Depth of field and sensor size. Is there a relationship?

The answer is no. There is no relationship between sensor size and depth of field. It's the focal length of the lens that matters.

I think that one of the under appreciated aspects of focal length and depth of field occurs when we are comparing focal lengths across different sensor sizes. Since we tend to talk about a 1" sensor equipped camera having greater depth of field compared to a full frame camera, the impression is left that it is all about sensor size. It's actually the coverage of the lens that changes.

Imagine we have a large format 4X5 film camera that we can exchange the film back for one with a digital sensor. When we compare the effect of using a 200mm large format lens with the 4X5 film back mounted on our large format camera, to when we have the full frame sensor or a 1/2.3" sensor mounted, we find that the depth of field is the same. Only the image size (coverage) has changed. A 200mm remains a 200mm regardless of the sensor strapped behind it. Only the coverage (image size and angle of view) changes.

This chart shows the equivalence factor for various formats as compared to 35mm. Under the Focal Length column, we see the coverage equivalence (angle of view) of a 200mm lens on the various film and sensor formats. So a 200mm lens on a 4X5 view camera is equivalent to a standard lens on 35mm camera in terms of its coverage. A 200mm on a 1/2.3" sensor equipped bridge camera is equivalent to a 1120mm super telephoto on a 35mm full frame camera. The depth of field of these 200mm lenses on these cameras, remain the same as a 200mm lens on a 35mm camera.

This explains why a 28mm equivalent lens on an APS-C equipped camera has greater depth of field than a 28mm on a full frame camera. That 28mm equivalent lens on the APS-C camera is actually an 18.5mm lens, so it has the same depth of field as an 18.5mm lens on a full frame camera.

So the bottom line is, the focal length of a lens determines the depth of field it is capable of delivering for any given aperture, not the sensor size behind it.

Why is this distinction important? With mirrorless cameras, we often have the option of mounting other brands of lenses on our mirrorless camera bodies, via the use of adapters. We can end up with a full frame lens mounted on an APS-C or MFT body. Once we start doing this, we can be left wondering what the depth of field will be. Well, it'll be the same as when that lens was mounted on its intended full frame camera.

Our choices around macro photography are also impacted. If we don't need the resolution of full frame, it makes more sense to go to the smallest sensor size that suits our needs. Doing so lets us work with a shorter focal length lens which will have a greater depth of field for any given aperture.

Something to keep in mind whenever depth of field becomes an important issue.