Hi Q.G.,
> Print dpi is often used to calculate the number of pixels an
> image file must contain to print to a certain size.
If talking about printers that do halftones (such as typical inkjets), the printer could be 2440DPI or 720DPI, your print size will therefore vary. If you want to do any up-front calculations to make sure you have a certain or minimum PPI in your output to halftone printer, calculate the PPI you want to show up in your output, independant of the printers DPI (for typical inkjets, they are not one in the same).
> If you want a print of 30 cm wide (about 11.5 "), printed at
> 300 dpi, you need an image that is 3450 (300 x 11,5) pixels wide.
For a halftoned image, that would be PPI not DPI. If it's not a halftoned printer, than DPI can possibly be used and intermixed with PPI.
> If your negative is 56.5 mm (about the size of the 6x6 format),
> or approx 2,22", wide, you need to scan it using a scanner
> resolution of 3450 / 2,22 = 1550 dpi(rounded).
It appears to me you are suggesting that one should figure out a scan resolution up front and scan based on *that* resolution, therefore not scanning at the native resolution of the scanner. In my experience, this does not give the best results, and I would strongly advise against it.
The scanner ALWAYS scans at it's native resolution, no matter what you ask it for. If you ask for data back that is not at that native resolution, it will decimate the image data inside the scanner and they typically don't do near as good a job as PS can do. It also means you have less data to do any post-processing you may want to do, and therefore will have a degraded image to start with.
I have found that always scanning at the native resolution of the scanner gives the best scans. Then sending that full resolution to the printer has given me the best results, but there is nothing wrong with, depending on the printer as I have outlined previously, providing a "magic PPI" to the printer driver. But, keeping in mind the print size and how many PPI I'll be sending to the printer so I can maintain at least 180PPI (for Epson inkjets).
Regards,
Austin