This will be a short series about how to make a lightweight AR projector with an optics solution that lets in the real world. A few curves are thrown in for a twisted scheme which no-one seems to be using.
This first post will introduce an optical ideal solution we probably can’t build yet, though it does not seem physically impossible. It just requires a lot of new techniques to build a curved-suface source. It is useful here to describe what we can’t build because its properties are easily calculated and then it gives us a starting point to twist in a direction we probably can manufacture.
An ideal view
If we could make a transparent spherical projector in front of the eye and concentric with the eye, with all the light going outwards, then it would be the basis for an almost perfect wide-angle viewer. It is ideal because the optics are the same every direction that the eyeballs can swivel.
We will talk about whether this is feasible below, but first the system will be explained.
The ideal projector would be a transparent spherical dome on which outward-facing light emitters are scattered. Dense enough for high resolution, small enough to see through the space between them.
The light shines outwards towards a partial reflector which has twice the radius of the projector. The reflector creates an external image at infinity (or a closer finite distance, by reducing the reflector radius slightly below twice the projector).
The outside world would be visible directly since both the outer reflector and the projector dome will be partially transparent, much like sunglasses. An A/V solution will still need sensors for eye-tracking and for spatial orientation and tracking, but the need for external pass-through or for imitating your eyes for other people can be eliminated.
The optics are the same no matter which direction the eyeball swivels, so the field of view can be as wide as needed, in this ideal form.
Image quality
One determinant of image quality comes from the distortion of an image at the center of view. The rays reflected from the outer shell form an almost parallel beam from any one projector pixel,
with a roughly 4mm diameter bundle passing through the pupil under medium lighting (50 lumens). Pupils can go wider but the lens is imperfect and loses resolution, so calculating resolution at 4mm is realistic.
ɸ = asin(2mm/(R/2))
Θ = asin(2mm / R)
ɸ*= 2 Θ
Angular error = ɸ - ɸ*
We can make a simple calculation of line pairs per degree by using the angular error at the 2mm radius (4mm diameter) edge of the beam compared to its center.
which turns out to be quite high resolution for modest lens distances. A human eye is typically 24 mm in diameter so a 50mm radius is about 38 mm from the front of the eye, which for most people is about the distance from their eye to the tip of their nose. At that radius 100 lines, each line using 2 pixels (line, space), would be 12,000 pixels for a 60 degree wide view. That resolution is beyond what we can see or build.
Side Eye
We also have peripheral vision and it is important for the image not to disappear when it is not in the center of view.
The geometry will compress the periphery. If you swivel your eye for a direct look at something it will be further around than when it came from a peripheral angle.
The geometry here does reduce the peripheral vision angle. The projector needs to be wider than the staring FOV in order to fill in peripheral vision. This angle compression affects all kinds of optics which offer wide field of view in a short optical path, so headset processors track the eye and make periphery adjustments to keep things less distorted.
The staring or direct FOV depends on the eye’s ability to swivel. Horizontally it turns +- 35°, vertically +25 -30. The pixel resolution outside the swivel ranges can be reduced because there will be no foveal vision.
The Projector
The half-radius geometry is old but needs some modern magic to make this projector.
Consider making a design with a 60mm R and a pixel pitch of 100/degree, or 1/6,000 radian. This is roughly the pixel count of an 8k projector if we aim for an oval high resolution center, 70° wide by 55° tall plus lower resolution periphery. That is a lot of pixels to drive - and they need to be attached to the spherical projector dome facing outwards in a way which does not send any glare back into the eye.
The projector has a radius of 30mm so we would have 30mm/6000, or about 5 microns distance between pixels. If each pixel source could be 2 micron with a future nano-LED, that might leave clear space around them so the outside world is visible.
That space around each pixel source is also needed for the reflected light to pass backwards to the eye.
Such small pixels on a domed surface are possible in principle, but not nearly feasible today.
The Reflector
The reflector needs to be lightweight, hold an accurate shape, allow outside light through, and to selectively reflect the projector light almost completely to minimize outside visibility in social interactions.
A polycarbonate spherical shape seems most likely to meet the structural and transparency needs. Selective reflection of the projected light could be done with polarization, or with dichroics.
If the nanoLEDs or other projector elements are naturally polarized then a polarized reflector would be a good choice. A polarized pass-thru from the real world is accepted in sunglasses, and a 99% selectivity for reflection is possible. Source polarization should be > 95% to minimize other people seeing the projector.
Dichroic mirrors on the reflector would allow a three color bandpass matching the projector. These will slightly alter the color of the real-world pass-through, but remain quite transparent otherwise. The projector would need to have sharp, stable spectrum. Blocking ratio > 90% will be unlikely.
Both techniques can be combined to minimize external visibility. Perhaps in partial combination, for example we might have full spectrum reflection for polarized light but add dichroic reflection just for blue if its source is not polarized.
Power and Weight
The surface area of an eye is about 1cm2. When the sun is shining on your eye that is about 100mW of power. Matching sunlight would be a dangerous goal for the projector. There seems no reason that the total light projected on the eye should exceed 10mW and no pixel should need to project more than a nW – yes, nano.
If the reflector is 90% efficient for either polarized or dichroic method, if adding peripheral light doubles the illuminated area, if the projector passes 50% of light from the reflector back to the eye, and if the nanoLED is 10% efficient, we need about 500mW electrical peak to run one projector (per eye). When indoors the power needed is probably a tenth of that.
The weight should be quite low compared to other goggles. The lens and projector can probably be a couple of mm thick but there will need to be non-optical structural elements to keep distances accurate, and places to mount the electronics and sensors. It might have an open frame like a large set of sunglasses though the space between the projector and reflector is likely closed to minimize contamination. The reflector and projector assembly might be replaceable at a fraction of the cost of the whole headset with sensors and electronics. That form of assembly would also simplify producing headsets for different faces and eye separations, allowing some level of mix and match of subunits to customize per user.
Putting it all together
A video may help visualize this in front of the eyes. There are clearly some problems of overlap in the nose region where the projectors will be truncated to allow space for the nose and the outer reflectors will have a compromise join limiting the field of view from each eye over the nose.
If we ever really can build this projector then there will need to be some experiments to figure out the most pleasing compromises at the join in the middle over the nose. Our brain is pretty good at eliminating the nose blockage to vision without us being aware of it - take a moment to try to see your nose!
The video is to scale for a large device, with a 60mm outer-reflector radius. A 50mm radius (the size used in calculations above) will reduce the amount of overlap but might have other drawbacks in accomodating corrective lenses or riding closer on the nose.
Next Week
That concludes our overview of an “ideal” optics, at least in terms of possible resolution, field of view, and good efficiency.
Next week we will look at a twist that keeps some of the attractive optical properties along with low power and weight, but greatly simplifies construction of the projector.