When comparing DoF issues, we must be very careful about what the conditions of the two situations are. We may say, "all other things being equal", but what does that mean? Same focal length? Same field of view?

For now. let's compare a situation of the same lens with and without a 2x focal length converter. Let's assume that focus is at the same distance, the focal length setting of the base lens is the same (and thus the focal length of the combination is twice that), and the f-number of the base lens is the same (so the f-number of the combination is twice that). And we will assume a consistent circle of confusion diameter limit (COCDL)

Then, in the configuration with the focal length converter in place, the depth of field will be substantially less than for the configuration with no focal length convertor.

If the setting of the base lens is f = 100 mm and f/3.5, with focus at a distance of 10 m, then, using a COCDL of 0.031 mm, the full depth of field is:

No focal length converter: 10.62 m

2x focal length converter: 4.50 m

But perhaps for our purposes it would be best to think in terms of a constant field of view (a constant focal length). Thus, with the focal length converter in place, we would set the focal length of the basic lens to (for our example) 25 mm. Then the results would be:

No focal length converter: 10.62 m

2x focal length converter: 67.98 m

Woof!

If we look at out-of-focus blur performance (which is what we are sometimes more interested in than depth of field), we also see interesting results.

Suppose that in both cases we assume focus at 10 m and are interested in the blur on a background object at 50 m. We will always use the base lens at its maximum aperture, f/2.0.

First suppose that with no focal length converter aboard, we set the focal length of the base lens to 50 mm, and we leave it set thus when we add the focal length converter. Then the results are (in terms of the diameter of the circle of confusion (blur figure) produces for a point on the background object:

No focal length converter: 0.10 mm (3.24 times our reference COCDL)

2x focal length converter: 0.20 mm (6.52 times our reference COCDL)

This time, when we mount the focal length convertor, we reset the focal length of the base lens to 25 mm (to hold the actual focal length and thus the field of view). Now the results are:

No focal length converter: 0.10 mm (3.24 times our reference COCDL)

2x focal length converter: 0.05 mm (1.62 times our reference COCDL)

Best regards,

Doug