Eyes on the iPhone 4: Is the iPhone's screen resolution superhuman?

Apple introduced what it called the "Retina Display" when it unveiled the iPhone 4, which is a high resolution screen of 960x640 pixels packed into a 3.5 inch screen. Other phones, such as the Nexus One, have increased pixel count by using what is known as a PenTile configuration of the pixel on the display, where each pixel is either a Red/Green unit or a Blue/Green unit. Apple instead used what we could consider the "normal" definition of a pixel that contains three colors but reduced the size of each pixel to a fourth of what is was on all the previous iPhone models, which is not an easy feat.

While this increase in resolution is certainly welcome, Apple decided to add a little bit of marketing buzz by claiming that the resolution of the display "is so high that the human eye is unable to distinguish individual pixels". The president of DisplayMate, Raymond Soneira, sent out an email soon after the iPhone unveiling to a variety of news outlets saying that our resolving power is directly related to our distance from the object, which is in part due to the fact that our eyes have the ability to slightly alter in shape in order to accommodate different optical scenarios. Additionally, he stated that at the Apple recommended 12 inch distance that the iPhone's pixels would be distinguishable. A slew of bloggers have since commented on this issue, either blaming Apple for false advertisement or praising the screen because it is damn gorgeous anyway.

What I have found interesting is how one measures the resolving power of the eye, which most people have for some reason neglected in talking about our resolving power. The human eye is a complex system that has the ability to adapt to several situations, most notably to the different intensities of light by altering pupil size and to distance by altering shape. There is also the question of how the visual cortex in the back of the brain processes this information, and whether it makes assumptions and calculations on what we are perceiving. We currently have no way of calculating what kind of data processing is done on the light that hits the eye.

This visual computation problem, however, have never been a reason to stop scientists from using a laser to prod an object. A paper published by a researcher named Guirao in January of 1999 describes the most popular method of measuring the performance of the human eye: by shooting a laser into the eye and seeing what happens (see the picture below). This figure is displaying two techniques at the same time. The first is that a low power green laser (5mW at 543nm) is directed at the eye, bounces back out, and the result is captured by a camera. The motion of the eye is also tracked with an IR LED so that the scientists know that the laser is going into the pupil (which has been artificially dilated) and not just bouncing off the iris. I am still curious how they managed to get sixty people to agree to be in their experiment, especially their "group c" was made up of people who are 60-70 years old.

Ow. Apparently there is "minimal discomfort" according to Santamaría 1987.

The image processing of the laser light that comes back from the eye is where most of the magic occurs. The laser light focused onto the eye has known properties such as the diameter of the beam. By the time this light hits the camera, it has been distorted. Scientists then use what is called the modulation transfer function to measure the change, which roughly comes out to how much of the sharp shape of the beam is lost by the time it hits the camera. A significantly detailed paper on the mathematics behind this is described by the Santamaría reference below.

The data that comes relates how sharp the resulting image is in relation to what is called cycles per degree, which is just a measure of resolution that can be though of as similar to a washboard in pattern, where one bump plus one dip make a cycle. The lower the sharpness, the less one can see the difference between one cycle and the next. Then the researchers choose a sharpness value that is too low for the eye to distinguish to calculate the highest resolution we can see. This procedure has been performed on a variety of people and at a variety of pupil sizes, which has most notably found that old people have poor vision (shocker).

So are Apple's claims correct on not being able to see the individual pixels of the iPhone (at 12 inches)? It very much depends on the person. People older than 60 will not be able to see pixels even after they hold the phone right up to their face. Young people between 20 and 30 might be able to distinguish it if they have had great eyesight all their lives and have no other problems such as keratometic astigmatism, amblyopia, any retinal or ocular disease, diabetes or nervous system disorders, or have previously had surgery on their eyeballs. On top of that, these studies still do not take into account motion (I dare you not to move your hand while holding your phone), stereoscopic vision, or how the visual cortex processes such fine grained information. So Apple's claim appears to be valid except for a very, very small number of people who are probably between the ages of ten and fifteen. While I think it would be ridiculous to have an iPhone at this age, you might hear high pitched squeaking as the younger masses complain that their iPhones suck because they can see that Pikachu is actually made up of a bunch of blocks.



References:
Campbell and Green. Optical and retinal factors affecting visual resolution. The Journal of Physiology (1965)

Guirao et al. Average optical performance of the human eye as a function of age in a normal population. Investigative Ophthalmology & Visual Science (1999)

Santamaría et al. Determination of the point-spread function of human eyes using a hybrid optical-digital method. Journal of the Optical Society … (1987)