A Simple Question Can Open a Can Full of Worms
A Simple Question Can Open a Can Full of Worms
In short, there are a couple of significant relationships between DPI and LPI.
A number of people here have offered opinions and self-made rules, as well as a divergence that includes relevant information about PPI. Let me try to provide some factual answers, because it's worth a detailed explanation of how all three of these numbers interact. I've taught a lot of printers and graphic designers how these three figures interact in a print environment for nearly 20 years now, so I'm willing to take a shot.
Be forewarned that this will include some math. But I'll provide answers as I go through this explanation that should reduce the pain factor dramatically.
First, let's break these abstract numbers into simple mechanics: Pixels, Dots and Spots.
Pixels=PPI. Pixels are magical things. They are what are input into your computer prepress system when you bring in a digital image through a digital camera, a scanner or most types of digital image files. They're also what you see when you look at digital images on the computer screen. The great thing about pixels is that they're square, so they fit together perfectly and there are no gaps in the information. Another great thing about them is that they are the actual color they portray -- green really is Green, not some approximation made up of Cyan and Yellow, with maybe some Magenta and/or key color BlacK thrown in.
The only problem is, you can't print a pixel. You have to translate that information into Output Dots and Printer Spots (halftone cells) to translate those pretty pixels into printable pictures.
Output Dots-DPI. This is the resolution of your output device. if you'll allow me to set aside some imagesetters/platemakers that have switchable resolution settings, these numbers are the constant of the process. A 600 dpi laser printer has output dots that are 1/600th of an inch. They don't get any bigger, and they don't get any smaller. A 1200 dpi imagesetter or platemaker, like you'd find at many newspaper plants or a typical small job printing shop, makes output dots that are exactly 1/1200th of an inch.
Printer's Spots/Halftone Cells=LPI. To give the impression of darker and lighter shades of printing, your output device groups bunches of Output Dots together to create Printer's Spots, also known as Halftone Cells. The more of those Output Dots that are clumped together and the less space there is between those clumps, the darker the shade appears to our eyes. The smaller those clumps are and the more space there is between them, the lighter the shad appears to the human eye.
So that's the first relationship there is between DPI and LPI. DPI defines -- literally -- how finely we can construct those halftone cells.
The second relationship between DPI and LPI is that it defines how many shades I can define between absolutely solid black and absolutely no shade at all.
Let's talk about grayscale halftones, because the math is easier -- though it's not exactly simple. The mathermatical relationship between Output Dots and Printer Spots/Halftone Cells is:
(DPI/LPI)squared, + 1 = number of shades of gray you can define. In absolute terms, more is better.
Let's take that abstract equation and translate it into real terms, using a 600 dpi laser printer and a 1200 dpi imagesetter. Let's say that we want to run a job at a 133 linescreen, as a typical image screen for commercial printing.
With a 600 dpi laser printer, at a 133 linescreen, the math is as follows:
(600/133)squared + 1 = # of shades
600/133 = 4 (actually 4.511278 and a whole lot of other numbers for the fraction, but fractions don't count)
4x4=16 + 1 = 17
That's the maximum number of shades we can reproduce between 0% white and 100% solid black.
So, why do you care?
Well, because we said more shades are better. And 17 shades aren't much. Let's say that you need to print a 20% screen. That's not going to happen with a 600 dpi laser printer and a 133 linescreen, because the gaps between shades are roughly 5.88 percent. You can print roughly a 17 1/2 percent screen or a 23 1/2 percent screen. In simple terms, 20 percent ain't gonna happen. and if you try to print a 133-linescreen image on that 600 dpi laser printer, the wide range between shades will translate into poor-quality, posterized pictures.
Using the same linescreen with a 1200 dpi imagesetter or platesetter works a heck of a lot better:
(1200/133)squared + 1 = # of shades
1200/133=9 (actually, 9.022 and a bunch of other numbers, but remember fractions don't count)
9x9=81 +1 = 82
We still can't print a screeen at precisely 20%, but the gap between 19.5 percent and 20.7 percent is a lot finer. And when you conside the human eye can detect between 80-100 shades, printing a good digital file from a 1200 dpi imagesetter or platemaker will give the impression of a quality photographic image.
This doesn't even take into account highlight or shadow dots -- the lightest and darkest shades you'll actually be able to reproduce on press. Nor does it account for dot gain as ink is absorbed by paper. Sorry about the novella. But this does precisely answer the original question: Is there any relation between DPI and LPI? The short answer is: absolutely.
Randy Hagan
htech
415 Congress, Suite 202
Portland, ME 04101
207-699-1316
