Know the words
In image processing, there are overlapping terms that tend to get interchanged. Especially for image and print resolution: dpi (dots per inch), ppi (pixel or points per inch), lpi (lines per inch). In addition to this, the resolution of an image is stated by its dimensions in pixels or in inches (at a certain ppi or dpi resolution). Yes, we can understand if your head is swimming. Let’s understand this:

When an image is captured using either a camera or a scanner, the result is a digital image consisting of rows – known as arrays – of different picture elements that are called pixels. This array has a horizontal and vertical dimension. The horizontal size of the array is defined by the number of pixels in one single row (say 1,280) and the number of rows (say 1,024), giving the image a horizontal orientation. That picture would have a “resolution” of “1,024 x 1,280 pixels”.  

The size of the image displayed is dependent o the number of pixels the monitor displays per inch. The “pixel per inch” resolutions (ppi) of monitors vary, and are usually in the range of 72 ppi to 120 ppi (the latter, lager 21.4” monitors). In most cases, however, with monitors the resolution is given as the number of pixels horizontally and vertically (e.g.1,0240 x 1,280 or 1,280 x 1,600). So the “size” of an image very much depends on how many pixels are displayed per inch. Thus, we come to a resolution given in ‘pixels per inch’ or ppi for short.

With LCD monitors, their ppi resolution is fixed and can’t be adjusted (at least not without a loss of display quality). With CRT monitors you have more flexibility (we won’t go into this further0.

 

When an image is printed, its physical size depends upon how many image pixels we put down on paper, but also how an individual image pixel is laid down on the paper.

How image pixels are reproduced by printer dots
There are only a few printing technologies where a printer can directly produce a continuous color range within an individual image pixel printed. Most other types of printers reproduce the color of a pixel in an image by approximating the color by an n x n matrix of fine dots using a specific pattern and a certain combination of the basic colors available to the printer.

If we want to reproduce a pixel of an image on paper, we not only have to place a physical printer’s ‘dot’ on paper, but also have to give that ‘dot’ the tonal value of the original pixel. With bitonal images, that is easy. If the pixel value is o, you lay down a black printed dot, and if the pixel is 1, you omit the dot. However, if the pixel has gray value (say 128 out of 256), and you print with a black-and-white laser printer (just to make the explanation a bit simpler), we must find different way. This technique is called rasterization or dithering.

To simulate different tonal values (let’s just stick to black-and-white for the moment), a number of printed dots are placed in a certain pattern on the paper to reproduce a single pixel of the image. In a low-resolution solution, we could use matrix of 3 printed dots by 3 printed dots per pixel.

Using more printed dots per image pixel allows for more different tonal values. With a pattern of 6 x 6 dots, you get 37 tonal grades, (which is sufficient). For a better differentiation let’s call the matrix of printer dots representing a pixel of the image a raster cell.

Now we see why a printer’s “dot per inch” (dpi) resolution has to be much higher than the resolution has to be much higher than the resolution of a display (where a single dot on a screen may be used to reproduce a single pixel in an images, as the individual screen dot (also called a pixel) may have different tonal (or brightness) values.

When you print with a device using relatively low resolution for grayscale or colored images, you must make a trade-off between a high resolution image (having as many “raster cells per inch” as possible) and larger raster cells providing greater tonal value per cell.

The image impression may be improved when the printer is able to vary the size of its dots. This is done on some laser printers, as well as with some of today’s photo inkjet printers. If the dot size can be varied (also called modulated), fewer numbers of dots (n x n) are needed to create a certain number of different tonal values, (which results in a finer raster). You may achieve more tonal values from a fixed raster cell size.

There are several different ways (patterns) to place single printed dots in a raster cell, and the pattern for this dithering is partly a secret of the printer driver. The dithering dot pattern is less visible and more photo-like, when the pattern is not the same for all raster cells having the same tonal values, but is modified from raster cell to raster cell in some random way.