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The FL will also depend on the gain of your screen material
This is true because foot lambert (fL) is a measurement of screen LUMINANCE which is the amount of light reflected from a surface
. The amount of light hitting a surface
(like a projector beam) is called ILLUMINANCE which is measured in foot candles (fc). If the screen is a true white (reflects all the light that hits it) Lambertian (reflects the light in all directions from the surface) reflector the luminance and illuminance values will be the same. If the screen is a gray Lambertian surface (absorbs some of the light that hits it) the luminance will be less than the illuminance. Only when the screen surface has "gain" can a darker-than-white screen have the same, or greater, amount of luminance than the light illuminating it. When this is true the surface cannot be Lambertian, but must have some amount of specular or retroreflective reflectance. You can think of it as "robbing Peter to pay Paul" which means that while the reflectance on-axis with the PJ may be the same (or greater) than a white Lambertian surface the off-axis reflectance will be less than even what the gray screen would have had if it were Lambertian. We measure this screen attribute by taking multiple gain measurements from different angles.
A foot lambert represents the same amount of light as a foot candle, the only difference is the former is being reflected from the screen and the latter is striking the screen.
When we talk about screens and projectors we generally just use the term foot lambert for both luminance and illuminance even though that is technically incorrect.