closing down the lens by one stop would give a similar depth of field, its not a perfect match if you look at a dof calculator, but close enough for most people.

By closing down the aperture by 1 stop you are recording 1 stop less light the image would be 1 stop under exposed
I chose to raise the ISO by 1 stop to compensate the alternative would be to half the shutter speed (1 stop difference).

if the shutter speed was 1/60th then 1/30th would be needed to keep the same exposure. This particular scene it doesn't particularly matter about the shutter speed.

with micro 4/3rds as the original camera at 18mm you would want 36mm on full frame and close down 2 stops and raise the iso 2 stops.

If you flip this on its head trying to match a full frame photo with a crop sensor or m43 camera. The surprising thing is you need a better lens for the smaller format. With 1 and 2 stops difference for each format.

You are also enlarging the negative more which is going to reveal more of a lenses defects e.g chromatic aberration.
It probably is fair to say the larger the format of the negative the less demanding is the Image Quality required from the system, big is beautiful

Heavy not so easy to take to a location but perhaps why people still love the medium and larger formats even 35mm film.

Yes, the focal length of an 18mm lens is always 18mm, but the Field of View and DOF of that lens on a FF or Crop body will be different if using the exact same lens on each body. I agree if you use the lenses designed for FF or Crop body, but I understood the question as if using only one FF lens. Perhaps I misunderstood the question. On a FF the Field of View will be wider so you would have to move in closer with a FF to get the same FOV as the Crop body. The DOF will also be shallower on the FF so you would want to close down the aperture one stop roughly and you would need to compensate elsewhere to get the same exposure.

Best,
Todd Ferguson

Yes, the focal length of an 18mm lens is always 18mm, but the Field of View and DOF of that lens on a FF or Crop body will be different if using the exact same lens on each body. I agree if you use the lenses designed for FF or Crop body, but I understood the question as if using only one FF lens. Perhaps I misunderstood the question. On a FF the Field of View will be wider so you would have to move in closer with a FF to get the same FOV as the Crop body. The DOF will also be shallower on the FF so you would want to close down the aperture one stop roughly and you would need to compensate elsewhere to get the same exposure.

Best,
Todd Ferguson