The dpi written to the image are just a factor to tell the system how large to scale the image when printing it. If they are omitted, most 2D imaging apps simply assume ’72′. To be correct, these are indeed actualy the ppi (pixels per inch). The ppi don’t affect the actual image resolution in pixels. For example, lets say you like to print the image with a 4:3 aspect at 4″×3″ inch size. Your printer is capable of producing 1,440 dpi. The image is 8 bits deep. This means 256 intensity levels per color. This number is slightly decreased by the CMYK conversion (assuming your image was RGB before) but this is negligible. Now you only need to calculate the ppi of the image from the lpi (lines per inch — or the ‘screen frequency’) being printed.
The formula to calculate the number of intensity levels printed is:
levels_printed = (dpi ÷ lpi) ^ 2 + 1
ppi should be calculated as
ppi = lpi × 2.5
Note that lower values will also work, depending on the frequencies in the source image, but 2.5 is said to be a save value.
Since levels_printed is known (should be 256 for 8 bits), as are dpi (1,440), we can reorder the above term like this to find out the value of lpi:
lpi = dpi ÷ √(levels_printed – 1)
in our case 1440 ÷ √(255) ≈ 90; since 90 × 2.5 = 225 your image should have 225 ppi.
4″ × 225 pixels/inch = 900 pixels
3″ × 225 pixels/inch = 675 pixels
Voila; your image needs to be 900×675 pixels in size if you want it to print at 90 lpi on an 1440 dpi printer w/o banding.
This is all that counts. Even if f.e. a TIFF file of the pixel dimensions in our example is set to 72 ppi, arriving being 12.5″ × 9.375″ large in your DTP/imaging program, you could still scale the image to 4″ × 3″ w/o physically touching it, i. e. by plain changing the ppi to 225; and everything will be all right.
For example, in Photoshop, open the ‘Image Size’ dialog, uncheck ‘Resample Image’ and enter the new ppi in the ‘Resolution’ field. You see that the ‘Print Size’ ‘Width’ and ‘Height’ are changed accordingly while the (grayed out) ‘Pixel Size’ ‘Width’ and ‘Height’ stay fixed.