**8. The continuous parallax**

We see the need to approach the perception of a continuous view sequence to have a threedimensional image with good quality. There is a white-light imaging process whose parallax is inherently continuous, as in holography. It matches depth coding by diffraction naturelly happening when the diffracted light is collected in a small region after a diffraction grating, with its also natural decoding happening after projecting that light on a second diffractive element (14, 15). Each wavelength represents a viewpoint based on a small area of the first

Fig. 4. Up: Photograph of an object directly projected on a holographic screen. Above:

We see the need to approach the perception of a continuous view sequence to have a threedimensional image with good quality. There is a white-light imaging process whose parallax is inherently continuous, as in holography. It matches depth coding by diffraction naturelly happening when the diffracted light is collected in a small region after a diffraction grating, with its also natural decoding happening after projecting that light on a second diffractive element (14, 15). Each wavelength represents a viewpoint based on a small area of the first

anaglyphic stereo representation of the same scene, with color channel.

**8. The continuous parallax** 

diffracting element and as the spectrum is continuous the parallax also is. We can better understand the basic process of a diffractive screen considering it as a primary element, a diffraction grating. If we further approximate the projecting lens to a simple pinhole camera corresponding to its central part, we can see in Figure 5 how the ray tracing based on an object point explains the resulting image by central symmetry (16).

Fig. 5. Symmetry in double diffraction imaging intermediated by a slit.

DG1 and DG2 are two identical diffraction gratings intermediated by a slit. Each object point has a corresponding image point symmetrically to a central point. Because the observer looks to the image from behind, he sees an inverted depth. In this case of perfect matching between two diffractions, it is interesting to notice a property which resembles a holographic one: the diffraction at a symmetric order, on the second grating for example, generates an image with inverted depth. An image in normal depth is so obtained (17).

property a second diffracting element may have. Enlargement is the same for all three dimensions of the object. A small transmission hologram made with a lateral reference beam on 35 mm film can be enlarged on the screen by illuminating it with a halogen lamp (19). To obtain a better luminous efficiency the scene was recorded employing a photographic objective covered with a horizontal slit and it was projected by reversing the light path as in Komar's technique but enlarged and in white light. It was possible then to have an image on

The observer's space depends vertically on the height of the diffuser and laterally on its width and on the screen dispersion. The angle between the object and the reference beams being of 45 degrees, no more than four observers seated in two rows can see the scene simultaneously. A similar system not enlarging holograms but projecting pictures of classic movies was presented to the public (21). There, the images appeared from six meters behind the screen coming closer little by little until traversing it to one meter from the observer,

The recording and white light projection of holographic movies was not accomplished due to the lack of resources and concentration of efforts in the application of electronic images. The recording of holograms in white light which is based on an interesting proposal (22)

**10. Continuous parallax in electronic images projected on diffractive screens**  The depth coding-decoding diffractive principle allows projection of a point source image at any position with respect to a diffractive screen. A computer-controlled figure generator was developed having a thin white light beam being focused at some millimeters from a diffraction grating whose lines were vertical. Because the beam was reflected on a mirror which was made to rotate through a vertical axis, the distance from the focus of the beam to the grating changed. This distance made the necessary degree of coding, which constitutes the horizontal size of a white-light spectrum. The movement was complemented with another two computer-controlled rotating mirrors to generate a luminous point located in any three dimensional position floating in front of the screen (23). A software was in charge of generating animations in the format of line figures. Figure 7 shows that a cube could be drawn without the need to correct any distortion. The image volume is about 100 l, no more is possible due to its reduced brightness. The possibility of white-light laser beams now

a 0,84 m x 1,10 m screen (20) at x40 enlargement (Figure 6).

Fig. 7. Luminous points in a cube shape in front of the screen.

located two meters away from the screen.

was not accomplished up to now.

In a second approximation, we can consider the diffractive screen as a diffracting lens, that is, a bi-dimensional grating which puts the light it receives converging to a unique position, as a convergent ordinary optical element. A diffracting lens is obtained directly by a hologram made with two point sources. If we project in monochromatic light, the screen acts as the one of Komar, but, projecting in white light and making the screen with the point sources from the same side of the film, the diffracted transmitted images are affected by a horizontal dispersion. The same basic property that gives orthoscopic and pseudoscopic images with two gratings corresponds now to the same images but seen all over the screen extension. When the observer moves laterally, he receives continuous view sequences of the object. In this way it has been possible to observe the enlarged image of objects on a one square meter screen but an intense reduced size projection lamp and a dark ambience is necessary. To avoid the need of having the observer watching at a very precise height, one point source in the the interference process process is substituted by a thin vertical diffuser. It gives the vertical size of the observation region but with a reduced image brightness. Besides the limited diffraction efficiency, another brightness limitation results from the need of a thin slit on the projecting lens to get maximum focal depth.
