Chasing the 6.4 Megapixel Unicorn
The folks over at OS X Daily took note that the latest Developer Preview for Mac OS X Lion includes a new wallpaper for Japan’s Mount Fuji. I usually pay no attention to this minutia — I mean, seriously, wallpaper is news? — but before clicking past, I noticed that they wrote that it is “a rather large 3200 × 2000 pixels.”
3200 x 2000 pixels is large. As a matter of fact, it is greater than the native resolution of the Apple 27” LED Cinema Display and even beyond the specifications of the now-discontinued 30” Apple Cinema Display, the largest display Apple has ever shipped.
It seems odd that Apple would intentionally ship an image with those dimensions when no current display is capable of rendering it. Those well-versed in Apple Kremlinology will tell you that this is a signal that new hardware is on its way, something spec’d with a whopping 6.4 million pixels.
But who knows, really, except Steve Jobs and John Gruber? Besides, raw resolution is much less interesting to me than pixel density, the so-called “DPI” or “dots-per-inch.” The iPhone 4’s Retina Display demonstrates the superiority of this metric to me every day. My iPad has 28% more pixels (1024 x 768 versus 960 x 640) for example, but they are distributed across 4 time the area. The resulting difference in sharpness between the two is nothing less than dramatic.
How long until we see a similar “Retina Display” for other devices? Might this mythical new 3200 x 2000 hardware — let’s call it the “Unicorn Cinema Display” — be capable of showing Mount Fuji pixel-for-pixel in all its glory? And would it represent a new Retina Display for Apple, the first outside of the iPhone? The unsatisfying answer, of course, is “it depends.”
Defining a Retina Display
First, it depends on what a “Retina Display” means. Apple’s page on the iPhone’s Retina Display defines it as “pixel density…so high, your eye is unable to distinguish individual pixels.”
Steve Jobs, at the announcement of the iPhone 4, had a similar description:
It turns out there’s a magic number right around 300 pixels per inch, that when you hold something around to 10 to 12 inches away from your eyes, is the limit of the human retina to differentiate the pixels.
But exactly when individual pixels “disappear” is not a simple calculation. Notice that Jobs doesn’t simply mention the DPI of the display, but also the distance from which you view it. This makes sense, if you think about it. A foot away from your eye, an iPhone 4 is pixel-free. Move it 6 inches closer, however, and now your eye is able to resolve some of the “jaggies” that were hidden before.
Let’s start off, then, with a few baseline measurements for existing displays and compare them to the heavily-anticipated “Unicorn”1:
|27” LED Cinema Display||30” Cinema Display||iPhone 4 Retina Display||New “Unicorn” Cinema Display|
|Dots Per Inch||109||101||326||??|
But wait. Why the question marks? Well, obviously, we cannot calculate a DPI for the new “Uni” unless we know its size. And since that kind of information is what Donald Rumsfeld would call “a known unknown,” we are going to need to approach this problem from the other side.
Now, wait a cotton, pickin’ arc-minute
We need two things to answer our Retina Display question. We have to calculate the “Unicorn-dog’s” DPI, and we also need to know the distance at which it will be viewed. Let’s focus on this latter one first.
In his exploration into this topic last year on Discover.com, Phil Plait went into great detail on the biomechanics behind Apple’s iPhone 4 Retina Display claims. It is definitely worth a read, but it comes down to this: if an individual pixel is smaller than the smallest element a person can resolve at a given distance, then that display can be considered a “Retina Display” by Apple’s definition.
But what value should we use for “a given distance”? The United States Department of Labor’s Occupational Safety & Health Administration suggests that the optimal distance to sit from a display is 20 to 40 inches. Forty inches seems quite far to me, and besides, it makes the DPI needed to qualify as a Retina Display much lower. Even 20 inches seems generous, especially for a laptop. There is no one “best” distance, so for the sake of this exercise, I’m going to use three: 18, 20 and 24 inches.
With that information, we can now look at the pixel size demanded of a Retina Display. Plaitt notes that a person with 20/20 vision has a visual acuity of 1 arc-minute, the equivalent to 1/60th of a degree. At 18 inches, that means your eye can resolve pixels larger than 0.00524 inches (5.24 thousandths of an inch). At 20 inches, a pixel needs to be larger than 0.00582 inches to be resolved individually. And at 24 inches, that number grows to 0.00698 inches.2
How big is a unicorn?
We now have everything we need, except the DPI of the “Une.” And since we don’t know its size, let’s consider the various sizes that it might be. In terms of monitors, Apple offers only the 27” LED Cinema Display today, and the “Jimmy-Cracked-Unicorn” could be another, higher-resolution version of that hardware, perhaps even marking the return of a 30” model. But might it also be a component, an LCD panel designed to replace the one inside an existing device? Let’s consider both possibilities.
Apple currently ships products with display sizes that range from 1.5 inches to 27 inches. I doubt we’ll see the Nano sporting 3200 x 2000 pixels anytime soon (ever?), so let’s start at the iPad and its 9.7-inch screen. Working up from there, we have the 11.6-inch one from the MacBook Air, a 13.3-inch component in the larger MacBook Air and the MacBook Pro,3 and so on, up through the 27-inch unit in the LED Cinema Display and largest of the iMacs.
If the displays on each of these devices were replaced with one of equal physical size but with the “Unicorn-on-the-Cob’s” 3200 x 2000 resolution, you would end up with the specifications shown in the table below:
|Pixel Size (in.)||0.00257||0.00292||0.00345||0.00397||0.00450||0.00556||0.00714||0.00794|
The question now is which one of these possible options represents a Retina Display? Using the visual resolution for 20/20-sighted people we calculated above, we simply need to note whether the pixels on the display at a given size and distance from the screen are smaller than the resolving power of the human eye. If so, then Apple could reasonably be expected to market it as a Retina Display:
|Retina Display @ 18″?||Yes||Yes||Yes||Yes||Yes||No||No||No|
|Retina Display @ 20”?||Yes||Yes||Yes||Yes||Yes||Yes||No||No|
|Retina Display @ 24”?||Yes||Yes||Yes||Yes||Yes||Yes||No||No|
Notice that even for the closest viewing distance of 18 inches, a 3200 x 2000 resolution represents a Retina Display for display sizes up to and including 17 inches. And of course, that covers the entire range of Apple laptops on the market today.
For smaller display sizes, a “Full Unicorn” would obviously not be needed to achieve the same Retina Display label. A 13.3” MacBook Air, for example, would need a screen providing approximately 2200 x 1375 pixels (191 dpi) to be considered a Retina Display at an 18-inch viewing distance.
So, what does this tell us, other than the fact that I had a lot of spare time on a Sunday evening? Well, just as I said at the start, “it depends.”
There are a lot of “ifs” in this exercise. If the 6.4 megapixel Mount Fuji wallpaper is not some sort of fluke, and if Apple does indeed have a “Unicorn” in its labs that can display Fuji at its full resolution, and if they ship it in their laptop or iPad line, then Retina Displays might be coming to nearly all Apple products.
Or, it could just be a very large photo of Mount Fuji.