virtual {mo}ritz

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.