Printing Halftones

Screen frequency, line screen, lines per inch (lpi); these are the commonly used names that refer to the method of simulating intensity levels using a laser or other printer that has only two physical levels; ink or no ink, dithering or half-toning.

Using the nominal resolution (dots per inch, dpi) of such printers only binary images (black&white or line art) can be produced. In order to simulate intensity levels (lightness or saturation levels) a group of dots must be combined into an image element (or printing element PEL). If such element is formed for example by 8 * 8 dots then the printer is capable to produce 8 * 8 + 1 = 65 levels of intensity. In this case the apparent, perceived resolution of the printed image is dpi / 8 that is the the same as the value of the line screen or lpi. 

LPI = apparent resolution

The printers dot resolution, line screen and the resulting number of intensity levels are related by the equation:

Intensity levels = (dpi / lpi)^2 + 1

With a halftoning printer the image quality is thus a balance of the apparent resolution (lpi) and the number of perceivable gray tones or colors. 

Higher apparent resolution may often be more favorable than a high number of intensity levels.

Not all of the printers do halftoning, a dye-sublimation printers and CRT printers produce so called continuous colors, they print full color pixels very similarly as CRT shows them. An 8400 dpi color laser would nearly match a 300 dpi dye-sub. 

There are new laser- and ink-jet printers that are able, to some extent, to put ink on top of ink and/or to use many ink colors instead the common four. These of course will improve the appearance of the image and a simple calculation of the intensity levels and lpi values are not valid for them.