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The reason you can't expect accurate results from LRG, LRB or LGB imaging is demonstrated by the attached image showing the transmittance of a set of Astrodon LRGB filters. You'll notice that the L filter admits wavelengths that none of the colour filters admit and also that there is an overlap between the B and G filters, so there are wavelengths that would be "counted twice" if you use these two filters.
If you had a set of colour filters that didn't overlap and covered the transmittance of the L filter perfectly then you could do imaging as suggested, but it doesn't provide any real advantage. You still need to achieve the same amount of integration time if you want the same SNR.
Cheers,
Rick.
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