Angles Of View
Diffusion screens take many forms. Some are flexible and roll up, others are rigid, with substrates of glass or plastic. Some can be tensioned while others cannot be stretched. But these are all mechanical properties; they are not optical. What unites diffusion screens optically is that they all have a surface which interacts with light falling on it. What are the properties of these
Screen Surfaces?Surely the screen surface with which we are all most familiar is Da-Lite's Matte White. An industry standard, this surface is often thought of as the "plain vanilla" of screen choices. But is the Matte White screen really that pedestrian? Or could it be that Matte White is one of the most remarkable projection screens of them all? Let's see.
Imagine that we are seated directly in front of a Matte White screen and, because we are not prepared to trust our own eyes, further imagine that we have an extremely accurate photometer which reads brightness over a 1o angle. (We don't want the spot meter to read too large an angle as that might obscure the brightness differences we're expecting to find.) When we point the photometer at the center of the screen, it measures, say, 10 units of light. When we pivot in our seat and point the meter out at a corner of the screen we see that it will read, once again, 10 units of light. Intrigued, we get up and move to some other position that is not normal to the screen and we repeat our measurements, pointing our meter back at screen center and then at numerous other points anywhere and everywhere on the screen. And no matter how often we do this we always get the same, exact reading: 10 units of light, anywhere we look.
We referred to this remarkable phenomenon in our discussion of Uniformity [Vol I, 1] but now it is time to try and understand it. First, however, let us perform a little experiment which will nicely demonstrate the case.
Take a piece of blank white copy paper and, grasping two of its opposite sides, hold it up before you. Notice its whiteness. Now slowly move one of your hands away from you until the paper is perpendicular to your eyes and you are sighting straight across the edge of the flat surface. Notice that the sheet is still white; and notice that it will remain white no matter how you orient it. At no time does it become dark, even when your viewing angle is 90o .
Both common sense and our scientific intuition suggest that Matte White projection screens should not behave as they do. One would think that the center of the screen should be brighter than the corners when we are positioned directly in front of it. Lambert's Law (which governs the physical dynamics of light reflecting off a radiating surface, a screen) tells us that the radiant intensity emitted in any direction from a unit radiating surface falls off as the cosine of the angle between the normal to the surface and the direction of the radiation. Yet despite the certainty of this mathematically prescribed fall off, we still see the same amount of brightness wherever we look at a Matte White screen.
The explanation for this spectacular uniformity involves the geometry of our viewing angle and is easily illustrated.
If we turn off the projector and substitute a flashlight for our spot meter, we will notice that the shape of the beam as it strikes the screen directly in front of us is perfectly circular. As we pivot and sweep the beam out toward the edge of the screen we notice that the shape of the spot is no longer circular, it has become elliptical. The farther out we point the light, the more stretched out it becomes. In fact, if we get up and hold the flashlight right against one edge of the screen, the "spot" turns into a fanlike band which extends down the entire length of the surface.
Both the photometer and our eyes behave in the same fashion as the flashlight. The surface area of screen they include when they are aimed at a portion of the screen directly in front of them (the circle) is smaller than when they look to the side (the ellipse), which in turn has a smaller surface area than the band.
And it just so happens that this increase of surface area is exactly inverse to the intensity fall off dictated by Lambert's Law. This means that although the amount of light per unit area coming from the projector is indeed reduced as our viewing angle from that unit area is increased, the number of unit areas included by our enlarged viewing angle will in total exactly make up for the loss in intensity from each of them.
In practice, of course, finding a uniform projection source is extremely difficult. Almost all projection lenses transmit very much less light out of their edges than they emit from their centers. Additionally, the classical inverse square law dictates that since light reaching the edges of a screen has travelled farther than light falling on the center, the outer light rays will arrive with less intensity. Neither of these factors, however, involves the screen and thus the sheet of paper is always white and the Matte White screen is always uniform.
Matte White screens are not, however, made out of paper (which is, however, both matte and white). Their surfaces are actually created with a substance known as Magnesium Carbonate (MgC03) - or a variant thereof. Magnesium Carbonate looks like white chalk and technically may be called a "perfect white diffuser." That phrase implies that no light striking such a surface will be absorbed and that all light so impinging will be reflected in a pattern that is isotropic. Thus the energy from any light ray arriving normal to the screen will be scattered identically in all directions.
Given these splendid optical properties, why would anyone want any other surface than Matte White on a projection screen? And the answer is because frequently it is desirable for a projection screen to have gain. By definition Matte White is unity gain surface. It does not have a gain greater than 1.
Screen gain is achieved by using a diffusion material which does not behave as a perfect white diffuser and which does not, therefore, reflect projected light isotropically. Da-Lite's Pearlescent and Video Spectra screens have a gain of 1.5 and consequently will be brighter when viewed from a small viewing angle than from a large one. What is going on at the surface of these Video Spectra and Pearlescent screens which produces this gain is interesting.
Examined under magnification their surface looks like a large series of flat stepping stones regularly laid out across a white field. The stones are actually platelets of mica and the field beneath them is a Matte White diffuser. From the discussion above we already know what will happen to light rays incident to the diffuser. But what about light striking the platelets?
These crystals have had their flat sides coated with Titanium Dioxide (Ti02) which renders them highly reflective. Thus they can be thought of as forming an array of tiny mirrors. As Figure 1 illustrates these platelets reflect light quite differently than the diffuser beneath them. The Pearlescent and Video Spectra screens turn out actually to be clever hybrids of two surfaces: one highly reflective and the other extremely diffuse. The platelets (shown on the right) give these screens their on-axis gain and the diffuser (sketched on the left) provides their uniformity.
Now that we've had a look at front projection diffusers, what about rear screen surfaces? How different are they? The answer is that are hardly different at all.
In fact the only real distinction between the material constituting a rear screen diffuser and a front is chemical. Instead of choosing substances that efficiently reflect light, we now need to utilize coatings which proficiently transmit it. A suspension of finely ground silica (Si02) is a typical example of a good optical transmitter for rear projection screens.
Although the projectors in Figures 2 and 3 point in different directions notice that for an audience seated to the left the two screens have identical distribution patterns. Varying the gain of either screen would obviously alter its pattern but otherwise, if we took the projector out of each Figure, we could not tell which screen was Front and which was Rear.
In rear screens gain is controlled by varying the density of the surface coatings. Lower density diffusions contain fewer particles to scatter the projected light rays so more of them pass through the screen at small exit angles which produces more on-axis brightness.
Higher density coatings will more thoroughly disperse the incoming light which will contract the on-axis gain but expand the size of the audience field.
Gain from a front projection screen is not governed by the density of the diffusion material but by the degree to which its reflectivity is allowed to be directional. The more specular or mirrorlike a front screen becomes, the more its gain will increase and its viewing angle will shrink.
Lastly it should be noted that screen surfaces do not have to be thick. Relative to the wavelengths included in the projected light surface depths of only a few microns are more than adequate. Microscopically, of course, these surfaces are not at all smooth and resemble instead a plain strewn with millions of irregularly shaped boulders through which the light waves must pass (if its a rear screen) or off of which they must bounce (if its front).
Mechanically, a projection screen, front or rear, is really just a wafer-thin surface which, if it could stand upright by itself, would need neither a backing nor a substrate.
Optically the function of a projection screen is quite independent of its substrate. It is the diffused surface and only the surface which does all the work.