I’m planning on following up on my earlier articles about AR/VR Head Mounted Displays
(HMD) that also relate to Heads Up Displays (HUD) with some more articles, but first I would like to get some basic technical concepts out of the way.  It turns out that the metrics we care about for projectors while related don’t work for measuring HMD’s and HUDs.

I’m going to try and give some “working man’s” definitions rather than precise technical definitions.  I be giving a few some real world examples and calculations to show you some of the challenges.

Pixels versus Angular Resolution

Pixels are pretty well understood, at least with today’s displays that have physical pixels like LCDs, OLEDs, DLP, and LCOS.  Scanning displays like CRTs and laser beam scanning, generally have additional resolution losses due to imperfections in the scanning process and as my other articles have pointed out they have much lower resolution than the physical pixel devices.

When we get to HUDs and HMDs, we really want to consider the angular resolution, typically measured in “arc-minutes” which are 1/60th of a degree; simply put this is the angular size that a pixel covers from the viewing position. Consumers in general haven’t understood arc-minutes, and so many companies have in the past talked in terms of a certain size and resolution display viewed from a given distance; for example a 60-inch diagonal 1080P viewed at 6 feet, but since the size of the display, resolution and viewing distance are all variables its is hard to compare displays or what this even means with a near eye device.

A common “standard” for good resolution is 300 pixels per inch viewed at 12-inches (considered reading distance) which translates to about one-arc-minute per pixel.  People with very good vision can actually distinguish about twice this resolution or down to about 1/2 an arc-minute in their central vision, but for most purposes one-arc-minute is a reasonable goal.

One thing nice about the one-arc-minute per pixel goal is that the math is very simple.  Simply multiply the degrees in the FOV horizontally (or vertically) by 60 and you have the number of pixels required to meet the goal.  If you stray much below the goal, then you are into 1970’s era “chunky pixels”.

Field of View (FOV) and Resolution – Why 9,000 by 8100 pixels per eye are needed for a 150 degree horizontal FOV. 

As you probably know, the human eye’s retina has variable resolution.  The human eyes has roughly elliptical FOV of about 150 to 170 degrees horizontally by 135 to 150 degrees vertically, but the generally good discriminating FOV is only about 40 degree (+/-20 degrees) wide, with reasonably sharp vision, the macular, being about 17-20 degrees and the fovea with the very best resolution covers only about 3 degrees of the eye’s visual field.   The eye/brain processing is very complex, however, and the eye moves to aim the higher resolving part of the retina at a subject of interest; one would want the something on the order of the one-arc-minute goal in the central part of the display (and since having a variable resolution display would be a very complex matter, it end up being the goal for the whole display).

And going back to our 60″, 1080p display viewed from 6 feet, the pixel size in this example is ~1.16 arc-minutes and the horizontal field of view of view will be about 37 degrees or just about covering the generally good resolution part of the eye’s retina.

Now lets consider the latest Oculus Rift VR display.  It spec’s 1200 x 1080 pixels with about a 94 horz. by 93 vertical FOV per eye or a very chunky ~4.7 arc-minutes per pixel; in terms of angular resolution is roughly like looking at a iPhone 6 or 7 from 5 feet away (or conversely like your iPhone pixels are 5X as big).   To get to the 1 arc-minute per pixel goal of say viewing today’s iPhones at reading distance (say you want to virtually simulate your iPhone), they would need a 5,640 by 5,580 display or a single OLED display with about 12,000 by 7,000 pixels (allowing for a gap between the eyes the optics)!!!  If they wanted to cover the 150 by 135 FOV, we are then talking 9,000 by 8,100 per eye or about a 20,000 by 9000 flat panel requirement.

Not as apparent but equally important is that the optical quality to support these types of resolutions would be if possible exceeding expensive.   You need extremely high precision optics to bring the image in focus from such short range.   You can forget about the lower cost and weight Fresnel optics (and issues with “God rays”) used in Oculus Rift.

We are into what I call “silly number territory” that will not be affordable for well beyond 10 years.  There are even questions if any know technology could achieve these resolutions in a size that could fit on a person’s head as there are a number of physical limits to the pixel size.

People in gaming are apparently living with this appallingly low (1970’s era TV game) angular resolution for games and videos (although the God rays can be very annoying based on the content), but clearly it not a replacement for a good high resolution display.

Now lets consider Microsoft’s Hololens, it most criticized issue is is smaller (relative to the VR headsets such as Oculus) FOV of about 30 by 17.5 degrees.  It has a 1268 by 720 pixel display per eye which translates into about 1.41 arc-minutes per pixel which while not horrible is short of the goal above.   If they had used 1920×1080 (full HD) microdisplay devices which are becoming available,  then they would have been very near the 1 arc-minute goal at this FOV.

Let’s understand here that it is not as simple as changing out the display, they will also have to upgrade the “light guide” that the use as an combiner to support the higher resolution.   Still this is all reasonably possible within the next few years.   Microsoft might even choose to grow the FOV to around 40 degrees horizontally rather and keep the lower angular resolution a 1080p display.  Most people will not seriously notice the 1.4X angular resolution different (but they will by about 2x).

Commentary on FOV

I know people want everything, but I really don’t understand the criticism of the FOV of Hololens.  What we can see here is a bit of “choose your poison.”  With existing affordable (or even not so affordable) technology you can’t support a wide field of view while simultaneously good angular resolution, it is simply not realistice.   One can imaging optics that would let you zoom between a wide FOV with lower angular resolution and a smaller FOV with higher angular resolution.  The control of this zooming function could perhaps be controlled by the content or feedback from the user’s eyes and/or brain activity.

Lumens versus Candelas/Meter² (cd/m² or nits)

With an HMD or HUD, what we care about is the light that reaches the eye.   In a typical front projector system, only an extremely small percentage of the light that goes out of the projector, reflects off the screen and makes it back to any person’s eye, the vast majority of the light goes to illuminating the room.   With a HMD or HUD all we care about is the light that makes it into the eye.

Projector lumens or luminous flux, simply put, are a measure of the total light output and for a projector is usually measure when outputting a solid white image.   To get the light that makes it to the eye we have to account for the light hits a screen, and then absorbed, scattered, and reflects back at an angle that will get back to the eye.  Only an exceeding small percentage (a small fraction of 1%) of the projected light will make it into the eye in a typical front projector setup.

With HMDs and HUDs we talk about brightness in terms candelas-per-Meter-Squared (cd/m²), also referred to as “nits” (while considered an obsolete term, it is still often used because it is easier to write and say).  Cd/m² (or luminance) is measure of brightness in a given direction which tells us how bright the light appears to the eye looking in a particular direction.   For a good quick explanation of lumens, cd/m² I would recommend a Compuphase article.

Hololens appears to be “luminosity challenged” (lacking in  cd/m²) and have resorted to putting sunglasses on outer shield even for indoor use.  The light blocking shield is clearly a crutch to make up for a lack of brightness in the display.   Even with the shield, it can’t compete with bright light outdoors which is 10 to 50 times brighter than a well lit indoor room.

This of course is not an issue for the VR headsets typified by Oculus Rift.  They totally block the outside light, but it is a serious issue for AR type headsets, people don’t normally wear sunglasses indoors.

Now lets consider a HUD display.  A common automotive spec for a HUD in sunlight is to have 15,000 cd/m² whereas a typical smartphone is between 500 and 600 cd/m² our about 1/30th the luminosity of what is needed.  When you are driving a car down the road, you may be driving in the direction of the sun so you need a very bright display in order to see it.

The way HUDs work, you have a “combiner” (which may be the car’s windshield) that combines the image being generated with the light from the real world.  A combiner typical only reflects about 20% to 30% of the light which means that the display before the combiner needs to have on the order of 30,000 to 50,000 cd/m² to support the 15,000 cd/m² as seen in the combiner.  When you consider that you smartphone or computer monitor only has about 400 to 600 cd/m² , it gives you some idea of the optical tricks that must be played to get a display image that is bright enough.

You will see many “smartphone HUDs” that simply have a holder for a smarphone and combiner (semi-mirror) such as the one pictured at right on Amazon or on crowdfunding sites, but rest assured they will NOT work in bright sunlight and only marginal in typical daylight conditions. Even with combiners that block more than 50% of the daylight (not really much of a see-through display at this point) they don’t work in daylight.   There is a reason why companies are making purpose built HUDs.

The cd/m² also is a big issue for outdoor head mount display use. Depending on the application, they may need 10,000 cd/m² or more and this can become very challenging with some types of displays and keeping within the power and cooling budgets.

At the other extreme at night or dark indoors you might want the display to have less than 100 cd/m² to avoid blinding the user to their surrounding.  Note the SMPTE spec for movie theaters is only about 50 cd/m² so even at 100 cd/m² you would be about 2X the brightness of a movie theater.  If the device much go from bright sunlight to night use, you could be talking over a 1,500 to 1 dynamic range which turns out to be a non-trivial challenge to do well with today’s LEDs or Lasers.

Eye-Box and Exit Pupil

Since AR HMDs and HUDs generate images for a user’s eye in a particular place, yet need to compete with the ambient light, the optical system is designed to concentrate light in the direction of the eye.  As a consequence, the image will only be visible in a given solid angle “eye-box” (with HUDs) or “pupil” (with near eye displays).   There is also a trade-off in making the eyebox or pupil bigger and the ease of use, as the bigger the eye-box or pupil, the easier it will be the use.

With HUD systems there can be a pretty simple trade-off in eye-box size and cd/m² and the lumens that must be generated.   Using some optical tricks can help keep from needing an extremely bright and power hungry light source.   Conceptually a HUD is in some ways like a head mounted display but with very long eye relief. With such large eye relieve and the ability of the person to move their whole head, the eyebox for a HUD has significantly larger than the exit pupil of near eye optics.  Because the eyebox is so much larger a HUD is going to need much more light to work with.

For near eye optical design, getting a large exit pupil is a more complex issue as it comes with trade-offs in cost, brightness, optical complexity, size, weight, and eye-relief (how far the optics are from the viewer’s eye).

Too small a pupil and/or with more eye-relief, and a near eye device is difficult to use as any small movement of the device causes you to to not be able to see the whole image.  Most people’s first encounter with an exit pupil is with binoculars or a telescope and how the image cuts offs unless the optics are centered well on the user’s eye.

Conclusions

While I can see that people are excited about the possibilities of AR and VR technologies, I still have a hard time seeing how the numbers add up so to speak for having what I would consider to be a mass market product.  I see people being critical of Hololens’ lower FOV without being realistic about how they could go higher without drastically sacrificing angular resolution.

Clearly there can be product niches where the device could serve, but I think people have unrealistic expectations for how fast the field of view can grow for product like Hololens.   For “real work” I think the lower field of view and high angular resolution approach (as with Hololens) makes more sense for more applications.   Maybe game players in the VR space are more willing to accept 1970’s type angular resolution, but I wonder for how long.

I don’t see any technology that will be practical in high volume (or even very expensive at low volume) that is going to simultaneously solve the angular resolution and FOV that some people want. AR displays are often brightness challenged, particularly for outdoor use.  Layered on top of these issues are those size, weight, cost, and power consumption which we will have to save these issues for another day.