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One thing that concerns me a bit about using "white" LEDs - particularly if you are using a one-shot colour (RGB) digital sensor:
"White" LED displays do not actually produce "white" light. Depending on the LED technology, they either have 3 fairly narrow-band spectral peaks, corresponding to the RGB LED elements, or the newer "bright white" LEDs use a strong narrow-band blue LED as the main driver, and yellow phosphor which produces a broad-band yellowish light which combines with the blue to simulate white light.
In addition, the peak wavelength and "width" of the Red, Green and / or Blue LEDs can vary depending upon the technology used - I'm sure we've all seen how some "white" LEDs seem to be "bluer" than others.
Either type of "white" LED can work well for human perception, which is remarkably adaptable in "filling in the blanks" when the source "white" light is actually missing some wavelengths - but I wonder what happens when you are using a digital sensor?
Your digital RGB sensor has three rather narrow (but overlapping) spectral sensitivities (for the RGB filters of the Bayer matrix respectively). These will typically be calibrated to simulate human perception of a wide range of colours, but what if the peaks of the emission spectra of your "white" source happen to not correspond with the peaks of sensitivity of the sensor? E.g. if you are using a "Bright White" (yellow phosphor + blue LED) source, the "white" light might actually be quite low in true "red" light. Will the process of capturing and processing the "white" flats introduce imaging errors by thinking your Red sub-pixels have a lower sensitivity than the Green and Blue sub-pixels (because there is less red light actually being emitted from your light source), and therefore give an inaccurate flat calibration?
Just a thought - I've captured plenty of spectra from various LED and fluorescent sources, and I know they can have very variable spectral signatures across Red, Green and Blue, but I've never tried to use a "white" LED source to produce a "white" flat calibration.
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