Halftone patterns are defined by the spacing of the dots measured in dots per inch (dots/inch), called screen frequency, and the percentage area covered by ink in the resulting patterns, called dot area. The dot spacing defines the sharpness of the resulting image, with 133-150 dot/inch screens being typical for magazine quality offset printing. The percentage area defines the light-ness or darkness of the resulting area. Figure 1 shows halftone patterns for different dot areas.

Figure 1 shows the round dots that would be produced using a traditional mechanical halftone screen, but other shapes can be used, either to produce textures for artistic reasons or to accommodate a scanning output device such as a film plotter. When a halftone pattern is generated on a raster printer, a pattern like that shown in Figure 2 is often used [Holladay].

In color printing, the four separations are printed one over the other. To minimize interference between the different colors, the halftone patterns on each separation are oriented along lines of different angles. Mechanically, this difference is produced by rotating the halftone screen when photographing the image. Digitally, the effect of this rotation must be simulated. Typical screen angles are: 105, 75, 90, 45 for cyan, magenta, yellow, and black respectively, though some recommendations exchange the values for magenta and black.

When printed on film, a halftone pattern should contain only opaque and clear areas. Gray areas in the pattern will make the pattern overly sensitive to exposure time when making the printing plate. The dot area of a properly screened film can be accurately measured using a densitometer, which is crucial for maintaining quality control of the film printing process. Film fog (which affects the transparency of the background film), inadequately opaque dark areas. and insufficiently sharp edges will all invalidate this measurement and jeopardize the reproduction process. It is essential to use high-contrast film and carefully control the development process to achieve reliable results.

The basic measure of a reproduction technology is its tone reproduction curve, abbreviated ``TRC.'' This function defines the mapping from the input gray or tone values to the output values. In traditional printing, these tone values are measured as density, a logarithmic function of reflectance. The tone reproduction curve relates density values in the original image to those in the reproduction, and ideal reproduction maps the original values to the identical values on the print. Where the original image is in digital form, however, the concept of a TRC must be redefined as there is no set of density measurements for the original image. The optimal mapping from monitor intensity to print density has not yet been defined, although a metric based on the colorimetric quantity L* has been considered. In practice, visually compensating the monitor and the printer so that a set of gray patches of different values (a gray step wedge) appear evenly spaced in lightness on both devices is adequate to ensure reasonable tone reproduction.

Another use of the term TRC describes the function that controls the mapping between the requested tone values and those actually produced by the mechanics of the printing process. The spots produced by any mechanical device are not the idealized squares or disks shown in the illustrations above, so the bit patterns sent to the printer must be modified to accommodate the tone reproduction characteristics of the device. This compensation can be provided by a table that is the inverse of the tone reproduction curve for the device. When setting up a digital printer, it is very important to control the printing process so that the dot area or density requested is actually the same as what is produced on the film. This does not happen ``automatically'' for most real devices.

One of the most important criteria for a good color reproduction process is that it be able to accurately reproduce the neutral colors in a picture. The three guns on a color monitor are usually balanced so that equal amounts of the primary colors produce a neutral gray color. In printing, it is not usually possible to use equal amounts of the primary colors to produce a gray. The process of adjusting the mix of the three primaries to produce a neutral color is called gray balancing. It is a straightforward task to find an approximately neutral progression of grays from a set of color patches containing nearly equal amounts of the primary colors. This data is used to produce a table of values that compensates each of the primaries to produce a neutral gray scale. For example, a color whose ideal value is a 50% gray might actually be produced as [C: 50%, M: 47%, Y: 47%].

Given that we are going to adjust the mix of cyan, magenta, and yellow to produce gray colors, what about colors that are nearly gray? If we don't compensate those also, there will be a discontinuity in our color space. Most colors contain some amount of gray, called the gray component, which is simply MIN[C,M,Y]. For example, the color defined as [C: 100%, M: 75%, Y: 80%] has a gray component of 75%. The obvious solution is to balance the gray component exactly as we would a gray color, and this is what is usually done. For one printer, however, we found that we got better results by gray balancing less than the full gray component for colors off the gray axis, using a function inversely proportional to the distance the color was from the gray axis. For this calculation, distance from the gray axis was defined as MAX[C,M,Y]-gc.

The three primary colors of the offset printing process are cyan, magenta, and yellow. In four color printing, black is used as well. The black separation is used to accomplish two things in offset printing: to increase the contrast by increasing the density in the dark areas of the picture, and to replace some percentage of the three primaries for economic or mechanical reasons. For example, to keep the paper from getting too wet with ink on high-speed presses, the SWOP standard recommends restricting the maximum dot area in any one area of 280% (4 solid colors = 400%). To achieve this, it is necessary to substitute black ink for mixtures of cyan, magenta, and yellow, a process called undercolor removal, or more recently, gray component replacement (gcr). Printing is distinctly non-linear, so it is difficult to predict how much black ink is required to match the density of the colored ink removed. If not done correctly, dark areas of the print, which are subject to gcr, will actually appear lighter than supposedly lighter tones not subject to gcr.

The correct design of the black separation is a topic of much interest in the color printing field today. Traditionally limited by effects obtainable with photographic processes, the use of computer controlled scanners and printers has made a wide range of effects possible [Johnson].

On raster devices, the set of brightness values available is quantized. Computer driven displays typically restrict monitor output to 256 different levels per primary. For film output, the number of halftone patterns available is quantized by the resolution of the printer. Each halftone dot is built on an array of printer pixels as shown in Figure 2. The maximum number of gray levels attainable for a particular array size is N2+1, where N=the number of pixels along the side of the array. The number of gray levels can be increased by making the array larger, with a corresponding decrease in image sharpness. Further quantization effects occur when approximating the different screen frequencies and angles. These effects can introduce moire patterns.

In practice, the total number of levels obtainable may be significantly smaller than the ideal due to limitations in the printing process. For example, a single pixel in isolation may not reproduce, so patterns with single dark pixels are effectively unpatterned. Similarly, single white pixels in a dark area may tend to fill, in so the darkest patterns will also be limited. For example, when using a 10 by 10 array on a 1200 spots/inch printer to approximate a 120 dots/inch printing screen, we've found that after compensation we had approximately 80 intensity levels, rather than the ideal 101. This is sufficiently restricted that it can produce visible contour lines on smoothly shaded portions of an image. This problem can be masked by adding small quantities of random noise to the pictures. Commercial quality scanners for producing halftones use resolutions around 2500 spi, which minimizes this problem.