It might be a fun project for those mathematically inclined and it is not difficult to identify the extra information required and how one might go about obtaining it. It would be more involved and likely less accurate but is revolving a large and heavy speaker through 4pi preferable to simply lifting it and moving a microphone around it?
That's easier to accomplish than rotating the microphone(s). Automated rotating tables for loudspeaker measurements have been around for decades. I don't see why this would need to be reinvented.
Also, rotating the speaker in the room will change the sound field. The Weinreich/Klippel method requires a fixed sound field. The speaker therefore needs to remain fixed and the mic(s) need to move to scan the sound field.
If the speaker is rotated on a turntable the mic would need to move in 2 axes rather than 3 to measure vertically and above and below the speaker. If you wish to move the speaker and avoid measuring over 4pi then an effective measurement correction is likely going to involve (partial) simulations of both the speaker and the room rather than just the room. In which case one might as well just simulate the low frequency response and measure the high frequency response.
Instead of going full 180 degrees with the mic, maybe a hybrid approach is possible?
Meaning rotating the speaker as well as the microphone.
That makes the mechanical structure already a lot less awkward.
It's a bit unclear how much points of freedom per axis (in space) are needed for the full moving mic solution?
If one wishes to correct for the influence of the room in a reasonably accurate manner then a full 4pi surface has to be measured and possibly 2 depending on how one goes about it. The number of points will determine the highest frequency that can be corrected. A speaker radiates into the room over a full 4pi which then come back as reflections picked up by the mic so a full 4pi has to be measured unless some large assumptions are made.
If a room is (nearly) symmetrical, I don't see why measuring a full 4pi surface is needed, since both sides are a perfect copy.
Or in other words, if I just measure 2pi and after flip the speaker 180 degrees (either manually or automatically), we have the same data.
The question remains how much error will be involved when the room becomes less symmetrical?
Besides the room reflection, there is also the first floor/ceiling bounce (as well as backwave at DUT and mic).
I think this will also influence that highest frequency, since it's possible to combine gated measured with the rotating mic method.
Just plain gated measurements are already able to measure from about 150-170Hz and above.
This also limits the frequency resolution, so also from that point of view, it's interesting to see how that can be improved with the other method(s).
Maybe a weird idea, but...
Assume a spherical room, and the microphone would be rotated around the center of the sphere. That would be equivalent to rotating the speaker, and leaving the microphone fixed relative to the room.
What about building a large sphere, fix the mic to it, and put the speaker inside on a rotating table?
(Don't ask me how to build a large sphere.)
Assume a spherical room, and the microphone would be rotated around the center of the sphere. That would be equivalent to rotating the speaker, and leaving the microphone fixed relative to the room.
What about building a large sphere, fix the mic to it, and put the speaker inside on a rotating table?
(Don't ask me how to build a large sphere.)
I see there is no lack of ideas 
For the moment I'm sticking to the Klippel way and see where we end up. I'm planning a cute little version. For me the journey is as important as the destination. If we get it working, others can try to scale up everything when needed. And if other ideas work better: great!
For the moment I'm sticking to the Klippel way and see where we end up. I'm planning a cute little version. For me the journey is as important as the destination. If we get it working, others can try to scale up everything when needed. And if other ideas work better: great!
This paper points out that field separation can be accomplished by making pressure mic measurements on two concentric spherical surfaces (the Klippel approach, apart from their non-spherical surfaces), or by making both pressure and velocity measurements on only one surface. The latter approach is intriguing because it halves the number of positions required so it halves the measurement time and eliminates the need for motorized radial mic motion.
I made an MS mic (mid-side mic) using two electret capsules facing opposite directions to get the required dipole pattern for the “side” signal. Perhaps something similar could be done to make a velocity mic without having to rely on a ribbon design? A conventional measurement mic provides the pressure signal, and the audio interface probably has two channels to handle the two signals. Not sure how to fit the loop-back into the system, though.
Few
I started reading that thinking you were going to continue with "...and a completely frictionless microphone in a vacuum."
But I digress.
It is intriguing, and I hear that latter approach (AKA "PU Method") is better than the "PP Method". The downside for us being the only device currently on the market that can directly measure the particle velocity of a sound wave is a Microflown sensor. They even make dedicated PU probes and 3D vector sensors. It's quite cool, but I don't know what they cost and the "contact us for a quote" on their website makes me think we're looking at new B&K levels of money.
You are kind of describing how the PP Method works.
The pressure gradient between two omni's is what allows calculation of the particle velocity. But using a figure 8 (or a ribbon) in place of a Microflown... hmm... I don't know if they would behave the way we need them to... but it's an interesting and potentially worthwhile thought experiment. Or actual experiment!Neither of the rooms I might use to measure are symmetrical and my guess would be that is the case for most people. If a room is accurately symmetrical and the speaker and mic placed accurately to maintain symmetry it could halve the number of measurements points but I would expect this to be pretty rare.
Floor and ceiling reflections are no different to reflections off the walls when it comes to compensating. Or were you referring to something else?
Gated measurements below about 1 kHz or so tend to be overly smooth and hide details one is likely trying to measure. I would have thought this was one of the major reasons for considering compensating for the room?
I just found this audioXpress article on making and analyzing a dipole mic from two omni mic capsules. I would ignore the “analog computer” portion of the 2009 article and just record the two raw signals before processing them with the recording computer.
…and one way to get a spherical room would be to hollow out a physicist’s spherical cow. I guess it might only work for bookshelf speakers, though.
Few
…and one way to get a spherical room would be to hollow out a physicist’s spherical cow. I guess it might only work for bookshelf speakers, though.
Few
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Sorry...here's the info:
JANUARY 01 1933
Frank Massa
JANUARY 01 1933
USE OF PRESSURE GRADIENT MICROPHONES FOR ACOUSTICAL MEASUREMENTS
Irving Wolff;Frank Massa
What insane problems are you expecting below 500Hz that can't be seen on near-field measurements, impedance graphs or burst decay plots in combination with the maybe somewhat smoothed response?
I am mostly thinking where the boundaries are in general?
Or in other words, how much error can be expected?