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Digital Printing Explained 2 – PPI vs DPI

Digital images are created by a grid of colored pixels.  The number of pixels in the grids x and y dimensions determine the resolution.  This creates and easy to use system as a 3MP image with a resolution of 2048x1536 will always have 3,145,728 pixels, regardless of the colors used in the image.  The Pixel Per Inch system gives a relation between pixels and print size.  This allows a certainty of print size as a 300ppi images will always represent 300 pixels per inch, so a 1000x1000 pixel image at 250ppi will print at 4” x 4".  Typically each pixel can be any of 16.7 million colors from either the Adobe RGB (1998) or sRGB colorspaces. The 16.7 million colors is based on 8bit RGB images where each pixel can have any color created by 255 shades of each Red, Green and Blue (255 * 255 * 255).

Our Digital Image with pixel resolution.
Most home and office printers on the other hand typically have a much smaller color gamut when compared to the Adobe RGB (1998) or sRGB (we will ignore the RGB to CMYK conversion for now).  This is due to the limited colors that the printer will be loaded with. A six color photo printer will have Cyan, Magenta, Yellow, Light Cyan, Light Magenta and Black inks available, with the paper providing the white, while a 4 color printer will use Cyan, Magenta, Yellow and Black.  Below is a representation of the printer version of our digital image above.
Our Printed Image with Dot Resolution
Obviously, our imaginary print with its 4 color dots a bit more limited than the digital image as it could not exactly duplicate the 19 colors seen in the original image.  The sample image is achieved with a technique known as dithering (or halftoning).  At its' simplest, dithering allows the printer to space out or overlap the CMYK dots at its' disposal to give the illusion of more colors than are actually available.  From our example above, the printer can produce the shades by placing several CMYK printed dots, in this case 36, per digital pixel.  This is where the higher dpi resolution comes in as a printer with a max dpi of 1440dpi is capable of putting 1440 dots or less per inch. I say "or less" because unlike the digital image where every pixel must be represented, the printer is not required to always print 1440 dots at 1440dpi.  In a 250ppi image, this allows a 4 color printer put 0-6 dots per pixel at 1440dpi when printed 1:1 to closely replicate the original pixel.
The above explanation is a bit simplistic as print resolution is based on a combination of ink colors, paper coating, paper white, dot gain, dpi, ink opacity, and dithering algorithms.  The key point is that the printer is producing an "artistic" reproduction of what is seen on the screen based on a set of rules, not an exact duplicate.  For this reason, when purchasing a printer for photographic work it is important to look at the number of color positions that the printer uses, as well as, the type of ink, color accuracy, supported paper types and archival rating of the ink.  Typically, printers that offer a higher DPI allow for not only more dots per inch, but also allow of varied dot size, with a tradeoff in slower print speed as the DPI is increased.  For this reason, a higher DPI (ignoring ink and paper type for now) will typically lead to a higher quality overall print, though due to limitations in human vision 1440/2880 DPI seem to be the realistic limit where print speed vs quality becomes the deciding factor..

The next installment of Digital Printing Explained with cover the Adobe RGB vs sRGB and the RGB to CMYK conversion.

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