Some terminology is confusing.
If you're printing a 360 dpi image on a 1440 dpi printer, the two terms mean different things. The 360 is actually pixels-per-inch and has nothing to do with dots, and the 1440 is 'printer dots.'
'Dots per inch' (dpi) can mean different things in different contexts. A lot of the terminology we use originated in halftone printing, where the final product, like a book or magazine, is printed with little dots, but these are a completely different kind of dot.
I think that we should always refer to file resolution in pixels per inch (ppi), no matter what. What you mean is always obvious if you do this.
A continuous-tone printer actually prints solid-color pixels that look just like what you see on the screen - little square tiles that butt up to each other. If an area has a 25% value of a color, there's a solid 25% value there, with no dot pattern in it. No dots are involved in the process, so I personally think that these should also be referred to as pixels-per-inch.
An inkjet cannot produce a continuous-tone image. Instead, nozzles spit tiny droplets of ink onto the paper. If you have a 25% value of a color in a certain area, the nozzles spit enough little droplets there so that 25% of that area is covered with ink and 75% is left blank. These little droplets correspond to 'printer dots' - there are 1440 possible printer dots per inch. The dots are much too small to see, so you see the spattering of tiny dots as a 25% value of that color; also, the droplets blot into the paper, spread, stick together, etc., so they don't stay as little perfect dots. It's all really a way of delivering a precise quantity of ink into a very tiny area.
An inkjet printer divides up the surface area it is going to print into 'cells'. Each cell covers one pixel's worth of surface area, so when printing a 360 ppi file, there are 360 cells per inch, one for each pixel in the original file. The nozzles then spit the correct number of droplets of each ink color into each cell to make up the color value of that pixel. So, the final image is both 360 dpi (pixels per inch and cells per inch) and 1440 dpi (printer dots per inch).
You have a big tradeoff here - the more pixels per inch you have, the more fine texture and detail your image will have, but the fewer subtle colors - higher resolution means more pixels/cells per inch, so each cell has fewer printer dots in it. As you decrease the resolution, the opposite happens - you get more dots in each cell, and therefore have more possible tones. If you have 360 cells per inch, and 1440 printer dots per inch, divide 1440 by 360 and you'll find that each cell can contain 4 x 4 printer dots (or 16 dots total). That means that there can be only 17 possible values of each color - 0 dots, 1 dot, 2 dots, etc. up to 16 dots, or solid coverage. Since high-end printers have 6 or more colors, you have in theory a maximum of 16 x 16 x 16 x 16 x 16 x 16 total possible colors (although a lot of these are not actually useable). If you printed at 288 dpi, you'd have 25 dots/values per color, and at 240 ppi you'd have 36 dots/values per color. So, make the resolution too high, and you risk color banding and possible posterization problems because higher resolution limits the number of available values of each ink. A large part of the reason that higher-end inkjets have additional colors like light magenta and light cyan (and sometimes two or more blacks) is to be able to create more values of these important colors with the same number of dots in as tiny a cell as possible. In a final print, there are so many dots and so many ink colors that it's almost impossible to see individual printer dots even under extreme magnification - again, this is all a way to get the right amount of ink in the right place.
When you print, no matter what the resolution of the original image, the printer software will divide the image up into the number of cells equal to the resolution you told it to print at. If there are more pixels in the original image than cells in the final print, the printer will simply average together the values of more than one pixel to get the final value of each cell. No matter what the original resolution, the printer will end up with the same number of cells and use the same quantity of ink. The only tradeoff is that it will take a little longer to compute each cell's value, which means a slightly longer delay between when you hit the print button and the when image actually starts printing. I prefer to do this most of the time, so that I'm not making different sizes of file each time I print something at a new size. However, if you're trying for ultimate quality, things like sharpening should be done specifically for the size the image will be used at, and in these cases I'll size the file to fit.
2880 printer dots per inch theoretically give you four times as many printer dots per cell (8 x 8 = 64 instead of 4 x 4 = 16), but it's difficult to keep the droplets small and regular enough to see a lot of difference, and the right paper surface is critical. The difference between 1440 should not be increased resolution and detail, but more subtle colors and smoother color transitions. Resolution of fine detail is pre-determined by the number of pixels in the original file; a 1440 and 2880 print from the same file will have identical levels of resolution. In a photo print, grain limits the smallest details you can resolve. In the case of inkjet prints, the grain (the printer dots) are already much smaller than the pixels, and no detail can be smaller than one pixel (remember that 'pixel' is an abbreviation of 'picture element', the smallest possible piece of a picture).
If you're printing with only black ink, at 1440 dpi and 360 ppi you'll only have 17 possible values (including white). Printing at a lower ppi or with a higher number of printer dots with black only would give you a much more dramatic improvement than you'd get doing the same thing in full color.
- Paul
