To stack or not to stack

gardenersassistant wrote:

There was no extra DOF from the smaller sensor.

Following on from that ...

Beyond a certain magnification (which varies depending on the kit used) it is possible to get greater DOF using a single capture with an interchangeable lens camera than from a fixed lens camera with a much smaller sensor. The greater the magnification, the greater is the difference in achievable DOF.

An example. First, a scene captured with a camera with a small (1/2.3") sensor (around the same size as the sensor in a smartphone). This used the camera's minimum aperture, and hence produced the largest possible DOF. The image is uncropped.

The subject was at an angle with the left hand side furthest from the camera.

Below is the same scene captured with a full frame camera. The DOF is considerably larger (and the image is considerably softer).

This image is full height but has been cropped at the sides to give the same 4:3 aspect ratio as the previous image.

So what is going on here?

The full frame image was captured with a Sony A7ii with a 1.4X teleconverter, a 2X teleconverter and 68mm extension tubes, on to which was reversed a 28mm Minolta legacy lens.

The scene width was around 3mm wide and so the magnification was around 12:1.

The lens was set to f/22.

For a given f-number, the effective f-number varies with magnification. The approximate formula used to calculate the effective f-number is this, where "Nominal f-number" is the f-number set on the lens:

Effective f-number = Nominal f-number * ( 1 + magnification )

So in this case the effective f-number is 22 * ( 1 + 12 ), which is in the region of f/256.

The small sensor image was captured with an FZ330 bridge camera with a 1/2.3" sensor, with a Raynox MSN-505 close-up lens.

With close-up lenses the effective f-number does not change with magnification, so the effective f-number was f/8, the same as the nominal f-number. This gives the same depth of field as f/45 on a full frame.

So, in terms of the amount of DOF we need to compare f/45 to f/256.

DOF roughly doubles for each doubling of f-number. So, f/45 doubles to f/90, and doubles again to f/180, and then increases by another 1.4 to 256. This would mean that the DOF would be roughly 2 x 2 x 1.4 = 5.6 times larger in the full frame image.

As to whether either of the images is usable is obviously a different matter. Stacking looks like the obvious approach to take in such cases, but where that was not practical one or other of the images might be usable, depending on the use case.

The general point here is that with a fixed lens camera all you can do to increase magnification is to place something in front of the lens, and this does not alter the effective f-number. With interchangeable lens cameras you can place something between the camera and the lens, such as extension tubes, bellows and teleconverters, and this does alter the effective f-number.

When you use close-up lenses on both a small sensor camera and larger sensor camera, as in the previous examples above, the effective f-number is not altered for either, so the only adjustment that needs to be made is for the difference in equivalent f-number stemming from the difference in sensor size. (e.g. three stops difference between 1/2.3" and MFT, and another two stops from MFT to FF.)