I cannot find a circular fisheye lens with an Canon EF-M mount. Is there one? There are a couple of regular fisheye lenses, but no circular fisheye with equisolid angle projection. If I use an EF-M/EF adapter on my EOS-M6 and something like the Sigma 4.5mm f/2.8, will the image be cropped?
I cannot find a circular fisheye lens with an Canon EF-M mount. Is there one?
Canon doesn't make one (they don't make any EF-S fisheyes, either), but the Sigma 4.5mm f/2.8 EX DC HSM is a circular fisheye for APS-C.
Sigma's lenses are a little different from Canon's. All of them can be mounted onto either full-frame cameras or APS-C cameras, unlike Canon's EF-S lenses having a "safety bumper" to keep them from being mounted onto full frame. But Sigma does designate the size of the image circle being able to cover full frame (DG) or only APS-C (DC). See: What do all those cryptic number and letter codes in a lens name mean?
... If I use an EF-M/EF adapter on my EOS-M6 and something like the Sigma 4.5mm f/2.8, will the image be cropped?
Because the 4.5mm is designed for APS-C, you will see the entire image circle of the lens within the frame. That does mean you'll get black edge and corners, though. But you'll only see the halfway-between a circular and diagonal fisheye look (black corners) if you try to adapt a full-frame circular (like Sigma's 8mm f/3.5 DG) to APS-C.
It will work as expected. Any fisheye that projects a circular uncropped image on an EF-S camera does so also when attached to an EF-M mount with an EF/EF-M adapter. Correspondingly, the image of a full-frame circular fisheye gets cropped like it would with an EF-S camera. The sensor size being the same (APS-C), any adapted lens functions optically exactly like when attached to a native EF-S body.
Those websites list all the types of fisheye lenses and the mathematical derivation of their projections on the sensor or film. Quite simply a perspective fisheye crops top and bottom to provide a wider coverage on a 16:9 ratio and an equisolid fisheye lens doesn't crop top and bottom of the lens on a 16:9 format ratio, while a equidistant projection allows easier angular measurements (it's in between the two); but there's no reason not to use a different ratio.
The Canon EOS-M6 shoots 16:9 video and photos in 3:2, 16:9, 4:3, and 1:1 aspect ratios, shooting 1:1 maximizes lens to print coverage with a fisheye lens.
I cannot find a circular fisheye lens with an Canon EF-M mount. Is there one? There are a couple of regular fisheye lenses, but no circular fisheye with equisolid angle projection.
Pierre Toscani's website shows cutaways and gives a lot of info about specific fisheye lenses, the above links will give a a great lesson to apply in your own searches for price vs. results for your particular camera.
If I use an EF-M/EF adapter on my EOS-M6 and something like the Sigma 4.5mm f/2.8, will the image be cropped?
No, not with that particular lens, for others it depends upon what ratio you shoot at and which style of fisheye lens. Check out the above links for more than you would ever want to know.
"The Sigma 4.5mm fisheye. This lens is built for cropped sensors, giving them a full 180° field of view withing a single frame. To achieve this field of view, the front element protrudes from the front metal of the lens, giving it the typical fisheye look.".
You can get a bit wider than the Sigma (and better quality) with the 'made in Japan' "Entaniya Fisheye 250 HAL 4.3", they have a video and images showing the crop for various sensors on their website, but expect to pay U$3K (over 3x compared to the Sigma 4.5mm).