Printers make dots. They have a printing resolution in Dots Per Inch (DPI). This is not related to a digital file's PPI.
The formula is LPI * 1.5 = PPI.
Hello dwig and welcome to the club of people confusing others ;-)
I believe you know exactly what you're doing and you do it probably right! Please don't blame me too much for a little criticism!
You write in one sentence that dpi is not related to ppi and in another sentence you explain a formula (that actually works) where you make a relation between lpi (line [of dots] per inch) and ppi -> joining the club!
I'm not the master of all printing, but really seriously interested in the topic, that's why I reply!
Legacy offset printing uses some form of screen to break up the ink to effectively the impression of a lighter tone by revealing some white paper between the spots of ink. Classically, this is done with an Elliptical Dot Halftone Screen. These screens vary in what frequency of dots they produce and that frequency is marked with the term Line Per Inch (LPI).
That's not wrong, but I think it's too generally spoken and can be confusing, too! I'd like to confuse a bit more ;-)
I'm not sure what you mean with "Legacy offset printing", because offset printing in general isn't really legacy just because there are other digital printing techniques.
I'd say from the perspective of today legacy offset printing is the conventional offset printing with an AM (amplitude modification) halftone screening, even though still used. With an AM raster your dots sizes varies based on the tonal values, not only the frequency of dots is changing. If you consider the way the halftone screen is generated, I think that for example a round or diamond dot shape is as classical as an elliptical dot shape.
Then came up strict FM (frequency modulation) screening around Y2K, where the size of a dot is/was fixed, but very small compared to AM. Closer placed dots gave darker colors and wider placed dots brighter ones. The next steps were parallel developments and I don't know what was first. The hybrid screening (some call it cross modulated XM screening) combined AM and FM, means variable dot size from very small to large. That XM screening was immediately combined with more complex mathematical algorithms in the Raster Image Processor (RIP) resulting in stochastic screening. In stochastic printing any kind of shape of the dot is combined including round, elliptical or diamond like shape. That is also known as a FM staccato (stochastic) raster. All techniques are used for different purposes. Maybe the strict FM screening was a necessary step and is not used so much anymore, because of more advanced technology that incorporated this method. The transition from AM to FM screening was made possible with the help of powerful computers and the computer-to-plate (CTP) technology. It just didn't make sense to expose an analog film with such small dots a FM screen can have and transfer it afterwards back to a plate. Direct transfer to a plate without a film made this possible.
And here it comes: These modern offset printing machines in reality have multiple times the dots per inch on their plates as your or my formulas are able to proper calculate. That's why we are confusing people, especially those that know a bit of what is going on. But why are we then confusing? We want to help! Ooops, that confuses me!
Why are our formulas useful?
We have at least the additional factors human and the printing material to take into account. For an explanation of the human factor and how we see image detail and sharpness, I've found
Norman Koren's website useful. For the factor printing material I couldn't really find a comprehensive site but here is a small chart in the middle of the page that is freely available in an
American Printer article where one can find some guide values of what lpi to use for different kind of papers. And that's where the formulas we gave are coming together.
Printing machines might evolve fast, but materials for printing not so much (except our Mac's nice retina ePaper displays). There is a limit of the dots that make sense to print on a paper. The cheapest magazine paper can show more dots like a high quality newspaper paper and then imagine what happens if you print on wood or toilet paper. If I say to ask the man at the printer or in the printing shop, I mean that this is the only one who knows the machine, but also the only one that knows the surface you're printing on. And that is the limiting factor for offset, inkjet or whatever printing. If you ask, some will give you a dpi, some a lpi, some a l/cm. And then you can take a formula and get your PPI (long time incorrect named DPI in Photoshop). That ppi will feed the printers RIP with the minimal needed or maximal useful amount of different color information to make the selected output device print a nice image for you on the material you've chosen.
I've found this website on a
DePaul University server useful and easy to understand, but there are also more or less expensive books on the web.
Sorry, dwig, I guess you know all this and may think, that I'm a confusing fool to tell you all this. In reality I'm writing this, to get more confusing answers from people that know something else about it and want to share their knowledge.
If printing on an inkjet printer, ignore it.
What is so different for inkjet printing then?