticular lens, fly-eye lens, etc. as described above requires physical pixel structure (lens array). Thus, it is disadvantageous in that the product has low resolution and is too thick. Also, it requires fine and minute printing and the printing area is limited. In this respect, it is not possible to attain the following two purposes: the improvement of resolution and the increase of number of parallaxes.
According to the patent reference 1, pixels in limited size are cut in each direction of parallax and diffraction grating is assigned and used. This also requires a limited area, and it is not possible to attain the two purposes as given above: the improvement of resolution and the increase of number of parallaxes.
To solve the problems of the prior art as described above, it is an object of the present invention to provide a computer-generated holographic stereogram, which has very high resolution and many numbers of parallaxes.
To overcome the disadvantages of the prior art as described above, a first computer-generated hologram according to the present invention is a computer-generated hologram for selectively reproducing a plurality of images depending on the direction of observation where complex amplitude of an object wave is recorded, wherein:
a virtual point light source group is set up spatially on a side opposite to the observation side of the hologram, luminance angular distribution AWLci (θxz, θyz) of divergent light diverged from each of the virtual point light sources of said virtual point light source group toward observation side is divided by angular division, and within the divided angle, among the multiple images positioned on the plane of said virtual point light source group, a divergent light diverged from a point of amplitude equal to the density of pixel of the image corresponding to each of divided angle or equal to a value in a certain fixed relation with the density of the images at the position of the virtual point light source is recorded as the object light at one of the positions on the observation side of the virtual point light source group.
In this case, each of the virtual point light sources in the virtual point light source group is a point light source where the spreading direction of the light is mono-dimensional, and it may comprise a linear light source, which extends in a direction perpendicularly crossing the spreading direction.
A second computer-generated hologram of the present invention is a computer-generated hologram for selectively reproducing a plurality of images depending on the direction of observation where complex amplitude of an object wave is recorded, wherein:
when a predetermined illuminating light enters, a diffracted light is reconstructed, which advances as it is diverged toward observation side from each of the points of spatial virtual point group on a side opposite to observation side of the hologram, luminance angular distribution of the light is divided by angular division depending on the direction of diffraction angle so that the light is diverged from each virtual point toward the observation side of the hologram, and the diffracted light is equal to the divergent light diverging from a point with an amplitude equal to the density of pixel of the image corresponding to each divided angle or equal to a value in a certain fixed relation with the density at the position of the virtual point of the recorded images among the separate recorded images positioned on the plane of said virtual point group within the divided angle.
In this case, each of the virtual points of the virtual point group is a point where the spreading direction of the light is mono-dimensional, and it may comprises a straight line extending in a direction perpendicularly crossing the spreading direction.
A third computer-generated hologram of the present invention is a computer-generated hologram for selectively reproducing a plurality of images depending on the direction of observation where complex amplitude of an object wave is recorded, wherein:
a virtual light converging point group is spatially set up on observation side of the hologram, luminance angular distribution TWLci (θxz, θyz) of converged light entering from the side opposite to the observation side to each of the virtual light converging points of said virtual light converging point group is divided by angular division, and within the divided angle, among the multiple images positioned on the plane of said virtual light converging point group, these converging lights are converged to a point of amplitude equal to the density of pixel of the image corresponding to each of the divided angle or equal to a value in a certain fixed relation with the density of the images at the position of the virtual light converging point, and the converging lights are recorded as the object light at one of the positions on a side opposite to the observation side of the virtual light converging point group.
In this case, each of virtual light converging points of the virtual light converging point group is a light converging point where the spreading direction of the light is mono-dimensional, and it may comprise a linear light converging light extending in a direction perpendicularly crossing the spreading direction.
A fourth computer-generated hologram of the present invention is a computer-generated hologram for selectively reproducing a plurality of images depending on the direction of observation where complex amplitude of an object wave is recorded, wherein:
when a predetermined illuminating light enters, a diffracted light is reconstructed, which is diverged at observation side through each point of spatial virtual point group on the observation side of the hologram, luminance angular distribution of the light converged to each virtual point is divided by angular division depending on the direction of diffraction angle, and among the separate recorded images positioned on the plane of said virtual point group within each of the divided angles, these converging lights are the diffracted lights converged to a position of amplitude equal to the density of pixel of the image corresponding to each divided angle or equal to a value in a certain fixed relation with the density at the position of virtual point of the recorded images, and the converged lights are reconstructed in this manner.
In this case, each of the virtual points of the virtual point group is a point where spreading direction of the light is mono-dimensional, and it may comprise a straight line extending in a direction perpendicularly crossing the spreading direction.
In the present invention, on a plane where a plurality of images such as parallax images are reconstructed and which is separated from the plane of the hologram, a multiple of virtual point light sources with luminance equal to the luminance of the position of the images different depending on radiating direction or a multiple of virtual light converging points with luminance equal to the luminance of the directions of the images different depending on light converging direction are defined. Light components radiated from these virtual point light sources or light components converged to these virtual light converging points are regarded as virtual object light, and a computer-generated hologram is prepared by using these light components. As a result, a computer-generated hologram can be prepared by using a light radiated from these virtual point light sources or a light converged to these virtual light converging points. Thus, it is possible to obtain a computer-generated hologram, which has high resolution and can record and reconstruct a multiple of images and which does not require hologram photographing. The present invention provides, for instance, a computer-generated holographic stereogram, which has high resolution and has many numbers of parallaxes.
The basic principle of a computer-generated hologram according to the present invention is as follows:
On a plane where a plurality of images such as parallax images is reconstructed and which is separated from the plane of the hologram, a multiple of virtual point light sources with luminance of the positions of the images different depending on radial direction or a multiple of virtual light converging points with luminance equal to the luminance of the positions of the images different depending on light converging direction are defined. Light components radiated from these virtual point light sources or light components converged to these virtual light converging points are regarded as virtual object light, and a computer-generated hologram is prepared using these light components. As a result, images with high resolution and with many numbers of parallaxes can be recorded. Thus, a computer-generated hologram (CGH) is prepared, which requires no hologram photographing.
Description will be given below on general principle of the computer-generated hologram according to the present invention.
As shown in
It is supposed now that initial phase of the virtual point light source Qi is φWLci, and a distance between Qi and Pj is rij. Then, a complex amplitude value OWLc (x2, y2, z2) is given as:
where N represents the number of Qi.
A luminance AWLci (θxz, θyz) from the virtual point light source Qi (x1, y1, z1) is divided by angular division with respect to θxz and θyz. In each of the divided angles, the density of pixel of the image of the image corresponding to the divided angle at the position of the virtual point light source Qi (x1, y1, z1) of the image is assigned. For instance, the angle θxz is divided to θxz0˜θxz1˜θxz2˜ . . . ˜θxzm within angle range of −λ/2 to π/2, and the angle θyz is divided to θyz0˜θyz1˜θyz2˜ . . . ˜θyzn within angle range of −π/2 to π/2 to have equal angular distance. Then, the density I11i at the position of the virtual point light source Q1 of the image I11 is assigned to the range of θxz0˜θxz1 and to the range of θyz0˜θyz1. The density I21i at a position of the virtual point light source Qi of the image I21 is assigned to the range of θxz1˜θxz2 and θyz1˜θyz1. The density Imni at a position of the virtual point light source Qi of the image Imn is assigned to the range of θxzm-1˜θxzm and θyzn-1˜θyzn.
Explaining in simpler manner, in
Here, the density is supposed to be a value, which takes a bigger value when brightness is high as generally used in digital image. (It is considered that, when black and white are compared with each other, white has higher density.)
Here, it is supposed that incident vector of a reference light 2, which consists of parallel lights entering the CGH 12 is (Rx, Ry, Rz), and that the amplitude of the wavelength λc is RWLc0. Also, it is supposed that the phase at the origin of coordinates is φRWLc. Then, complex amplitude value RWLc (x2, y2, z2) is given as:
R
WLc(x2,y2,z2)=RWLc0·exp[j{(2π/λc)×(Rxx2+Ryy2+Rzz2)/(Rx2+Ry2+Rz2)1/2+φRWLc}] (2)
The intensity IWLc (x2, y2, z2) of interference fringes caused by the object wave 1 at Pj (x2, y2, z2) and the reference light 2 are given by:
I
WLc(x2,y2,z2)=|OWLc(x2,y2,z2)+RWLc(x2,y2,z2)|2 (3)
In the above, a distance rij between Qi and Pj is given as:
r
ij={(x2−x1)2+(y2−y1)2+(z2−z1)2}1/2 (4)
An angle θxz with respect to z-axis when the straight line QiPj is incident to the plane x-z is given as:
θxz=tan−1{(x2−x1)/(z2−z1)} (5)
An angle θyz with respect to z-axis when the straight line QiPj is incident to the plane y-z is given as:
θyz=tan−1{(y2−y1)/(z2−z1)} (6)
Initial phase φWLci of the virtual point light source Qi is set to a fixed value between the virtual point light sources Q1 regardless of the relation of the virtual point light sources to each other.
As it is evident from the above description, a multiple of virtual point light sources Qi (x1, y1, z1) are set up on planes of a plurality of images I11, I21, . . . , Imn, which can be recorded and reconstructed on the same plane as the CGH 12. Luminance angular distribution AWLci (θxz, θyz) of divergent light radiated from each of the virtual point light sources Qi is divided depending on the direction of the radiant angle. Within different divided angle, luminance is set to a value equal to the density I11i, I21i, . . . , Imni at the position of the virtual point light source Qi of different images I11, I21, . . . , Imn. The initial phase φWLCi of the virtual point light source Q1 is set to a constant value between the virtual point light sources Qi regardless of the relation to each other. Then, the phase and the amplitude of the divergent light from the virtual point light source Qi are holographically recorded (recording of interference with the reference light 2). As a result, by the CGH 12 of the present invention, images I11, I21, . . . , Imn different depending on the direction of observation can be obtained.
When an illuminating light 15 with the same wavelength λc as the reference light 2 is incident at the same incident angle as that of the reference light 2 to the CGH 12 as shown in
Explaining in simpler manner by referring to
Next, description will be given on a method to prepare the CGH 12 as described above as a binary hologram by referring to
In the case shown in
Also, a point light source within 2-dimensional plane is used as the virtual point light source, while it may be designed in such manner that a linear light source extending in y direction and not spreading in y direction may be used.
Further, in the case shown in
It is supposed here that the initial phase of the virtual light converging point Qi is φWLci, and a distance between Qi and Pj is rij. Then, a complex amplitude value OWLc (x2, y2, z2) of the object wave entering Pj (x2, y2, z2) is as given below, instead of the above equation (1):
where N represents the number of Qi.
Radiant luminance TWLci (θxz, θyz) emitted toward the observer from the virtual light converging point Qi (x1, y1, z1) is divided by angular division with respect to θxz and θyz. Then, the density of pixel is assigned at a position of the virtual light converging point of an image corresponding to each dividing angle for each image within the divided angle. For example, the angle θxz is divided to θxz0˜θxz1˜θxz2˜ . . . θxzm within the angle range of −π/2 to λ/2. The angle θyz is divided to θyz0˜θyz1˜θyz2˜ . . . θyzn within angle range of −π/2 to π/2 with equal angular spacing between them. The density I11i at the position of the virtual light converging point Qi of the image I11 is assigned to the ranges of θxz0˜θxz1 and θyz0˜θyz1. The density I21i at the position of the virtual light converging point Qi of the image I21 is assigned to the ranges of θxz1˜θxz2 and θyz0˜θyz1. The density Imni at the position of the virtual light converging point Qi of the image Imn is assigned to the ranges of θxzm-1˜θxzm and θyzn-1˜θyzn as luminance within the divided angle.
Explaining in simpler manner, in
An object wave 1 is generated, which has the densities at the pixel position i of the letters “A”, “B”, . . . “H” at the same time depending on the direction of parallax. The object wave 1 is as given in the equation (1′).
Here, it is supposed that incident vector of the reference light 2, which consists of parallel lights entering the CGH 12, is (Rx, Ry, Rz), that the amplitude of the wavelength λc is RWLc0, and that the phase at the origin of the coordinates is φRWLc. Then, the complex amplitude value RWLc (x2, y2, z2) of the reference light 2 is given, as in the case of
R
WLc(x2,y2,z2)=RWLc0·exp[j{(2π/λc)×(Rxx2+Ryy2+Rzz2)/(Rx2+Ry2+Rz2)1/2+φRWLc}] (2)
The intensity value IWLc (x2, y2, z2) of interference fringes caused by the object wave 1 and the reference light 2 at Pj (x2, y2, z2) is given similarly as:
I
WLc(x2,y2,z2)=|OWLc(x2,y2,z2)+RWLc(x2,y2,z2)|2 (3)
In the above, the distance rij between Qi and Pj is given as:
r
ij={(x2−x1)2+(y2−y1)2+(z2−z1)2}1/2 (4)
The angle θxz with respect to z-axis when the straight line QiPj is incident to the plane x-z is:
θxz=tan−1{(x2−x1)/(z2−z1)} (5)
The angle θyz with respect to z-axis when the straight line QiPj is incident to the plane y-z is given as:
θyz=tan−1{(y2−y3)/(z2−z1)} (6)
The phase φWLci at the virtual light converging point Qi is set to a constant value between the virtual light converging points Qi regardless of the relation to each other.
As it is evident from the above description, a multiple of the virtual light converging points Qi (x1, y1, z1) are set up on planes of a plurality of images I11, I21, . . . , Imn recordable and reproducible on the same plane as the CGH 12. Luminance angular distribution TWLci (θxz, θyz) of convergent light entering each of the virtual light converging points Qi is divided by angular division depending on the direction of radiant angle. Within different divided angle, luminance equal to the density I11i, I21i, . . . , Imni at the position of the virtual light converging point Qi of different images I11, I21, . . . , Imn is set up, and initial phase φWLci of the virtual light converging point Qi is set to a constant value between the virtual light converging points Qi regardless of the relation to each other. The phase and the amplitude of the converging light entering the virtual light converging points Qi are recorded holographically (recording of interference with the reference 2), and the CGH 12 of the present invention can be obtained, in which the different images I11, I21, . . . , Imn can be reconstructed depending on the direction of observation.
When it is designed in such manner that an illuminating light with the same wavelength λc as the reference light 2 enters the CGH 12 recorded at the same incident angle as the reference light 2 as shown in
Explaining in simpler manner by referring to
Next, description will be given on a method to prepare the CGH 12 as a binary hologram by referring to
In the case shown in
Also, in
Further, in the case of
Further, in the description given for
A plurality of images to be recorded on the CGH 12 of the present invention as described above may be parallax images obtained by changing the direction of observation of a 3-dimensional object or of a changeable picture, which is turned to an entirely different picture when the direction 1C of observation is changed, or a series of animation images to be changed when the direction of observation is changed.
Further, the divergent light emitted from the virtual point light source or the converging light converged at a virtual light converging point may be recorded on the plane of the CGH 12 so that these light components may be superimposed on the divergent light from adjacent virtual point light source or on convergent light converged to adjacent virtual light converging point, or these may be recorded separately from each other and not superimposed on each other. In other words, in the former case, when the spacing of arrangement of the virtual point light source or virtual light converging points is narrower than the width of the object wave from one point light source or from the light converging point spreading on the plane of CGH, the number of the images to be recorded increases, and the resolution is also turned to be higher, while noise may be increased because interference fringes are superimposed on each other. With regard to angular division in x direction and y direction of the luminance AWLci (θxz, θyz) and the luminance TWLci (θxz, θyz), may be equal angle division or angle division to have equal spacing on the plane of the CGH 12 or may be the other division. In case the images are recorded as superimposed on the plane of the CGH, if the initial phase φWLci is set to a constant value regardless of the relation to each other, unevenness in the reconstructed image is decreased, and this contributes to the improvement of the quality of the images. In case the 1) images are not superimposed on the plane of the CGH, the initial phased φWLci may be set to a constant value so that these are related to each other.
If the distance of the image from the plane of the CGH is set to within 1 mm, more distinct image can be obtained, and this is desirable.
Also, in the computer-generated hologram of the present invention, it may be arranged in such manner that the hologram of
In the above, description has been given on the computer-generated hologram of the present invention based on its principle, while the invention is not limited to these embodiments, and various changes and modifications can be made.
As it is evident from the above description, according to the computer-generated hologram of the present invention, on a plane where a plurality of images are reconstructed and which is separated from the plane of the hologram, a multiple of virtual point light sources with luminance of the positions of the images different depending on radial direction or a multiple of virtual light converging points with luminance equal to the luminance of the positions of the images different depending on light converging direction are defined. Light components radiated from these virtual point light sources or light components converged to these virtual light converging points are regarded as virtual object light, and a computer-generated hologram is prepared using these light components. The present invention makes it possible to provide, for instance, a computer-generated holographic stereogram with high resolution and with many numbers of parallaxes.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2003-101736 | Apr 2003 | JP | national |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 10551986 | Oct 2005 | US |
| Child | 12483879 | US |
