PPI and the problem with Retina displays

I have always had Macs of one form or another. All have the ubiquitous Retina display. In earlier Macs, you could easily change the resolution to whatever was required, but the Retina displays are somewhat bewildering when it comes to their resolution. A 13.3″ display has a resolution of 2560×1600 pixels at 227ppi, but it isn’t actually possible to obtain that sort of resolution using the system control on the Mac, i.e. there is no 1:1 correspondence between image pixel and screen pixel. The best they can do is “Scaled” resolution which provides one of four options:

  • 1024 × 640 = ×2.5
  • 1280 × 800 = ×2
  • 1440 × 900 (default) ×1.77
  • 1680 × 1050 = ×1.52

Why? Because the Retina display uses pixel-scaling, so the display at the setting of 1280 × 800 is scaled at 2 times the actual resolution, giving a “high-resolution” of 2560 × 1600 pixels. So every pixel is doubled to four times the detail. So a 280 × 280 pixel image displayed using the default setting is scaled 1.77 times, which means it displays as 496 pixels, which at 227ppi, means it is 2.1875 odd inches on the screen.

Pixels shown on a standard versus Retina display (at 2× scaling)

How to fix it? Use one of the 3rd party utilities like EasyRes. It installs in the top menu, and you can easily convert between screen settings… although the negative is that at 2560×1600 pixels, things other than images appear *very* small.

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PPI vs. DPI: what is the difference?

Image resolution for devices is commonly expressed in one of two forms: PPI or DPI. Two terms that are both similar and different. Both relate to pixel density in different mediums, and although many use them interchangeably, there are differences between the two. Neither one has any direct relation to the content of an image, because regardless of how it is acquired, images are made of pixels, which are dimensionless. Both relate to how an image is either viewed on screen, or printed.

PPI

PPI stands for pixels-per-inch, and is the pixel density associated with digital devices typically used to view images. PPI only becomes useful when an image is brought into the real world, for example displaying it on a screen. It refers to the number of pixels that a device (e.g. screen) can display within one inch of space. For example the iMac Pro has 5120×2880 pixels in its display, and its pixel density is 218ppi. The 6.1″ iPhone 12 has a 2532×1170 display with 460ppi. The higher the value for PPI, the greater the pixel density, and the smaller the size of the pixels. Images shown on devices with higher dpi often appear sharper than those displayed on low resolution devices. However this is also dependent on your distance to the device, and the how good your eyes are. The examples in Fig.1 show examples of various pixel densities.

Fig.1: Various pixel densities

To illustrate how PPI of a device affects the display of an image, consider the example shown in Fig.2. A 280×280 image has been shown simulated on four devices with differing values of PPI: 210, 280, 140, and 70. Higher pixel densities makes the image look sharper – for example at 280ppi, the entire image fits into the 1″×1″ region on the screen. At 70ppi it takes 4″×4″=16in2 to display the same image, which means a much lower resolution where parts of the image may start to look “blocky” and edges appear jagged.

Fig.2: An example of a 280×280 image shown on devices with differing PPI.

Different sized devices, can have the same resolution, but differing pixel densities. For example consider a series of televisions with 55″, 60″, and 65″ displays. The display resolution for each of these TV’s is the same, at 3840×2160 pixels. The 55″ TV will have 80ppi, the 60″ 73ppi, and the 65″ 68ppi. All have differing PPI because although the number of pixels is the same, the size of the pixels on each device is slightly different. To determine the size of an image on a particular screen, take the dimensions of the image and divide those values by the resolution of the screen. For example, an image that is 3000×2000 pixels in size shown on a device that has a resolution of 218ppi will display as 3000/218=13.76″ wide, and 2000/218=9.17″ high.

DPI

DPI implies dots-per-inch, and refers to the resolution value of a physical printing (or scanning) device. Printers reproduce an image by spraying out tiny dots, and the number of dots per inch affects the amount of detail and overall quality of a print. Figure 3 shows the 280×280 image printed out on three devices, one with 280dpi, one with 560dpi, and a third with 140dpi. The lower DPI results in a larger, if somewhat coarser, image. In all cases, the ratio of dot to pixel is 1:1, it’s just the size of the dots that changes. In the first case, 280dpi means that each dot is 1/280″ in size, and the image is printed in an area of 1″×1″. In the second case, the size of each dot is 1/560″, so the image printed in a space of ½”×½”. In the final case, the size of each dot is 1/140″, so the image printed in an area of 2″×2″.

Fig.3: The effect of DPI on printing.

The trick with DPI is how many dots can be packed into an inch? An inkjet printer can produce a resolution of between 720-2880dpi, whereas a laser printer produced images between 600-2400dpi. Theoretically the more dots, the crisper the image, but 300 DPI is already packing 90,000 dots on colour in a square inch, so how much better 1200dpi is, is likely debatable.

Sometimes, the metadata for an image will include the DPI, e.g. DPI=72. This makes no difference to the how an image is viewed on a screen, nor does it impact the size of the image file. Three different copies of the same file can have DPI values of 72, 150, and 300. All three will have the same number of pixels, and the same file size. Only when they are printed out will they appear as different sizes.

DPI and scanning

DPI also relates to scanning. The larger the DPI set on a scan, the more detail the image will contain, however there are limits with respect to the quality of the scanner, and the quality of the image. For example, a 5″×7″ photographed scanned at 150dpi will result in an image of size 750×1050 pixels in size, whereas if it were scanned at 300dpi, the resulting image would be 1500×2100 pixels.

What about LPI?

There is of course a third measure, LPI, or lines-per-inch, which is used in offset printing. This is used to measure resolution in images that are converted into a pattern of dots – halftones. Standard newspapers are printed at 85lpi, and offset-presses are 130-150lpi.

The 72dpi Myth

There is still a lot of talk about the magical 72dpi. This harkens back to the time decades ago when computer screens commonly had 72ppi (the Macintosh 128K had a 512×342 pixel display), as opposed to the denser screens we have now. This had to do with Apple’s attempt to match the size of the text on the screen to the size when it is printed, known as WYSIWYG (What-You-See-Is-What-You-Get). Apple basically matching the 128K to their dot matrix printer, the “ImageWriter”.

Dots and printers

There are different types of printers where dots are perceived a little differently. For example a colour inkjet printer can only create droplets of a few different colours for each dot, so small dots are combined to simulate continuous colour. Modern inkjet printers have high resolutions like 2400×1200, or 2880×1440. A dye-sublimation colour printer on the other hand produce continuous tone colour, meaning that every “dot” in an image can be an arbitrary colour (although there aren’t really any dots). Dye-sub printers normally have a resolution of between 300-500dpi. Many inkjet printers have resolutions like 2880×1440dpi, however this usually describes how many droplets of ink are placed in the 1in2 area, considering many are overlaid to create various colours.

How big are pixels?

A pixel is an abstract, size-less thing. A pixels size is relative to the resolution of the physical device on which it is being viewed. The photosites on a camera sensor do have a set dimension, but once an image is acquired, and the signal are digitized, image pixels are size-less.

For example, let’s consider TVs, and in particular 4K Ultra HD TVs. A 43″ version of this TV might have a resolution of 3840×2160 pixels (w×h). The 75″ version of this TV has *exactly* the same number of pixels – about 8 million of them. What changes is the pixel size, but then so does the distance you should view the TV from. The iPhone 11 in comparison has a screen size of 1792×828. For example, the 43″ 4K TV has dimensions of roughly 37″×20.8″, which means that the size of a pixel is 0.24mm. A 75″ 4K TV would have a pixel size of 0.41mm. An Apple Macbook Air with a 13.3″ screen (2560×1600 pixels) has a pixel size of 0.11mm.

As an example consider the image below. Two sizes of pixels are shown, to represent different resolutions on two different physical devices. The content of the pixel doesn’t change, it just adapts to fill the physical pixels on the device.

Pixel sizes on different screens

Likely more important than the size of pixels is how many of them there are, so a better measure is PPI, or pixels-per-inch. The iPhone 11 has 326ppi, a typical 43″ TV has 102ppi, and the 75″ TV has 59ppi.