The deal about retina displays

When Apple announced the iPhone 4 yesterday I was shocked to hear that its display has a pixel density of 326 pixels per inch. That’s an incredible number. Steve Jobs was quick to say that this is more than a human eye can resolve. He called it a retina display. The vocabulary and units used in the discussion about the iPhone’s greatness are somewhat exotic, so let’s see what this is all about.

 

Pixels per inch (ppi) is the unit expressing how densely pixels are placed on a visual display unit. The iPhone 4 has 960 x 640 pixels on a 3.5 in display (aspect ratio: 3 to 2).

So based on the definition of pixel density (pixels / inch = ppi) we can calculate how large one pixel is rendered on the iPhone 4:

960 pixels /(326 ppi * 960 pixels) = 0.00307 inches or 0.07791 mm.

Just for comparison: the size of a pixel on a standard 19-in LCD monitor (aspect ratio: 5 to 4) running 1280x1024 pixels is 0.01159 inches or 0.29441 mm (almost 4 times larger).

OK, that’s what the iPhone 4 is providing. Now let’s look at what we as humans add to the equation. Visual acuity is the measure of the eye's ability to distinguish the smallest identifiable spacial pattern, like two pixels next to each other on a smart phone. Based on the spacing of receptors in our eyes, we can resolve the presence of two distinct pixels down to where they are separated by just one minute of arc (= 1/60 degree). According to the picture below, we can only see two pixels as separate objects, if their distance h is large enough to create a line-of-sight angle Φ of 1/60 degree. With the trigonometric formula below, we can calculate the distance h between the two pixels for a given viewing distance d.

 

Let’s use 1/60 degree for the line-of-sight angle and 12 inches for the viewing distance. The minimum distance h between the two pixels is then:

 12 inches * tan(1/60) = 0.00349 inches or 0.08866 mm.

So for us to be able to perceive two pixels as separate objects on a smart phone, they have to be at least 0.00349 inches apart, but the iPhone 4 can show things as small as 0.00307 inches. That’s what they mean with retina displays. These displays are so packed with pixels that they match (and even exceed) the visual acuity of our eyes. Indeed, 287 ppi had been enough for the iPhone 4. That’s the limit, we cannot resolve higher pixel densities (at least for a 12 inch viewing distance).

I can’t wait to see the display live and in action. Can you imagine having that pixel density on large screens as well? Paradise!