rAVe HomeAV Edition Volume 4, Issue 12 – June 28, 2007

Angles of Reflection
Too Close for Comfort?
By Blake Brubaker, Da-Lite Screen Company

Too Close for Comfort?

If you recall not too many years ago, many in the industry decided that the rules that were used for sizing a screen needed to be evaluated due to the changes and advances that occurred in projection technology and the ever increasing need for audiences to not just look at a projection screen but be able to read or evaluate what was being presented on the screen. Much of this need was driven by the fact that software manufacturers were developing programs that allowed a presenter to put the highlighted text points in front of their audience, on a projection screen rather than on a piece of paper. For those of us in the PC world, we know this as the introduction of Microsoft’s PowerPoint software. When this occurred, we learned that the rules we had been using, when all we were doing was looking at video images, were outdated and inadequate for the task at hand. From the reevaluation, we determined that for a commercial venue we needed a screen height that was at least one sixth (1/6) the distance from where the screen will be placed and the most distant viewer for applications where we had to read the content and one fourth (1/4) if we were to inspect the image. To date, this has served us well. Now, let us take a look at whether or not the new 1080p formats will have an affect on this rule.

Perhaps one of the biggest challenges we face with these new high resolution formats is making sure that the font size of the projected text is large enough for everyone in the audience to be able to read. It seems that every time I get a new monitor or computer it is higher resolution. When I turn it on for the first time, I am taken back as to how small the fonts on Windows have gotten. This is a result of the same font size being used by Windows but at the larger resolution. In other words, a 10 point text in one resolution might look like this, while the same 10 point text might look like this with a higher resolution. The reason this occurs is because the computer is using the same number of pixels to create the letters but since the pixels are smaller, and more of them, the same text is much smaller. For that reason, it is very critical that in any presentation we have control over the ability to change the font size in order to compensate for these discrepancies between resolutions.

Let us then look at this from a more mathematical standpoint. For purposes of this example, let us take a screen that is sized to 45" x 80". If we are using a projector that has a native resolution of 720 x 1280, we can easily multiply those two by each other and determine that we have 921,600 pixels being displayed on the screen. From that, we can determine that each pixel is 0.0625" in height by 0.0625" in width. By contrast, if our projector has a resolution of 1080 x 1920, keeping the screen size at 45" x 80", the pixel height now becomes 0.0417" in height by 0.0417" in width. As you can see, there is a fairly significant disparity between these two. Now let us look at how a computer presents text and fonts. How this occurs is worth an article in itself. So, for the purposes of this example, we will assume that for most Windows based software the 10 point Arial letter T is made up of a pixel structure that is 10 units in height. Armed with that information, we can now determine the percentage of difference between our Arial letter T in the two different resolutions. The smaller of the two resolutions will result in a height of 0.625" for our character versus 0.417" for the denser of the two resolutions. As you can see, with the new 1080 resolution our character is nearly 50% smaller.

To take the character height issue one step further, we learned from Volume III of “Angles of View” that in order for the human eye to recognize the smallest character being projected, that it must subtend at least 10 arc minutes. (An arc minute is a unit of angular measurement equal to one sixtieth of a degree or 60 arc seconds.) Through a long and involved set of calculations, this equates to the rule we have used to date that states we need at least ¼ inch in character height for every 7-feet of viewing distance. Considering that this rule is not impacted by the resolution of the display, it is still valid and should be followed. However, as we just learned, with a higher resolution display it is very likely that the font size that was used with a lesser resolution may not work with the higher resolution and is the reason why it is critical that we can change font size on our presentations.

Alright, so we know that we can potentially have a problem with the current rules and we need to make sure that our font sizes are large enough to ensure all of our audience members can read the text. However, what about seating distances and the screen size? When most of us see a movie at the local cineplex, we generally like to sit somewhere between half way back and in the middle of the screen. This, we feel, is the best seat in the house. No doubt this is in most cases just that. However, show up a little late to the screening of that “must see” new movie and you will find that the only seats left are those in the front row and perhaps are the seats that are to the far left or right of the screen. These are by most standards considered the worst seats in the house. Why is that the case? Well, as you would assume, the angles at which you are required to watch the movie, both horizontally and vertically, are sometimes uncomfortable. The human eye’s visual field of view is 135° High by 160° Wide. Although this is a very impressive range of vision, it is possible, as we know from the movies, to be too close for comfort. So, exactly when is this the case in a commercial boardroom or a residential home theater?

In Volume I of “Angles of View”, we learned that for most commercial applications that the closest we should sit to the screen is 1½ times the width of the screen and furthermore we learned that this row could be 2 screen widths across. So, does this still apply in the 1080p revolution? In order to answer this question, we need to see how this rule came into being. The calculations behind this recommendation were based on the off-axis angle at which a text character becomes more elliptical and less recognizable. The maximum angle at which we can acceptably view this character is 45º. Therefore, by drawing sight lines from a respective screen out from the left side of the screen to the right side of the audience and vice versa, we end up with an ever increasing cone which has an intersection point that is .5 widths out from the screen. At this point, only one person would be within the acceptable viewing position. Taking this out, further reveals our rule of 2 screen widths at 1½ times the width back from the screen. So as you can see, this rule has nothing to do with the resolution of the screen. It has only to do with the angle of which we are viewing the screen. Therefore, in the commercial world, we can make the assumption that our guidelines are still applicable.

As for the residential side of the equation, things become a bit stickier. If the room in which the screen is located is one that is multi-purpose and has seating that may be off-axis at harsh angles, the rules we use for the commercial world should be applied. However, if instead, we have a dedicated theater room with seating arranged much like the local cineplex, the rules change just a bit. If we apply the same logic that was used for the commercial boardroom application above, then we would say that a row that is 1 width back from the screen is able to be 1 width across. After all, the math works correctly.

However, let us think about this from a real world perspective. As an example let us look at the same 45" x 80" screen that was used above. Our normal rules for sizing a screen say that we should be no further back than 3x the height or 11.25 feet. In order to then determine the closest seating distance, we would say that it is equal to the width or 80". Is this too close? According to our maximum off-axis viewing angle, no it is not, but what about the pixels? Will we see them seated this close? In order to answer this question, we need to look at the human visual system. If we are lucky enough to have 20/20 vision, that basically means that we can clearly distinguish one arc minute of contrasting information, from 20 feet away. Converting that to inches, tells us that in order for us to distinguish the contrast of that item, in this case the gap between two pixels, the pixel will need to be larger than 0.069 inches in height.

Looking at our examples from above, we learned that our pixel is 0.0625 inches in height for the lesser of the two resolutions and 0.0417 inches in height for the greater of the two. As you can see from 20 feet back, neither one of them becomes an issue. However, once we move forward on the 1024 x 720 resolution we begin to have potential issues where as the 1080 x 1920 image does not cause problems until we get to somewhere around 12 feet from the screen. So as you can see the scenario where we would be seated one screen height or 80 inches from the screen is way too close and we would likely be able to see the pixels. Since we have determined that at 12 feet is where we will potentially begin to see the pixels, let us use that information to determine the optimum seating area for the screen and ultimately provide us with a formula for determining the proper screen height. By taking the 12 feet and dividing our screen height of 45 inches, we have determined that the optimum viewing distance for a 1080p projected image is equal to 3 screen heights. So, our 1/3 rule that we have been using in the residential world is indeed still applicable and is not too close for comfort.

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