**1. Introduction**

256 Advanced Holography – Metrology and Imaging

Zhang, Z.; Lu, G. & Yu, F.T.S. (1994). Simple method for measuring phase modulation in

What is a hologram? Even if holography was described in a single paper by its creator, there are many descriptions for such a widely divulged phenomenon, known all around the world. Many techniques and elements are entitled "holographic", but they can be classified in two main groups, the "academic" and the "popular" ones. I realized this in July 1989 in a Bulgarian holography meeting when showing my white light holographic screen to Yuri Denisyuk, whom I consider to be the second inventor of holography. He asked if the image I was showing came from a hologram, and my answer was the question "What is a hologram?" His answer was: "Does it employ a reference beam?". My answer was no and then I learned how to introduce the holographic screen techniques in science, not as holography, which is a combination of interference, recording and diffraction, but as a combination of interference, recording, projection of images acquired by any other technique, and diffraction. The projection is made on a fine diffracting structure of about 1,500 lines/mm in such a way that each eye receives a different image which corresponds to the parallax of a 3D scene. But when I showed my projections to people they mostly believed they saw holograms. For them, a hologram is an element which shows 3D in an at least apparent parallax without needing any complementary goggles for the eyes. I call this a popular definition of holography and it can be applied to holographic screens and to autostereoscopic systems, provided they reach at least apparent continuity. Non-diffracting auto-stereoscopic techniques are hardly trying to reach this.

A holographic screen, which from now on I will name commonly as a diffractive screen, consists basically of the hologram of a diffuser whose format is designed to create an observation space for the image projected on the screen. This observer's position field is obtained using reverted illumination, i.e., illuminating the screen in the opposite direction to the reference beam. In this way we can generate the more directional screen which is possible nowadays, in large format and employing lightweight and unbreakable materials. Gabor himself tried some ways to make stereoscopic screens without the need of additional goggles or filters (1). The screen obtained by recording an interference pattern, in a holographic manner, is a way for doing that.

### **2. The hologram as a diffuser**

The construction of a surface that generates a luminous distribution at will is not a simple task. Even assuming that, as the light is going to reach a long distance, its distribution in a

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

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

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

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

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)

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

resolution can be considered as the square of the present capability of 2D screens.

received as object information, as it happens in 3D computer drawing rendering.

accommodation, one important element of visual discomfort.

employing LEDs instead of projectors was proposed (6)

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

3D auto-stereoscopic cinema (7) in 1945.

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 define as the desired one on the lighted plane.

How can one construct such a microstructure on the surface? Which machining technique would be useful? Could we replicate it in a rapid and cheap way?

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).
