From Chapter 1 - "Modern Digital Halftoning" by Daniel L. Lau and Gonzalo R. Arce

Halftoning refers to the physical process of converting a continuous-tone image such as a photograph to a black and white dots for its reproduction in a printing device that is only capable of printing or not printing a dot at any location.  When analog halftoning was perfected in 1880 the predominant form of printing was letterpress, which was incapable of printing intermediate tones, only black and white.  Continuous-tone, monochrome photographs were reproduced as line drawings done by highly skilled craftsman, usually on a scratch board.  With halftoning, newspapers and magazines could cheaply reproduce photographs in their publications, making photography a lucrative industry and resulting in a technical revolution in photographic equipment.

In terms of photo-lithography (a process introduced in 1855), the early halftoning processes involved projecting light from the negative of a continuous-tone photograph, through a mesh screen such as finely woven sik onto a photo-sensitive plate.  Bright light, as it passes through a pin-hole opening in the silk screen, would for a large round spot on the plate.  Dim light would form a small spot.  Light sensitive chemicals coating the plate would then form insoluluble dots that varied in size according to the tones of the original photographs.  After processing, the plate would finally have dots, where ink was to be printed, raised slightly above the rest of the plate.

Today, printing is far more advanced with the introduction of non-impact printing technologies and the emergence of desktop publishing.  Brought on by advancements in the digital computer, the photo-mechanical screening process introduced in 1880 has, in many instances, been replaced by digital imagesetters.  In some instances, printing is no longer binary as continuous-tone dye-sublimation printers are now readily available ... but have not reached the wide-spread acceptance of four color ink jet or electo-photographic (laser) printers.

In these digital printers, the halftoning process of projecting a continuous-tone original through a halftone screen has been replaced with a raster image processor (RIP) that converts each pixel of the original image from an intermediate tone directly into a binary dot.  One form of doing this is based upon a pixel-by-pixel comparison of the original image with an array of thresholds.  Pixels of the original with intensities greater than their corresponding threshold are turned "on" (printed) in the final halftoned image while pixels less than their corresponding thresholds are turned "off".  For large images, the threshold array is tiled end-to-end until all pixels of the original have a corresponding threshold. 

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Initially RIP's set up threshold arrays that approximated the results using photo-lighography.  This approach known as amplitude modulated or AM digital halftoning results in dots placed at regular intervals with each dot's size varying to achieve the desired tone.  Two difficulties arise from this approach.  The first is that detail can be limited to the frequency that dots are placed.  The second is that different "screening" is needed represent printing with different primary colors.  When different angles are used moire patterns can result.

With the ability of digital printers to be able to accurately address individual pixels tone values can be represented by the total number of pixels placed in an area rather than trying to change the size of the dots.  This technique is known as frequency modulated or FM halftoning.  With FM halftoning details can be more easily represented without as great of a risk of introducing moire patterns.

With the advent of multiple dilutions of inks and the ability of some ink jet printers to form variable drop sizes the binary halftoning processes have been altered to multi-toning processes that "halftone" multiple levels.