**3. The diffractive screen helping to fulfill the observation field in multiple projections**

The surface which, like a plane mirror or a hologram, should generate a light ray distribution which is equivalent to the originally generated by a three-dimensional object must have the capability to emit in a large angular field with directional intensity and color values corresponding to the scene which is being reconstructed. Each ray is the component of a luminous point to be constructed outside the surface, generally, in front of it. The threedimensional image which floats in front of a screen is the one that most impresses the public, even more when the observer can pass his hand through.

Fig. 1. Left: Ordinary diffusion at a screen. Right: Rays in an ideal three-dimensional display.

The capability to make such an element within a so-called pixel for a TV or computer display does not yet exist. A theoretical way to achieve it was patented (4) based on the

plane may correspond to the Fourier transformation of the transmission or reflection surface properties. It is not completely correct to suppose that, because the Fourier transformation can only be applied in a paraxial approximation, and the angles we need to achieve do not always have this limitation. But, assuming the hypothesis, we could obtain the desired surface profile by using the inverse Fourier Transformation of a light distribution that we

How can one construct such a microstructure on the surface? Which machining technique

We understand that if we make the hologram of a surface of any profile the surface of the resulting hologram is effectively a diffuser with the diffracted light intensity profile of the original surface. It is a fact that diffractive elements made by holography begin to be employed for designing illuminating systems, working with monochromatic or nearly monochromatic light (2). Although the efficiency of an easily replicated hologram is less than 25%, the concentration of the light strictly at a desired region may compensate and even overcome the problem in many cases, and holographic diffusers are on sale by many companies, one of the applications being the internal illumination of computer displays (3).

**3. The diffractive screen helping to fulfill the observation field in multiple** 

Fig. 1. Left: Ordinary diffusion at a screen. Right: Rays in an ideal three-dimensional

The capability to make such an element within a so-called pixel for a TV or computer display does not yet exist. A theoretical way to achieve it was patented (4) based on the

The surface which, like a plane mirror or a hologram, should generate a light ray distribution which is equivalent to the originally generated by a three-dimensional object must have the capability to emit in a large angular field with directional intensity and color values corresponding to the scene which is being reconstructed. Each ray is the component of a luminous point to be constructed outside the surface, generally, in front of it. The threedimensional image which floats in front of a screen is the one that most impresses the

define as the desired one on the lighted plane.

**projections** 

display.

would be useful? Could we replicate it in a rapid and cheap way?

public, even more when the observer can pass his hand through.

location of a 2D micro-display at the focus of a small lens, each micro-pixel element being a ray generator. The number of pixels of a modern display should correspond to the number of volumetric pixels, also called "voxels". Each voxel is the origin of many rays and each ray comes from a sub-pixel of the ideal complete screen, so that we may think these as "ray pixels". An image in a volumetric space with the present pixel display capability for each voxel involves the need for much more pixelation at the emitting surface. The required resolution can be considered as the square of the present capability of 2D screens.

The addressing of those micro-pixels could be facilitated by coding techniques because in each micro-display one pixel's position would always have a corresponding pixel position in its neighbor micro-display, both beginning to a unique three-dimensional display point so that its color and intensity would be very close. Usually, colour does not change with the observation perspective, and the intensity angular change is a relationship which corresponds to a diffusion surface law that could be predetermined and does not need to be received as object information, as it happens in 3D computer drawing rendering.

A fixed relationship interconnects then each family of micro-pixels, each one belonging to one specific micro-pixel display element, and its implementation could be automatic to reduce the need for transmitted information. As such a system is not yet possible, the Holografika company (5) produces one in which a certain number of projectors is located behind a diffracting screen whose function is to produce a diffuse lobe so that as the observer moves, the transition of the light coming from one projector to the light coming from the neighbor projector does not have dark regions. The space region for the observer is then continued and no dark regions are present. The number of projectors must be about 18 and until now only images made by the computer have been shown and animated through simple movements. We can understand that the name "holographic display" given by the company to the system can only be accepted within the popular meaning described above; no light interference is present during the process, neither in practice nor in concept. It is the only commercial system claiming to have the appearance of a continuous parallax. It also claims that the light is directed so that the observer's eye focalizes effectively at the point where the image is represented, eliminating the difference between convergence and accommodation, one important element of visual discomfort.

To support such an assertion, it is necessary to prove that more than one ray exiting from different positions on the screen, those rays converging at the image, are seen by one eye. The commercial system has only a horizontal parallax, so that a certain degree of vertical astigmatism should be present in direct proportion to the eye's aperture. A similar system employing LEDs instead of projectors was proposed (6)

### **4. Non-diffractive screens for stereo imaging**

Dennis Gabor asserted (1) that he and Semioj Ivanov simultaneously studied the possibilities of achieving a screen which could eliminate the need of special goggles. The original idea was developed almost fifty years before by Gabriel Lippmann (1), who employed thin cylindrical transparent elements assembled side by side. Gabor's description is very complete, but it was Ivanov who succeeded in installing the first (and still the only) 3D auto-stereoscopic cinema (7) in 1945.

Based on two cinema projectors placed side by side, the 3 m x 4 m screen was made of a set of thin vertical cylindrical lenses whose surfaces were as shown in the upper part of Figure

After having performed some tests he thought that, if the depth of the scene could be limited, the observer could see the scene normally when one eye is receiving any view or even when the eyes are at positions when inverted views were received. That is, the

monocular or pseudoscopic image could be seen as an orthoscopic one.

Fig. 3. Elements and vision zones at Ivanov's autoestereopic system (from Ref.1).

certainly possible to perceive the depth in such situations.

**5. Diffractive screens for stereo imaging** 

In my test of similar situations employing diffractive screens, I could mention a few people who could tolerate those cases. When there is lateral movement of the camera or some relative movement between objects, some 3D perception can occur to be explained by a sort of Pulfrich effect. For people who are very keen on 3D observation, as Gabor would be, it is

Once holography was discovered and its first practical applications performed, the possibility of employing a hologram not for creating images but for generating vision zones of projected images appeared. The roughness properties that Gabor wanted for the screen to

2, where the light that is focused at a short distance of the back surface is reflected with different angular orientation due to the different transversal position of each projector and in a multiple way because each lenticular element receives the reflected light with a different angle. Figure 3 shows the conical distribution of the elements necessary to converge the whole scene at the observer's positions. It is to be noted that much accuracy is needed to keep the distance corresponding to the right and left eyes positions so that there are limitations to the positions where observers can be, something common to every stereo system, if mainly auto-stereoscopic.

Fig. 2. Surface structure of Ivanov's screen (from Ref.1).

It is reported (1, 7) that Ivanov's theater could receive 180-200 spectators and that some movies were made for it, but it was discontinued because of the fact that the spectator needs to keep his or her head in an almost fixed position.

After Ivanov died Gabor tried to improve the technique by experiencing with mirrored elements with only vertically diffusing properties, eliminating the need for the conical assembly of elements, but he finally concluded that the production of such a screen would be too expensive and abandoned the idea.

2, where the light that is focused at a short distance of the back surface is reflected with different angular orientation due to the different transversal position of each projector and in a multiple way because each lenticular element receives the reflected light with a different angle. Figure 3 shows the conical distribution of the elements necessary to converge the whole scene at the observer's positions. It is to be noted that much accuracy is needed to keep the distance corresponding to the right and left eyes positions so that there are limitations to the positions where observers can be, something common to every stereo

system, if mainly auto-stereoscopic.

Fig. 2. Surface structure of Ivanov's screen (from Ref.1).

to keep his or her head in an almost fixed position.

be too expensive and abandoned the idea.

It is reported (1, 7) that Ivanov's theater could receive 180-200 spectators and that some movies were made for it, but it was discontinued because of the fact that the spectator needs

After Ivanov died Gabor tried to improve the technique by experiencing with mirrored elements with only vertically diffusing properties, eliminating the need for the conical assembly of elements, but he finally concluded that the production of such a screen would After having performed some tests he thought that, if the depth of the scene could be limited, the observer could see the scene normally when one eye is receiving any view or even when the eyes are at positions when inverted views were received. That is, the monocular or pseudoscopic image could be seen as an orthoscopic one.

Fig. 3. Elements and vision zones at Ivanov's autoestereopic system (from Ref.1).

In my test of similar situations employing diffractive screens, I could mention a few people who could tolerate those cases. When there is lateral movement of the camera or some relative movement between objects, some 3D perception can occur to be explained by a sort of Pulfrich effect. For people who are very keen on 3D observation, as Gabor would be, it is certainly possible to perceive the depth in such situations.
