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I', trying to understand difference between DPI and PPI.

I learned that a DOT is the smallest physical entity a device can show or printer can print and a DOT may consists of R,G,B elements.

A pixel is the smallest amount of information within a digital image.

So, does that mean in coloured picture each R,G,B value are individual pixel?

If so, then each dot consists of more than one pixel, am I right?

If I'm right is there some attribute like pixel per dot?

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I like a lot the reasoning of the question. I will break a little a rigorous analysis for the sake of making this answer as simple (and practical) as possible.

Each dot consists of more than one pixel... Is there some attribute like pixel per dot?

This could be, to some extent, be the other way. One pixel formed by several dots.

And my short answer is Yes. There are some correlations.

A dot. To be or not to be

A printed "dot" (as the basic unit of a printer) can contain only 2 types of states. Or is it printed or not.

A pixel is not only a digital "dot" it can contain different levels of information. The most basic type of pixel is a monochromatic 1bit pixel. It is the same case. Either you have a black pixel or you have a white pixel.

If you use a monochromatic bitmap the relationship can be exactly 1 to 1. One black pixel = one printed dot.

Halftones

Most of the time we do not use a monochromatic image.

If I have a pixel that can have for example 3 values: 1-white 2-Gray 3-Black I could resolve this using a 2x1 dots grid. 0dot=white, 1dot=Gray, 2dots=black.

This means that the reproducible levels of gray depending on how many dots we assign to match the depth of the pixel.

Normally on commercial print we have 8-bit images producing our printed images. If we have a basic grid of 16x16 dots we can have 256 combinations of dots to have 256 levels of gray.

That is the basic relation you are looking for n_n

It is not a direct dependency, (It is an optimization issue) so it is not a direct relationship or it is carved in stone. But you will find on commercial print this numbers together: 300ppi, 150lpi, 2400dpi (150x16=2400).

Things are a bit more complicated than that. But that relationship is a base to optimize these conversions.

I need to finish a paper and video about this. I am preparing physical tests, macro images, etc.

Some other variables, for example, Screen angle

Let us analyze a bit more the case of the commercial print 300ppi, 150lpi, 2400dpi

16x150=2400 is a direct transformation when your screen angle is 0° and is the easiest to understand.

But we have some other angles, like a halftone screen at 45°, where we need a file resolution of at least 212ppi

enter image description here

Double the resolution

So, why do we use 300ppi instead of 150ppi when we have 150lpi?

Here is a simulation of a 150lpi screen at 0°. Watch the red circle.

On the left, we have a 150ppi file. The circle could start growing for example from the center.

On the right, we have a 300ppi file. Now the rip has better information on how to start to grow the circle. Both are 150lpi but the extra information helped a bit to produce a better halftone, but after that, the extra information is lost.

enter image description here

Pixelation

If we use a lower resolution, for example, 75ppi, each line-dot is repeated 2x horizontally and 2x vertically. and this will be noticeable as a pixelation.

enter image description here

In normal halftone screens for commercial print we need:"

  • Some amount of pixels assigned to a line to produce enough different shades of gray (16x150=2400).

  • A workable, optimized range of pixels assigned to produce a nice line-dot. 300-212ppi on a 150lpi output. We can push this in some cases to 150ppi.

A lot of other things to consider

If we want to get rough I'm listing some other things to consider.

  • Halftone or dither

  • Viewing distance

  • Type of paper

  • Print technique

  • The pixel on electronic devices

  • Pixel density

  • Sensors

  • What really is a pixel

  • Types of pixels

  • etc.

Error diffusion

That was the easy part.

On inkjet printers (and other systems) we do not use a line. We shoot the dot directly into the paper.

The error diffusion shoots "random" amounts of ink droplets according to the percentage of the color they want to reproduce.

But they do not need to fill a grid, so it can shoot for example some droplets and shoot a different amount of droplets if it has some new color information next to it.

Think of the difference with the other approach. Using LPI will be like if "it's a military formation". But here we have "a bunch of civilian dots playing around". They produce an overall shade, but no formation is detectable.

This means that using the same 300ppi file will have a bit more final detail printed on a photographic inkjet printer that on a magazine (remember that the information is lost in sake to produce a nice 150lpi dot)

This also means that you can use a 200ppi image and still will have more detail than the 150lpi counterpart.

But as this is random it would be impossible to say "this droplet corresponds to this pixel."

I ignore the internal algorithm used to produce the "randomness percentage", but there is a chance they have a 16x16 "grid" or 256 unit somewhere in the mathematics of it. They need to produce some density of droplets shoot according to one maximum unit.

You can stop reading here

Just a note on joojaa's comment about "a pixel is not a little dot"

If we treat a pixel just as an array of digital information, the trick is how to convert this information between information systems.

If our system A supports 1bit information (2 states) and our target system B also supports 1-bit information per unit, the relation is 1 to one.

If our system A supports 2bit information, and our target system B only supports 1-bit information, we need to grab two units to reproduce the same amount of information as our the system A.

And so on...

PixelDepth Vs Dot

There is a direct correlation between a pixel depth and a dot array in terms of information.

  • If an image is 150ppi and printer has 150 lpi and 2400 dpi then each 16 by 16 grid will represent one pixel, right?(assuming 150x1 pixel resolution)<br/>If the image is of 450 ppi then each 16 by 16 grid will have 3 pixel? (assuming 450x1 pixel resolution) – Jaiaid Mobin Sep 21 '16 at 15:13
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    @JaiaidMobin No, like i said it can be weighted. There is no equivalence as such. No point in thinking that the lpi raster equals to one pixel as it does interpolate data inside itself. It is just the nearest thing to a pixel, not being a pixel tough. You usually send about 4 pixels per raster Its a but like sub pixel rendering. – joojaa Sep 21 '16 at 15:32
  • I'm confused, you state that you "don't agree with my logic" and down vote my answer.. then post "It is not a direct dependancy ...." -- which entirely supports my answer. – Scott Sep 21 '16 at 17:11
  • Jaiaid Mobin I added an example of a range of optimized ppi-lpi relation. "450 ppi then each 16 by 16 grid" No. The exceding information the extra ppi provide, will be averaged and then will be vaporized into oblivion. – Rafael Sep 21 '16 at 18:33
  • Good explanation of how halftones see grey values... but has nothing to do with pixel counts... 1 pixel can create a 4x4" 50% grey area... guess what.. that'll still create a halftone. :) And now you're getting into what you refer to as "pixel depth" .. which I referred to as "pixel density" ... same thing. :) – Scott Sep 21 '16 at 20:04
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Pixels have no size. Pixels are not a physical entity, they don't exist. You can't hold them, you can't touch them, you can't measure them. A pixel is merely the smallest increment your screen can display. The key words there are "your screen". The pixel size on a 1980 monitor will be different than the pixel size of a 2016 4K display. But they are both still pixels.

There is absolutely zero correlation between pixels and dots. None.

Now I fully understand where confusion sets in.

When software was being created in the 1980s there had to be some way to create a correlation between what is seen on screen and what is physically printed. So someone somewhere decided to make it so in applications referencing 1 pixel would see that reference as 1 dot when printing/outputting. But realize this was just an arbitrary designation and not based on any sort of equal measurements. They merely took the smallest digital increment for the screen and made that equal to the smallest physical increment on press in the application user Interfaces. That's all.

A "dot" on press could be 1 pixel... it could be 4 pixels ...it could be 5 pixels.. there's really no standard formula which can calculate how many pixels were used by looking at a dot.

Pixel density effects dots. The tighter the pixel density the more pixels there are in a dot. This is where the conversion happens between pixels and dots. And it's why Pixels Per Inch (PPI) is important, but still not the same as Dots Per Inch (DPI).

Pixels change size based on density. The more dense the pixels are the smaller they become. Dots do not change size. A dot is always the same size. The only difference with dots is the line screen. The line screen will control how dense, or close together dots are, but it never alters the size of the dots themselves, unlike pixels density.

This is why "print" images are suggested to be 240PPI or greater. To coincide with standard printing dots. A printer will use 150, 300, or more dots per inch. So the goal is generally to get the pixel density (how many pixels fill 1 inch of screen) to the same or close to the same increment that a press/imagesetter requires.

Since most commercial printing is done at 300DPI, getting a pixel density close to 300PPI is as close as you can "guestimate" to get pixels to be relatively close to the same size as a dot. In reality, it's not an exact measurement or science. it's just that this has proven to be the least troublesome method to get what's on screen to look relatively the same off press. But you will find that a 400PPI image prints pretty much the same as a 240PPI image because, when printed, the dots are the same for both images even though the pixels may be different.

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    Hum. I disagree with the overall logic of the arguments. :o) – Rafael Sep 20 '16 at 21:25
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    @Rafael no this is true please read a pixel is not a square (read A pixel is not a square) It is important. – joojaa Sep 20 '16 at 22:37
  • @Rafael for some nice pictures see this post Altough i do not disagree with the last part its still fine on a overall level – joojaa Sep 20 '16 at 22:47
  • Just some of my disagreements. 1) There are diferent meanings of pixels. A pixel of a screen is diferent as a bit-map-unit also called pixel (as information) A pixel on a screen has a phisical dimension. 2) You say that one pixel on a screen will be diferent that other screen, true. Also a dot will vary depending on the printer used. 3) "Pixel density "does not convert the unit into a dot. They are pixels and remain pixels. It is to measure screen devices. – Rafael Sep 21 '16 at 19:18
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    @Stan.. nope.. you may want to ask Microsoft why their displays have always used 96ppi then.. I mean.. if things were "specifically engineered" and all. Computers were in use long before anyone thought of using them for prepress. The notion that they were "specifically engineered" for prepress is, well, not accurate at all. – Scott Sep 22 '16 at 0:50
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No, each pixel is represented by multiple dots*. See unlike a monitor your average offset/laser printer can only make dots of the colors you have inks for. A pixel can be dimmed down but a dot is always the same intensity. So you have to use other tricks to create different tints of color.

Also the primary colors on paper are not Red, Green and Blue but rather Cyan, Magenta, Yellow and Black. These are essentially the inverses of R, G, B since on paper you remove incoming light whereas a monitor creates light which are inverse processes. Black has been added to the mix for other technical reasons. So your average offset print shop prints with 4 colors.

To produce hue they do something called a halftone raster. A halftone is essentially a pattern that contains a mixture of dots that are on and off so that on the average they seem like some tone of a color. Due to this a printer needs more resolution to simulate the same thing as a monitor.

enter image description here

Image 1: color on screen vs zoomed in Halftone on paper. Each pixel in the simulated image represents one dot.

Your inks are transparent (except black) so that they are just printed with halftones on top of each other. There is lot to be said about halftoning, the pattern does not have to be a round dot it could be a diffusion patter etc. In any case the printer driver/printer software developer can affect the size of each halftone raster which is the closest equivalent to a pixel. Though because its made out of multiple elements it can be weighted differently so normally you can have more pixels than rasters size leads you to believe.

The size of a raster is measured in LPI (good luck finding that info due to it being a controllable setting) and you should have about 1.6-2.2 pixels per LPI which means that a 300 PPI image is suitable for a ~150 LPI image since a sufficiently wide raster is about 16 by 16 to 12 by 12 dots wide it translates to about a 2400 DPI output which is typical for many commercial prints, but could be less than this.

Inkjet printers are a bit special in that they can have multiple sized dots so they can have some variation in color but even then they do not have the kind a range as a monitor and need to halftone though they usually use stochastic methods for this.

Additional clarifications

* generally speaking. You could print many pixels inside a dot but that would be purposeless one dot can still only make one color per ink. Whoever downvotrd has a point i am not being exact enough.

Scott is right pixels do not have a size, nor do they have any information between them. The printer has to resample the image to get the difference solved. So what it basically does it converts the image to a function and then rebuilds a sample field it can use. For more info see here the process is the same in both directions.

net effect is that sending too many pixels makes no sense and sending too few will just get blurred. Logic varies and can be tuned. But lots and lots of experimentation has been done on this and generally somewhere between 240-300 PPI is good enough. 240 being only slightly less good for most print work held in hand. Going beyond 300 is technically challenging and should involve your printer.

  • a minor technical comment on a very technical topic: "each pixel is represented by multiple dots". Pixels are samples and halftone dots are samples. So that statement is only true if the (pixel samples) frequency is equal to or greater than the (dot samples) frequency. If you provide 300px for an inch-wide area on a 150 LPI screen, you have satisfied this, but it is not an intrinsic property. – Yorik Sep 20 '16 at 20:42
  • @Yorik true. But if you do not supply a image that is big enough the computer will continue and resample the image as if it would be. Of sorts anyway so the end result is that you get blurring just like if you would be upsampling an image. Like Scott says pixels are point samples and as such do not exist between the areas so resampling is thechnically allways there even if it were just box aka nearest filtering. – joojaa Sep 20 '16 at 22:33
  • does that mean color combination in each raster is decided using lpi value of printer and ppi value of image? For example in case of 300 ppi, 2 pixels will be mapped to each raster(roughly)<br/>If that's the case who do this mapping printer/display driver software or it's done in h/w? – Jaiaid Mobin Sep 21 '16 at 15:21
  • @JaiaidMobin no just the LPI value. The image is scaled to meet the sampling patterns demand. It is done by a RIP engine that is either in the printers software or in the driver or a separate program – joojaa Sep 21 '16 at 15:30
  • I did not downvoated this, but the link you posted is to resample and smoothing in the same information system (a pixel with specific bit depth) Transforming between pixels and dots involves transforming information between diferent information capable systems. Full coment on my answer. – Rafael Sep 21 '16 at 20:15
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In short PPI is when you're talking about the image data and DPI is for when you're describing the physical output. i.e. displayed on screen or printed on paper.

There is definitely a lot of confusion all around on this. PPI and DPI although technically different are usually used interchangeably since in both cases it's only value is for an image's printed physical dimensions.

From the Wikipedia page on DPI:

In printing, DPI (dots per inch) refers to the output resolution of a printer or imagesetter, and PPI (pixels per inch) refers to the input resolution of a photograph or image. DPI refers to the physical dot density of an image when it is reproduced as a real physical entity, for example printed onto paper. A digitally stored image has no inherent physical dimensions, measured in inches or centimeters. Some digital file formats record a DPI value, or more commonly a PPI (pixels per inch) value, which is to be used when printing the image. This number lets the printer or software know the intended size of the image, or in the case of scanned images, the size of the original scanned object. For example, a bitmap image may measure 1,000 × 1,000 pixels, a resolution of 1 megapixel. If it is labeled as 250 PPI, that is an instruction to the printer to print it at a size of 4 × 4 inches. Changing the PPI to 100 in an image editing program would tell the printer to print it at a size of 10×10 inches. However, changing the PPI value would not change the size of the image in pixels which would still be 1,000 × 1,000. An image may also be resampled to change the number of pixels and therefore the size or resolution of the image, but this is quite different from simply setting a new PPI for the file.

https://en.wikipedia.org/wiki/Dots_per_inch#DPI_or_PPI_in_digital_image_files

Since this is the Graphic Design Forum and not the Computer Science forum I'll say yes a pixel is a smallest unit of a raster (bitmap) image and consists of at least Red, Green and Blue data.

The relationship of dots to pixels is different for every output device and display technology. The output device has to interpret the image data to be able to output it in it's own specific way.

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