How to understand the brightness of a projector

In the installation of a video projector, what counts is not what comes out of the projector, but what the screen gives; It is an important nuance. Once this has been understood, almost everything is understood.
The fact that a projector has a luminosity of 1,000 lumens indicates that the luminous power, with a totally white image, at the exit of the objective, is 1,000 lumens.
The contrast ratio that is usually given is the on / off, that is, the quotient, measured on the screen, between the following two situations:

1. Projector powered with a 100% white signal;
2. Projector powered with a 100% black signal.

These two parameters are not related to each other.

The brightness on the screen (and the black level) is usually measured with a unit called "foot-lambert" (fL), which gives the measured illumination. 1 foot-lambert = 1 candela per square foot. Some prefer to use the candle per square meter (Cd / m2).

When it comes to projectors, it can be said that 1 lumen = 1 candela. In other situations, it is not necessarily so, since the two units measure different magnitudes. But in the projectors, this simplifies the calculation of the final luminosity on the screen, which is simply the number of lumens that the projector gives, divided by the surface of the screen, and multiplied by the gain of it.

The SMPTE (Society of Motion Picture Television Engineers) recommends a value of 16 fL for cinemas. Sometimes, a home theater can be darker than a movie theater, so for the home theater, it is usually recommended between 12 and 16 fL. It also depends on the particular taste: those who prefer luminous images will shoot at 16 fL, while those who prefer softer images will opt for 12 fL or even less.

The luminosity must be calculated with care since, other things being equal, a too bright projector will give "burned" targets and grayish blacks and will tire the eye. At the opposite end, a low-light projector will give an anemic, pale, lifeless and without relief.

With respect to the contrast, there is nothing to calculate. The highest level of contrast should be sought, whatever the brightness.

The only variable in relation to the contrast is the level of ambient light: if this is excessive, that is, higher than the black level given by the projector-screen assembly, the contrast of the projector will be wasted, and it will be useless to look for a contrast projector very high. Remember the maxim: no projector can project black; it can only not project light.

In that case, the contrast measured will be the quotient between the light emitted by the projector and reflected by the screen (16 fL, for example), and the ambient light reflected by the screen. Imagine that we light a fluorescent tube in the room and that the screen reflects 0.5 fL of the tube (hypothetical value). In this case, the contrast of the system will be 16 / 0.5 = 32: 1, no matter how much the projector gives 10,000: 1

Some examples
Let's take a 500-lumen projector with an on / off contrast ratio of 1,000: 1. On a gain screen 1.0, 16/9, 2 meters wide, that is, a surface of 24.2 ft2, the target level will be 500 / 24.2 = 20.66 fL. The black level will be 20.66 / 1000 = 0.02066 fL. The image would be more or less.

Now, let's take a projector with the same contrast, but twice as bright, that is, with 1,000 lumens, with the same screen. The target level will be 41.3 fL (well above the specifications of the SMPTE) and the black level, 0.04132 fL. It would give an image more or less like this (nothing satisfactory):

Finally, let's take that second projector, but with a screen with twice the surface, that is, 48.4 ft2, which corresponds approximately to a 16/9 screen. 2.8 m of a base. The target level will be 1000 / 48.4 = 20.66 fL and the black level will be 20.66 / 1000 = 0.02066 fL. The image would be:

Thus, it is demonstrated that a projector of 500 lumens and 1,000: 1 contrast will give on a screen of 2m width exactly the same level of black and white as a projector of 1,000 lumens and 1,000: 1 contrast on a screen of 2.8m wide

Summing up, to choose the brightness and the contrast:

1. Choose the projectors whose brightness (lumens) is suitable for the installation according to the method indicated above;
2. From among them, choose the one with the highest contrast (taking into account also the other factors – color, resolution, video processing, etc., etc.).
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