JPH0380311B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a three-dimensional image display method for obtaining a three-dimensional image by computer-generated holography.

[Prior art and its problems]

Holography is a hologram that records a pattern created by interference between diffracted waves from an object and a separately prepared reference wave, and is then irradiated with a reproduced wave that has the same wavefront as the reference wave. A method of reproducing a three-dimensional image. Generally, an object and a hologram have a Fourier exchange relationship, so by sampling the object and numerically Fourier transforming it, the complex amplitude transmittance of the hologram can be calculated. A hologram obtained in this way is called a computer generated hologram. Regarding computer generated holograms, see, for example, the magazine Applied Optics, Volume 5, 1966;
The paper written on pages 967-969 entitled “Binary Fraunhofer Holograms Generated by Computers”
by Computer).

In the computer generated hologram described above, an object is sampled, and the hologram surface is decomposed into sample points (cells) using the sampling theorem. The sampling theorem is the function g(x)
1/2f when does not have a component higher than spatial frequency f
This theorem states that if a function g(x) is sampled at an interval of , the shape of the function can be uniquely determined. Therefore, for example, when the size of the hologram in the x direction is Δx, and the number of sample points N in the x direction is set as N=Δx/2f (1), the image can be reproduced without losing information. This holds true in exactly the same way in the spatial frequency plane. Therefore, the sample points on the object and the sample points on the hologram may be the same, and the number N expressed by the above equation (1) may be used.

FIG. 5 shows the structure of a conventional hologram sample point. According to this figure, the complex amplitude of one sample point is represented by an aperture 51 in a cell 50, and its position p
The phase is expressed by , and the amplitude is expressed by its area c·h (c is a constant), thereby creating a binary hologram. However, this method requires a large number of decomposition points and is impractical. In order to solve this problem, a method was devised in which a cell is represented by three apertures and any complex amplitude is represented by combining these apertures. This method was published in Applied Optics magazine, Volume 9, 1970, 1949.
The paper “A Simplification of Lee’s Computer/Hologram (A Simplification of Lee’s Method of
Generating Hologram by Computer). In this method, if the complex amplitude distribution on the hologram surface is A _H (ξ, η)=a _H (ξ, η) exp{iφ _H (ξ, η)} ...(2), then this equation becomes It can be expressed as A _H (ξ, η) = a ₀ (ξ, η) + a ₁ (ξ, η) exp(i2π/3) + a ₂ (ξ, η)exp(i4π/3). That is, in this method, the phase is 0,
An arbitrary complex amplitude is expressed by adding each component of 2π/3 and 4π/3 vectorwise. For example, in the case of phase π/2, the result is as shown in FIG. Also 2
Since it is a value hologram, a ₀ , a ₁ , and a ₂ in the above equation are each expressed by the size of the aperture. For example, the shape of the sample point with phase π/2 is as shown in Figure 7.
It is represented by two apertures. According to this method, since the phase can be easily displayed and the amplitude is expressed by the area of the aperture, the number of resolution points in the ξ direction is greatly reduced as shown in FIG. 7, but the number of resolution points in the η direction is relaxed. It is not an essential solution.

On the other hand, research is also being conducted on creating multivalued holograms using plotters such as CRTs that can express halftones. This method is used, for example, in the magazine Applied Optics (Applied Optics).
Optics, Vol. 8, 1969, pp. 2461-2471.
Its Application for Digital Optical
Information Processing)”.
In this method, as shown in FIG. 8, the amplitude is expressed by the density of a circular aperture displayed on the CRT, and the phase is expressed by the center position. Also in this method, η
Although the number of decomposition points in the direction is significantly reduced, the number of decomposition points in the ξ direction is not relaxed.

Incidentally, there is the following relationship between the number of decomposition points of a hologram and the size of a reconstructed image. If the size of the sample point on the hologram surface is δx×δx, the size Δx of the image reproduced from the hologram is expressed as Δx=λf/δx (3). In equation (3), λ is the wavelength and f is the focal length of the Fourier transform lens used for reproduction. According to equation (3), in order to enlarge the reconstructed image,
The size of the sample points must be made smaller, and the smaller the number of decomposition points per sample point, the larger the reconstructed image becomes.

Therefore, when the conventional method described above is applied to a hologram using a material with a small number of resolved points, the number of resolved points per sample point increases, resulting in a small reconstructed image, making it unsuitable for three-dimensional image display. There was a problem.

[Purpose of the invention]

An object of the present invention is to provide a three-dimensional image display method that can obtain a large reconstructed image even when applied to a hologram using a material with a small number of resolution points.

[Structure of the invention]

The present invention provides a method for displaying a three-dimensional image using a hologram in which the phase and amplitude of a transmitted or reflected wavefront are expressed by a plurality of cells including a plurality of apertures, in which the aperture inside the cell is ,
The present invention is characterized in that three holograms are arranged at positions of 2π/3 and 4π/3, and the amplitude transmittance of the aperture can be changed in three or more steps.

〔Example〕

An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 shows the configuration of a three-dimensional image display device that implements a three-dimensional image display method according to a first embodiment of the present invention. In this figure, three light beams L emitted from a monochromatic light source 1, such as a laser array made up of three semiconductor lasers, are transmitted through a beam shaping optical system 2 made up of a plurality of lenses. The light beam is then irradiated onto a light spatial modulation element 5 such as a liquid crystal light valve by an optical deflection device 3 made of an acousto-optic element and the like and an optical scanning device 4 made of a rotating polygon mirror etc., and is scanned. In this case, each of the three light beams L scans each phase resolution point of one sample point of the optical spatial modulation element 5. On the other hand, a hologram of a three-dimensional image generated by an image processing device 6 such as a computer is generated using a fast Fourier transform processor 7 having an interface such as GP-IB. This calculation result is quantized according to the number of density gradations of the light spatial modulation element 5 by a control device 8 such as a microcomputer having an interface such as GP-IB.
The control device 8 controls a power supply 9 having three outputs and is equipped with an interface such as a GP-IB, and causes an injection current corresponding to the quantization level to flow through each semiconductor laser of the monochromatic light source 1. Make it. As a result, the intensity of each light beam emitted from the monochromatic light source 1 changes, and the transmittance of the light spatial modulation element 5 changes depending on the intensity of the irradiated light.

In the optical deflection device 3, a waveform forming device 10 such as a function generator having an interface such as GP-IB generates a frequency corresponding to the scanning position, and this frequency is used to generate a frequency corresponding to the scanning position. It is configured to be applied onto the optical deflection element via the optical deflection element driving device 11. Further, the optical scanning device 4 is controlled to always scan the optical spatial modulation element 5 at a constant speed. A hologram is drawn on the optical spatial modulation element 5 with the above configuration.

After the hologram is drawn as described above,
The monochromatic light source 1 is stopped from emitting light, and another monochromatic light source 12 having the same wavelength as the monochromatic light source 1 is caused to emit light by a power source 13. The light emitted from the monochromatic light source 12 passes through the beam shaping optical system 14 and is irradiated onto the light spatial modulation element 5 . The angle of incidence of the beam on the optical spatial modulator 5 is set in the direction of diffraction of the hologram.
Thereby, the virtual image of the object reproduced from the optical spatial modulation element 5 can be observed through the Fourier transform lens 15.

Next, the principle and operation of the three-dimensional image display method using the three-dimensional image display device will be explained. If the complex amplitude distribution on the object plane is A ₀ (x, y) = a ₀ (x, y) exp{iφ ₀ (x, y)} ...(4), then the complex amplitude distribution on the hologram plane A _H ( ξ、
η) can be obtained by Fourier transforming equation (4) as A _H (ξ, η)=∫∫A ₀ (x,y) exp{2πi(xξ+yη)}dxdy (5). Here, A _H (ξ, η ₎ =a _H (ξ, η) exp{iφ _H (ξ, η)} ...(6 ₎ ) can be expressed in an appropriate way. By sampling the object, the hologram is also sampled according to the sampling theorem described above. As described above, one sample point can be expressed by a combination of apertures at three positions of phase 0, 2π/3, and 4π/3. In the case of the conventional method, the amplitude is expressed by the area of the aperture because it is binary, but by using multiple values, the amplitude can be expressed by the amplitude transmittance of the sample point.

Next, assuming that the number of samples on the object plane is 1000×1000, the method according to the present invention requires the number of decomposition points in the hologram to be 1000×3000. If we consider the case where a hologram is realized using a liquid crystal light valve with dimensions of 30 x 30 mm and a number of resolution points of 3000 x 3000, the number of resolution points of one sample point is 1 in the modulation direction, as shown in Figure 2. 3 in the direction perpendicular to the modulation direction. In this case, the quantization number is this 1×
It depends on the number of density gradations of the 3 decomposition points. There are several types of liquid crystal light valves, but for example, a thermal writing type uses transparent substrates 16, 16 as shown in FIG.
It has a side switch structure. In FIG. 3, 17, 17 is a transparent electrode, 18 is a light absorption film, 1
9 and 19 are liquid crystal alignment films, and 20 is a liquid crystal layer. For example, a liquid crystal light valve having such a configuration is used as the light spatial modulation element 5. When the focused light beam L is irradiated onto the light spatial modulation element 5 made of such a liquid crystal light valve, the light energy is converted into thermal energy by the light absorption film 18, and the orientation of the liquid crystal layer 20 in that portion is changed. It becomes disordered and scattered. In this way, data is written into the optical spatial modulation element 5 by the light beam L, and a hologram is created. Note that in order to erase the written data, a voltage may be applied to the transparent electrode 17 to align the liquid crystal. In FIG. 1, reference numeral 21 denotes an erasing power source, which applies voltage to the optical spatial modulation element 5 at appropriate times.

Also, as a liquid light valve, for example, 0%, 25
Use one that can express 5 levels of concentration: %, 50%, 75%, and 100%. As shown in FIG. 2, each phase of 0, 2π/3, and 4π/3 of one sample point has three resolution points. Different densities can be expressed for the sample points as a whole depending on when all three decomposition points are used and when only the central decomposition point is used. In the case of the five gradations, a quantization level of 9 can be achieved.

The size of the reconstructed image according to the above embodiment is δx
= 11 x 11 mm image can be reproduced for 30 μm. If this is done using the conventional method, δx = 80 μm, and the image size will be 4×4 mm.

Next, a second embodiment will be described based on FIG.
FIG. 4 shows the configuration of a three-dimensional image display device similarly to FIG. 1, and since the configuration for drawing a hologram is the same as in the first embodiment, the same parts are given the same reference numerals. In this embodiment, the three-dimensional image display device is configured as a projection type when the image size or visual field is insufficient.

In FIG. 4, after the monochromatic light source 1 stops emitting light, the monochromatic light source 12 is made to emit light, and the light is passed through a beam shaping optical system 14 composed of a plurality of optical systems and irradiated onto the light spatial modulation element 5. There is. Then, the real image of the object reproduced from the optical spatial modulation element 5 by the Fourier transform lens 15 is projected onto the screen 22, and the image is observed from the optical spatial modulation element 5 side. The real image is in a conjugate relationship with the virtual image, resulting in an image whose perspective is reversed. To correct this, it is necessary to reverse the perspective of the input image.

In the above, the field of view can be increased by sacrificing vertical parallax. When an image is reproduced using this method, a 33 x 33 mm image can be created on a screen 3 meters away from the hologram, for example. In the conventional method, the image size is 12 x 12 mm
It was hot. For details on projection holography, please see the magazine "Optics Communications", Volume 3,
The paper “Reduced Information Projection Holography Using Horizontal Self-Focusing Stereo Screen” on pages 85-88
Type Holography Using A Horizontally
Direction-Selective Stereoscreen).

Further, according to the three-dimensional image display method according to the present invention shown in each of the above embodiments, since writing and erasing are possible, real-time recording and reproduction can be performed. The calculation time required to create a hologram using this method is as follows. It takes 100 seconds to Fourier transform a 1000 x 1000 point two-dimensional image using a fast Fourier transform processor that Fourier transforms 1024-point one-dimensional input data in 100 msec. The calculation time when decomposing 10 points in the three-dimensional depth direction is 17 minutes. If the number of sample points is reduced to, for example, 128 x 128, the calculation time will be 32 seconds and display close to real time will be possible.

Furthermore, since three light beams L are used during writing, information on one sample point can be written at once, and the writing time can be further shortened.

〔Effect of the invention〕

As is clear from the above description, according to the present invention,
Since the number of decomposition points per sample point decreases,
Even in a hologram material with an insufficient number of resolution points, it is possible to reproduce an image of a size that can be recognized as a three-dimensional image.

[Brief explanation of drawings]

Fig. 1 is a block diagram of a three-dimensional image display device according to the first embodiment of the present invention, Fig. 2 is a diagram showing the structure of a hologram sample point, and Fig. 3 is a liquid crystal light valve used as an optical spatial modulation element. 4 is a block diagram of a three-dimensional image display device according to the second embodiment of the present invention, FIG. 5 is a diagram showing the structure of a conventional hologram sample point, and FIG. 6 is a diagram showing the structure of a hologram. A diagram showing that the phase of a sample point can be expressed by a combination of 0, 2π/3, and 4π/3, Figure 7 is a diagram showing the structure of a sample point in a conventional hologram, and Figure 8 is a diagram showing the structure of a conventional hologram. FIG. 3 is a diagram showing the structure of sample points. DESCRIPTION OF SYMBOLS 1, 12... Monochromatic light source, 2, 14... Beam shaping optical system, 3... Light deflection device, 4... Light scanning device, 5... Optical spatial modulation element, 6... Image processing device, 7... Fast Fourier transform processor, 8...
Control device, 9, 13, 21... Power supply, 10... Waveform forming device, 11... Optical deflection element driving device, 15
...Fourier transform lens, 22...screen.

Claims (1)

[Claims] 1. In a method of displaying a three-dimensional image using a hologram in which the phase and amplitude of a transmitted or reflected wavefront are expressed by a plurality of cells including a plurality of apertures, the aperture inside the cell is expressed by a phase of the wavefront of 032π/3,
A three-dimensional image display method, characterized in that three holograms are arranged at positions of 4π/3, and the amplitude transmittance of the aperture can be changed in three or more steps.