Thankfully , I agree changing the enlarging apeture has nothing to do with Depth of Field.
Oh boy. Where is my latest strip of Patented Flavored Inner Tube... This month - TURI Estonian Vodka.
Not what I said, Bob. What I said was depth of field / focus is the same for both enlarging and taking lenses; and that any change in sharpness you described was probably NOT due to change in the depth of field.
f/stops DO have an effect on depth of field. Tried to show it by the math...
I am going to go home now to drink 5 Old Milwakkees and try not to think of this thread for a 19hr stretch. If I can add a few shots of Bourbon I will. Tommorow is another day see you then.
If sharp at full opening, it should be sharp at all apertures. But since no lens is perfect, "sharp" is a relative term. The plane where sharpness is best will not be perfectly flat, but slightly curved. So best sharpness in the center doesn't mean the corners are as sharp as possible.
So we need more DoF to make the corners acceptably flat. We get this by stopping down the aperture.
A theoretical lens will have maximum resolution at maximum aperture, decreasing due to diffraction as the aperture is closed down. But since weære dealing with real-life bits of glass, our enlarger lens is not perfect. So there will be some point where DoF is sufficient to get a good sharpness over the whole easel, while not yet losing definition to diffraction.
Incidentally I just received four old lenses in the mail (I bought them for the shutters). They seem to have been used in some sort of repro setup, or perhaps printing. On one of them the aperture was taped stuck at f:8 - a reasonable value for the optimum working aperture for an f:4.5 lens in reproduction work!
You finally struck the right chord. Depth of field can in fact cause focusing errors because the sharpness of the image changes more gradually when the depth of field (or focus) is large. That is why there is such a thing as depth of field (or focus).
A perfect lens or even a very good one may be sharpest at maximum aperture. Diffraction has nothing to do with lens design, only with diameter of the aperture. The formula for diffraction does not contain any elements that have to do with lens design. ANY practical lens shows an increase in resolution as it is stopped down, and ANY lens shows an increase in diffraction when it is stopped down. Where the two cross over is the optimum aperture for resolution. A poor lens may not show much change in resolution over its entire aperture range. Don't buy one like that.
For focusing, use the widest aperture. If your lens does not have a flat field, you will have to stop down to flatten it. The same will apply to most of the other possible aberrations. There are many old wives tales connected with lenses and their use. If you can dig up the article on "Hazards of the Grain Focuser" that I wrote fot Photo Techniques, you will see the experiments that you can do for yourself to resolve the questions that have arisen here. I'm not bragging, just telling the truth.