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Since optical filters can be made out of diffraction gratings, could a reflective filter be made by printing black dots on a sheet of white printer paper?

If so, this filter could be tuned at each pixel location using the density of black dots to reflect a desired color of light and produce a color photo.

Assumptions:

  1. A highly precise printer is available.
  2. Very flat printer paper is available.
  3. The observer's gaze is directed perpendicularly into the photo.
  4. The observer is standing far enough away so that the photo does not appear to change color with small changes in his/her position & gaze angle.

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Yes, in theory this is possible. In fact several animals, such as peacocks and butterflies, use this trick to create bright colours out of dark materials. Google for Structural coloration.