Trying to Maximize Light from LED Source

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Hi There, i am building a DIY 4k projector and have a question on maximizing the light reaching the first fresnel lens. I currently have a condensor over the source light, but was wondering if there was a way to further increase it.

I was thinking of creating a 4 sided rectangular mirror tunnel (think of a pylon) that would go from the light source to the fresnel. One end of the tunnel will be small just enough to encapsulate the light source and the other end will be the size of the fresnel itself.

The hope would be to maximize all the light from the LED to the fresnel.

Has anybody done this before or are there any concerns with this approach?
 
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