Justwalking wrote:We are talking about same F-working for both systems.
No problem there. If you want to have same F-working on large and small sensors, with same FOV, then for sure DOF will be less on the large sensor. But at the same time, the large sensor will resolve more detail. This is because you have swapped the lens for one with larger NA. That case is the third line in the diagram I posted,
HERE.
Nobody is debating whether the formulas are
correct. The formulas are fine. I know them forwards and backwards and I use them often. All the formulas referenced by Justwalking are correct.
The debate about the formulas is really about
what numbers to plug into them.
The numbers that Justwalking chooses, correspond to changing the lens system so that the larger sensor does have less DOF. The same change means that the system will also resolve finer detail on subject. I don't know if Justwalking doesn't understand that, or if he's trolling us.
What the formulas show, when correct numbers are plugged in, is that at same FOV and same NA, all size sensors produce images that have the same DOF and same resolution on subject. Experiment shows the same thing.
To repeat myself, the formulas are correct.
Likewise the articles are correct. The question there is, what are the articles correct
about? That is, what do they hold constant, and how do other things change besides the ones that they mention?
It is completely true that if you shoot the same FOV at the same F-number setting of the lens, then a larger sensor will have less DOF. At the same time, the larger sensor will capture finer detail on subject. Both of those happen for the same reason: at same F-number, the larger lens will have a larger aperture, resulting in larger NA on the subject side. The articles mention the loss of DOF, but they do not mention the finer detail. If, instead, they just stopped down the larger lens so as to maintain the same diameter hole in both lenses, then both cameras would capture the same DOF and the same level of diffraction-limited detail. But this is complicated to explain to a general audience, so almost no articles mention it.
There is one very useful article that has not been referenced yet: Richard F. Lyon's
"Depth of Field Outside the Box".
Quoting from page 8 of 39:
4. If you reduce the focal length as above, but fix the aperture diameter d by also scaling to a lower f-number by the same format-size factor, then d/e and S remain the same, giving you the same DOF. From the “outside-the-box” viewpoint, your camera is no different, as it has the same aperture diameter, same position, and same field of view. Its format doesn’t matter. You also get equal amounts of blur due to diffraction in this case, but likely worse aberrations in the smaller camera since it is working at a lower f-number.
Notice that changing to a smaller format can make your depth of field higher, lower, or unchanged, depending on what you keep fixed.
This is, of course, exactly the same thing that I've been saying. But it's not consistent with what Justwalking wants to believe, so I assume that he will find some way to reject it.
--Rik