Why Birdbaths Optics? Because the Alternative (Waveguides) Must Be Worse (and a teaser)

The idea for this article started when I was looking at the ODG R-9 optical design with OLED microdisplays. They combined an OLED microdisplay that is not very bright in terms of nits with a well known “birdbath” optical design that has very poor light throughput. It seems like a horrible combination. I’m fond of saying “when intelligent people chose a horrible design, the alternative must have seemed worse“

I’m going to “beat up” so to speak the birdbath design by showing how some fundamental light throughput numbers multiply out and why the ODG R-9 I measured at CES blocks so much of the real world light. The R-9 also has a serious issue with reflections. This is the same design that a number of publications considered among the “best innovations” of CES; it seems to me that they must have only looked at the display superficially.

Flat waveguides such as used by Hololens, Vuzix. Wave Optics, and Lumus as well as expected from Magic Leap get most of the attention, but I see a much larger number of designs using what is known as a “birdbath” and similar optical designs. Waveguides are no secret these days and the fact that so many designs still use the birdbath optics tells you a lot about the issues with waveguides. Toward the end of this article, I’m going to talk a little about the IMMY design that replaces part of the birdbath design.

As a teaser, this article is to help prepare for an article on an interesting new headset I will be writing about next week.

Birdbath Optics (So Common It Has a Name)

The birdbath combines two main optical components, a spherical mirror/combiner (part-mirror) and a beam splitter. The name  “birdbath” comes from the spherical mirror/combiner looking like a typical birdbath. It is used because it generally is comparatively inexpensive to down right cheap while also being relatively small/compact while having  good overall image quality. The design fundamentally supports a very wide FOV, which are at best difficult to support with waveguides. The big downsides are light throughput and reflections.

A few words about Nits (Cd/m²) and Micro-OLEDs

I don’t have time here to get into a detailed explanation of nits (Cd/m²). Nits is the measure of light at a given angle whereas lumens is the total light output. The simplest analogy is to water hose with a nozzle (apropos here since we are talking about birdbaths). Consider two spray patterns, one with a tight jet of water and one with a wide fan pattern both outputting the exact same total amount of water per minute (lumens in this analogy). The one with the tight patter would have high water pressure (nits in this analogy) over a narrow angle where the fan spray would have lower water pressure (nits) over a wider angle.

Additionally, it would be relatively easy to put something in the way of the tight jet and turn it into a fan spray but there is no way to turn the fan spray into a jet. This applies to light as well, it is much easier to go from high nits over are narrow angle to lower nits over a wide angle (say with a diffuser) but you can’t go the other way easily.

Light from an OLED is like the fan spray only it covers a 180 degree hemisphere. This can be good for a large flat panel were you want a wide viewing angle but is a problem for a near eye display where you want to funnel all the light into the eye because so much of the light will miss pupil of the eye and is wasted. With an LED you have a relative small point of light that can be funneled/collimated into a tight “jet” of light to illuminate an LCOS or DLP microdisplay.

The combination of light output from LEDs and the ability to collimate the light means you can easily get tens of thousands of nits with an LCOS or DLP illuminated microdisplay were OLED microdisplays typically only have 200 to 300 nits. This is major reason why most see-through near eye displays use LCOS and DLP over OLEDs.

Basic Non-Polarizing Birdbath (example, ODG R-9)

The birdbath has two main optical components, a flat beam splitter and a spherical mirror. In the case a see-through designs, the the spherical mirror is a partial mirror so the spherical element acts as a combiner. The figure below is taken from an Osterhaut Design Group (ODG) patent which and shows simple birdbath using an OLED microdisplay such as their ODG R-9. Depending on various design requirements, the curvature of the mirror, and the distances, the lenses 16920 in the figure may not be necessary.

The light from the display device, in the case of the ODG R-9 is a OLED microdisplay, is first reflect away from the eye and perpendicular (on-axis) to the curved beam splitter so that a simple spherical combiner will uniformly magnify and move the apparent focus point of the image (if not “on axis” the image will be distorted and the magnification will vary across the image). The curved combiner (partial mirror) has minimal optical distortion on light passing through.

Light Losses (Multiplication is a Killer)

A big downside to the birdbath design is the loss of light. The image light must make two passes at the beam splitter, a reflective and transmissive, with a reflective (Br) and transmissive (Bt) percentages of light. The light making it through both passes is Lr x Lt.  A 50/50 beam splitter might be about 48% reflective and transmissive (with say a 4% combined loss), and the light throughput (Br x Bt) in this example is only 48% x 48%= ~23%. And “50/50” ratio is the best case; if we assume a nominally 80/20 beam splitter (with still 4% total loss) we get 78% x 18% = ~14% of the light making through the two passes.

Next we have the light loss of the spherical combiner. This is a trade-off of image light being reflected (Cr) versus being transmitted  (Ct) to the real world where Cr + Ct is less than 1 due to losses. Generally you want the Cr to be low so the Ct can be high so you can see out (otherwise it is not much of a see through display).

So lets say the combiner has Cr=11% and the Ct=75% with about 4% loss with the 50/50 beamsplitter. The net light throughput assuming a “50/50” beam splitter and a 75% transmissive combiner is Br x Cr X Bt = ~2.5% !!! These multiplicative losses lose all but a small percentage of the display’s light. And consider that the “real world” net light throughput is Ct x Bt which would be 48% x 75% = 36% which is not great and would be too dark for indoor use.

Now lets say you want the glasses to be at least 80% transmissive so they would be considered usable indoors. You might have the combiner Ct=90% making Cr=6% (with 4% loss) and then Bt=90% making Br=6%. This gives the real world transmissive about 90%x90% = 81%.  But then you go back and realize the display light equation (Br x Cr X Bt) becomes 6%x6%x90% = 0.3%. Yes, only 3/1000ths of the starting image light makes it through. 

Why the ODG R-9 Is Only About 4% to 5% “See-Through”

Ok, now back to the specific case of the ODG R-9. The ODG R-9 has an OLED microdisplay that most like has about 250 nits (200 to 250 nits is commonly available today) and they need to get about 50 nits (roughly) to the eye from the display to have a decent image brightness indoors in a dark room (or one where most of the real world light is blocked). This means they need a total throughput of 50/250=20%. The best you can do with two passes through a beam splitter (see above) is about 23%.  This forces the spherical combiner to be highly reflective with little transmission. You need something that reflects 20/23=~87% of the light and only about 9% transmissive. The real world light then making it through to the eye is then about 9% x 48% (Ct x Bt) or about 4.3%.

There are some other effects such as the amount of total magnification and I don’t know exactly what their OLED display is outputting display and exact nits at the eyepiece, but I believe my numbers are in the ballpark. My camera estimates for the ODG R-9 came in a between 4% and 5%. When you are blocking about 95% of the real world light, are you really much of a “see-through” display?

Note, all this is BEFORE you consider adding say optical shutters or something like Varilux® light blocking. Normally the birdbath design is used with non-see through designs (where you don’t have the see-through losses) or with DLP® or LCOS devices illuminated with much higher nits (can be in the 10’s of thousands) for see through designs so they can afford the high losses of light.

Seeing Double

There are also issues with getting a double image off of each face of plate beam splitter and other reflections. Depending on the quality of each face, a percentage of light is going to reflect or pass through that you don’t want. This light will be slightly displaced based on the thickness of the beamsplitter. And because the light makes two passes, there are two opportunities to cause double images. Any light that is reasonably “in focus” is going to show up as a ghost/double image (for good or evil, your eye has a wide dynamic range and can see even faint ghost images). Below is a picture I took with my iPhone camera of a white and clear menu through the ODG R-9. I counted at least 4 ghost images (see colored arrows).

As a sort of reference, you can see the double image effect of the beamsplitter going in the opposite direction to the image light with my badge and the word “Media” and its ghost (in the red oval).

Alternative Birdbath Using Polarized Light (Google Glass)

Google Glass used a different variation of the birdbath design. They were willing to accept a much smaller field of view and thus could reasonably embedded the optics in glass. It is interesting here to compare and contrast this design with the ODG one above.

First they started with an LCOS microdisplay that was illuminated by LEDs that can be very much brighter and more collimated light resulting in much higher (can be orders of magnitude) starting nits than an OLED microdisplay can output. The LED light is passed through a polarizing beam splitter than will pass about 45% P light to the LCOS device (245). Note a polarizing beam splitter passes one polarization and reflect the other unlike a the partially reflecting beam splitter in the ODG design above. The LCOS panel will rotate the light to be seen to S polarization so that it will reflect about 98% (with say 2% loss) of the S light.

The light then goes to a second polarizing beam splitter that is also acting as the “combiner” that the user sees the real world through. This beam splitter is set up to pass about 90% of the S light and reflect about 98% of the P light (they are usually much better/more-efficient in reflection). You should notice that they have a λ/4 (quarter wave = 45 degree rotation) film between the beam splitter and the spherical mirror which will rotate the light 90 degrees (turning it from S to P) after it passes through it twice. This  λ/4 “trick” is commonly used with polarized light. And since you don’t have to look through the mirror, it can be say 98% reflective with say another 3% loss for the λ/4.

With this design, about 45% (one pass through the beamsplitter) of the real world makes it through, but only light polarized the “right way” makes it through which makes looking at say LCD monitors problematical. By using the quarter wave film the design is pretty efficient AFTER you loose about 55% of the LED light in polarizing it initially. There are also less reflection issues because all the films and optics are embedded in glass so you don’t get these air to glass index mismatches of off two surfaces of a relatively thick plate that cause unwanted reflections/double images.

Google Glass design has a lot of downsides too. There is nothing you can do to get the light throughput of the real world much above 45% and there are always the problems of looking through a polarizer. But the biggest downside is that it cannot be scaled up for larger fields of view and/or more eye relief. As you scale this design up the block of glass becomes large, heavy and expensive as well as being very intrusive/distorting in looking through a big thick piece of glass.

Without getting too sidetracked, Lumus in effect takes the one thick beam splitter, and piece-wise cuts it into multiple smaller beam splitters to make the glass thinner. But this also means you can’t use the spherical mirror of a birdbath design with it and so you require optics before the beam splitting and the light losses of the the piece-wise beam splitting are much larger than a single beamsplitter.

Larger Designs

An alternative design would mix the polarizing beamsplitters of the Google Glass design above with the configuration of ODG design above.  And this has been done many times through the years with LCOS panels that use polarized light (an example can be found in this 2003 paper). The spherical mirror/combiner will be a partial non-polarizing mirror so you can see through it and a quarter waveplate is used between the spherical combiner and the polarizing beam splitter. You are then stuck with about 45% of the real world light times the light throughput of the spherical combiner.

A DLP with a “birdbath” would typically use the non-polarizing beam splitter with a design similar to the ODG R-9 but replacing the OLED microdisplay with a DLP and illumination. As an example, Magic Leap did this with a DLP but adding a variable focus lens to support focus planes.

BTW, by the time you polarized the light from an OLED or DLP microdisplay, there would not be much if any of an efficiency advantage sense to use polarizing beamsplitters. Additionally, the light from the OLED is so diffused (varied in angles) that it would likely not behave well going through the beam splitters.

IMMY – Eliminating the Beamsplitter

The biggest light efficiency killer in the birdbath design is the combined reflective/transmissive passes via the beamsplitter. IMMY effectively replaces the beamsplitter of the birdbath design with two small curved mirrors that he correct for the image being reflected off-axis from the larger curved combiner. I have not yet seen how well this design works in practice but at least the numbers would appear to work better. One can expect only a few percentage points of light being lost off of each of the two small mirrors so that maybe 95% of the light from the OLED display make it to the large combiner. Then you have the the combiner reflection percentage (Cr) multiplying by about 95% rather than the roughly 23% of the birdbath beam splitter.

The real world light also benefits as it only has to go through a single combiner transmissive loss (Ct) and no beamsplitter (Bt) loses. Taking the OGD R-9 example above and assuming we started with a 250 nit OLED and with 50 nits to the eye, we could get there with about an 75% transmissive combiner. The numbers are at least starting to get into the ballpark where improvements in OLED Microdisplays could fit at least for indoor use (outdoor designs without sunshading/shutters need on the order of 3,000 to 4,000 nits).

It should be noted that IMMY says they also have “Variable transmission outer lens with segmented addressability” to support outdoor use and variable occlusion. Once again this is their claim, I have not yet tried it out in practice so I don’t know the issues/limitations. My use of IMMY here is to contrast it with the classical birdbath designs above.

A possible downside to the the IMMY multi-mirror design is bulk/size has seen below. Also noticed the two adjustment wheel for each eye. One is for interpupillary distance to make sure the optics line up center with the pupils which varies from person to person. The other knob is a diopter (focus) adjustment which also suggests you can’t wear these over your normal glasses.

As I have said, I have not seen IMMY’s to see how it works and to see what faults it might have (nothing is perfect) so this is in no way an endorsement for their design. The design is so straight forward and a seemingly obvious solution to the beam splitter loss problem that it makes me wonder why nobody has been using it earlier; usually in these cases, there is a big flaw that is not so obvious.

See-Though AR Is Tough Particularly for OLED

As one person told me at CES, “Making a near eye display see-through generally more than double the cost” to which I would add, “it also has serious adverse affects on the image quality“.

The birdbath design wastes a lot of light as do every other see-through designs. Waveguide designs can be equally or more light wasteful than the birdbath. At least on paper, the IMMY design would appear to waste a less than most others. But to make a device say 90% see through, at best you start by throwing away over 90% of the image light/nits generated, and often more than 95%.

The most common solution to day is to start with LED illuminated LCOS or DLP microdisplay so you have a lot of nits to throw at the problem and just accept the light waste. OLEDs are still orders of magnitude in brightness/nits away from being able to compete with LCOS and DLP with brute force.