A quick google search:
Aperture can be stated in units of length. It's perfectly correct to give an answer "5mm" when asked what aperture was set on a shot. Of course, no photographer would ever say it that way. It's also correct to give it in F-numbers which is the ratio of the focal length to lens diaphragm opening. When stated that way an aperture setting at a given F-number will give the same exposure rate independent of lens focal length or sensor size.
yes, same f-number = same exposure, as we are dealing with f-numbers when we shoot and, more important here, when we calculate DOF. That was my point.
If magnification is not a functon of sensor size, what is your defination of magnification. My defination of magnification is sensor size / subject size. Clearly a function of sensor size.
For example the subject is an 11mm shrimp. On a small sensor camera this is 22/11 or 2:1. But on a large sensor camera this is 36/11 or ~3:1
1:1 or 2:1 defines the relation between real world size and size on the sensor, not the final print. A smaller sensor does not magnify – it’s “just” cropping. Eric stated in the 5D thread he could put tape on his sensor leaving a small surface in the sensor's centre uncovered. By wrong definition, he would get 5:1 or something:http://wetpixel.com/...indpost&p=61817
You are right that you need a lens with higher magnification / reproduction ratio in order to fill a full frame (35mm) with the same subject. This is important in order to find out what real life size would fill the frame for the final print. But 1:1 stays 1:1 in terms of optical magnification. And that's what goes into the formula and determines how many millimetres DOF you get. Cropping doesn't change the reproduction ratio / magnification. You don't change the DOF when cropping an image with Photoshop. No difference to what a smaller sensor does all the time compared to full frame (being exactly, DOF would change a little bit if you print a cropped image on the same print size as COCs change a bit, but this has nothing to do with the magnification / reproduction ratio).
As written in the 5D thread:http://wetpixel.com/...indpost&p=61279
Well then even if it wouldnt work in real life, which effect in theory should be stronger?
I haven't worked it out. It depends what value of COCs you use for the different sensors. Classic film way would be ~ 0,03mm for 35mm recording surface.
Formula: circle of confusion = sensor/film diagonal (43,27mm for 35mm film) divided by 1500. For a Canon APS-C sensor, this would give ~ 0,018mm. But this is "just" the value when looking at a certain size of print from a certain distance giving the viewer a "sharp" image within the defined DOF. But you won't see the same sharp image if you look at a 13 megapixel image in Photoshop in detail or at a real large print.
You can also use the pixel pitch as COC value. Not easy to state an overall law if you for example compare a 6 megapixel APS-C camera vs. a 13 megapixel 35mm sensor camera and want to give recommendation on effective DOF limits in regards to the different resolutions.
You have to be careful in how you ask the question. Craig Jones and I went back and forth on this awhile back and I think we've managed to converge on the way to look at this question. The best way to look at it is to ask, for the same subject, eg. a 1 cm nudi, a same final print, eg. 24x16", the same diffraction limited resolution, eg 1500 lines across the frame, which sensor has an advantage. For a given resolution, the larger sensor uses a smaller aperture for the same diffraction limited resolution, and this more than offsets the longer focal length lens needed to get the same FOV. The larger sensor has a slight advantage.
I know that my above statement contradicts to a definition with fixed COCs (adapted to sensor size) as you have mentioned. But I think the different resolutions (6 vs 8 vs 12 MP) and print sizes call for taking different COCs into account. You are absolutely right if you point out the DOF relation based on the same COCs on the final print and provide a comparison between sensor sizes in general. But I think, if you have a 12 MP camera, you want the images to look sharp within DOF @12MP, not just @6MP or whatever. So I would take the used camera into account.
I know my point of view is not very academic. But I have experienced (especially when determining COCs for hyper focal distances) that standard film values like 0,03mm won’t lead to the best results in real life. Especially not if you take a digital camera outresolving film. And even with largely projected slides 0,03mm is kind of weak.
Beside providing an answer which sensor size has an advantage in terms of DOF in conjunction with macro in general, I think it’s difficult to translate this into real life shooting as we are shooting with different resolutions (COCs).