Angles Of View
The ability our industry enjoys to provide our customers with an ever burgeoning variety of visual displays is enabled by two, consecutive technologies. The first is the computer which, with its ever faster chips and graphics boards, is continually reinventing what's possible in digital image formation. The second is the projector which is continually improving the quality of the images it can deliver to a screen. The connector which binds the two together is their maximum pixel counts. Anyone interested in contemporary displays must, therefore, think carefully about
Resolution - How Much Should We Count On?To begin with the obvious, all electronic displays are comprised of pixels, a term whose etymology is a contraction of the phrase "picture element." A pixel is the smallest unit used to create a digital image. Thus the specification of a display's resolution is given by the maximum number of pixels it may contain. This quantity is generally expressed as a pair of numbers describing a matrix of the pixels' horizontal and vertical distribution.
When we see "640 by 480 (VGA)" labeling some device, we know that the maximum number of pixels available for writing images is 307, 200. We also know that the larger of the two numbers specifies the number of columns of pixels running horizontally across the display, while the smaller number tells us the maximum number of rows running down it.
If we use these pixels to draw a line across some image area, we are able to specify the precise number and locations of the "points" which make it up. In contradistinction, the number of "points" making up a line within an analog image is theoretically infinite and cannot be specified. The analog line can be diced up into as few or as many sections as we wish. The number of pieces comprising the digitized line cannot be either increased or decreased. It has a fixed and immutable count.
Extending this line analogy a little longer, we can go on to see that if we want the pixellated version of a line to be a convincing imitation of its analog version, we need to put together a large enough number of points that we can place close enough together so that from any reasonable viewing distance, we cannot tell them apart. In this way the illusion of the perfectly continuous analog line can be created.
For the illusion to be successful three major thresholds must be crossed. The horizontal resolution must be high enough, the viewing distance large enough, and the image size must be small enough that we can see only what we want to see: the picture, not the pixels.
We are able to perceive the line as continuous because the resolving power of our eyes fortunately is not infinite. If it were, our line would always be made up of unconnected dots and we could never see a forest for the trees.
When we come to look at projection screens in connection with resolution, we can establish promptly that the role played by diffusion screens is always small. This is so because the largest units used to make up a diffusion layer are particles whose absolute size is measured in microns. Pixels, on the other hand, get measured in millimeters and are resultantly three orders of magnitude larger.
The picture changes radically, however, when we look at screens which have large scale structure. The best example here are lenticulated rear projection screens. All of these have surfaces which contain a series of tangible grooves which can be expressed as a frequency. Thus a lenticulated screen which has a "pitch" of 1 millimeter (meaning that there is 1 lenticulation for every 1mm of screen width) has a frequency lower than one which has a pitch of .6mm (meaning that there are 5 lenticulations in every 3mm of screen width).
After noting that we are looking here at frequencies which are spatial and not temporal, let's return to our digital projection devices for a moment and notice that, come to think of it, they too can be described as having spatial frequencies.
If the horizontal resolution of some projector is 800 (SVGA), we know that when that row of pixels is projected across some screen its spatial frequency will obviously be 800. Varying the size of the screen which displays that row will change the size of the individual pixels, but it will not alter their frequency. Equally, varying the size of a lenticulated screen displaying the 800-pixel row will not change the size of the individual lenticulation, but it will alter their total number.
We have, then, the beginnings of an interesting mathematical relationship. Our projection device is dicing up our image into an exact number of horizontal pieces and our lenticulated screen is interestingly able to do the very same thing. What happens when we bring the two devices together depends largely on the relationship between their frequencies.
Another way to define a series of pixels and a series of lenticulations is to state that they are both wave forms. (The lenticulations actually look like waves and the projected pixels actually behave like waves.) Since we know that all types of waves are capable of interfering with one another, will we not be surprised to discover that the two we are presently considering are no exception.
The magnitude of their interference is visually detectable through a phenomenon called Moir fringing. It is mathematically calculable according to the expression
where W is the frequency of the lenticulations and W0 the pixel frequency." If we make W0 always equal to 1 and crank a long list of incrementally increasing values for W through this formula and then graph the results, we get figure 1.
As the number of lenticulations per pixel is increased, the extent to which the interference line moves away from the Y axis decreases. Thus the amplitude of the effect diminishes as the frequency of the lenticulations is increased.
When we look at a screen which is exhibiting Moir¨Ś interference patterns, the text or data we are trying to read or discern will appear indistinct and blurry. Often the severity of the effect will vary according to our viewing angle - the greater the angle, the greater the illegibility. Although we might at first suppose the projection lens is not focused properly, a closer look makes clear that the information content in the pixels themselves is somehow being scrambled.
But wait. We have established above that a pixel by definition is the smallest building bock with which we can create a display. If that is really so, then its content must be homogeneous and, therefore, impossible to scramble. Have we somehow misrepresented?
No, not exactly. Let us imagine a single pixel chosen at random from within some display. At the time we examine it, its assigned content is some particular shade of some particular color. And, as soon as we utter the word color, we begin to glimpse the origin of this sort of Moir¨Ś.
Almost all digital projection devices create color by blending light from three distinct sources, each of a primary color. What is essential to see here is not that the sources, the Red, the Green, and the Blue are chromatically separated but that they are spatially separated. Thus with a CRT projector, for instance, a colored pixel is actually a stack of three pixels, one overlaying the other, which in combination create the desired color. In most LCD, light valve, and DLP projectors there are also three, spatially separated color sources. Thus the chromatic information inside a given pixel is not always homogenous and, therefore, is capable of being scrambled.
Interestingly, a projection device which utilizes only a single light source and which creates its color by spinning a tripartite translucent wheel before that light source will not be susceptible to resolution loss when combined with a lenticulated screen. (Neither, of course, would a solely monochromatic projector.)
But when "red" light rays contributing to a single pixel are different in their source from the "blue" which are in turn different from the "green," the intended mix of their combination can be significantly altered by the lenticulations which sample them on a screen. If the number of lenticulations per pixel available to do that sampling is small, the resultant effect will be proportionately coarse and noticeable.
Today, when projectors are becoming ever brighter, and images ever more detailed, the decision to use a lenticulated screen must be accounted for carefully. If our customers are counting on us to provide them with top quality displays, we may just be well advised to offer them a diffusion screen on which we ourselves don't have to count but on which they most surely can.