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In order to truly move all of the photons from the emitter to the target, you need to effectively surround the target with lenses, such that it looks from the surface of the target as if the emitter is filling the sky.

If that is the case, then there is no extra room to fit the optics to focus another source onto the target.

If you shrink the optics enough to make room for another source, then you also aren’t delivering all of the photons from the original source (you can’t be, since you aren’t covering all incoming angles), and therefore it’s not the same temperature as the source.

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