Retina iMacs
In anticipation of the upcoming Apple event, speculation has swirled (to varying degrees) about the possibility of Retina iMacs.
While I personally have no information on what Apple will, or will not, release, I think some very simple math on the concept and definition of a “Retina iMac” is worth exploring.
Retina and Pixel Doubling
First of all, Retina and Pixel Doubling are two distinct concepts. While the iPhone and iPad both received exact pixel-doubled screens, the Retina MacBook Pro did not exactly receive the same treatment.
Yes, the resolution of the MacBook Pro with Retina display (Apple’s terminology is a mouthfull, hereafter rMBP) is 2880 by 1800, or exactly double 1440 by 900. However, the “traditional” (for lack of a better term) MacBook Pro offered a 1680 by 1050 display as well - a choice almost every “professional” or “power user” selected. If pixel doubling were really the Only Way, we would see a shockingly high resolution of 3360 x 2100 available as a CTO option for the rMBP. This is not the case.
In fact, I’m typing this very post on a 13" MacBook Air, which has that same 1440 x 900 resolution. Would a theoretical 13" “MacBook Air with Retina display” offer the same 2880 by 1800 resolution as the 15" rMBP? Likely not.
Sufficient versus Necessary
Pixel doubling is therefore sufficient to achieve Retina resolutions, and is and was convenient for the iPad and iPhone, but it is not necessary.
So what is necessary?
This is where it becomes slightly complex. Apple’s definition of Retina is not completely explicit, but in essence boils down to “When the average person, at the normal viewing distance, can’t see individual distinctions between pixels.”
It doesn’t mean no person can distinguish pixels at the normal viewing distance, and it doesn’t mean an average person can’t distinguish pixels at any arbitrary viewing distance.
This excellent article on Retina mathematics by Richard Gaywood on The Unofficial Apple Weblog goes into the mathematics in-depth, and is definitely recommended reading. As he notes:
The usual figure quoted in the literature for 20/20 vision is that the eye can tell the difference between two lines that are more then one arc minute apart – i.e., 1/60 of a degree.
What this boils down to, simply, is that there is a series of mathematical equations you can compute involving viewing distance, and 20/20 vision, and the necessary resolution to achieve Retina status.
Viewing Distance
Viewing distance is where things get a bit more complex. With a phone or tablet, we can already compute Apple’s “intended” Retina viewing distance by assuming they intend you to view the device at the maximum distance at which the assumptions behind Retina still hold. In other words, the farthest distance from the device at which it is still Retina.
For the iPhone 4 and 4s, with a ~330ppi display at 3.5" diagonal, that viewing distance is around 10.4". For the New iPad, a ~264ppi display at 9.7" diagonal, the Retina distance is roughly 13".
And for the only laptop Apple has thus far released with a Retina display, the ~220ppi display at 15.4" diagonal yields a Retina distance of around 15.6"
I’ve charted below the approximate values for all three of Apple’s current Retina products:
| Product | Screen | Display | Distance |
|---|
| iPhone 4/4s | 3.5" | ~330 ppi | 10.4" |
| The New iPad | 9.7" | ~264 ppi | 13.0" |
| Retina MBP | 15.4" | ~220 ppi | 15.6" |
We can see two trends here:
* As the display gets larger, the Retina viewing distance increases.
* As the display gets larger, the ppi decrease.
In fact, with the rMBP, the Retina viewing distance is already equal to the screen size.
HDTV Viewing Angles
The iMac has never truly been a television, or a television set competitor, but nonetheless it is often used to watch television and film content. From wikipedia THX recommends:
THX recommends that the “best seat-to-screen distance” is one where the view angle approximates 40 degrees….
Their recommendation was originally presented at the 2006 CES show, and was stated as being the theoretical maximum horizontal view angle, based on average human vision…
This equates to multiplying the diagonal measurement with about 1.2.
This can be thought of in a sense as a a minimum viewing distance - if you get any closer, you’re not going to be able to see the whole screen at one time. We noticed previously that while the ppi of Retina displays decreased with size, the viewing distance increased. The 1.2x multiplier factor would suggest the minimum viewing distance for the rMBNP has already been exceeded for the Retina displays, implying that most individuals view the screen from a position farther away than the Retina resolution would imply.
It is worth considering that for the iPhone 4 and 4s, this distance would be 4.2", which seems ludicrously close for viewing iPhone content (though not, perhaps, a motion picture in landscape mode). For the iPad, this corresponds to 11.6", which is still somewhat close than the distance at which most people likely view iPad content. For the iPhone and iPad, however, these 1.2x distances are closer than the Retina distance. For the rMBP, this distance is farther than the Retina distance.
In other words, if you fill your field of view with the content on a rMBP, it will all appear Retina, whereas for the iPhone and iPad, at fill-your-vision distances pixels might still be visible.
This observation squares well with experiences in the field - to me, personally, the rMBP seems “magically sharp,” even more than my iPhone or iPad. Others have likewise commented (I seem to recall Gruber stating this on an episode of the Talk Show) that the rMBP feels the sharpest at their personal normal viewing distances.
Amending the previous chart:
| Product | Screen | 40° Distance | Retina Distance |
|---|
| iPhone 4/4s | 3.5" | 4.2" | 10.4" |
| The New iPad | 9.7" | 11.6" | 13.0" |
| Retina MBP | 15.4" | 18.5" | 15.6" |
The MacBook Pro with Retina display is the first product where the Retina Distance is less than the fill-your-vision 40° distance recommended by THX. Apple went ahead and used, roughly, the size of the screen as a guide for the Retina Distance.
We can therefore use the 40° angle (1.2x diagonal display size) and the size of the screen itself (1.0x diagonal display size) as the bounds for viewing distance on a Retina iMac. Most people’s viewing distances will likely fall somewhere in-between these two ranges. If watching or observing content over the whole screen, perhaps people will move back to 1.2x, and if looking at a portion of the screen they perhaps will move closer, as close as the diagonal screen size, or even further.
Aspect ratio
I will confess to glossing over the various differing aspect ratios above, as well as throughout the rest of this piece. Suffice to say, I am ignoring the effect aspect ratio has on viewing distance, and assuming that any possible iMacs would all feature the same 16x9 or 1.77778 aspect ratio of the current iMac line.
I think this is reasonable, and it simplifies the process of thinking about the question of Retina iMacs.
PPI and Display Manufacturing
Apple, in the modern “Tim Cook era” has been extremely conservative with manufacturing, and likes to execute on tried-and-true processes. They reuse technology, test processes in low volume products (e.g. die-shrunk AppleTV) and don’t like to take unnecessary risks in unproven manufacturing processes.
Many speculate that an upcoming iPad Jr. (credit to Dan Benjamin at 5by5.tv) would have a screen size of around ~7.8 inches, and reuse the extremely mature LCD fabrication in the iPhone 3GS, simply cut into larger sheets.
It’s worth exploring this as a concept for Retina iMacs.
There are two products that stand out as already having very high ppi for use in Retina iMacs.
The first, most obviously, are those iPhone 3GS screens. At 164.8 ppi, they would offer a huge resolution increase over the current 27" iMac’s display density of 108.8 ppi. However, while it might be possible to cut these displays in 7.8" iPad Jr. sizes, it may be less feasible to scale them up to 21.5", 24", or 27".
The second would be another less-explored display from either Apple’s 11" MacBook Air or the iPad ½. These displays have pixels density of ~135.2 ppi and ~132 ppi, respectively. Either of these displays could serve in a Retina iMac, and the choice would likely come down to whichever display was more mature. Apple has shipped far more iPads than they have 11" MacBook Air computers, and the scale-up of either display would likely present a similar challenge; scaling up to 27" from 11" is not likely to be more difficult than scaling up from 9.7".
Thunderbolt and Bandwidth
The rMBP has a display density of ~220.5 ppi, but this is simply not feasible at iMac sizes for the simple reality of video bandwidth. Ignoring the cost issue, a Retina iMac at 27" build with a display density of 220.5 ppi would require a resolution of around 5188 by 2920. That is 15,148,960 pixels, or around 15.1 Megapixels.
This stack exchange discussion indicates that (rephased) thunderbolt allows 20Gbps for a display, which at 32bpp and 60Hz yields around 10 Megapixels.
Internally, however, Thunderbolt currently uses DisplayPort for sending the video signal to monitors. Assuming Apple is using 4 lanes for the forward-link DisplayPort inside Thunderbolt, it can transfer up to 17.28 Gbps for a monitor. (From Wikipedia’s article on DisplayPort)
Wikipedia also suggests 30bpp as the correct display depth, or even 24bpp, since there is no alpha channel necessary for a display and computer display standard is 8bpp x RGB, with “large gamut” displays offering 10bpp per color channel.
We can therefore divide up 17.28 Gbps by 30bpp and 60Hz to get around 9.8 Megapixels, or at 24 bpp this yields 12.3 Megapixels.
All these numbers, regardless of calculation, are significantly below the 15.1 Megapixels a 220 ppi Retina iMac would require.
It seems logical that Apple would want to both stay within the engineering constraints of their current iMac line, and at the same time be able to product a Retina thunderbolt display. Thunderbolt target display mode, external Retina monitors in the iMac form factor, and other engineering constraints would all seem to point to a display below the constraints of current thunderbolt/displayport technology.
Furthermore, it is simply not necessary to use a 220 ppi display to achieve retina resolutions at iMac screen sizes.
It is therefore prudent to assume that whatever display density Apple elects to build for a theoretical Retina iMac, they will stay within this ~10 Megapixel limit of thunderbolt.
Two Possible iMacs
From the previous section on PPI, it seems likely Apple would use a display at either 132 or 164.8 ppi. Personally, it is my inclination that for cost and manufacturing reasons, the iPad 2 screen process would be used, but it could admittedly go either way. What kind of screens would we see with these display densities?
Recall from the previous chart:
| Product | Screen | Display | 40° Distance | Retina Distance |
|---|
| iPhone 4/4s | 3.5" | ~330 ppi | 4.2" | 10.4" |
| The New iPad | 0.7" | ~264 ppi | 11.6" | 13.0" |
| Retina MBP | 15.4" | ~220 ppi | 18.5" | 15.6" |
Now, since the viewing ranges we have (from 1x display size to the 1.2x THX 40° angle) are fixed, we can make some tables and see what combinations of ppi, viewing distance, and monitor size quality for Retina status.
So for iMacs at 132 ppi (iPad 2 display density):
| Display | Viewing Distance | Retina ppi | % of Retina |
|---|
| 27" | 27.0" (1x) | ~127 ppi | 104% |
| 27" | 32.4" (1.2x) | ~106 ppi | 124% |
| 24" | 24.0" (1x) | ~143 ppi | 92% |
| 24" | 28.8" (1.2x) | ~120 ppi | 111% |
| 21.5" | 21.5" (1x) | ~160 ppi | 83% |
| 21.5" | 25.8" (1.2x) | ~132 ppi | 100% |
I’ve bolded the ones which qualify under our definition as Retina, but to summarize, the 27", thanks to its extended viewing distance, qualifies as retina regardless. All other display sizes require the 1.2x 40° viewing distance to qualify as Retina.
Now, if Apple were instead to use the higher 164.8 ppi (iPhone 3GS display density):
| Display | Viewing Distance | Retina ppi | % of Retina |
|---|
| 27" | 27.0" (1x) | ~127 ppi | 129% |
| 27" | 32.4" (1.2x) | ~106 ppi | 155% |
| 24" | 24.0" (1x) | ~143 ppi | 115% |
| 24" | 28.8" (1.2x) | ~120 ppi | 138% |
| 21.5" | 21.5" (1x) | ~160 ppi | 103% |
| 21.5" | 25.8" (1.2x) | ~132 ppi | 124% |
In this case all theoretical iMacs, at all viewing distances, meet and in some cases drastically exceed the required Retina ppi.
So if Apple meets the standard set by the 15" Macbook Pro with Retina Display, which is to say a 1:1 ratio of display size to Retina viewing distance, they would have to use 3GS display densities at somewhere around 164.8 ppi.
If instead Apple moves to something like the THX standard for viewing at 1.2x the display size, they might use 132 ppi screens from the iPad ½ process (or 11" MacBook Air).
Without any other information, the trend does seem to be towards increasing the viewing distances with monitor size. The only question is whether Apple will stabilize at a ratio of 1x or 1.2x for viewing distances for the purpose of their internal definition of Retina. However, we can judge the implications of that decision.
iMac Resolution and Thunderbolt, revisited
Recall that we have assumed thunderbolt at an absolute maximum, can carry just under 10 Megapixels of resolution for a display monitor. What are the implications for the size assumptions made above?
The current 27" iMac features a resolution of 2560 x 1440, which works out to around 3.7 Megapixels. High-Resolution 30" displays (such as the models sold previously by Apple, and currently by Dell and HP) push 2560 x 1600, or around 4.1 Megapixels.
Thunderbolt currently has no issues connecting to either display.
The minimum resolution of a retina-qualifying iMac would be the 132 ppi 21.5" iMac, assuming a 1.2x viewing distance, at roughly 2474 by 1390. This is obviously within reach of current Thunderbolt display capacity.
The maximum resolution of a retina-qualifying iMac would be the 164.8 ppi 27" iMac, which would have a resolution of 3878 by 2182. This is around 8.5 Megapixels and while it would fit in the theoretical display bandwidth of Thunderbolt / DisplayPort I have calculated previously, this does seem like pushing the boundaries of what is possible.
At 132 ppi that same 27" model would have native display dimensions of 3106 by 1748 pixels, or 5.4 Megapixels. This isn’t so much higher than the current resolution required by 30" displays.
Usable Points
Despite my previous explanation of why pixel-doubling of the current iMac resolutions is both impractical and unnecessary, we must briefly return to pixel doubling in the context of the points versus pixels divide.
OS X, in this Retina era, finally supports what used to be called HiDPI mode through 2x assets. In other words, The OS pixel doubles. The vagaries of how this is implemented are somewhat more complex (with non-native resolutions involving higher scale factors) but for the purposes of this discussion we can assume the “native” retina resolution of these monitors to be half the pixel doubled resolution.
For the two possibilities we explored - 132 ppi and 165 ppi - this yields, with some rounding, the following charts of possible native resolutions in horizontal and vertical points.
For 132 ppi (iPad 2 density) at 2x:
| Display | Horizontal Points | Vertical Points |
|---|
| 27" | 1600 | 900 |
| 24" | 1366 | 768 |
| 21.5" | 1280 | 720 |
And for 164.8 ppi (iPhone 3GS density) at 2x:
| Display | Horizontal Points | Vertical Points |
|---|
| 27" | 1920 | 1080 |
| 24" | 1720 | 966 |
| 21.5" | 1600 | 900 |
We can see from this simple chart that if Apple wants to be able to offer a pixel doubled 1080p, they will have to use a higher ppi, such as the 164.8 ppi display of the iPhone 3GS.
This for me is perhaps the clearest indicator that Apple will not, despite my previous inclinations, use the iPad ½ or 11" MacBook Air display process. It would seem silly not to offer a native pixel doubled 1080p at a minimum. While Retina makes things look beautiful, screen real-estate is still important for the 27" iMac purchaser.
In summary, I think Apple can and will release Retina iMacs. Maybe not the near future, but the obstacles aren’t as high as people make them out to be, simply because the resolutions necessary aren’t as extreme as intuition (pixel-doubling existing screens) would suggest. Thunderbolt can probably support them, and Apple can probably fab them.
Whether it’s an iPhone 3GS resolution screen at 164.8 ppi, or more like an iPad or Macbook Air screen at 132 ppi, I don’t know. But I’m leaning towards the higher number.