I'll start with some poetry: ¿Is it possible Capturing the color of the sky?
(Note the -spanish exclusive- opening question mark to make the rethoric question even more dramatic).
I have no idea of the characteristics of colour sensing sensors nor of coloured LED ones (that seem to be the most appropiate for this project?), so the following is just thinking in loud voice.
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Colours perception is a quite subjective (personal) issue. Some people see the swimming pool green some see it blue.
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Nevertheless, comparing colours is not so subjective: two colours seem to be the same independently of the name one uses to designate it.
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Brain has a fundamental role on light perception: everybody knows that the same grey square may seem white when opossed to a black one and black in a white foreground.
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Colours are basically defined by the amount of basic ones in them: blue, red and yellow. Other characteristics (as, for example, the texture of the coloured body and saturation) are too important.
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I'd start by capturing the color of the sky by a simple method (the ones described seem to be valid -parabolic mirror, lens. I wonder if a plain piece of pipe -white coloured inside- looking to the sky with the sensor in the other end will do); then I'll try to get the simple (see "4") decomposition; I would say that there exist some cheap sensors that do exactly that.
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Then, I'll try to feed a multicoloured LED (or whatever device that achieves a similar result) with that recipe -the decomposition- and study what the results are. First of all, trying to adjust the ambient light (see "3") depending on the conditions you have to reproduce the sky (it wouldn't be the same the perception just by looking to the LED than the colour you get on a screen that is illuminated by three -red, blue, yellow- projectors whose intensity is adjusted according to the recipe).
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If this procedure gives an acceptable result (meaning than the reproduced sky varies acording to the sky colour, even if the perceived colours are different), I'll try to "map" -not exactly using the map C function- the incoming colours to a different intensities to get more similar final colours (sky and fake ones).
At the end: who -and how- is going to determine if the result is acceptable? (more poetry?).
Best regards.
Vicente ..