A Tutorial on Printing

James C. Owens

A. Analog and Binary Printing

Photography is an analog or continous-tone process; the density (darkness) produced is a continuously increasing function of the amount of light falling on a given area of the film or paper. This is ideal for accurately and smoothly reproducing the wide range of light and shadow of pictorial images, but not for producing the sharp edges of text because lens aberrations and light scattering in the paper blur edges somewhat. Printing, on the other hand, is binary; the process can either deposit ink on the paper to give full darkness or deposit no ink to leave the paper white. There are no intermediate shades, and the boundary between inked and non-inked regions is very narrow. For crisp, sharp, black text and line art, this is ideal, but if a pictorial image is to be printed, a means for creating areas of intermediate density has to be found.

In 1875, Ives invented the needed process for printing pictorial images. He realized that since the printing process gave only two states, inked and not inked, the only way to produce intermediate levels of gray was to modulate the fractional area of paper covered by ink. If the image were subdivided into small regions by putting it in contact with a screen, each region small enough that it was reasonably uniform and, more important, not readily visible to the eye, and if within each region he could deposit a spot of ink that covered enough of the area to absorb just the right fraction of light, the printed image would look as if it exactly reproduced the gray tones of the image. For example, if half the area of a region is covered with ink, the region will reflect about half of the light falling on it; we call this a "50% gray" region. Ives called the process "halftoning" for this reason, because midtones were reproduced by "toning" (inking) about half of the area.

B. Important Concepts and Definitions

If the printing process is not intrinsically capable of reproducing all shades of lightness or color, the image must be subdivided into elementary areas, called picture elements or pixels, and the printing colorant deposited in such a way within each of them that its average reflectance approximately matches that of the original image. If the areas are small enough, the eye will not resolve them and the image will appear natural. No image detail smaller than the pixel can be reproduced.

The process of subdividing the image into pixels is called spatial sampling. The sampling frequency is expressed in pixels per inch (pixels/inch or pix/in); this is the correct specification for printer resolution.

Resolution, then, is a measure of the smallest object that can be replicated by the printing process. For example, if we wished to print a pattern of alternating light and dark lines, each one of which is 1/100 inch wide, the printer must have a resolution of 1/100 inch, or 100 pixels/inch, to do so. A related concept, but not identical, is addressability. It is common practice in low-resolution desktop printing to print in such a way that the smallest possible spots of ink overlap significantly. We might, for example, print using ink spots 1/100 inch wide, but place them on centers only 1/200 inch apart so that they overlap by 50%. Making addressability higher than resolution reduces artifacts such as stairstepping of diagonal lines, but it of course does not increase the visibility of fine detail.

The process of controlling deposition to reproduce the apparent lightness of an image is called rendering. The form of rendering commonly used in binary printing is called halftoning, a process in which an appropriate fraction of each pixel is covered with ink so that the average reflectivity of the pixel is correct. Halftone screen resolution is traditionally specified in lines per inch rather than pixels/inch because early screens were made by depositing parallel lines on a clear substrate. It was difficult to deposit two sets of crossed lines, so two screens, each having only lines, were crossed and the pair placed between negative and plate. For example, a "200-line screen" means that the halftone resolution is 200 pixels/inch.

There is significant confusion and inconsistency of nomenclature in the literature. We will always refer to the basic image elements, the smallest regions that actually represent image information, as pixels. If a halftone pixel consists of a single continuous region of ink, whether it has been created by a single droplet of one ink or a cluster of droplets of different colors of ink, we will call it a dot. Dots, therefore, must appear in regular patterns having the same spacing as pixels. If the halftone pixel is built up from a regular array of smaller regions, each of which is independently covered with ink or not, we will call such a region a subpixel. If a dispersed halftone pattern is used (as described in the tutorial section) without an obvious regular structure, we will call each area covered with ink a spot. When appropriate for a particular printing process we will use physical terms such as droplet to describe the smallest physically realizable image element.

Analog or continuous-tone printing uses a process capable of generating a full range of levels of each color (typically 256) at any location. Binary or halftone printing uses a process capable of only two levels, ink or no ink, and halftoning must be used to reproduce pictorial images. Gray-scale printing refers to intermediate systems, those capable of generating a few different levels of gray with each spot, as for example by using several inks of differing pigment concentration, but still requiring some degree of spatial halftoning to reproduce the full range of image density and color.

Raster printing simply refers to the pattern in which pixels are laid down during printing, along parallel scan lines running across the page. In most ink jet printers, the print head shuttles back and forth across the paper, advancing only a fraction of the head width at each pass, so that the image is laid down along a number of parallel scan lines in several overlapping passes, a process called shingling. This procedure is very important in giving time for the ink to dry, in avoiding artifacts, and in giving an opportunity for inoperative nozzles to be replaced by working ones. In optical printers, a laser beam is rapidly scanned across the page while the page itself moves slowly forward. The resulting pattern of pixel laydown along parallel lines is called a raster, after the Latin rastrum, or rake.

C. Digital Halftones

In binary or gray-scale digital printing, which require halftoning, each pixel must be created by filling in only part of the pixel area. How is this done?

The halftone pixel is subdivided into an array of NxN subpixels, and it is the subpixels, not the full pixels, that are individually colored. For example, most graphic arts scanners divide each pixel into a 12x12 array of subpixels. We can then expose (and deposit ink from) 0, 1, 2, 3,...up to all 144 of them, giving 145 different average reflectance levels that the pixel can have. The obviously unfortunate consequence of this is that the exposing spot must be very small, only 1/12 the width of the pixel, and hence the writer resolution must be high. Writing a 200-line screen image requires a printer resolution of 200x12 = 2400 subpixels per inch! This is why digital platesetters and halftone proofers for graphic arts always have resolutions between 1800 and 3000 subpixels per inch - it is needed to approximately match the tone reproduction capability of digital silver halide prints printed at 200 pixels/inch. Matching the quality of 500 pixel/inch, 256-level (8 bits per color) photographic prints would require a resolution of 16 x 500 = 8000 subpixels/inch. Of course, such high-resolution writers can make superb text and graphics, much sharper than photographic systems can.

A second disadvantage of binary printing processes is that much more data needs to be transferred to the printer. Instead of 8 bits per pixel per color, the graphic arts system must send 1 bit per subpixel; to achieve the same 256 levels of density requires 256 bits per pixel per color, a factor of 256/8 = 32 times as many. This is why digital graphic arts printers usually have a high-speed RIP (raster image processor) built into the printer and why they usually use several laser beams to write several subpixels simultaneously.

We can understand at this point why, if a digital printer can write even a few different levels of density rather than just the two (0 and 1) of a binary system, fewer subpixels are needed to generate the necessary number of pixel densities, and this gives significant advantages in reducing the writer resolution required and in reducing the data rate. This is the reason why multiple density inks, or, better yet, multiple drop size capability is so important in inkjet printing.

D. Color Reproduction and Color Halftoning

The eye can distinguish tens of thousands of shades of color. Fortunately, we need not have that many shades of ink; it has been known for centuries that good color reproduction can be accomplished by using only three primary colors. For "additive" systems such as television monitors, which produce the three colors independently from triads of phosphors (which you can see if you look at the screen with a magnifying glass), the primaries are red, green, and blue, referred to as the RGB set. If all three are present, white is seen. For "subtractive" systems such as photography and printing, where the colorants are partially or fully overlapped, the three primaries are:

cyan (white minus red = blue plus green)
magenta (white minus green = blue plus red)
yellow (white minus blue = green plus red)

which are called the CMY set. If all three are present on a print at full coverage, black is seen (or neutral gray if coverage is less than 100%).

Note #1 on printing: Printers often refer to these colors as "blue, red, and yellow," but this is not correct; the first two of these actual colors are critically different from blue and red.
Note #2 on printing: Although three primaries are adequate to reproduce neutrals and a range of colors, printers usually add a fourth ink, black (denoted by K, making the four-color set CMYK), for three practical reasons:

First, black ink is cheaper than colored ink, so if a neutral color is required they will use black ink rather than equal amounts of C, M, and Y.

Second, if a color is required which needs unequal amounts of C, M, and Y, they can replace the common amount (which would give a neutral) with K and only use the differential amounts of the two remaining colored inks. This is called "gray component replacement" or "undercolor removal" depending on how it is done.

Third, for black text, using only one ink gives a sharper image because misregistration of the three colored inks is precluded.

We cannot reproduce the entire gamut of visible colors, such as the pure spectral colors seen in a rainbow, for example, with any set of three real primaries, but if the primaries are well chosen a reasonable range can be printed using the four "process colors" CMYK. If a larger gamut or special colors are required, printers add more inks and call the process "hi-fi color." Orange and green are often added to extend the printable gamut in directions where it is limited, and also special highly saturated colors may be added for company logos and trademarks.

Ink Overlap and Layering Effects

In photography, the three emulsion layers and hence the three colorants formed during development are fully superimposed; light must pass through all three layers to reach the eye. Hence the dyes must not only control the three primary colors independently, with as little overlap and interaction as possible, but the dyes must be transparent. If the colorant layers were heavily pigmented and therefore opaque because all the light not absorbed were scattered, no colors could be seen except that of the top layer.

The same problem of overlap exists in printing. It is desirable to use pigmented inks for permanence, for their sharp-cutting spectral absorption, which gives good color saturation, and for their high optical absorption and hence relatively low cost compared with dyes. Unfortunately, they may scatter a significant part of the light.

Printers using conventional halftone patterns partially avoid the problem by rotating the four halftone screen patterns with respect to each other (angles of -15, 0, 30, and 45 degrees are a common choice) so that the centers of the C, M, Y, and K pixels do not coincide. The principal reason for screen rotation is to avoid the appearance of moire patterns, the coarse banding patterns that appear if the halftone screens do not have exactly the same spacing. An important secondary reason is to avoid depositing all four inks on top of each other. For low densities and hence low percentage coverage, the spots of each color do not overlap but form circular rings called "rosettes." For high densities, of course, when the spots are large, they will overlap, and at maximum density, full coverage, the inks will overlap completely just as in photographic prints. Using heavily pigmented inks would give rise to a significant problem in producing strongly saturated colors that require nearly full coverage by two or more of the inks.

In practice, the black ink can be quite opaque, while the CMY inks must be reasonably transparent. They can be pigmented, but the pigment particles must be very small so that there is relatively little scattering of the light passing through each ink layer.

We conclude that it is generally desirable in systems using pigmented inks that the spots of each color be deposited so that they overlap as little as possible, although they must overlap at high densities. The details of ink deposition strategy and the resultant appearances of color and visibility of spot patterns are complex and must be carefully worked out for each type of ink, substrate, and printing application.

E. Digital Marking Technologies for Desktop Printing

1. Processes

Many novel photochemical systems have been invented for copying or printing monochrome or color images without wet chemical processing. Those having the highest quality for pictorial images have, not surprisingly, been based on silver halide, such as laser and LED printing onto Polaroid instant film or 3M Dry Silver material, and Fuji's Pictrostat and Pictrography systems. They were all, however, relatively slow and expensive. A number of photochemical systems not based on silver halide have also appeared; the most recent of these to be widely known have been the Mead Cycolor and the Fuji Thermal Autochrome systems.

If we restrict ourselves to only those processes suitable for desktop digital printing at rates of about one page per minute or more, there are only three:

Electrophotography and closely related processes such as electrography, ionography, and magnetography, in which dry toners are deposited imagewise onto paper and fused is the oldest and most widespread. Although multilevel and even continuous-tone processes have been demonstrated, process control problems have limited almost all practical systems to binary operation. Some printers have used suspensions of very fine toner particles in dielectric liquids to give high resolution and high density with thin layers of toner, such as the Indigo printer. Other related processes such as photoelectrophoretic migration imaging and Elcography have been demonstrated. Overall, dry toner conventional electrophotography has proven to be a versatile, reliable process capable of very good binary imaging, both monochrome and color, for text. It can be quite good for pictorial images as well, but would not be credited with photographic quality because its resolution is too low.

Thermal transfer printing, in which dye is heated and transferred to a receiver sheet, is a true continuous-tone process capable of excellent pictorial images. There are two types of thermal transfer printers. In the first, a linear array of resistors (similar to the writing bar in old fax machines) writes an entire raster line of pixels at once as the donor and receiver are pulled over it. This is called the D2T2 (Dye Diffusion Thermal Transfer) process, introduced commercially about ten years ago. The Kodak printers, in particular, have excellent control systems and give images that are as good as, and in some respects better than, conventional photographic prints. Text is good but not excellent because resolution is only 300 pixels/inch and there is some thermal spreading of the pixels. Unfortunately thermal transfer printers are relatively slow (about 90 seconds per A4 print) since four passes over the bar are required to deposit three colors and a protective covering layer, and relatively expensive (over $5000).

The second type of thermal transfer printer is laser thermal printing; an array of high-power (about 1 Watt) diode laser beams are focused to very small spots to transfer dye at high resolution for halftone proofing, as in the KODAK Approval System. In this process the dye is actually sublimed or ablated from the donor onto the receiver rather than merely softened and diffused into it. Hence we have the odd situation of a process capable of continuous-tone imaging being used to simulate a binary printing process.

Inkjet printing is the third technology, and one that has made remarkable progress in the last fifteen years, building on the continuous-jet inventions of Hertz and Sweet, the drop-on-demand thermal "bubble jet" printers of Hewlett-Packard and Canon, and the piezoelectric heads of Epson and Tektronix. Less than ten years ago the expensive printers by Iris and Stork were showing that inkjet could produce very high quality, but desktop printers were still primitive. The resolution of the inexpensive printers was below 200 pixels/inch and image quality, even for text, was poor. Now, however, the best desktop inkjet printers surpass electrophotography for pictorial image quality and are much lower in hardware cost. They lag significantly only in speed and in media cost. The technology is continuing to develop so rapidly that comparisons of printers are of only transient value. Both improvements in existing head technologies and new approaches to drop ejection, such as the methods suggested by Silverbrook, are under intense study.

2. Characteristic Problems of Low-Resolution Binary Printing

Electrophotographic and inkjet desktop printers share several characteristics and problems because they are both primarily binary printers. Laser electrophotographic printers generally produce binary toner spots of fixed size, and inkjet printers generally produce single-volume droplets and hence binary ink spots of fixed size. Such binary printers having 200 to 300 pixels/inch, which was the maximum resolution available before the HP of 1991, were widely utilized as office printers but had problems with text and graphics and even more serious problems with images. Using these spots as subpixels meant that halftone pixels were very large and visible. The resulting problems included:

  • Text sharpness
  • "Jaggies" in text and in fine lines at shallow angles to the raster
  • Highly visible halftone patterns
  • Poor color reproduction and color transitions
  • Banding, streaking, and nonuniformity

Because increasing the resolution of the marking engines appeared to be very difficult, a great deal of work was done (and still is being done) in an effort to use image processing to reduce the visibility of these artifacts. One type of work addressed jaggies (reconstruction artifacts), the other addressed halftoning.


The only real solution to jaggies, which are visible offsets when an edge crosses from one row of pixels to another, is higher resolution, but increasing the number of gray levels can help, and these efforts were called "antialiasing algorithms" even though the problem was not aliasing but reconstruction. The best known of the solutions was Hewlett-Packard's original Resolution Enhancement Technology (Ret), which a method of smoothing the jaggies of text edges but recognizing that certain patterns of pixels generated by font software could be replaced by other patterns, individually designed, that looked smoother. More important, HP added the capability of reducing the laser power in their printers to write a smaller spot which looked less dense. Although the actual addressability of their printers was not increased, the lighter spot could be used to make text and also near-horizontal and near-vertical lines look smoother by partly filling in the most obvious pixel steps.

Halftoning Algorithms

Hundreds of papers have been written on the development of new digital halftoning methods having less visible patterns than conventional growing-dot halftones, which were quite unacceptable. An excellent review has been given in Robert Ulichney's book, Digital Halftoning (MIT Press, Cambridge, MA, 1987). In all cases the idea was to distribute the subpixels so that the pixel area was covered by a regular or random pattern of separated subpixels. Some of the most noteworthy approaches were:

  • Bayer patterns: minimizing power spectral density at low spatial frequencies
  • Fixed threshold scatter: specifying different but fixed subpixel patterns for each step in filling the pixel
  • Stochastic scatter: subpixels are randomly located in different pixels having the same fill
  • FM scatter: subpixel groupings of random size as well as random location in the pixel
  • Blue noise: adding high-frequency noise to the thresholds of fixed patterns
  • Error diffusion: using the error between the desired pixel density and that achievable to modifythe number of subpixels filling in adjacent pixels

All of these helped, and all had their own characteristic problems and artifacts. Error diffusion is especially interesting because it has the effect of expanding the size of pixels in uniform or nearly uniform areas in order to achieve finer control of density and color at the expense of resolution. In other words, areas of detail reproduce edges well but density and color are inaccurate; broad, uniform areas of little detail can show density, color, and gradients well. Unfortunately error diffusion had its own artifacts, visible wiggly lines of subpixels called "snakes," but further work combining some of the approaches listed have helped. In the end, though, higher resolution and/or modulation of subpixels to give more gray levels are the only solutions to the problems.

A Note on Reverse Engineering: When error diffusion halftoning or one of the stochastic halftoning methods is used, the original image data is still specified by pixels per inch, but the rendered and printed image may not show the periodicity of the pixels. Hence microscopic examination of a print may not allow determination of the actual pixel size.

F. Inkjet Printing

1. Technologies and Companies

Many approaches to inkjet printing have been explored, and a considerable number have been introduced as products. We summarize the most important in the following table.

Continuous Jet
  • Sweet Method (deflected drops write)
    • Binary deflection: Scitex
    • Multiple deflection: Videojet, Linx, Imaje
  • Hertz Method (undeflected drops write)
    • Iris, Stork
Drop on Demand
  • Thermal
  • Piezoelectric
    • Sqeeze: Siemens
    • Bend: Tektronix, Sharp, Epson
    • Push: Dataproducts, Epson
    • Shear: Spectra, Xaar, Nu-Kote, Brother, Topaz
  • Other
    • Electrostatic: IBM, ESI, Minolta, Kodak
    • Acoustic: Xerox
    • Surface Tension

2. Resolution and variable dot technology

As we have discussed, for text and fine lines, resolution is very important. A value of 500 pixels/inch or more is generally considered to give very good text, although the conventional printing industry would more than double that number. Variable dot technology to give at least a few levels of gray can significantly improve the appearance of low-resolution text by filling in jaggies.

Figure 1
Figure 1. A typical plot of perceived text quality versus number of gray levels per pixel

For photographic images, resolution is less important if the imaging process is analog, but even more important than for text if the process is binary. As was pointed out in Section C of this tutorial, a resolution of over 2000 subpixels/inch is required for good photographic quality for a binary process. The dependence of image quality on resolution and number of bits follows the same general shape as in the plot above, but the requirements are higher. With 64 levels of gray, a resolution of 500 pixels/inch is probably enough. Even a few levels of gray per dot significantly reduces the subpixel resolution required.


We have discussed several key issues in inkjet printer design:

  • Printhead technology
  • Rendering methods
  • Color reproduction
  • Ink/media interactions

All of them are currently under extensive study in many laboratories, and developments are occurring very rapidly. Some of the interesting questions include:

  • What is the maximum practical number of nozzles?
    1. Could full-width heads be made, and would they be practical?
    2. Could ink drying be fast enough?
    3. Could nozzle reliability be high enough?
  • What is the minimum droplet size?
  • What is the maximum droplet rate?
  • What is the best method for obtaining variable dots?
  • Can full-color, full-size A4 pictorial images, each one different, possibly be made at a rate of several per minute?


Print Unchained: Fifty Years of Digital Printing, 1950-2000 and Behond; Edward Webster. Published by DRA of Vermont, Inc., West Dover, VT (available from IS&T)