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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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    $\begingroup$ I don't remember ever seeing colours or diffraction from printed black lines on an opaque white surface. $\endgroup$ – Keith McClary Apr 8 '17 at 3:04
  • $\begingroup$ Are you saying that it's not possible or you have not personally experienced colors or diffraction from printed black lines on an opaque white surface? $\endgroup$ – ElecEng2016 Apr 8 '17 at 5:19
  • $\begingroup$ The paper will have a combination of specular reflection and diffuse reflection (glossy vs. "flat white" paper). Diffuse reflection is due to surface roughness which I think disrupts phase relations needed for interference. $\endgroup$ – Keith McClary Apr 8 '17 at 15:19
  • $\begingroup$ Ok, that makes sense. Let's add the assumption of ideally non-rough, glossy paper. $\endgroup$ – ElecEng2016 Apr 8 '17 at 16:44
  • $\begingroup$ If it looks white then there is diffuse reflection. "Milky" transparent materials with smooth surfaces can also look white. Somerelatedquestions. $\endgroup$ – Keith McClary Apr 8 '17 at 18:50
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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.

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