Basically, is there a commercially available camera (or an image sensor) that can capture all 3 (NIR, Visible and UV) in one photo.
There are lots of examples online of people taking pictures in NIR, then Visible, then UV and 'stitching' them together, but nothing that can do this in a single shot.
Depending on your definition of "commercial availability" (it is pretty unavailable to me) Phase One Achromatic might fit the description.
One more comment: the relative intensity / sensor sensitivity (it ends up the same) of visible and invisible light differs greatly. Getting the exposure in invisible light right is more art than science (in my experience - near UV is about about 4 stops off, and near IR about 5, but a lot of bracketing is required).
Using filters and separating the three (UV, visible, IR) shots allows for longer times / wider aperture for the invisible light ones. Shooting with the same settings as for visible light would result in a dark image.
Combining all three spectrums in one image would in most cases lead to the visible light image "crowding out" the two invisible ones.
You have been told that your camera sports optical filters meant to exclude UV and IR. These are not perfect. I will bet that your digital camera will likely capture the cusp of the IR region. To test, focus on the business end of a TV IR remote. If your camera has any residual sensitivity to infrared, you will see the tip of the remote glow. Same is true for UV. Try and image using a black light (UV light source). I will bet you will get a smidgen of an image.
Photo science has come a long way when it comes to presenting images from the various regions of the spectrum that are above and below our vision range. X-ray imaging greatly advanced medical science. It doesn’t stop there. We can image heat sources. This is the infrared (IR) that allows us to see heat leaking from an improperly insulated building or nocturnal animals romping in the woods. Not to mention night vision military imaging paraphernalia and aerial reconnaissance. We can even image radio and microwaves (RADAR). And of course the electron microscope camera images the super tiny.
When we image above (ultra) and below (infra) the range of human vision, we by necessity, are imaging in false colors. “False” because we can only guess how these frequencies would appear to our eye/brain combination if we could see them. Mostly we image these unfamiliar sights in black & white. We often tint or shade the resulting image to help us make sense of what we are seeing. An X-ray in false color can help the doctor diagnose.
Imaging the infra and ultra-frequencies has opened up a new chapter when it comes to our understanding of our universe.
Normal DSLRs do record NIR (and some UV); they typically contain filters to avoid that from happening. Google 'remove IR filters' to find out how to make them do just that.
Not that - as others described - each wavelength has a different focus plane, so you would hardly be able to get them all in focus at the same time, maybe closing the aperture all the way (to f/32 or f/45) does it.
Here's one problem with any camera that attempts to capture such a broad range of light: The display medium must be able to show what it has captured in only the visible spectrum because if it displayed the UV in the UV spectrum and/or the IR in the IR spectrum you wouldn't be able to see it. This means the colors in the visible spectrum would need to be shifted to make room on either end for the UV and IR.
The main problem, though, is the way that most digital cameras detect color. They use a Bayer mask that is most sensitive to very near the same wavelengths of light that the cones in our retinas are. Even if IR and UV weren't filtered prior to the light reaching the sensor, the sensitivity curve of the sensors would mean the visible light would dominate the image to the point the UV and IR would have very little influence (other than the IR might cause highlights to blow at slightly lower exposure levels).
Any light past the red end of the visible spectrum invokes a fairly equal response from sensels under all three filtered colors in most digital cameras. The sensors used in typical digital cameras are also unable to discriminate very well between various wavelengths on the UV end. Because most digital cameras are designed to reproduced visible light only, the sensors have filters in front of them to block infrared and UV light from reaching the sensor.
