First, off, I think my previous formulas was wrong: it should have been DOF ratio 1.6*sqrt(22/15)=1.93, and for your 10MP vs 12.7MP case, 1.6*sqrt(12.7/10)=1.8, a difference of 1/7 stops. But now that I read your procedure involving up-ressing for very large prints, that traditional approach does not apply, so you have inspired me offer a new one. But the formulas comes out the same! So in your test with a one stop difference the ODF ratio is predicted to be 1.3, or 0.73 stops. Is that close enough to what you see?
Why my new calculation:
I always compare equal size images.
Good: with equal size images, ignore my formula, which was for equal PPI (before upressing).
Since I have a wide format printer and fairly low-pixel-count cameras, many of my prints require the image to be interpolated beyond its native resolution.
That probably makes the tradition DOF reckoning not applicable, as it is based on the assumption of the resolution being high enough that it is not a factor in perception of sharp vs OOF. That is, the resolution length scale on the print is assumed to be substantially smaller than the circle of confusion threshold at which OOF effects are noticeable. Remember that the traditional reference for DOF scales was 5"x7" prints viewed from 10". So to check that guideline of "4/3 stops from 35mm to EF-S", it would be better to use a print size not needing any up-ressing, maybe A4.
But the traditional DOF results that I described are giving the right answer to the wrong question for your situation! Instead you have raised an interesting new question:When images are viewed at sizes so large that the resolution limits of the sensors are visible (roughly, when up-ressing is needed), how is DOF related to format size, focal length, aperture, degree or enlargement and the underlying resolution of the image?
The answer might be one advocated by Jonathan Weinke (sp.?): the parts of the image that are perceived as out of focus are those where the circles of confusion are noticeably larger than the resolution length scale of the sharpest, fully in-focus parts of the image. So in traditional DOF formulas, the CoC threshold value to use would be roughly the pixel spacing, or some suitable fixed multiple of that.Computational Details
Assume focal length proportional to linear sensor size, for equal FOV, equal focus distance, equal aperture ratio.
Use numerical values LSS for linear sensor size, PC for pixel count.
The pixel spacing is roughly proportional to LSS/sqrt(PC), so we use a value CoC that is proportional to this. The traditional formula says that the DOF is proportional to
so in our case this is proportional to
To compare formats that differ in linear sensor size by ratio LSSR and with pixel counts in ratio PCR, the DOF varies inversely withLSSR*sqrt(PCR)
which is the formula I used above.
If the aperture ratio is also adjusted in ratio NR, the DOF varies in proportion toNR/(LSSR*sqrt(PCR))Example
Comparing the 10MP EF-S 40D to the 12.7MP 35mm 5D, we have LSSR=1.6 and PCR=12.7/10=1.27, so the suggested DOF ratio is
1.6*sqrt(1.27) = 1.8
Close enough to a factor or two, or two stops. To be precise, get stops by taking twice the log of this divided by the log of 2, getting 1.7 stops.
With your difference in aperture by a factor NR=1.4, the DOF is less for the 5D by factor
1.4/(1.6*sqrt(1.27)) = 0.77, or 0.73 stops. Doe that match your observation of "only one stop?"