To create a High-Fidelity virtual acoustic environment using headphones, it is absolutely necessary to compensate for the headphone response, which varies considerably between different headphone models. To make things trickier, the headphone response varies significantly also between different persons due to the acoustical interaction with an individual’s ears. Thus, individual headphone measurements are needed.
However, headphone measurements on real ears is a tricky business. Ideally one would like to know the sound pressure at the eardrum, which is what matters for what we hear. Alas, putting a microphone at the eardrum can be risky, uncomfortable, and requires special equipment. A common alternative method is to seal the ear canal and measure at the blocked ear canal entrance instead. Under special circumstances, i.e, that the headphones are acoustically “open” and passes the sound reflected back from the head completely through, this measurement provides sufficient information about the sound at the eardrum.
In this post I describe a new measurement method that I’m quite excited about, that potentially solves many of the drawbacks of the aforementioned methods. I think it will be useful both in research on personalized binaural rendering, and research on headphone equalization for stereo music reproduction. The method was presented by me at the 2023 AES International Conference on Spatial and Immersive Audio in Huddersfield, England (link to paper).
During last year, my co-author Sead had started experimenting with building miniature MEMS microphones for measurements in the ear canal. And he demonstrated that with these microphones, it was possible to measure the room response of the speaker system in our lab, and a pair of headphones, then calculate digital filters that would use the headphones to replicate the sound pressure in the ear canals of the speaker system. This is not completely new – and we have been working on headphone-based binaural rendering for a decade – but it was amazing how good it sounded, in many cases we could hear no difference between the headphone reproduction and the speaker system. It convinced me that open ear canal measurements are superior to the blocked-canal method in this application.
There’s one major problem though with the single-mic in the open ear-canal method – robustness. If you accidentally move the microphone in the ear canal even a fraction of a millimeter between measurements of the sound system and the headphones, the illusion can be lost. This is because the ear canal acoustics is surprisingly complex, as we’ll see below. Fortunately, I found that the robustness issue can be solved by using two microphones in the ear canal instead. Below I’ll explain how.
Here’s a close-up picture of our prototype two-microphone MEMS array to the left, and the picture to the right shows the cabling and connectors together with an ear replica that we used for validating that our proposed method works as intended. We use a replica ear because it’s a lot more convenient than a real ear, no risk for harming a living subject and easier to control the measurement process.
Some basic theory about ear canal acoustics is useful for understanding the principle behind the two-microphone array. A simplified model of the ear canal is a tube where sound waves propagate in one dimension. The sound field can be decomposed into an incident wave (p+) and a reflected wave (p–) that has been reflected in the eardrum, with reflectance factor R. The total sound pressure in the tube is then the sum of p+ and p–.
We can measure the total sound pressure in the replica ear by putting a single miniature microphone in the ear canal and playing a sine sweep with a speaker to measure the frequency response.
When performing this measurement at different points along the ear canal and normalizing to the measured response at the eardrum position, we get the following graph (the ear canal of the replica ear is around 28mm long):
What can be seen in the above graph is that there is strong interference in the ear canal between the incident and reflected waves, giving a standing wave pattern. A consequence of this is that the measured frequency response depends very much on the microphone position, giving the robustness problem discussed above.
The idea with the two-microphone array is to measure the response of the incident and reflected waves separately instead. To do this, one can implement a cardioid pickup pattern on the two-mic array using digital filtering. A cardioid polar pattern is illustrated below, it picks up sound only in one direction along the tube:
When measuring the response of the incident wave p+ in the replica ear, in the same locations along the ear canal as in the graph above, the following is the result:
Here we can see that the standing wave notches are absent from the measurements. The measured response also varies much less with the microphone position. The cardioid measurements in the above graph are normalized to the response at the eardrum position, and they are much closer to the actual response at the eardrum than the single microphone measurements shown above.
Finally, here’s an example of a measurement of a pair of Sennheiser HD650 headphones on a real person, comparing a single-mic measurement with a cardioid measurement in the ear canal:
It is clear that the single mic. measurement is affected by standing wave pressure minima in the ear canal whereas such effects are hardly seen with the cardioid measurement (the notch around 10kHz is due to another pinna-related effect).
This is a quite specialized subject, but if you read this far I hope you got a bit inspired. Feel free to send me a message if you have any questions or feedback on this topic. And for more information, check out the related published article, which of course contains a much more detailed treatment with proper referencing.
The work I describe in this post is part of my PhD studies conducted in collaboration with Dirac Research and the Signals & Systems group at Uppsala University, Sweden.
