What type of camera adapter should I choose?

[coprinus]

I have an Olympus CX31 microscope with a trinocular head.
The camera I want to use has a 4.3" sensor, dimensions in mm: 17.47x12.86
The camera manufacturer proposes an adapter that has a 1.2 times magnification.
Because of the 1.2 magnification, the field of view the camera sees will be reduced by that same factor.
Alternatively I could use a camera adapter from the same manufucaturer with a 1.0 magnification.
This would not reduce the field of view which I prefer, but I wonder if the camera sensor will still be sufficiently illuminated at the edges.
How can I know or calculate the size of the view field that the microscope would project on the camera sensor if no magnification is used in the camera adapter ?
Probably there is a relation with the Field number of the trinocular tube which is 20 for the CX31.

[PeteM]

You can directly project with an infinite scope such as your Olympus CX. A direct path from the trinocular port to your camera sensor (no lens) wouldn't be far off for a Micro 4/3 sensor. You might try it, hand-held, and see if you want to magnify (crop) the image that 1.2x further. If it's a cheap projection lens, it may degrade quality. If it's an expensive projection lens, you might decide you don't need it.

"1X" is usually just an empty tube (for infinite type optics) to go from the head to a mount on your camera. You could likely find something on Ebay for around $50 and also a variety of cheap but good quality used MFT camera bodies.

[Scarodactyl]

Agreed, if I were you I would direct project if possible. I know some of the low end objectives are only rated for 20mm coverage but I am not sure this is a hard limit, I doubt it would introduce vignetting on m4/3

[coprinus]

OK thank you for the information. I did not buy the camera yet, the plan was to order it together with the adapter. I am going to try it handheld with an APC sensor photography camera and see what the size is of image circle I get.
If it cannot accommodate the 4/3" sensor without vignetting, I'll try to find a camera with a 1" sensor and use a 1X empty adapter tube.

[coprinus]

Is it only the field number of the objective that is going to be the limiting factor or could the optics of the microscope also play a role?
I know there is a lens and a prism in the optical path to the trinocular head.

[Scarodactyl]

The head can certainly be a limiting factor, but outside of custom setups the scope will come with a head that's rated for at least the field number of the objectives. I don't know what the limits are like on the cx series heads because I haven't tried one, but usually it isn't a hard cutoff leading to vignetting when going past the rated field number but instead a decrease in image quality, which is less important for the extreme corners of photos. The eyepieces are more likely to show hard image cutoff issues when their field number is too high because the image gets cut off by the prism edges.
That all said, I would also go for a 1x adapter because it is much cheaper and could even be DIY'ed. Even if the corners had hard vignetting it would make little sense to spend a bunch of money to chase a particular tiny increase in image quality on what is still a student scope.