CLEAR PROJECTIONS
Sep 1, 1998 12:00 PM, M. K. Milliken Jr.
Fonts have been around for more than 500 years, ever since Herr Gutenberg invented movable type in 1437. And, as anyone who owns a computer knows, there are plenty of them to choose from. All fonts have faces, and all faces belong to a family. Thus, this font appears here in its standard face, but there are also italic and bold as alternative and additional faces. To see the elements that distinguish one font from another, consider Figure 1. These are the principal parts of the characters and symbols which make up any font family. Note particularly the dimension marked as "x-height." This term is printers' language for the height of a character, excluding (if any) its ascender or descender. I suggest that the x-height is also convenient for measuring the minimum height for any lowercase character or symbol.
A property that does not belong to any given font family is size. Fonts, especially computer-generated ones, are scalable. We can describe their printed size by specifying the number of points a letter is to occupy. There are approximately 72 points to the inch (25.4 mm), and 12 of these points are a pica. Precise as those measurements are, however, they are of little or no use when the font is not to be printed but projected. Approximately 1/12 inch (2.1 mm) high letters are fine for this page but would be hopeless on a 100 inch 92.5 m) diagonal projection screen.
Some interesting things may be observed about the legibility of fonts in general. One of them is that mixed case text is easier to read than TEXT WHICH IS PRINTED ALL IN CAPITAL LETTERS or even Text Which Has Just The First Letter Of Every Word Capitalized. Another is that legibility depends on the tops of words. (See Figure 2.) Notice how much more difficult it is to decipher the lower half of the same sentence.
An enormously important attribute of fonts is whether any particular face is serif or sans serif. Serifs are small, usually horizontal cross strokes that are added to the ends of a letter's main strokes. This type is serif, but typeface without serifs is sans serif. Because of their ability to coax the eye along the line of type, fonts with serifs are generally acknowledged to be more readable.
Becoming sensitive to these observations is helpful, but it still doesn't really answer, "How can we think about fonts for projected displays, and what guidelines can we follow for their manipulation?" Fortunately, there are some valuable answers that emerge from research undertaken by Dr. Joy Ebben of JME International in Alta Loma, CA. Dr. Ebben breaks the design of projected characters into five principal categories: shape, height-to-width ratio, pixel matrix, stroke width and character, and word and line spacing. With respect to the shape of the possibly ambiguous characters, she offers case-sensitive criteria. A needs clearly delineated space above its horizontal stroke. B needs approximately equal loops. C and G are easily confused with each other and with O if the C break is not clearly discernable or if the horizontal stroke of the G is not long enough. D and O can be confused if the O appears to square. E requires clearly delineated spaces. M and W need sufficiently long center sections. P requires a large enough loop. S and 5 are easily confused if the S is too square and/or the horizontal top of 5 is not long enough. The number 1 and l must look different. U and V will be confused unless the uprightness of vertical strokes of the U is maintained. Y needs a long tail to differentiate it from V, and it needs a distinctly v-shaped top to differentiate it from a T. The number 6 and 9 need apparent (but not too large) loops and fairly straight tails. Other likely confusions are that X can be called K (and vice versa); H can be thought to be M or N; J or T can be called I, and K can look like R. Additionally, B can look like R, S or 8; 0 (zero) can seem to be O, or both can look like Q, and Z can often look like 2.
Based on the typical width of a set of capital letters, the height-to-width ratio should be not less than 70% and not more than 90%. The pixel matrix available for any character or symbol is absolutely critical to adequate legibility. Unfortunately, however, here is a case where the increased and increasing resolution from better visual displays does not help. When you upgrade either your computer or projector from a 800 X 600 device to a 1,024 X 768 unit, the first thing you'll notice is how much harder it is toread. Why is that so? Although your new machine will display 306,432 more pixels than your old device, not one of those extra pixels is devoted to the improvement of your font. Thus, if your SVGA machine reserved, a 7 X 5 pixel array to write each of its lowercase characters, then your new machine also will allocate only the same 35 pixels to the same task even though each of those pixels is only 60% the size of its predecessor.
Dr. Ebben's rule of thumb for visual tasks that require the continuous reading of projected text is that the minimum matrix be nine pixels high by seven wide. Clearly, however, even more pixels will always result in even better character definition.
Next, we come to stroke width for which the historical ANSI (American National Standards Institute) standard has been that it be greater than 1/12 of character height. Dr. Ebben and others believe, however, a stroke width of approximately 1/4 character height is preferable for projected text. Furthermore, she has discovered that there is marked discrepancy between what she calls forward video (light characters on a dark background) and its inverse. The rule, then, is to use at least a double-pixel-wide stroke for large screen displays (forward video). Interestingly, this is true because double-stroke-width in reversed video (dark on light) appears to be narrower than single stroke width in forward video.
The ANSI standard for mixed case horizontal character spacing has historically been given as not less than 10% of character height. Because of even moderate off-axis viewing angles, however, Dr. Ebben believes that the minimum space should be increased to 25%. In terms of a 9 X 7 pixel matrix, this corresponds to two dot elements, but this spacing should be increased to 50% whenever viewing angles become large.
With regard to the appropriate spacing between words, Dr. Ebben reports that the distance between one projected word and another should not ever be less than the width of one character. Spacing between lines (leading, which rhymes with bedding) has been established by ANSI to be a minimum of two stroke widths or 15% of character height, whichever is greater. Dr. Ebben contends that there is good reason to increase this minimum to 50% of character height for projected text.
These typography criteria are worth attending because all of us in the A-V industry who work hard together to create better visual displays are discovering that the task contains more science and less instinct. If we all were pilots, we'd be flying less by sight and more by instruments.
This development should not surprise us because most of us have seen it coming for a long time. Always remembering that ours is a business driven primarily by a much larger industry (the computer industry), we can easily see how more complex the information that a computer can output to its screen is today compared with what it could do only a few years ago. Desktop publishing, Web sites, presentation software and multimedia in general have all become sophisticated. System requirements are routinely calling for 100 MHz (and sometimes as much as 300 MHz) processors and 32 MB RAM as minimums just to get the programs to run. All that speed and memory (to say nothing of the huge amounts of space required from the hard disk) is designed to aid us. We want to be able to pack increasing amounts of information onto our screens, and we want to have those high-density data communicated to other people in many other venues.
This article emphasizes the critical significance of this data concentration, particularly in terms of the visual task necessary to its assimilation. To put it simply, it all boils down to the fact that we are not looking at projection screens anymore. We are reading them, and reading something is much harder than simply looking at it. When the material we are expected to read is projected and then reflected or transmitted by some screen, comprehension becomes downright demanding. Because the degree of this difficulty cannot be overestimated, efforts needed to manage it must be considerable.
The problem is that if you want to ensure that everybody lookin g at a display can discern and decipher the data projected upon it, you must absolutely guarantee that every single character and symbol is large enough to be identified reliably and accurately. This is not a question of font choice alone. Nor is it a question of the contrast or color palette that is available. It is a question of size, pure and simple. If the characters and numbers are not big enough to be read by the person positioned at the back of the room, he will not be able to figure them out. Period.
So, how do we ensure that letters and symbols generated by computers projected onto screens are big enough? We define the minimum size in a way that can be reliably generalized over all of those cases in all of their variations. The height of no lowercase character shall subtend less than 10 minutes of arc on the retina of any viewer. That's the mathematically expressed rule, and once we understand it, we can use it in any and all cases always. To see exactly why the concept of minutes of arc is so useful, consider Figure 3 (for which we are indebted to Dr. Ebben). The Greek letter alpha, (a) is the angle in which we are interested, and for the moment, it is an unknown. Now notice that there's a second a, the little one, pointing into the intersection of the two lines at the back of the eye. That is what we are really interested in. Fortunately, there's a provable theorem in geometry stating that all vertical angles are equal, and vertical angles are the two opposing pairs of angles created wherever two straight lines intersect. Thus, if we can find a way to measure or calculate a, we will automatically know the value of the one inside our eye that nearly impossible to measure.
Next, we have to think about angles and how we see. If you get up from your chair, and with your eyes open, slowly turn completely around, your eyes will have swept over everything in your horizontal field-of-view. Because that field is a complete circle, we can define at as divisible into 360 equal slices called degrees. Because you do not have eyes in the back of your head, however, the only way you can see in all 360 degrees is to turn completely around. Otherwise you can see only what's in front of you, which is only a part of 360 degrees, which is about 200 degrees. Because 200 degrees is not equal to the complete 360 degrees circle, we will have to recognize that it is only a section of that circle, and any section of a circle is called an arc. When we look to see how much of that available 200 degrees gets used by our eyes when reading something, however, we discover that it is only the central part of our visual attention that gets used. It is encompassed by something less than 30 degrees. If we're reading a page of text, it should therefore be simple enough to divide each line by 30 and discover how many degrees are taken up by each character. Unfortunately, when we do that, we soon see that there are many more characters to a typical line than 30. Projected displays, for instance, often include lines that are 80 characters in length.
To deal with this problem, mathematicians came up with a way to subdivide each degree into 60 smaller slices which, for numerically obvious reasons, they call minutes (and each minute may be subdivided into 60 arc seconds). This enables us to divide a 30 degrees field-of-view into not only 30, but also 1,800 equal parts.
The final things we have to think about there are easy; they are just vocabulary. The verb subtend is simply a mathematical word meaning to be opposite to and delimit. All it means here is that if we can measure the height of a symbol on a screen; we know that the angle (the big a) subtends on the screen will be the same angle that is subtended on the tiny screen inside our eye, which is called the retina.
Having dealt with the math, we can return to our rule and notice its usefulness is that it holds true for all viewing distances and for all screens. This is so because the size of the little screen, the retina, does not change even as all the other variables may.
The way that the number of requisite arc minutes was proved to be 10 had nothing to do with calculation. It was established by long and arduous empirical research, which entailed asking lots of audience volunteers, "Can you read this from there, or do I need to make it bigger?" When people positioned on-axis to the projected characters stopped saying that the symbols were hard to make out, they were measured to be subtended by at least 10 minutes of arc. If you take the trouble to calculate it, you'll discover that 10 arc minutes translates to just over 1/4 inch (6.4 mm) for every 7 feet (2.1 m)of viewing distance.
For off-axis viewing, 10 has to be increased because trying to read something from an oblique viewing angle is much harder than looking at it straight on. You figure out what it takes to read from those through the equations in Figure 4. The first formula solves for minutes of arc for on-axis reading in still another way-it divides the product of 3,438 and the character height (in inches) by the viewing distance (in inches). Hence, if the height of a symbol is 0.65 inches (165 mm), and the viewing distance is 25 feet (7.6 m), then .65 X 3,438 = 2,234.7 / (25 X 12 ) = it subtends only 7.45 minutes of arc and is therefore not big enough. Working the numbers backward, we see that 300 X 10 = 3,000 / 3,438 = 0.88 inches (22.4 mm) of symbol height, which is big enough.
Figuring out how big to make symbols for off-axis viewing is a little more complicated. Notice that the viewing distance in both equations is along the line-of-sight. So it gets measured the same way but will always be longer for a viewer positioned at the edge of a row of seats than it will be for a viewer at the center.
Unlike v1, however, v2 depends for its size on two additional variables, a and the superscript K. As indicated, a equals the off-axis angle from which the character will be perceived. (For now, we'll assume K will equal one.) Recalling that all of these computations are based on pretty straightforward triangles (like the ones illustrated in Figure 5), we can understand that the angle a is also an internal angle of a triangle and will have a cosine.
If we want to, we can recall that a cosine of an acute angle in any right triangle is the ratio of the length of the adjacent leg to the hypotenuse. But we really don't have to know that to solve the equation. Instead we can simply activate a calculator and have it tell us what the cosines are of whatever angles we wish. Thus, when we iterate through the off-axis viewing equation for the example we used above (a row of seats 25 feet or 7.6 m back from a screen), we discover that the requisite height of a character increases.
Slight increases are necessary when the angle is small, but by about 30 degrees, the 0.88 inch symbol (22.4 mm) height has surpassed 1 inch (25.4 mm), and by 45 degrees, the growth accelerates even faster, exceeding 2 inches (50.8 mm) by 60 degrees. Even though this is fairly intuitive, it is extremely helpful to see exactly how the relationships between the variables may be controlled.
That leaves us to discuss K in the second equation. Interestingly enough, it turns out that the human eye does not respond to the demands of off-axis viewing exactly according to the cosine law. Instead, it does just a little better than that. Thus K, which we'll call the human compensation factor, is actually equal not to 1, but to about 0.9. On the other hand, Dr. Ebben, who was one of the first to work all of this out (and to whom we are indebted for Figures 4 and 5), is cautious about letting the K factor influence her design calculations. It's true, she says, that the eye performs a little better than you think it will at large angles; but relying on that fact removes even a modest fudge factor from both the computations and their outcome. Thus, she counsels, let K = 1. It certainly makes the calculation easier.
Large viewing distances and large viewing angles combine to make small characters unreadable. That much we've always known, but if we are to keep our display systems from failing their purchasers, we now have to know more. Arduous though it may be, the results of a careful and mathematical analysis are now always worthwhile. Indeed, without them, display systems can fail and there could be no end in sight.
In addition to Dr. Ebben's original research, other sources used in the preparation of this article are:
Shurtleff, Donald A., How to Make Displays Legible, Human Interface Design, 1980
Cavanaugh, Sean, Digital Type Design Guide, Hayden Books, 1995
Carter, Rob, Working With Computer Type, Rotovision, 1997
Figure 1: http://www.adobe.com/type/browser/samples/Hfgx.gif
Figure 2 : http://info.med.yale.edu/ caim/manual/pages/graphics/legibility_top.gif and _bottom.gif
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