In which I question the NEX APS-C Shallower DOF argument

Sensor size matters because it will affect your FOV, which will affect DOF. You can’t assume that FOV is unnecessary in the equation because you only want to compare sensor size and DOF. Well then, we could eliminate any other variable that is integral to the argument (distance, for example) and arrive at a customized conclusion.

Here is an example, taken with Sony 16-50mm f/2.8 SSM (at 50mm, f/4) on Sony A55:

That makes it a 75mm equivalent on FF, taken at a comfortable distance. Assuming 2m for distance, the DOF would be about 25cm. Now, I could have captured this image with Sony F828, which has a 4x crop factor. For the same shot, I’d have needed about 19mm for focal length (75mm FF equivalent) but at the same distance and aperture, the DOF would be 85cm.

We can’t assume 50mm focal length on F828 here. That would be 200mm equivalent and while DOF will shrink considerably, we will end up with only capturing the eye (a whole different FOV). This describes the challenge of control over DOF with smaller sensors.

The telephoto reach is an advantage of a smaller sensor and wider angle is an advantage of larger sensor. However, you can crop to extend your reach towards telephoto but you can’t recover wider FOV from a narrow one. And again, sensor size is at play.

As far as aperture size relationship to crop factor, I think it has already been presented and it is actually within the way aperture is defined (focal length divided by 3.5, below). Keeping FOV and distance constant:

1-inch sensor’s 10mm f/3.5, aperture size: 2.9mm

APS-C sensor’s 18mm f/3.5, aperture size: 5.1mm

FF sensor’s 28mm f/3.5, aperture size: 8mm

--
Sony A55, Sony NEX-3, Sony F828