Do the optical power and energy of LED vary with distance?
Assuming that you're shining the LED beam through some non-dispersive, non-absorbtive medium (clean air or vacuum, etc.) then the total energy impinging on the surface won't change.

This is basic physics -- the light energy coming out of the LED continues being light, unless it smacks into something that absorbs it, and it goes in a straight line, unless it smacks into something that disperses it.