I'm sure this could be sorted out really easily. Does anyone have the instructions which came with their focusers?
The problem is we have two respected printers, Fred Picker and Gene Nocon mentioned in this thread who's suggestions are complete opposites.
One says use paper, the other says don't. I know the majority do and I don't. It is human nature to defend the way you do something as being right even if you have no proof so a bit of guidance from the focuser manufacturers would be really useful.
Considering the enlarger as a camera, I came to these assumptions:
For 1:1 reproduction, I agree with your 'reversed proportional' theory. i.e. distances and depth of field/depth of focus being equal.
When focused at greater distances, a huge change in subject distance translates to a small change in lens to film distance. e.g. a change from infinity focus to ten feet may result in a lens position change of about 1" (thinking about a view camera here).
My thinking then is that if you go in the opposite direction, e.g. the image on the film (or paper on the enlarger) is larger than the subject, then the reverse should be true. i.e. a small depth of field at the subject (negative) translates to a larger depth of focus at the paper.
[QUOTE=RalphLambrecht;789553Picker and Nocon, both give good advise, because both approaches work.[/QUOTE]
Yet they both suggest that the other's method is wrong! I think we need to stop worrying about it and do whatever works for us personally.
A little OT, but to continue with these thoughts. If I were in a "Resolution Contest" with someone doing contact prints of 8x10, then my personal 0.15mm CoC may not be good enough. So a process lens (with a flat field) and good MFT curve at f5.6 may be needed. Again this is if the prints are going to being closely scrutinized side-by-side.
Now, that first example I gave (9x enlargerment) was more typical of a 35mm enlargement. I used f2.8 in that example, but, as you suggest, using a more realistic f8 would increase the focus spread way beyond 2mm, further discounting the 'paper thickness' myth.
One thing I would like to summarize is that when enlarging, understanding depth of field is just as important as when taking pictures. Every enlarging system suffers from the following things to some extent:
1) Lack of parallelism
2) Lack of field flatness due to the lens
3) Curved or wavy negatives
4) concave, convex or wavy paper easels
The question of "how much to you need to stop down" to correct those things can be answered, to some extent, by the Peak magnifier. The main problem, is that things can look a little fuzzy under the Peak, and still be OK in a print viewed from a distance.
Therefore, determining the acceptable F-Number from the focusing equation takes into account a personal "acceptable circle of confusion" for viewing a print from a distance, and can take some of the guesswork out of interpreting the image under the Peak.
I have considered writing up an article on focusing the enlarger but,
a) Jeff Conrad came up with the math that substantiates that equation,
b) Jeff already has two good articles on focusing the view camera on the LF site,
c) the math in those articles is difficult to follow,
d) if you can follow the math for the view camera model, you don't need a separate article for the enlarger (its just a large format macro camera) and
e) if you can't follow the math in the view camera focusing articles, you probably won't be able to follow it in an enlarger focusing article :)
However, if there were interest I could try to come up with some kind of article like "The Basics of Optimum F-number Selection for Projection Printing Using Modular Transfer Function Criteria." Problem with that title is that no one will understand the title. If I called it "How to Focus the Enlarger" no one will read it :)