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Pixels, Dots, and Inches: How Big Can I Print It

By Dave Etchells

 

Based on what I've seen in various discussion forums on the ‘web, printing resolution has to be one of the most confusing topics in digital imaging. The question is simple: "How large can I print images from my digital camera (scanner, photo-on-floppy, etc.), and still have them look their best?" This month, we’ll take on this question, and hopefully clear up a few misconceptions along the way.
Our Standard: PPI
Since an image file can be any size at all, in this article we’ll speak in terms of printing resolution, expressed as pixels per inch, or PPI. As you’d expect, "pixels per inch" is just a measure of how "big" the pixels of our images will be on the printed page. For example, a 640x480 pixel image printed at a size of 6.4 x 4.8 inches has a printing resolution of 100 PPI. A little later, we’ll talk about how to choose the most appropriate PPI value for your combination of camera/scanner and printer.
Millions of Colors, Four Crayons
Before we go any further, it’s important to understand a basic fact about digital color printers: They actually can only print four colors! (Or, in the case of some of the newer special-purpose "photo" printers, six colors.) The four colors are the so-called "subtractive primaries" (cyan, magenta and yellow), plus black. The special "photo" printers typically add a light cyan and light magenta to the mix.
Cyan, magenta, and yellow are called primary colors because you can create virtually any visible color simply by mixing them in various amounts. (The "subtractive" label refers to the way these colors affect light reflecting from them, subtracting specific wavelengths, and reflecting everything else.) If printing inks were perfect, the three primaries would be all we'd need, but in practice the three colors combined at full strength usually produce only a muddy, brownish black. To make up for this, a true black ink is used to create richer dark tones.
Ideally, a photographic printer would work by mixing exactly the right proportion of the primary colors at each spot on the page. True "continuous tone" printers do just this using dye-sublimation or dye-diffusion processes. Unfortunately, the technology to do this is complex and costly, meaning that most full-page continuous-tone printers cost several thousand dollars.
Diversity Through Dithering
Modern inkjet printers use very tiny dots of the primary colors mixed in random patterns to simulate continuous-tone printing, relying on our limited vision to blur the result enough for the dots to merge together. All the dots are the same size, but by carefully controlling how many dots of each color appear in a given area, an amazing gamut of colors can be created. The range of possible colors depends on how many dots of each of the primaries can be packed into that "given area" we just mentioned.

It Takes a Lotta Dots...
Think of it this way: Suppose we have an area on our page, say 0.01 x 0.01 inches, that we'd like to color a particular shade. How many shades can a given printer create? To make the math easy, suppose our printer is rated at 1,000 dpi. What this means is that the printer can lay down 1,000 tiny dots of ink per inch of each primary color, vertically and horizontally. That’s a million dots of ink per square inch, but only a hundred dots (ten by ten) of each primary color in the 0.01 inch-square area we're coloring. Since each of these potential dots can only either be there or not (remember, we can't vary the size of the dots), this gives us a hundred possible shades for each primary color. (Each possible shade corresponding to a number of ink dots ranging from one and one hundred.) Thus, the total number of colors we can produce is something on the order of 100 shades of cyan times 100 shades of magenta times 100 shades of yellow, for a total of a million, extended into various tints of black when you add-in the effect of the black ink as well.
This sounds pretty good, but a hundredth of an inch is a pretty big chunk of area when you’re talking about printed output: If we actually divided a picture up into 0.01 inch chunks, it would have a bad case of the "jaggies." Suppose we decided to double the printed resolution, by shrinking our coloring grid to units of 0.005 inches (200 little squares per inch)? Suddenly, the range of colors drops from a million to only 125,000 (25 x 25 x 25). That still may sound like a lot, but take my word for it, you’d see pretty severe "banding" in areas of subtle gradation. Of course, inkjet printers don’t arbitrarily divide images into square chunks to decide what colors to put down, but this simplified illustration makes it clear why printers rated at more than a thousand dots per inch of resolution can’t actually show anywhere near that level of detail in a printed image.
From dpi to PPI
The key to answering the "How big can I print?" question is to figure out how big your pixels can get on the page: Too big, and the printer will be able to distinguish their edges and corners, revealing the dreaded "jaggies." Below a certain pixel size (that is, above a certain PPI value), the random scattering of printer dots hide the edges of the image pixels. The trick is to find out what this limiting PPI value is for your printer. More accurately, you want to find out what the lowest usable PPI value is for the combination of your camera/scanner and printer, since the way your digital camera or scanner handles its pixels is an important part of the overall equation.
Testing, Testing...
Fortunately, it’s not too hard to figure out what works for your printer and image source: All that’s needed is a good test image, a few sheets of paper, some ink, and a bit of patience.
What you’ll want for your test image is something that will show pixel "jaggies" and compression artifacts (JPEG "blockies") most clearly. Jaggies will appear most noticeably along slanted lines of strong contrast, while JPEG artifacts are most noticeable in areas of fine detail. One of the best test images for this sort of work is a newspaper page, preferably with large headline type to give you some angled straight edges, and some smaller type to provide the fine detail. If your camera doesn’t focus close enough for the newspaper trick, almost anything else that will give you a sharply focused dark-on-light or light-on-dark edge at an angle will do: Perhaps a piece of dark furniture against a white wall, with the camera tilted 45 degrees to get the angle you want.
Once you have your test image, print it at a range of different sizes, varying from quite small to large enough to obviously see pixels, jaggies, JPEG artifacts, etc. Find the size where the undesirable garbage is just starting to show, and divide the pixel dimensions by the length/width to find the PPI number that works best for you. (For example, if your 640x480 pixel image just starts to look ragged when printed at a width of 5 inches, the "magic" PPI number for your camera/printer combination would be (640 pixels) ¸ (5 inches) = 128 PPI.) In the future, to decide how big to print any given image, just divide its dimensions in pixels by the PPI number you arrived at to find the desired size in inches.
Examples and Conclusions
To show how this works, I prepared some files in Photoshop™, with type rendered at different resolutions, in a range of shades from solid black to light gray. These were printed on my elderly 720 dpi inkjet printer, and then photographed (digitally, of course) at extreme magnification. Several samples are included here as illustrations. Note how the "jaggies" are most evident on the pure black letter, since it has the most closely-packed ink dots. The black type starts to look a little rough at 120 PPI, and is clearly blocky at 90 PPI. By contrast, the lighter shades have so few dots it’s actually a little hard to tell where the edges are. On this printer, I’ve come to use 120 as a minimum PPI value, and stick to 150 PPI if I’m being picky. Of course, YPPIMV (your PPI may vary).

 


This series of images shows greatly magnified output from a 720 dpi inkjet printer. Notice how the edges of the type are reasonably smooth down to 180 PPI, roughen slightly at 120 PPI, and become quite ragged at 90 PPI. For this printer, the lowest printing resolution for best results is probably 120 PPI.

 


While I try to avoid overly-broad generalizations, I know that some of you reading this are shopping for digital cameras or printers, and could use a little guidance as to what to expect. With that in mind, I’ll stick my neck out (protected by a huge disclaimer) to say that you can probably plan on useful PPI values of 120-150 for 720 dpi printers, and somewhere around 150-180 PPI for the 1440 ones. For the special "photo" printers, expect to be at the high end of these ranges, as those devices hold more detail in highlight areas as well as in the shadows, revealing more jaggies than their lesser brethren.
A basic understanding of how inkjet printers work, combined with a little experimentation can save you time and hassle in printing your images, and insure top-quality results to boot. Dive in!


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