light engine.

hello nerds.
dust off those pointed hats, i'm looking for feedback on TWO (count them, 2) things here.

1. What is the most optimized shape?
2. What is a recommend method for construction, medium to retain the shape, and reflective surface/coating?

Problem:
I've about 220mm between the lamp and the lcd screen. the screen has a surface area about 30.5 cm across. 22.75 cm high. ~38cm diagonal. I'm looking for the 'best' reflective shape and surface (reasonable here people, like mylar, not gold) to get the MOST light through the screen and ideally EVEN on the screen, i don't want to burn a hole in the middle of the lcd!


link this got me thinking.


The bulb i'm using is about 1.8" in diameter and 9" long, just a cylandar. it puts out at startup about 40k lumens, and a mean lumens of 32k.



I was considering mounting it horizontal across the back (punch two holes and push the lamp through).
If the ellipse reflector is back enough from the focal point where the lamp is at, maybe those 2" holes wouldn't hurt as much.

I was considering building a modified egg ellipse (I beleive made with 3 points instead of two) so the light would spread out to the entire 15" panel instead of converging to a point.

check out the ellipse with pins and string method of construction . it looks like i was paying attention in geometry! because the 15" panel is not square, our best shape is going to be an Ellipsoid (rotate the render for another angel) but i'm still figuring out poors mans tools to make an egg ellipse into an ellipsoid with the right properties. who needs calculus? i've got a drill and a pen...

Anyone have any ideas for a reflective surface - whether paint, or film, like mylar?
mylar is listed as having a melting point of 254 degrees C. I wonder how much before that it starts to not reflect light like we want it to?