That iPhone 4 Display Thing: Sorting Out Retina Display

During the WWDC keynote Steve Jobs introduced the next version of the wildly popular iPhone. The new device, iPhone 4, has new display technology that decreases the size of each display pixel while increasing pixel density to a point where it is hard for the average personal to see individual pixels at a certain distance. The net effect is sharper images. Apple calls this technology Retina Display.

Jobs said, “…there’s a magic number, right around 300 pixels per inch, that when you hold something ten to twelve inches from your eyes, is the limit of the human retina to differentiate the pixels.”

What he wanna say that for?

A brainiac and owner of DisplayMate Technologies (yes, he’s selling something), Dr. Raymond Soneira, PhD, disputed Jobs’ statement, saying that the pixel density needed to be half again denser than what the iPhone 4 sports to be properly called a retina display. In an email to Jason Cross at PCWorld, Dr. Soneira said, “Steve Jobs claimed that the iPhone 4 has a resolution higher than the retina - that’s not right:

1. The resolution of the retina is in angular measure - it’s 50 Cycles Per Degree. A cycle is a line pair, which is two pixels, so the angular resolution of the eye is 0.6 arc minutes per pixel.

2. So if you hold an iPhone at the typical 12 inches from your eyes, that works out to 477 pixels per inch. At 8 inches it’s 716 ppi. You have to hold it out 18 inches before it falls to 318 ppi.

So the iPhone has significantly lower resolution than the retina. It actually needs a resolution significantly higher than the retina in order to deliver an image that appears perfect to the retina.”

Other folks have weighed in to the controversy offering opinion and math adjusted to suit number commonly used for measuring human visual acuity.

The resulting media crap-storm is, at least at the surface, laughable and strangely akin to Congressman Wilson’s “You Lie!” outburst to President Obama. The problem is that the more I think about this situation, the more the implications give me less reason to laugh and more reason to be concerned.

Who’s right?

I’ll admit I’m not smart enough to dispute Dr. Soneira’s assertion on my own, all I have is the Internet. The doctor’s got numbers to back up his math and I’m just ok with numbers, but what I’m seeing in other, older articles about human visual acuity leaves me scratching my head.

For instance, Dr. Soneria says, “the angular resolution of the eye is 0.6 arc minutes per pixel.” My search says that 0.6 arcminutes is about .01 degrees of arc, however, many other sites claim that human visual acuity ranges between 0.2 to 0.3 degrees, which equals about 1.2 arcminutes if we use 0.2 degrees.

Enter Phil Plait over at Phil worked through the math ( and I checked it …snicker) using 1 arcminute, which is a number agreed to by astronomers and other smart people the world over as being the average person’s ability to discern an object as being more than a dot at a given distance.

According to Mr. Plait (not a doctor nor does he have alphabet soup behind his name), if 1 arcminute is used then Jobs’ claim is correct, with some room to spare (which Jobs also claimed). Here’s an excerpt from Mr. Plait’s blog:
“Jobs claims the iPhone held at 12 inches from your face has pixels too small to be resolved by your eye. Soneira, the display expert quoted in the magazine articles, disputes that. He uses the 0.6 arcmin resolution for the human eye (so we use the scale factor = 5730). Let’s use that and run the numbers.
Something 12 inches away means your eye can resolve dots that are bigger than

12 inches / 5730 = 0.0021 inches

So if the pixels on the iPhone are smaller than 0.0021 inches in size, then Jobs is right. Your eye won’t resolve them. If the pixels are bigger, Soneira is right, and your eye can resolve them.
The actual iPhone 4 has 326 pixels per inch (the display is 960 pixels high, and about 2.9 inches in length). You have to flip that to get the size of the pixel in inches:

1 / 326 = 0.0031 inches

Uh oh! Things look bad for Jobs. The iPhone pixels are too big! At one foot away, your eye can resolve the pixels, and Jobs must be lying!
Or is he? Remember, Soneira used the 0.6 arcmin resolution of the eye, but that’s for perfect eyesight. Most people don’t have perfect eyesight. I sure don’t. A better number for a typical person is more like 1 arcmin resolution, not 0.6. In fact, Wikipedia lists 20/20 vision as being 1 arcmin, so there you go.
If I use 1 arcminute instead, the scale factor is smaller, about 3438. So let’s convert that to inches to see how small a pixel the human eye can resolve at a distance of one foot:

12 inches / 3438 = 0.0035 inches

Aha! This means that to a more average eye, pixels smaller than this are unresolved. Since the iPhone’s pixels are 0.0031 inches on a side, it works! Jobs is actually correct.”

If the math has left you wide-eyed then it basically says that Jobs’ claim is based on commonly accepted numbers for measuring visual acuity, and based on those numbers, Jobs is correct for anyone with average vision. If you’re able to see a lot better than 20/20 then you would see pixels on the iPhone 4 screen.

In another email to Jason Cross Dr. Soneira defends his use of 0.6 arcminutes as a measuring standard. He says, “ There have been some comments that my analysis is for perfect vision. Jobs’ statement is for the *retina* not the *eye* with a poor lens. If you allow poor vision to enter into the specs then any display becomes a retina display.”

It’s not just Wikipedia that lists average human visual resolution at 1 arcminute, as I mentioned earlier, that number can be found all over the Internet (see a few of these references below).

So, is Dr. Soneira right and does that mean Steve Jobs is full of it?

It seems that both are right depending on whether you take the purest point of view (Dr. Soneira) or the realist point of view (Jobs). The funny thing is that all of this could have been avoided if Steve Jobs had said, “…average human eyes…” instead of, “ human retina…” If he had, then any claim of “puffery” could have been avoided or dismissed. As it is, the media seems to have made a mountain out of this mole hill, and the good Dr. Soneira has made a name for himself at the expense of Steve Jobs.

Here’s the thing: what Jobs says on stage directly reflects on him as a person and Apple as a technology entity. If he makes false or exaggerated claims, then it dilutes Apple’s credibility. A lot of fun has been made of Jobs’ “Reality Distortion Field,” but most, if not all claims made while immersed in that field could be validated later once the affects have worn away.

This is different. While the display for the new iPhone will likely kick all manner of butt, to make unsubstantiated claims about it hurts Apple’s reputation as a reliable, dependable, and most of all, truthful company. Apple can’t afford that. No reputable company can. Luckily, Jobs’ display statements are NOT unsubstantiated and are, in fact, based on provable data, but the damage has been done by the tech news community who seems too eager to report any Apple related dirt without first checking the facts.

Now what?

I believe it’s time for another open letter from Steve Jobs to the public addressing the display issue. If Jobs wants people to believe him about Flash, and other controversial issues, then he needs to make it clear that this was not a breach of trust, and not an act of puffery, but a teapot tempest and is hardly worth all the attention.

During the WWDC keynote Steve Jobs showed that he is in touch with the people who use his products. He joked about many of the controversies surrounding the iDevices including Apple’s infamous application approval process. I’m hoping that he continues being open. This display issue is not a big deal in and of itself, but if left to fester it could haunt Apple and Jobs for years to come.

For more information about human visual acuity, check out along with the downloadable PDFs from the University of Arizona College of Optical Sciences and the National Institute of Standards and Technology.