Embedded Transparent Display for AR

Embedded Transparent Display for Augmented Reality (AR)

The goal is to overlay digital content onto visual passthrough of the real world in a wearable form factor, so that both the real world and the digital content are brought into focus.

The human eye can only resolve an object that is farther than 25cm from the eye.

For a Near Eye Display, meaning that the display sits < 25cm from eye, some optical system must diffract light to bring the display into focus.

At the same time, for an optical passthrough system, passthrough light from the surroundings must be unaltered by the optical system. This is referred to as an afocal system, because it does not focus the light at all, or simply a light relay, because it relays light unaltered.

Our solution is to embed a transparent display within an afocal system, so that the light from the display can converge and focus on the eye while the light from the surroundings is left unaltered.

Ideally, this design would be as compact as possible to make it possible to be wearablre

Image Reference: https://88guru.com/library/physics/aberration-of-lens

Compact design requires small focal lengths to bring a near-eye-display into focus when it is so close to the eye. Technical challenges lay in the design trade-offs for an optical system:

power of lens is inverse to focal length
lens aberrations increase with power of lens
lens size limits focal length, because the focal length can never be less than the aperture (without extreme aberration)
We want at least 25cm aperture of lens (for glasses lens)

Therefore, we must make tradeoffs between size of system and aberration, and aberration and lens size.

Starting out, we selected two standard light relay designs to test - Galilean Telescope and 4f system.

Here are two Galilean telescope systems back-to-back. Galilean telescope is an afocal system which results in some magnification. By stacking 2 galilean telescopes we can build a lens stackup with no magnification.

For a galilean telescope design, the display light must be brought into focus by the convergent lenses and 1 divergent lens in front of it.

The effective focal length of the lenses in front of the display is a function of their focal lengths and their distances.

The virtual image projection from the Galilean telescope is a function of this effective focal length and the distance between the display and the first lens. For a near-eye display, the virtual image must be projected farther than the near-point limit of the human eye (25cm)

This will result in magnification of the display.

Because of the complexities of Galilean telescope, we started with the 4f system, which is much simpler - just two lenses placed double the focal length apart from each other.

However, the 4f system results in an inverted view.

An embedded transparent display placed directly in between the lenses in a 4f system would appear to the viewer as if it is projected to infinity, with no magnification.

This is very desirable!

Prototyping a 4f system is very easy, just requiring two lenses placed 2 focal lengths away from each other, and a transparent display placed directly in between.

The advantage of the 4f system is that it quickly and easily overlaps the background and near-eye displays in focus.

First we looked at the lens aberrations over different sizes.

A 50mm DIA 50mm FL has minimal aberration - but the system is 100mm long! Which is quite bulky.

50mm system, with 2x 25mm FL lenses, has significantly more aberration, but is half the length of the first design! This system is only 50mm in length instead of 100mm.

After initial testing with 4f systems, we wanted to test out the Galilean telescope!

Multiple lens stack up works well in simulation, but this did not translate well to testing later on.

Here’s a spreadsheet describing a lens stack-up design using the system of equations defined by geometric optics. We can see the relationships between the lens focal lengths, distances between the lenses and display, the projected virtual image, and ultimately whether the near-eye display can be brought into focus while embedded within an afocal Galilean Telescope design.

This design requires a lot of lenses, and gets large very quickly. As you can see, to bring the near-eye display into focus while keeping f-number > 1, meaning that no individual lens can be too powerful, we must stack up multiple convergent lenses to increase power of the composite system.

We started experimenting with stacking lenses for increasing composite lens power.

Here are the results! We see significant spherical aberration from stacking convergent lenses.

On the left the display is placed closer to the stacked lenses than their EFL, so a virtual image of the display is projected beyond the display, which is what we would need for our design. However, we also see the expected magnification, which makes our display resolution unusable.

The image on the right is just to show the spherical aberration effect on the lens. On the right, the display is placed farther from the stacked lenses than their EFL, so it is not magnified nor is it projected farther away, which is useless for a near-eye display.

Clearly, spherical aberration from stacking convergent lenses is significant.

Next we want to look at the performance of the galilean telescope as a light relay.

The galilean telescope ended up not being a great light relay (because of lens aberrations from stacking 4 lenses and very small field of view).

Also, bringing the near-eye display into focus would have been very difficult because we would have had to stack multiple convergent lenses. Here we see the results of our prototype, which does not stack multiple convergent lenses and therefore cannot bring the display into focus.

We can only bring the display into focus if we significantly adjust the focus of the camera (beyond what our eyes can do). Here the camera is on a near-focus setting. Unfortunately, only part of the display shows up here - we believe because of misaligned frame rates of the camera and the display.

We used a checkerboard pattern to determine the approximate field-of-view angle for each system, and from the results of two equal-length systems in the same environment, the 4f system has a market angle of about 22°, which is twice as large as that of the Galileo system, so it appears that 4f is the best method we can come up with.

Results

For the final prototype, We stuck with two 25mm FL, 50mm total 4f system for a binocular view set-up!