Would it be possible to replace the backlight of an LCD with a high brightness lamp? I know it needs a lot of cooling, but using a lamp with a long filament and a reflector should work ?

The reason i ask, it looks to me as if a lot of the light from a standard HQI bulb gets wasted because it doesn't shine in the right direction. The standard backlight setup should do a better job.

I'm sure i'm overlooking something, but problems are there to be solved, right?

I would start reading info in wiki, about the optics,, this will explain..

a projector works the same way as 35mm slide projector,, it is all about providing collimated light to the panel then sending thru the field lens Fresnel (split optics version) to a projection lens, and out to the screen

a backlight in essence is just a diffuse illuminator,,, A light box for the panel, like when doctor clips the xray chart to the wall mounted light box, to look at it

In essence, i can't get a sharp image because the light is diffused ?

basically you won't get a bright projection as you need directed light into the triplet to get the brightness at the screen. the reason for the collimator fresnel is to collect light and straighten it out so it can then be directed by the field fresnel into the triplet, and onto the screen. the collimator is most efficient when a light source is used at it's focal point (or near there). using a diffused light source will lead to large losses in brightness.

cheers,
gs