How colour correction is achieved by camera's sensor?
Answers
Karel's sample shot has a strong greenish color cast because every "pixel" is processed without weighting, which therefor gives green twice the effect as red and blue. The result is an image processed from minimally amplified pixels, where as normally red and blue channels would be amplified by a factor greater than one to compensate for the greater number of green pixels. From a signal-to-noise optimization perspective, that would be most optimal.
From a digital "white balance" standpoint, I'm not really sure there is any way to determine exactly what the base output of the sensor is. It might vary between manufacturers, it may be handled simply by amplifying the signal from each pixel channel, or it may be performed entirely by image processing logic after read and amplification. I would think that a good baseline to work with would be to use a 1.0 weighting for each pixel channel, and a daylight temperature setting (5200-5500k). That should normalize the camera around about as pure "white" light as light can get.
If I understand what you mean by correcting white balance optically, you would then need to have a color filter that properly filtered out about half the green wavelengths of light to compensate for the change in how you are processing the sensor signal. Since you have twice as many green pixels as red and blue, and the signal is processed without weighting, you need to reduce the amount of green light reaching the sensor by a similar amount.
I would be a bit skeptical about this really improving anything. If it was the case that processing light this way before it hit the sensor was ideal, digital camera manufacturers would have already accounted for it with additional filtration in the pre-sensor filter stack that most digital cameras have these days. I think the decision to use twice as many green pixels as red and blue is done because more wavelengths of light fall within that color range than for red and blue. Having more sensitivity in that more prolific range of light frequencies is overall BENEFICIAL, not detrimental, to signal ratio. With an unweighted/filtered approach...you are reducing the overall light by at least 1/4, requiring amplification of the final signal across the board, not just in the red and blue channels.