Angles Of View

As an index of their flexibility and power CRT video projectors are often described in terms of bandwidth. The LCD projectors provide a similar indication when they announce the number of pixels they can display. Understanding the significance of these specifications is useful to predict what projected images will look like on a screen. The attribute they measure and a critical feature of all visual displays is called

Resolution

At first glance the concept of resolution is simple enough. A dictionary (American Heritage) defines it as "the fineness of detail that can be distinguished in an image, as on a video display." What is not so simple is the number of places and the number of ways it can be limited or measured.

When we look at a video image on a screen we are actually at the end of a projection chain with six links in it: Software → Hardware → Projector → Screen → Eye → Brain. Whatever resolution we perceive has been created, modified, and limited by each of the five preceding links.

Software and hardware combine to produce the nature, content and shape of a video image. All of those data are then electronically divided up into an exact number of small pieces or bits which, when transduced by a projector into a beam of light, have come to be called pixels.

The pixel (the word is a contraction of the phrase "Picture Element") is the fundamental building block of all video images. When we are told that a projector has a resolution of 640 horizontal by 480 vertical, we can determine that any image cast by that projector will be divided up into precisely 307,200 pixels which are formed by the intersection of 640 columns with 480 rows. (The reason there are not 640 rows is the 3:4 aspect ratio of the video signal; 480 is of course ¾ of 640.)

Video images, then, are partitioned just like a piece of graph paper where each little box is a pixel and all lines, curves, and colors can only be drawn by filling in (or not filling in) every one of them. Because filling in half a box is not allowed, if the pixels are large enough aspects of the image like diagonal lines will look like stair steps. Horizontal or vertical lines, of course, will be continuous as either of those can be made by filling in contiguous boxes in a row or column.

Although this pixellation causes a video image to be broken up like a jigsaw puzzle into thousands of little pieces which are all the same size and shape, the overriding benefit of this digital signal is that it can be collapsed or copied an endless number of times with no loss to its original integrity. Because each pixel is mapped to a specific address inside the image ( e.g. Column P, Row 423) the puzzle can always be electronically reconstructed within a tiny fraction of a second.

Even though they can provide vastly higher resolution (on the order of 10,000 lines for 35mm Kodachrome®), images made with film cannot be mapped in this way because their structure is chemical, not electromagnetic. If you enlarge a slide image far enough you'll detect the grain of the emulsion, but that in no way will resemble an orderly matrix of pixels.

As we have noted, CRT projectors state their resolving capacity in terms of bandwidth which is an index of how many bits of information the device can process every second. The units for bandwidth are expressed in kilo Hertz. Just as a six lane highway permits more vehicles to move along it in an hour than a two lane road could manage, a projector scanning at 80kHz (80,000 cycles/second) can display a lot more information than one scanning at 15kHz. Hence the broader the bandwidth, the greater the available resolution.

Once the projector has transmitted a video signal out through its lenses resolution is no longer specified as a function of time (cycles/sec) and becomes instead a function of space. Regardless of a signals' bandwidth, image resolution on a screen will depend principally on what we can perceive visually and, therefore, the appropriate measuring techniques will change.



Figure 1

When you look closely at Figure 1 you should be able to count each of the black and white alternating lines. When you hold this page out at arm's length, however, you should not.

If the box were moved farther and farther away from your eyes the size of the space it occupies in your overall visual field would get smaller and smaller. Eventually you would not be able to detect that the box was different from the blur of dark type around it.

If the box were to become a projection screen, is there a way to determine how big it would have to be to ensure that everybody in the audience could count all the lines? Yes there is; even if we don't know the room size or how many viewers are in it.

We do know the number of lines in our display and we know that number will not change as the screen gets bigger (or smaller). And we also know what is the minimum space in anybody's visual field that any single line needs to occupy in order to be countable. That space is most usefully measured not in inches or millimeters, but in degrees.

When you look out across a room, your eyes are taking in about a 30^o horizontal field-of-view. Fields broader than 30^o tend to make us uncomfortable if we have to look at them for extended periods of time. This is why the minimum recommended viewing distance from a projection screen is two times the screen's width. From that distance the screen fills up about 28^o.

At the other end of the visual range is the smallest object the human eye can perceive. And that is generally specified as measuring 1/60th of a degree or, 1 arc minute. A fighter pilot with perfect eyesight is predicted to be able to detect that there is something in the sky before him when the object subtends 1 minute of arc. This feat is equivalent to being able to pick out this dot ☻ when it's printed somewhere on a blank piece of paper from a viewing distance of 28.6 feet.

For images displayed on projection screens, of course, the practical resolution standard is a lot less demanding because it needs to include legibility. How big must a character be in order for us to read it? The answer is that the height of lower case letters must subtend not less than 9 minutes of arc.

Because measurements made in degrees of arc automatically account for distance, it is important that we determine the size of our smallest character cell from the position of the least-favored-viewer. This is the person occupying the seat that is farthest away from the screen. Once his distance from the screen is known, the 9 arc minute height is readily calculated. (Convert the viewing distance to inches and multiply by .0026.)

We must remember that absolute character size is not the only criterion for legibility. Contrast, color and font selection are among the other factors which influence whether text in a projected image can comfortably be read.

Some screen manufacturers like to specify the resolution available from their diffusion screens with a statistic such as "70 lines/mm." Common sense should quickly expose such an assertion as questionable. No projector could get that number of lines/mm onto a screen and no human eye could delineate them if they were there.

What accurately can be said about all diffusion screens is that the structure of their coatings is sufficiently fine to ensure that they will not degrade the resolution available from any conventional projection source.

When the surface of a projection screen is lenticulated, however, the possibility of reducing the overall resolution of a display becomes conceivable. Lenticulations have a fixed pitch or frequency across the width of a screen. If the pitch equals 1 mm we know that there will be about 2400 of these vertical ribs in a screen which is eight feet wide.

If a projector is capable of putting characters onto the screen which measure less than 2 mm in width, then elements of that character (the vertical stroke of the letter L, for example) could get lost from view. This can happen because the function of lenticulations is to divide the light rays which strike them into two separate bundles one of which is sent to the left side of the audience and the other to the right. For reasons that will be explained in detail later in this series [Vol.III,2], if the ratio between the pixels and the number of lenticulations dividing them is too small, significant image degradation can occur.

To combat this challenge Da-Lite has been careful to include in its line of profiled screens, surfaces which have the finest possible lenticulations. One of these models, called the Da-View, has a pitch of .28mm. This means that this screen has 90 lenticulations in every inch of its width. This sort of frequency is increasingly important as it is certain that the resolution of all the electronic devices in the projection chain will be rapidly and continuously improved. Users of projection screens are already demanding that the video images they project be the equal of the images they see on their computer monitors. The largest gap which divides the two is not brightness, but resolution.

Thus in a very important sense the resolution of a display is a completely appropriate gauge of how much information it can convey. So the number of pixels is going to get larger and the bandwidths are going to get broader and more and more information is going to be cast up on our screens.

Is there a practical limit to these inexorable technological advances? Probably. The human eye, after all, is not likely to change much in the decades ahead. And so, when the resolution of a video display eventually surpasses even the fighter pilot's ability to distinguish it (and one day it will), the issue may finally be resolved.