Angles Of View
In the issue preceding this one, efforts were made to persuade interested readers of the benefits to be had from watching entertainment media on rear projection screens. In fact, there are no optical disadvantages to rear projection whatsoever. There is, however, a physical drawback to rear projection which, of course, is the amount of floor space which must be sacrificed in order that it be enabled. This article will outline some useful ways to keep the size of that space to a bare minimum and, additionally, how to avoid certain optical problems which space compression techniques can sometimes cause. The forthcoming discussion will focus particularly, then, on
The Secondary Reflection IssueIn the world of commercial office space, it's bad enough that the square footage necessary to create a rear projection booth is, month after month, expensive to pay rent on. In the world of Home Theater, the notion of having to create some jet black closet which can't even be used to house the washer and dryer must surely in some families really be anathema.
Nevertheless, if we have done our audio/visual homework diligently we will have to acknowledge that, painful though the real estate investment may be, the benefits to be reaped are extremely profitable. How, then, may we keep our return at a maximum and make our initial investment as small as possible?
We'll do it, of course, with mirrors (blue smoke will not be necessary). By using one or two mirrors correctly positioned behind a rear projection screen, we can reduce the depth of its booth by more than 50 per cent. If we expect all of the rooms in our house to be rectangles, the width of that booth cannot be less than the width of our screen, but the depth which otherwise might need to be greater than the width can be reduced by half.
If we think about this for a moment, it all makes perfect sense. We know that light rays coming out of a projector (any projector) must pass through a lens which causes them to diverge. If they didn't do that and we shined a projector at a blank wall, the size of the image it casts could never be made bigger, no matter how far back from that wall we moved it. To say that last sentence in a different way, for whatever size image we wish to make, there will be a minimum distance back from that image at which any projector must be placed in order to cast it. In the parlance of the A/V world, this distance is called the "throw distance".
That "throw distance" is the bad news. The good news is that although the light rays making up our image have to travel that distance if they are to form a picture as big as we wish, they don't have to do it in unbroken straight lines. We can intersect their paths with mirrors and, as long as they are at the correct angles, no distortion of any kind will occur. Alert readers will immediately notice that a mirror will reverse an image but, relative to a front projection screen so, of course, will a rear screen. Fortunately, this is a non-issue as any projector we buy these days is certain to have a switch which, when flicked, will electronically "reverse" its image whichever way it appears.
As long, then, as the total path length of every light ray emanating from the projector is not changed by the insertion of a mirror or mirrors, the resultant image need not be degraded to any degree. Unless, that is....
There are, in fact, two "artifacts" which can intrude upon an image's quality. The first is what is called "ghosting" and the second is what is called a "secondary reflection." The first thing to say about them is that they are not the same.
"Ghosting" appears as a faint, double image wherein every object within the picture appears to be outlined by a slightly offset copy of itself. Instead of appearing sharply defined as in CLEAR, it looks something more like FUZZY. Ghosting is caused when there are, in fact, two image planes, one typically being the front surface of the screen and the other atypically being its back surface. In the case of a standard, acrylic rear projection screen, the two surfaces are separated by the thickness of the plastic sheet out of which it was made and, thus, are not more than 3/8 of an inch apart. That fractional inch, however, is quite enough to create a doubled image if the undiffused surface has had something done to it that has caused it to be other than transparent.
We, at Da-Lite, firmly recommend that the coated side of our diffusion screen always be installed facing the audience and that nothing (nothing) be done to the back surface including allowing it to become dusty. Lastly, it should be noted that ghosting is a phenomenon which is neither created nor worsened by mirrors.
The problem which mirrors can cause is Secondary Reflection(s) and it doesn't look at all like ghosting. Instead, what is most often seen is faint repetitions of parts of the picture properly projected above the screen's equator showing up as visible artifacts below it. What causes this is as easy to define as it has been difficult reliably to avoid.
A few paragraphs ago we stressed that the back surface of our diffusion screens be kept clean and uncoated. That means consequently that such a clear surface will definitely be reflective. Some amount of light from the projector will be reflected back (towards the mirror) on its first pass through the screen. Because mirror systems generally position the projector below the screen, the mirror closest to the screen will have its bottom edge farther away from the screen than its top and thus, looked at in elevation, its vertical plane will form some angle with the plane of the screen. Sort of like this: Screen Ž| \← Mirror.
Now, if we trace in our minds' eye these rays of light which are bounced back by the screen, we can follow them to see where they go. Some number of the light rays from the projector reaching the top of the screen will bounce back from it and then hit the mirror for the second time after which they will be reflected by that mirror at angles different from the one they traveled along after their first bounce. If those second paths are along angles that are too small, the secondary light rays will end up not passing below the screen but through it.
The challenge of figuring out correct geometries for mirror systems and projector angles behind a rear screen has bedeviled designers for years. The method by which Secondary Reflections can be avoided, however, has been rigorously worked out and is explained in detail on Pages 100 through 104 of Basics of Audio and Visual Systems Design written by Raymond H. Wadsworth, P.E. Although that invaluable handbook has long been out of print, an updated version (to be edited by the author of this series) is currently in the works and will be published in 2001.
In the meantime, the basic technique can be illustrated (with Mr. Wadsworth's help) as follows:
This drawing (first created in 1983, which explains why the projector icon is a slide projector and why the drawing is not in elevation but in plan) shows the various distances which need to be manipulated in order to calculate a, the angle at which the mirror must be set so that secondary reflections will not occur. In contemporary mirror systems, this drawing should be rotated 90o and "W/2" should more accurately be named "H/2" as "W" stands here for width and we want "H" for height.
All the angular relationships which Wadsworth details, however, are as useful today as they were seventeen years ago. To determine the minimum value for a, his equations require three data points:
1) The Height (for him it was the width) of the screen.
2) The throw distance.
3) The distance back from the screen to the closest edge of the mirror (in his drawing this is a side edge, in our case it is the top edge).
Plugging those three numbers into his formulae yields, for any mirror system, the minimum angle at which the mirror must be set so that all of the light rays reflected back by the screen strike the mirror in such a way that, when they are reflected by it a second time, they travel along paths leading either above or below the screen but never through it.
Back in 1983, the only way to make these calculations was actually to crank the various measurements through the requisite trigonometry. While that trig is still mandatary for those same purposes today, the effort to accomplish it, as it were, manually is not.