I hope you don't mean that resolution is a function of linearization.
Well, no... That was a joke.
Actually, I go into this very subject at 14:20 in Part Two of Correct Color Management: The Movie.
However...
To start:
In any case, the actual size of the mark the droplet of ink makes on the paper is unknown. For a 600 or 1440 "dpi" ink jet printer the "dot" it images most certainly is not 1/600ths or 1/1440th of an inch in size.
Sure it is. Dots per inch
means dots per inch, and that's precisely what it translates out to, since only at 100% coverage is a printhead only firing at each spot.
E.g. "This inkjet proofer prints at 2880 x 1440 dpi." does not mean that the resolution is finer, or that the droplets of ink are finer in one direction. Instead it simply means that the paper is moved more slowly in one direction...
Well, no. You are right that it doesn't mean the dots are any finer in the 2880 direction-- if by finer you mean smaller. What it does mean though is that in one direction the dots are generated at 2880 dpi, and in the other at 1440. The media transport speed has nothing to do with it.
As a result, with some inkjet printers, reference is sometimes made to "picoliters" in addition to dpi when the resolution of the device is described in the specifications.
There are some, notably the HP latex machines, who aren't real forthcoming with their dot size, but that's usually because their dots are a little on the largish side and they don't feel like sharing that with the class. I'm pretty sure though their dot size is around 10 pl, which, by the way, doesn't compare well with the 4.2 pl size of the dots on the Epson S80600, currently my favorite printer in that class. (My guess is the latex ink just won't fit through smaller nozzles, and they don't want to advertise that fact. Almost every other printer I'm aware of though, the drop size is in the spec sheet.)
But no matter, anyone who knows anything about inkjet printers knows that inkjet printer drop sizes are measured in picoliters.
Correct Color clients certainly do, and understand the significance.
A picoliter is a unit of fluid volume.
A picoliter is one trillionth of a liter.
Trillionth. That's a pretty small drop.
And currently, the smallest rated drop size out there on any commercially available printer is 3.5 picoliter on the Epson aqueous machines. There used to be some 1.5 picoliter printheads out there, but my understanding is they were very good at running dye-based ink, but not so good at running pigment-based ink... and dye-based ink does not last, while pigment-based ink does.
What you are right about is that drop size is equally as important as resolution in determining print quality of an inkjet printer. (I'll refer you again to 14:20 in CCMTM Part Two.)
3.5 picoliter dots though are still incredibly small; so small in fact that it's hard to even get a picture of them. Even scanning at 600 ppi, you can't get a close-up look at them, because as you zoom in, you find that they are significantly smaller than the pixels, and you get pixelation before you get a good actual look at the dots.
Now of course there are machines out there with significantly bigger dots. There are still some old Scitex 1500XL's chugging away out there with 80 pl dots. And you're right, 1440 of those dots would not fit in an inch. That's why their max resolution is in the 290x290 range.
I'd also note a couple more things:
I'm not a printhead engineer, but my understanding of the firing graph for every printhead in every resolution is that the center of each square is the firing point, and the goal is to hit the center of the square.
Also I'd note that very few printers have just one resolution. The Epson S80600 has -- for instance -- 360x720, 720x720, 1440x720, and 1440x1440. Also some have these have multi-dot or fixed dot mode. It is, or course, the same printheads and the same nozzles, and they're all the same size, it's a question of how they're fired. But for every resolution there's an individual graph.
I'd also quibble with the definition of a "splat." Again, I'm not an inkjet engineer, and again, the printers I work with have dots so small that I'm unable to get that close a look at them, but I'd bet folding money that they do not resemble the splotches in your illustration.
What I know for a fact after over 15 years of making a living profiling inkjet printers is that there is simply no other printing technology that is so consistently stable.
I can't see dots like that achieving that stability.
Mike