Dots, pixels, inches. Wha...?

Image to print: DPI, ppi, and pixels. How do they fit together?

People frequently ask questions such as “how many mega-pixels does my image have to be in order to be able to print it at 13” x 19” ?” “Do I have to upsize, resize, or re-sample to be able to print at 11” X 17” ?” Anyway, what does it all mean?

Translating the pixels that are recorded on a camera to the dots that are laid down in a print brings together four ideas:

  • camera sensor size and pixel resolution.
  • print dot density and human visual acuity
  • print head construction and ‘native’ printer resolution
  • how to match image pixels with print dots

Camera sensor size and pixels

A camera sensor is made up of a rectangular array of pixels. Each pixel collects the colour and tone of the light coming from a point in the scene being photographed.

The sensor on a 12 MP digital camera like the Nikon P7800 is made up of 4000 X 3000 pixels. Such a camera divides the scene into 12 000 000 points and collects and records the light from each point.

The Canon EOS 5D camera's sensor is made up of 4368 X 2912 pixels. The 5D divides the scene into 12 719 616 points and collects and records the light from each point.

The monster Nikon D800 divides a scene into 7360 X 4912 pixels, a whopping 36 152 320 individual pixels.

The total number of pixels on the sensor represents the maximum information that the camera can record. If you are looking toward printing a quality fine art print, you should set your camera to record at the highest resolution, that is to record the maximum number of pixels that it is capable of.

Of course, if you crop your image, it will have fewer pixels.

Print dot density and human visual acuity

If you look very closely at a photograph in a newspaper, you will see that the photograph is made up of a large number of individual dots or varying colour and/or tone.

In many print media, including ink-jet printers, print images are made up by laying down adjoining coloured dots that together make up a pattern of colours and tones which, in turn, viewed from a sufficiently large distance, make up a picture.

How small the dots need to be depends on the distance that the picture is to be viewed from and the degree of quality (lack of ‘grain’) that is expected.

If one looks at a very large picture on a billboard from a distance of 20m or so, individual dots could be nearly as big as ¼’’ (~8mm) across. From 20m we would see the picture as made up of continuous colours and tones because at that distance our unaided eyes would not be able to resolve the individual dots.

According to Wikipedia, the limit of resolution for a person with 20/20 vision is about 1 'arcminute', or 1/60 of a degree. (In other words, a 20/20-sighted person could not tell whether two objects are really two or just one, if they are less than 1/60˚ apart.) If the individual dots in the billboard picture are less than 1/60˚ apart we will see continuous tone and colour. There's a good discussion of the resolving power of the human eye here.

eyeandvisualacuityOf course, if we were able to get up close to the billboard individual pairs of dots would make bigger angles and become very apparent.

In high quality photographic reproduction, such as in a glossy magazine, we try to make the dots so small and so close together that they are imperceptible to the naked eye from normal reading distance of about 35 cm (~ 13.7”).

Using a little bit of high-school trigonometry we can work out that, when viewed from 35 cm, dots that are less than 1/250” appear not to be separated. Dots about that size, packed closely together, make up continuous colour. (Incidentally, these figures are almost always quoted in the feet and inches system, even in countries that have always used the more rational metric measuring system.)

In print terminology then, any print made at a dot pitch of 250 dots per inch or greater will be a high quality print whose individual dot structure will be imperceptible to a normal-sighted person viewing the print unaided at a normal viewing distance.

 

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