Digital BW, The Print

Bob writes:

> When you refer to a 160 ppi or 200 ppi printer,
> what exactly are you referring to, and how does
> this relate to dpi resolution of the printer?

Inkjet printers, like offset presses, use essentially opaque inks in four or
more colors, usually cyan, yellow, magenta, and black.  Since these inks are
opaque, their darknesss on paper cannot be varied, nor can one color be
printed on top of another to blend the two.  So, in order to create
variations in the darkness of the printing, the inks must be divided into
dots of variable size.  When the dots are large and closely spaced, the
printing appears dark (from a suitable distance).  When the dots are small
and widely spaced, the printing appears light.

Inkjet printers, like the imagesetters used to create plates for offset
printing, do not know about variable sizes for dots; they always print dots
of a fixed and very small size.  When dots of variable size are required (as
for printing halftone images, as described above), the tiny dots are
combined to form larger dots.  The range of densities on a print (from
darkest to lightest) depends on the number of different sizes of halftone
dot that can be printed, and this in turn depends on the number of machine
dots (the actual dots printed on the paper) that can be combined to form
each halftone dot.

Printing a single pixel on paper requires a halftone dot of each color.

As a result of all this, a 2880-dpi inkjet printer cannot print anywhere
near 2880 pixels per inch.  It prints far less, and there is an inverse
relationship between the number of intermediate tones it can print and the
resolution (because more tones requires more variability in dot size, but
that means that individual halftone dots must be made up of more machine
dots, which further reduces resolution).

So ... if the inkjet printer manages 2880 dpi, and you want 256 levels of
black or green or whatever, you'll need 256 machine dots per halftone dot.
That means roughly a square of eight machine dots on a side, and 2880/8 =
360, so 360 is the maximum number of pixels per inch that the printer can
manage with 2880 dpi, if 256 tone levels are desired.  If you want more
tones, resolution goes down; if you want less, resolution goes up.

Actual implementations are much more complicated, and shortcuts exist to
improve resolution a bit, but the above explanation illustrates why you
don't get anywhere near 2880 pixels per inch from a 2880-dpi printer.