Today, printing is a far more advanced technology having introduced non-impact printing and with the introduction of desktop publishing. Brought on by advancements in the digital computer [1], the photo-mechanical screening process has, in many instances, been replaced by digital imagesetters. In some cases, printing is no longer binary as continuous-tone dye-sublimation printers are now readily available but due to their speed and material requirements (special papers and inks), have not reached the wide-spread acceptance of four color ink jet or electro-photographic (laser) printers.

In digital printers, the halftoning process of projecting a continuous-tone original through a halftone screen is replaced with a raster image processor (RIP) that converts each pixel of the original image from an intermediate tone directly into a binary dot based on a pixel-by-pixel comparison of the original image with an array of thresholds (Fig. 2.1). Pixels of the original with intensities greater than their corresponding threshold were turned “on” (not printed or printed white) in the final halftoned image while pixels less than their corresponding thresholds were turned “off” (printed or printed black). For large images, the threshold array is tiled end-to-end until all pixels of the original have a corresponding threshold.

Most of the RIPs imitate the halftone patterns of contact screens by employing clustered-dot ordered dithering where the threshold array is small (8x8, 12x12, or 16x16) and is composed of consecutive thresholds arranged along a spiral path radiating outward from the array's center. These arrangements of thresholds result in a single cluster of “off” pixels centered within each tile or cell, forming a regular grid of round dots that vary in size according to tone. These techniques are commonly referred to as amplitude modulated or AM digital halftoning due to their modulating of the size of printed dots. Like contact screens, resulting patterns vary in their screen frequency, dot shape, and screen angle.

2.1 What is the screen frequency?

The screen frequency is the number of lines or rows of clustered-dots per inch of the resulting halftone pattern. Like the original glass plate screens, finer screens create patterns with higher spatial resolutions, but depending on the resolution of the printer (measured in dots per inch), screen frequency is limited by the number of unique gray levels required to reproduce an image without introducing banding artifacts (noticeable transitions between consecutive gray levels). This relationship is defined as:

Shown in Fig. 2.2 is an illustration of the effects of varying the screen frequency on a gray-scale ramp. For reference, studies have shown that AM dots become indistinguishable to the eye at screen frequencies above 200 lpi [3,4].

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Figure 2.2 The effects of varying screen frequency on a gray-scale ramp.

2.2 What is the dot shape?

Dot shape refers to the specific arrangement of thresholds within the dither array, which dictates how clusters vary in both size and shape according to tone. The shape of dots is most clearly recognizable at gray level 1/2 (number of black dots equals the number of white dots), and the most common dot shapes are round, square, and elliptical [5]. Special effect shapes have also been introduced [6,7]. Shown in Fig. 2.3 are examples of four proposed dot shapes.

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Figure 2.3 Various dot shapes proposed for AM halftoning.

2.3 What is the screen angle?

The last parameter of which to classify AM screens is the screen angle or the orientation of screen lines relative to the horizontal axis. This parameter is a function of the human visual system with directional artifacts least noticeable when oriented along the 45˚ diagonal [8]. It follows that for monochrome printing, this screen angle should also be 45˚. Shown in Fig. 2.4 are examples of several screen angles.

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Figure 2.4 The effects of varying screen angle on a gray-scale ramp.

For computational ease, screen angles are typically restricted to rational angles (rise over run equals integer over integer) where each tile is of the same size and shape. Shown in Fig. 2.5 (left) is the division of pixels into a tiling of halftone cells of size 6x6 pixels at a rational angle of 9.5˚. Note how each tile is identically shaped. Irrational angles create a tiling that requires multiple threshold arrays due to varying tile shapes. Fig. 2.5 (right) shows the tiling of cells of size 6x6 pixels at an irrational angle of 16.6˚ where tiles are not identically shaped as indicated by cells labeled A and B. Using irrational angles requires a RIP to generate threshold arrays on the fly to match the size and shape of a particular tile [6]. Rational angles allow for the use of a single array.

Figure 2.5 The tiling of 6x6 halftone cells at (left) a rational screen angle of 9.5˚ and (right) an irrational screen angle of 16.6˚.

Unlike screen frequency and dot shape, the screen angle plays a fundamental role in the elimination of moire, the interference patterns produced by superimposing two or more regular patterns. In color printing, the halftone patterns of cyan, magenta, yellow and black inks are superimposed with AM patterns, composed of regular grids of printed dots, exhibiting moire. Fig. 2.6 shows the moire patterns associated with superimposing just two regular grids. While this interference cannot be altogether eliminated, it is through the screen angles 15˚, 75˚, 0˚, and 45˚ for cyan, magenta, yellow, and black, respectively, that moire is minimized, creating the pleasant rosette pattern of Fig. 2.7.

Figure 2.6 The moire patterns created by offsetting two AM halftone patterns by (top-left) 5˚, (top-right) 10˚, (bottom-left) 15˚, and (bottom-right) 30˚.

Figure 2.7 The rosette pattern created by setting the CMYK channels to screen angles 15˚, 75˚, 0˚, and 45˚ respectively.