Projection Screen Gain

General

The screen gain is the equivalent of how equal the light is distributed to all viewing angles, compared to the center axis. With a perfect white screen, a gain = 1 indicates that the light is reflected evenly to all directions (theoretically up to 90 degrees sidewards).

Measurements on White Screens

The screen will be illuminated with a defined light source and the reflected light intensity on axis is compared to the light intensity after the screen is exchanged with a defined white test surface. This white test surface is reflecting light evenly to all directions, thus creating a screen surface with a gain = 1. Test materials are defined in several standards. It could be made of the chemical material MgO, BaSO4 or MgC3 (German standards DIN 5033 and DIN 19045 determine BaSO4). The projection screen under test shall be measured in comparison to this "perfectly white and diffuse reflective" surface as the test material.
Any real-world projection screen will not reflect light as evenly to all directions as these chemical materials, a measured gain = 1 just indicates that the reflection is equal to the test material on axis. But because a perfect white screen should not absorb too much light, the assumption could be made that the remaining reflected light off axis is quit evenly distributed. A higher light reflection on axis would indicate that the light off axis is smaller. (As all measurements invented by human creativity, it is not perfect but very helpful!)

 Gain = 1 Gain = 1.4 Gain = 1.4 with off-axis projection

Grey Projection Screens

To get more contrast in the projected image with available high light outputs it is more and more common to use grey projection screens. A grey screen made of perfectly neutral grey is theoretically still "white", as we define a white sheet of paper in total darkness still "white". But it is black! The nuances of grey between black and white are defined by the amount of white light reaching this "white" surface.
If we now take a neutral grey surface and illuminate it with enough white light, it looks perfectly white. Only by comparison with a "really white" surface in the direct neighborhood we realize that is is not "white" but "grey". Our brains told us it was "white" ...
This phycho-optical effect can be used to enhance the contrast in a projected image. The grey screen will always have a gain less than "1" and if the contrast is measured, the result will not show an improvement. Some would say: "if so, it doesn't have a higher contrast!" But here the measurement methods made for white screens don't fit!!

A projection screen of 70% grey (for instance) is made of grey 70% between black and white:

grey scale and equal contrast ranges

Comparing a white screen and a 70% grey screen in a slightly darkened room, the white screen will be 30% more white, or differently said: the white screen is white and the grey screen is grey. But if now the white screen is illuminated by a projector with a completely white image and the grey screen is also illuminated by a projector with a completely white image but 30% more bright (higher luminous flux, more lumens!), both screens will look the same ... (and it is even possible to get a brighter image on the grey screen by much more light than on the white screen).
Putting the right amount of light individually on both screens to make them look alike, the "white" is the same on both! But projecting a completely "black" image on both screens with these projectors will give a 30% lower black on the grey screen ... !!! This means we have a about 30% higher contrast! And this is not a mystical psycho effect, it is real! Just the standard contrast measurements for projection screens are not prepared for this.

projection on a grey screen (left) and a white screen (right), about 30% more light output for the grey scren
white parts are identical, black parts are darker on the grey screen

See: Contrast and Brightness
See: Projection Rules