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In traditional mirrors, some of the input light is absorbed by atoms in the mirrors surface and are 'lost' as heat, degrading the quality of the reflected image.

Could this loss be compensated by an array of "powered elements" arranged to reflect nearby photons repelling them with some sort of electo-magnetic force, to completely prevent loss?

This would realize the perfect mirror, reflecting all light back.

enter image description here

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There aren't mechanical oscillators that have the same frequencies as visible light. The most common oscillators with the same frequencies as visible light are the electrons orbiting atoms, which is why atomic transitions emit and absorb visible light.

If you're willing to accept a powered system, you could absorb all the light into an image-processing system and then project that image in another direction, possibly with much more light intensity than the original image had. For instance, folks with telescopes sometimes use video cameras to observe objects too faint to see naked-eye in real time.

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    $\begingroup$ Note that even if intensity is preserved, there will be loss of phase-information. An essential quality of a mirror is that it preserves phase so you can do for example a diffraction experiment. $\endgroup$ – alfC Aug 4 '14 at 18:36
  • $\begingroup$ You would need to do a phase sensitive detection method. Something like this might be possible, however there is always measurement noise. Even with unity gain detection efficiency there would still be shot noise in the measurement which would make the output beam a little different than the input. In practice the best detectors have 90% or so quantum efficiency. You are better off going with a 99.999% reflective mirror. $\endgroup$ – jgerber Jun 22 '19 at 14:34
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To make high-finesse cavities for instance, you can nowadays easily buy mirrors with reflectivity as good as 99.999%. There are also superconductor coated mirrors and other Bragg elements that reflect better but you cannot not buy them because some people want to keep their advantage in the design of IMU (inertial measurement unit) :).

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