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Ok, so maybe not all the magic happens before the phosphor but a solid 90% or more of the magic happens before it get to the phosphor screen.
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Something like that...
Realistically the older P20/P22 phosphors have fairly long persistence times, i.e. they glow longer when hit with an electron. Which in theory makes the "brighter" since they are "lit up" more of the time. These were mainly used in Gen0, Gen1 and early gen2 and a few early gen3 systems to squeeze out the last bit of "gain" out of a tube and they are fairly well matched to the human eye for most "contrast". The downside to this is that you can get "streaks" when you have highly dynamic scenes, which is a major downside in a fire fight or piloting applications.
The P43 phosphors used on most Gen3 stuff have a much lower persistance which means no streaks, and is better for piloting. Also, the wavelength they emit at, seems "brighter" to the human eye, but in theory show less contrast.
P45 emits across a broader span of the human visual spectrum, which in theory might offer some advantages for "Brightness perception" and contrast.
In practice, I have looked through phosphors made in the 50's all the way through modern day and honestly I don't know how much I buy into the above claims. The persistence thing is real for sure, especially with cascade Gen1 systems. Its alot less of an issue on gen2 systems.