For prints that are sharp from edge to edge we require film flatness and the alignment of the enlarger negative stage, baseboard and lens to be satisfactory. What precision do we need? Here is some information I found relevant to the alignment of my LPL4x5 enlarger, which I am using for medium format enlargements.
The critical factor is the depth of field (DOF) of the enlarging lens. This varies with lens aperture and the degree of magnification. For calculation of DOF a choice is required for the circle of confusion (CoC) value, in the case of enlarger optics this is the CoC of the image on the baseboard, which will be reproduced in the finished print. Recommended values for CoC fall in the range one thousandth to one fifteenhundredth of the diagonal of the finished image. Taking as an example the negative format 6x7cm and 6x enlargement we get a print size of roughly 12x16in, and for a print this size the diagonal is about 20in (500mm) so the CoC value is about 500/1000 or 0.5mm.
The depth of field (at the negative) may be calculated using a simple formula that is precise within a few percent:
DOF = 2Nc (m+1/m^2) where N is the lens aperture, c is the CoC, m is the magnification.
inserting values for our example print and a lens aperture of f5.6 we get
DOF = 2 x 5.6 x 0.5 x (6+1/36) = 5.6 x 0.194 = 1.086mm
Rounding this to 1mm we now know that for our 6x7 negative, with a lens aperture of f5.6 and an enlargement of 6x, to be in sharp focus, the permissible deviation from flat and square between the film and the lens is 1mm across the 6x7cm negative.
In my case I use a glass negative carrier so that film flatness is assured. In order to find the alignment accuracy of the negative carrier relative to the lens I used commonly available straight edge and ruler. I began with a test of the flatness of the baseboard, progressing thru measurement of the deviation of the negative carrier from being parallel to the base, and finally to adjustment of the lens so that it is perpendicular to the base.
In another recent thread on the subject of anti-newton glass (here (there was a url link here which no longer exists) see post #71) figures were given for calculated DOF that were approximately 0.06mm for the same conditions. These figures are incorrect and imply requirements for film flatness and alignment that are too stringent by an order of magnitude and which are not required for high quality work.