By using FM halftoning schemes, printers maximize their apparent spatial resolution and are relieved of the strict tolerances on screen angles and screen registration. They can also use more and more colors to produce larger color gamuts (the set of achievable colors that can be produced by the printer) [28]. Notably, though, with its associated advantages, FM halftoning has, with few exceptions, only been employed in ink jet printers. The problem is the  increased scrutiny placed on the printer's ability to print small, isolated dots.

Noting Fig. 4.1 (a), the ideal display produces dots that completely cover the sample area associated with a given pixel without overlapping neighboring pixels' sample areas. By printing all pixels, perfect black can be obtained. In a real printing device, individual printed dots are round, and in order to produce perfect black, must be large enough as to cover the entire sample area as illustrated in Fig. 4.2 (left) and (left-center) [29]. By overlapping neighboring sample areas, though, the resulting tone is darker than the fraction of all pixels that are printed. Assuming that dots are printed consistently (small variation in size and shape from printed dot to printed dot), this distortion in tone can be corrected by adjusting the intensity level of the input image before halftoning. The amount of compensation depends on the arrangement of printed dots with dispersed-dot (FM) patterns requiring greater degrees of correction than clustered (AM) [30,31]. Ink jet printers are such a device that prints (approximately) round dots that overlap neighboring pixels (Fig. 4.1 (b)). Being able to compensate for distortions introduced by the printing process for any arrangement of dots, ink jet printers can enjoy the benefits associated with FM halftoning.

Figure 4.2 Clusters of (left,right-center) one and (left-center,right) four printed round dots where the dots of (left) and (left-center) cover the entire sample area while the dots of (right-center) and (right) do not cover the corners.

In the electrophotographic printing process, the size and shape of dots varies greatly from printed dot to printed dot (Fig. 4.1 (c)), and this variation can only be minimized when dots are grouped together to form clusters. Images printed using isolated dots tend to show severe tonal distortion and exhibit a great deal of variation in tone across the printed page. Figure 4.3 illustrates the resulting variation in tone across a page for an error diffused halftone representing gray level 7/10 produced by a laser printer set at 1200 dpi. In this figure, the average variation in tone along the vertical axis is plotted along side an image of the page, and the average variation in tone along horizontal is plotted below the image. Due to distortions such as this, unreliable printing devices such as lithographic presses and laser printers continue to use AM halftoning schemes. So a real challenge has come to face researchers as they try to improve the image quality in these types of printers. What they are finding is that halftoning algorithms that cluster same color pixels together, in a random fashion, hold the key by creating patterns that are easier to produce consistently from page to page and by creating color halftone patterns without moire.

Figure 4.3 The resulting printed page produced by a laser printer at 1200 dpi where the gray level 7/10 is produced using error diffusion. The average variations in tone along the horizontal axis and the vertical axis are also shown, plotted alongside and below the picture of the printed page.