Human S cone channel = sum over bands of (intensity in that band) * (human S-cone sensitivity in that channel)
and similarly for M and L cone channels, which goes to the integral representing true color in the limit.
Are the bands too wide for this to work?
For wideband filters used for stars and galaxies, yes. Sometimes the filters are wider then the entire visible spectrum.
For narrowband filters used to isolate emission from a particular element, no. If you have just the Oxygen-III signal isolated from everything else, you can composite it as a perfect turquoise color.
But that said, I’m actually surprised that astrophotographers are so interested in calibrating stars to the human eye. The article shows through a number of examples (IR, hydrogen emission line) that the human eye is a very poor instrument for viewing the “true” color of stars. Most astronomical photographs use false colors (check the captions on the NASA archives) to show more than what the eye can see, to great effect.
I think when astrophotographers are trying to render an image it makes sense that they would want the colors to match what your eyes would see looking through a good scope.
I've only experienced dramatic color from deep sky objects a few times (the blue of the Orion Nebula vastly outshines all the other colors, for instance), and its always sort of frustrating that the picture show something so wildly different from what my own eyes see.
https://www.adept.net.au/news/newsletter/202001-jan/pushbroo...
Hyperspectral imaging is a really fun space. You can do a lot with some pretty basic filters and temporal trickery. However, once you’re out of hot mirror territory (near IR and IR filtering done on most cameras), things have to get pretty specialized.
But grab a cold mirror (visible light cutting IR filter) and a nighvision camera for a real party on the cheap.
Just rgb filters aren't really going to get you anything better than a bayer matrix for the same exposure time, and most subjects on earth are moving too much to do separate exposures for 3 filters.
The benefits of a mono camera and rgb filters is that you can take advantage of another quirk of our perception; we are more sensitive to intensity than color. Because of this, it's possible to get a limited amount of exposure time with the rgb filters, and use a 4th "luminance" filter for the majority of the time. During processing you can combine your rgb images, convert that to HSI and replace the I channel with your luminance image. Because the L filter doesn't block much light it's faster at getting signal, but it's only really a benefit for really dark stuff where getting enough signal is an issue.
Then I felt surprised that I was surprised by that.
Canon has made a few astrophotography cameras:
https://en.wikipedia.org/wiki/Canon_EOS_R#Variants
There are also modified cameras available with the filters removed: