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| Re: Image PPI to Printer DPI |
DPI is a historical printing standard / term of art and the 300ppi requirement for reproduction dates from the introduction of B&W laser printers. My career spanned analog screens > digital equipment and here's the historical background as I understand from using it, researching it, buying it, and managing it for a living.
DPI = dots per inch comes from letterpress and offset printing which original used "hard" dots space 85, 120, 133, 150, etc per inch to create intermediate gray tones on white paper with black ink. The screen ruling would be selected based on what the paper could handle without the 90% shadow dots filling together. 85DPI was pretty standard for letterpress newsprint, 133DPI or 150DPI screening on clay coated papers which don't absorb the ink like a blotter. I created halftones and color separations with screen like that in the 1970s at National Geographic where I worked as a lab tech.
I first saw PPI mentioned in the context of printing vs. DPI in the mid 80s with the introduction laser printers. Like a printing press gray tones on a B&W laser printer are created with regularly spaced dots of various sizes. But on a laser printer they are created with sub-dot patterns within each printing dot.
Each printing dot was actually and 8 x 8 grid which was exposed one 8 row at a time as the paper passed over the fixed print head. The process would repeat 8 times to complete on row of printing dots. If no parts of the grid were exposed the tone of the dot would be white (just paper). If all 64 of the grid cell were exposed by the laser to fuse the toner the dot would be black. If half the grid cells were exposed the tone for that dot would be gray. By varying the number of 0-64 sub cells of each PRINTING dot which were solid the overall image had 65 discrete tones of gray in it.
As I understand it from reading trade journals at the time the 300 pixel per inch standard was arrived at by testing. It was well established from years of offset printing how fine a line ruling was needed at reading distance for the eyes not to resolve the dots: 150 DPI or 150 discrete dots to the inch for B&W and 133 DPI for color. It was possible to use a courser screen ruling for color because the four colors overlapped at different angles to create more continuous coverage of the papers.
Different digital image (PPI) to 150 DPI sampling rates were tried and shown to people to rate which sucked and which fooled them. The consensus was that between a 1.7 to 2 pixel > printing dot ratio produced the best looking results ON A B&W LASER PRINTER. So to get a realistic image on the 150 DPI laser printer a pixel resolution of between 255 ppi (150DPI x 1.7) and 300 ppi (150 x 2) was needed.
Where it gets really confusing is how the 2 for 1 downsampling from 300 pixels per inch get translated (on a laser printer) into 64 block grids spaced 1/150th per inch center to center. That's done mathematically at a level beyond what I understand.
Like many conventions submitting 300ppi resolution images was used by people like magazine art directors who really didn't understand technically why it was a convention. But as with the laser printer development test it was obvious that files with lower resolutions sucked.
Back in the 80s - 2000s I was production manger and later director of a publication printing plant printing. Well into the 2000s we did most of our reproduction for magazines by scanning transparencies. The few digital images we used were reproduced in smaller sizes. If you took the pixel dimensions of the SOOC file and divided by 300 it told you the max. size it would print acceptably. A 2.1 MP camera producing a 1200x1800 file SOOC could make a decent looking 4 x 6 image. Push it any larger by resampling in Photoshop and the image quality deteriorated.
For a full page 8.25 x 10.75 magazine page you needed a camera that produced (8.25 x 300) x (10.75 x 300) = 2475 x 3,225 = 7.9 MP SOOC. For a two-page 16.5 x 10.75 = 4,950 x 3,225 = 15.9 MP SOOC. The 8MP sensors didn't arrive until around 2004. 16MP sensors several years later. Now the SOOC resolution of some cameras is so large is is necessary to downsize their SOOC files for use on a two-page magazine layout.
The 300ppi min for reproduction is still used as commercial standard because most commercial / editorial work stills winds up in print in a magazine at some point. But advances in post processing and inkjet printing has made it obsolete for images not printed on a high speed magazine press.
Inkjet work differently
Ink jets have discretely spaced jets on the print head (Typically 300 / 360/ 400 per inch) but the jets don't form discretely spaced dot on the paper as with offset printing. The paper and the print head can move in increments smaller than the jet spacing. For example by moving the paper 1/2 the speed as normal a 300 jet print head will put 600 "splats" of ink on the same area of paper as at normal speed. The printer can control the the movement of the head across the paper the same way, and control the frequency and volume of the ink spurts. All those physical design factors translate into needing fewer ppi to get acceptable results vs. printing on an offset press.
The best way to find out the best ppi for a printer you own or print on at a vendor is to take a section of a file, resample it in Photoshop so it is the same size image but changes in PPI resolution, print them and compare. Compare them side-by-side and like the laser printer testers 30 years ago you'll know by eye which suck and which are acceptable.
The min ppi which looks acceptable will vary with printer / paper choice and other variables, and with content. If an image doesn't have fine detail, like skin in a portrait, a lower ppi level will be acceptable. If the image has fine detail it will need more ppi to look good. But more ppi isn't always better. As with lens resolution as you stop down at some point, you need to determine with testing on your equipment, the test image IQ will start to deteriorate as ppi increases. Fine detail will get lost in the sea of overlapping ink spatters.
Personally I used a Apple Quick Take 100 .8MP camera in late 1994. Even at postage stamp size the IQ sucked.
In late 2000 I bought a 2.1 MP Kodak DC290. On a desktop inkjet I could get a 4 x 6 print that was an acceptable match to a 4 x 6 film neg photo print. Printing on more forgiving $25,000 dye sub proofer I was able to get acceptable looking 12 x 18 prints, some which are still on my wall. Experimenting with Genuine Fractals and a wide format ink jet I was able to create an acceptable 24 x 30 print for a portrait IF you looked at it on the wall from across the room.
I waited until 2004 and the 8MP Canon 20D before jumping to DSLR and giving up film completely so I would be able to produce 8 x 10 prints that looked as good as an 8 x 10 created on film. I upgraded to a 14MP 50D and can get the same quality in a 12 x 18 with a SOOC file and print larger as needed by applying PhotoChops. I don't feel any compelling need to buy a higher resolution body because I have not made a print larger than 12 x 18. When I make a 600 x 900 file for a web page I'm actually "throwing away" more pixels vs the SOOC file than I did with the 2.1 Kodak and must apply things like USM to compensate.
YMMV - If I was making a living selling large fine arts prints of landscapes or posters for commercial clients I'd buy the biggest MF sensor I could afford because I would have a compelling need for more pixels.