Angles Of Reflection

It is considered by many to be the single most important parameter in a projection screen’s specifications, and so it should come as no surprise that gain has been covered many times in many ways.  Given its position in the minds of those interested in screens, it is important that the concept of gain is well understood.  What is it?  What does it do?  How can it be used to enhance a display?  Let’s review and perhaps learn a bit more about: 

Gain Again

Quite simply put, gain is a number that tells us how bright a projection screen is.  Higher numbers indicate screens that are brighter than those with lower numbers.

Defined a bit less simply, gain allows us to predict how bright a screen of a given size will be when used with a projector of a given light output.  The output of the projector, typically indicated by the manufacturer in lumens, can be divided by the square footage of the screen to determine what amount of light energy will fall on one square foot of its surface.  This number, multiplied by the gain, will reveal the amount of light that is reflected from that square foot of material, and is measured in foot lamberts.  A movie theater screen will typically reflect around 16 foot lamberts, while for most commercial applications, 30 foot lamberts or more will be appropriate.

Finally, in more technical terms, a screen’s gain is measured as a comparison between the amount of light the screen reflects and what would be reflected by a reference standard under identical conditions.  That reference is typically magnesium carbonate (MgCO₃), a chalk-white substance which absorbs virtually no incoming light, diffuses it in a fairly even pattern, and represents a gain of 1.0.  

Under our current system, the gain measurement you find on most screen specifications represents the light measured returning from a screen at the perpendicular angle expressed as a multiple of what was measured from the reference standard.  If more light is returning compared to the reference, it will have a value greater than one, and if it is less, then it will be less than one.  A 2.5 gain screen will reflect 2.5 times the light of magnesium carbonate at this angle, and a 0.6 screen will return only 0.6 times as much.  As a result, these different surfaces will generally appear either brighter or darker than MgCO₃, respectively.  I say generally, because the way gain is manipulated into becoming greater or less than one is not quite as simple as it might at first seem.

To achieve a low gain, some amount of gray pigmentation is added to the screen material so that it will absorb a portion of the incoming light rather than reflect all of it.  This will make black appear darker, and will, therefore, improve the contrast ratio that the screen is capable of producing.  Naturally, the entire image will be darker, and not just black, but a change in black level is the most important factor in determining contrast.  For more on this, please consult "Contrast ", the fifth article in Angles of View.

As for a higher gain screen, these are often used to help brighten an image from an inadequately bright projector for a given screen size.  Recalling that the light falling on a square foot of material will be the total output of the projector divided by the square footage of the screen, it is possible for the light to be spread out over too large an area to see a bright enough image.  Increasing the gain will allow this light to be multiplied by a number larger than 1.0, and will increase the foot lamberts we’ll see reflected.  

To do this, the screen will use a reflective coating to create a sort of directionality in how the light is reflected, focusing a good portion of it along a single axis.  This, in turn, reduces the amount of light that is sent in all other directions.  The screen cannot create more light energy, but it can focus it in one direction at the expense of the others, and in most cases, the higher the gain the more light is aimed in one direction.  In the absence of directionality, such as with a Matte White screen or MgCO₃, light is diffused in a more even pattern.  This means that the measure of light returned at one angle will be almost exactly the same as at every other angle.  No one angle is increased, and no angle is forced to decrease its light emission to allow for an increase.

What complicates this process is that it is possible and even commonplace to combine pigmentation and directionality to create a gray screen with a gain close to or even greater than 1.0.  Doing this will both darken and brighten the image to some degree, allowing both contrast and brightness to be enhanced.  Being simultaneously darker and lighter does not invalidate our foot Lambert formula described above for determining how much light to expect from a screen, but it does reveal an important distinction between gain and what we’ve been referring to as directionality.  Two screens with the same white or gray base, and even two screens with the same listed gain measurement cannot be assumed to behave in the same way under projection, and the reason for this is that they may have a difference in their directionality.

To show this difference, most manufacturers take additional gain measurements and graph the results.  We measure at 5° increments around the center of the screen, and this is a fairly common approach.  A non-directional screen will diffuse light fairly evenly, whether its gain is 1.0 or less, and will show a graph with a very gentle curve.  What this means in the real world is that anyone seated anywhere in front of an evenly lit screen will see an evenly reflected image of uniform brightness.  With a directional screen, as the angle away from perpendicular increases, we will soon exit the area of directionality’s influence and the amount of light being measured will usually decrease.  At a certain angle, the measure of light reflected from the screen will be one half of what it was at perpendicular, and this is referred to as the half angle.  

Far from being a trivial or arbitrary consideration, this angle is significant not only because it will provide a clue as to a screen’s directionality (being significantly directional will create a narrow half angle, regardless of the actual gain), but also because when the light reflected measures half of what it was at the center, the screen will become unmistakably dimmer.  If enough of a brightness change is visible simultaneously across the screen, it can be perceived as a hot spot.  

This distracting artifact is the primary reason why we avoid creating outlandishly high gain screens to allow for dim projectors, or recommend using them in situations where the audience will be seated in a wide area around the screen.  The significant directionality in high gain screens will result in a very acute half angle, and a large portion of the audience will likely be seated outside of it.  Even in the case of a screen intended for a single viewer who promises not to move away from the seat centered in front of the screen, at large enough screen sizes and short enough throw distances, it is possible for a hot spot to appear if light from the projector is traveling to the corners of the screen at such severe angles that they will be essentially directed away from the viewer.

An exception to this rule may be expected from the retro-reflective materials you may have seen in highly reflective paints, road signs, and in Glass Beaded projection screens.  The important difference between these and the far more typical angular reflective screens is that retro-reflective materials reflect light primarily back towards its source.  This means that while the directionality of an angular reflective screen would cause it to behave like a mirror, aiming light at an angle equal but opposite to the light source, a retro-reflective material will be aiming light back towards the incoming light.

In practical terms, this means that although there will be a conspicuous change in brightness from one viewer to the next, what each viewer sees from his set perspective will be more uniform than one might otherwise expect.  This is because the majority of each light ray is reflected back towards the origin at each point on the screen instead of away from it at the edges.  A hot spot may still be seen by a viewer far enough away from the origin (ie, the projector), but retro-reflectivity allows for large screens with high gain that will be fairly uniform if viewed from inside the boundary of the half angle.

Interestingly, looking at the gain measurements taken from angles outside the influence of directionality will reveal that many screens will show a flat curve out towards the most oblique angles.  This may not be particularly significant in terms of the screen’s use, as the uniformity experienced by a presenter or someone standing in the wings is not a prime concern.  However, knowing the gain at the angle where the curve flattens out can potentially reveal the shade of the screen’s base in a way that is more accurate than making this judgment based solely on a photograph of it.

Figure 2 is an example of the sort of gain chart many manufacturers provide, but with a slight difference.  As you can see, the Y axis is not vertical as it is in most charts, but angled around a single point both to reflect the relative positions from which each measurement was taken, and also to present a shape that should ease in the visualization of each material’s reflectance pattern.

Looking at the Matte White material’s curve, it very closely follows the 1.0 line around the center axis which means it is diffusing light evenly in all directions with very little directionality.  The most obvious example of a directional screen would be in the Glass Beaded material which peaks at 2.5, and then dips sharply before settling into a gentle curve starting at 25°.  From this point on, it looks very similar to Matte White’s curve, but centered around the 0.9 line instead of 1.0.  As a result, the image will begin to appear uniform as the viewing angles increase beyond this point, but the picture will not be nearly as bright as it was at the center, or as bright as it would be on a Matte White screen.

The High Contrast material, which touches 1.1 before quickly descending below 1.0, is a clear example of how the curve beyond the influence of directionality can be a clue to the grayness of the base material.  Finding 1.1 gain on a screen would understandably seem to indicate a white base and some directionality, but looking at the actual curve tells a different story.  The gain on a Matte White screen would not fall very far below 1.0 at any angle, but the measured gain on this material reaches below 0.8.  At around 40°, the slope at which gain decreases evens out, and it begins to act more like a darker version of Matte White.  This is more or less what the High Contrast material is beneath the reflective coating.  Placing a sample of this particular High Contrast material next to a Matte White screen will prove that it is basically darker, but as far as incident light from a projector or light meter is concerned, its coating more than overcomes the absorption of the pigmentation.  A simple gain measurement might not reveal this to be the case, and it would be difficult to know that a 0.8 gain material with no directional coating is practically just as gray as a 1.1 gain material with that coating.

Figure 2 - Gain measurements of three screen materials plotted around a central point to represent the measurment angles more directly

Because of this, please look at both the gain and the half angle to get an idea of how the screen will behave.  From this, guide the arrangement of the room so that the audience is inside that half angle and able to enjoy the benefit of increased gain.  In addition to these considerations, the measurements the manufacturer provides will give some insight into the possible uniformity of the projected image.  The details of this have been covered by Kim Milliken in "Uniformity ", the first article of Angles of View, and also in "Uniformity – Revisited " by Blake Brubaker in the fifth issue of Angles of Reflection.  Their comprehensive work will be an excellent next step in exploring these matters regardless of your level of expertise.

-- Adam Teevan

(ateevan@da-lite.com)

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