Halftoning basics

Halftoning is the process of rendering an image with multiple levels of grey or colour (i.e. a continuous tone image) on a device with fewer tones; often a bi-level device such as a printer or typesetter.

The basic premise is to trade off resolution for greater apparent tone depth (this is known as spatial dithering).

There are many approaches to this, the simplest of which is to throw away the low-order bits of tone information; this is what the posterize filter does. Unfortunately, the results don't look too good. However, no spatial resolution is lost.

By using groups of device pixels in concert more tones can be reproduced. For example, consider the following patterns:

Fig 1: A dispersed dot ordered dither

As device pixels are darkened from left to right, the "grey level" of the grid increases from 0% to 100% (albeit in coarse steps of 25%). Note that it takes a 2 by 2 square in device space to make this pattern, so an image halftoned using this pattern will loose a factor of 2 resolution in both x and y-axes. By using different such patterns, a range of effects can be achieved.

The grid the pattern is formed on is known as a screen, after the etched glass screens used by the old photographic halftoning processes of the 1890's.

Modern digital halftoning divides into the following areas:

FM (frequency modulation) screening
AM (amplitude modulation) screening, which further divides into:
- AM dispersed dot
- AM clustered dot

FM screening is also known as stochastic screening, since it uses random dot placement. The common Floyd-Steinberg error diffusion algorithm is an example of such an FM screening technique. It generates blue (i.e. high frequency) noise with few low frequency components leading to a pleasing look.

AM dispersed dot patterns are also commonly (and incorrectly) called "ordered dither", but actually all AM schemes are ordered, since they share a common grid or cell structure (which is absent in FM screening techniques).

Below are 4 pictures which exemplify the differences between these screening techniques:


(a) original	(b) FM screened

(c) AM, dispersed dot	(d) AM, clustered dot

Fig 2: Comparision of halftoning techniques

FM screening is so-called because the spacing between dots (and thus their spatial frequency) changes as the image tone darkens. FM screens look much better than ordered dithers, and so are growing in popularity. In fact, if there is little difference between the original image above (2a) and the FM screened one (2b), this is probably due to your browser using FM screening techiques to render the original! FM and stochastic screening is a relatively new technology which may replace traditional ordered dithers in the future, but there are still plenty of people using clustered dot ordered dithers. FM screening is not covered any further on these pages.

Figure 2c shows the original image rendered using a 4x4 dispersed dot ordered dither - a larger tonal range is possible at the expense of resolution.

Finally, Figure 2d shows the image rendered using clustered ordered dithering. The cell size is 4x4, but this time the co-ordinate grid is skewed by 45°. The device pixels are now clustered together to form larger spots, which grow to fill the cell as the image tone darkens. Why not find out more about clustered dot ordered dithers?

The topic of halftoning is a large one, and much has been written on the subject. This list of reference material merely scratches the surface.

Robert Ulichney, Digital Halftoning. MIT Press, 1987: Rather rigourous mathematical treatment of AM screening, with a nod towards FM screening techniques. Emphasis is on asymmetric grids. Colour separation not addressed.
Peter Fink, PostScript Screening: Adobe Accurate Screens. Adobe Press. 1992: Packed with info on AM clustered dot screening. Includes supercell and CMYK separation. Rather PostScript-centric (surprise-surprise!). No other types of halftoning considered. Sadly, out of print these days. Peter has a website devoted to pre-press issues.
ESCOR Panther RIP: ESCOR make raster image processors (RIPs), and have some very good explanatory pages up about the general area of AM clustered dot screening.
Harlequin: Harlequin also make RIPs, and used to have some information on halftoning on their web pages, but they seem to have removed it.

[ On to clustered dot dithers . . . > ]

(c) 1998 Austin Donnelly <Austin_Donnelly@yahoo.co.uk>
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