As hinted at earlier in this thread, polarizers will work, in principle. The flashes or other sources would be filtered by polarizers oriented in the same direction (up/down, say) while the camera polarizer is set 90 degrees relative (right/left, say). Because of the way digital cameras perform metering, the camera polarizer should be of the "circular" polarizer type. Crossed polarizers work because specular reflections retain polarization, while diffuse reflections become depolarized. Note that at shallow angles, the reflectivity of nominally diffuse targets becomes ever more specular in the plane of the source-eye line of sight, so the light sources should be relatively normal to the plane of the object, but not so straight on as to be imaged by the camera if the target were a mirror. Expect a factor of 4 effective reduction of detected diffuse light relative to use of no polarizers. Specular light reduction will depend on the quality of the polarizers, which may not be spectrally uniform.
While it may be possible to use large diffuse light sources to obtain an adequate representation of the target details and colors, in principle any specularity that the target or its protective covering has will cause the addition of a haze to the image that is the color temperature of the light source(s) if the light sources are in a position from which they can specularly bounce off of the target and into the camera. (As a gedanken experiment, imagine a 25% reflective silvered mirror covering the target. The image of the target would be a combination of the reduced light from the target and a semi-transparent mirror view of any lighting within the reflected camera field of view, hence even taking the photo inside a giant white integrating sphere -- a perfectly diffuse world of light -- would not avoid the appearance of haze. Fortunately, AR glass coverings and an ink printed target surface itself have relatively low specular reflectivity and in the real world this haze may be too slight to be a distraction except perhaps at the blackest end of a gray scale test pattern.) I would think that shiny oil paintings with irregular surface angles would be most affected by this if lighting positioning is not carefully thought out.
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