First things first, I have to figure out what kind of projector I will need to successfully fulfill my brief. To gain insight into how large and bright the image has to be, I consult the director and the set designer.

I also receive technical drawings which detail the projection surface. It turns out that they want it to be 24 feet wide x 13.5 feet tall on the DS gauze/scrim.  I also find out that the material the set designer has chosen is a standard, gray, 8 point sharkstooth gauze, which will work well for bleed-throughs. (More about projection materials here).

I assume that given that the projection is used during moments dedicated solely to projection that the imagery does not have to compete with stage lighting. This in turn means I can get away with using a projector with a lower brightness rating than if it were for an application where the light of the projector has to compete with the stage lighting. Now what is that rating? Well, brightness of projectors is measured in ANSI lumens. There are other lumens variations, which is why the word ANSI is important. 

The technical approach to working out how bright the projected images needs to be goes like this... Decide how many (ANSI) lumens per square foot (or square meter) you need. The consideration of ANSI lumens per square foot is important because every projected image covers a distinct area (width x height). The size of this area determines how tall and wide the projected image will be stretched or how far in vertical and horizontal direction the brghtness will be distributed.  Consequently, the same projector will be brighter for a small area than for a large area. A measurement of ANSI lumens per area unit (square feet or square meter) will therefore be an universal way of measuring brightness levels on the projection surface. This is what we care about because we want the audience to see the projection as intended, regardless of the brightness rating of the projector.

Here is the rub though; whether 50, 250 or 500 ANSI lumens per square meter will be sufficient depends on a number of factors such as the projector's surface, the viewing angle, ambient light levels and the overall composition of the scene(s). By the latter, I mean how the projected images are used together with other elements within a scene. For example, if the projected image has to compete with the brightness of a lit actor standing in front of it, the projected image needs to be brighter than when the audience only sees the projected image on its own. The reason for this is that the human eye adapts to the ambient brightness of what is within his or her field of vision. The eye will focus on the brightest part of every composition instinctively. The rest will drop off until the eye gets "bored" looking at it. If the image is important to the action of the actor, the human eye should have the opportunity to perceive both equally well. Otherwise, there is a visual disconnect and neither element (actor/image) can support the other. I find that a good middle ground is 20-25 ANSI lumens per square foot. It not crazy bright, but it is bright enough to compete with lit actors most of the time. If it is a bright show, upwards of 30 is preferable.

The important fact is that the human eye does not measure luminance. Brightness is what the human brain perceives as intensity when it compares the darkest and brightest items in sight.

There are two further complications:

1. Projectors have a chip inside that determines the ratio of the area that can be covered. These chips are commonly either 4:3 (classic TV set image) or 16:9 (HD or widescreen TV set). There are others, but these two are the most common ratios used now. The size of the chips and therefore the distribution of brightness shot from the lens is fixed. If the area we are projecting on does not fit the ratio of the chip we can only overproject to cover the desired area. Alternative approaches involve more projectors, but I want to keep it simple in this example so I won’t cover these options here. Once you overproject, the brightness is stretched beyond the area you are interested in and as a consequence, is dimmer than it would be if you filled the projection area in as originally intended. In other words, if you can’t make the projected image fit the projection surface and are forced to overprotect, you lose brightness. More information about display ratios can be found here.

2. There are competing technologies for producing an image that can be projected known as DLP and LCD. These chip technologies create images in vastly different ways, thus creating higher contrast images.  A higher contrast image will appear brighter to the human eye than an image with less contrast. So even though a DLP projector might have a lower ANSI lumen rating than a LCD projector, the resulting image can look as bright or brighter than that of an LCD projector. Thus, I commonly use the term "perceived brightness" to describe what I or the audience will perceive as bright (or not).

For all the reasons above, the rating of a projector's brightness in ANSI lumens will not be any guarantee for a sufficiently bright and legible image. Luckily, the screen in the task at hand is 24 feet x 13.5 feet which is exactly an 16:9 ratio. So I will specify a projector with a 16:9 chip. If the budget is low, an LCD projector will be okay, but I prefer DLPs because the blacks are better and images can appear out of relative darkness as opposed to a dimly lit square. A rating at the lower end of the brightness spectrum will work, because the image is up in "projection-only" moments. So 20 ANSI lumens per sq foot should work. The brightness across the projection surface is 20 x 24 x 13.5 = 6480, that’s (target ANSI lumens per square foot) times (width of projection area ) times (height of projection area). As the surface almost matches the ratio of 16:9  which is a common projector chip ratio the selection of a DLP projector with 16:9 chip and a brightness rating of about 7000 ANSI lumens should work well.
Up until now I have left out another important consideration — the resolution. I need the image to look realistic because it is a photo: photos need resolution in order to looks good. I’ll get to that in the next part.