DIY 3D Speaker Scanner - the Mathematics and Everything Else

[NTK]

Based on this, its still possible to do with an additional rotation axis for the microphone then.

So essentially 4-degrees of freedom.

1 : Polar rotation axis , 2 Lateral (r) extension, 3 Z vertical extension, 4: microphone angle rotation.

This will allow you to do a spherical plot of measurements while keeping construction very simple.

Can you please provide a sketch? It is difficult for me to visualize. Thanks!

 

[maxxevv]

Can you please provide a sketch? It is difficult for me to visualize. Thanks!

Let me assemble a simplified model. Get back to you shortly.

 

[Dave Zan]

...offset the center of the measurement sphere ...So we can just scan one sphere and not...adjust the mic at all. Of course I want to run a few simulations to see if it will work.

My first intuition is that this won't work well, (or at all?).
Hence I didn't consider it for my proposal.
But fascinated to see if I am mistaken and you can make it work.

...the speaker stand next (offset) to the ϕ rotary table axis...will place some limits on the measurement positions

Yes, I did think about this but concluded it's not a problem.
The stand can pass between two measurement positions and underneath the speaker is not an area that requires detailed resolution.

...our coordinate system does not need to match that of CTA-2034. So what is the "best" location of our coordinate system
...I think the center point of tweeter or midpoint between tweeter and mid...

Nice point that I hadn't considered much.
Aren't your proposals essentially what CTA 2034 recommend anyway?

Best wishes
David

 

[NTK]

I found out that Igus (better known for their cable tracks) also makes robotics rotary axes with center pass-throughs.

... Nice point that I hadn't considered much.
Aren't your proposals essentially what CTA 2034 recommend anyway? ...

My new proposal regarding the coordinate system origin is to address Krunok's post (quoted below) due to the controversy in the Neumann KH80 thread. Some speaker manufacturers have specified their speakers' reference axes quite a bit away from the "default" CTA 2034 locations. For our purposes, we need ours to be as close to the acoustic center as possible.

From your document: "When it is not provided by the loudspeaker manufacturer, we may define the loudspeaker’s reference axis as the line pointing in the forward direction either from the center point of the tweeter or the halfway point between the tweeter and the mid-range driver. "

Adding to the discussion about reference axis in Neumann KH80 thread, isn't the latter in most cases better idea than the former?

 

[maxxevv]

Pardon the delayed reply, had to run some errands.

Here's what I meant.

You have a main rotation Axis Z.

You then have a lateral extension slider.

Its coupled to the vertical axis lifter using a ball/leadscrew.

The microphone at the end of the boom can be rotated for angle.

With the above, you can achieve a spherical reach around a speaker as long as the lengths of the various extension points are specified correctly at build.

Can you please provide a sketch? It is difficult for me to visualize. Thanks!

 

[NTK]

Pardon the delayed reply, had to run some errands.

Here's what I meant.

You have a main rotation Axis Z.

You then have a lateral extension slider.

Its coupled to the vertical axis lifter using a ball/leadscrew.

The microphone at the end of the boom can be rotated for angle.

With the above, you can achieve a spherical reach around a speaker as long as the lengths of the various extension points are specified correctly at build.




View attachment 47505

That looks just like a Klippel NFS So there is no reason it won't work, even though my simulations had different assumptions.

But after all, it will ultimately be the decision of the brave soul(s) who takes the plunge to actually build one on which configuration(s) to build. As I have said in the opening post, I won't be able to do it in my foreseeable future (which currently is months). I don't even have a pair of speakers in my apartment right now (not counting my Yamaha clock radio), let alone measuring gear. I am currently exclusively listening with my 15 years old pair of UE Super.fi 5 Pro and a 10 yo Sansa Clip Zip

 

[maxxevv]

Engineering solutions converge given the same set of functional parameters if distilled to its most elemental form.

The same functionality can be achieved with something more fanciful. Such as a 6 DOF robot arm too.

 

[NTK]

My first intuition is that this won't work well, (or at all?).
Hence I didn't consider it for my proposal.
But fascinated to see if I am mistaken and you can make it work.
...

Ha! It turns out that you are correct. The spherical wave expansion function matrix (i.e. the matrix [ψ]) becomes less than full rank in all cases. Can't do sound field separation

The little issue with double spherical scan, at least how I understand it, is that it requires the two measurements (i.e. at radial distance r1 & radiation distance r2) to have identical angular coordinates (i.e. same θ and ϕ). This, I think, will halve the angular resolution in our measurements, possibly requiring double the measurement numbers.

If time efficiency is not so important, a double layer spherical scan saves us at least one robot axis. So we can get by with 2 rotational axes and 1 manual translational axis (as you described).

The double layer sound field separation method is described in this paper. I haven't run any simulation to verify this method myself yet.
https://www.researchgate.net/public..._separation_method_application_to_a_car_trunk

BTW, the equi-distance points on a sphere grid (which I suggested in part 4) performed better than the equal angular spacing grid (which I used in my original part 2 and 3 reports) on the same test cases.

Cheers!

 

[Dave Zan]

Ha! It turns out that you are correct. The spherical wave expansion function matrix (i.e. the matrix [ψ]) becomes less than full rank in all cases. Can't do sound field separation

My intuition was based on the physics but it makes sense that that's how the maths works out.
It's some consolation that I understood it correctly, to be honest, but sad we can't simplify it.

The little issue with double spherical scan, at least how I understand it, is that it requires the two measurements (i.e. at radial distance r1 & radiation distance r2) to have identical angular coordinates (i.e. same θ and ϕ). This, I think, will...double the measurement numbers.

More unsubstantiated intuition but I think we don't need to double the measurement numbers.
I expect we can do an outer scan at low resolution for the field separation because it only applies at lower frequencies and then do the inner scan at hi res to do both the low frequency field separation and the fine resolution, time windowed component.
Or maybe the other way around, hi res outer scan, lo res inner - my proposal was only based on practical consideration that we check we don't hit the furniture before we leave it unattended.

The double layer sound field separation method is described in this paper. I haven't run any simulation to verify this method myself yet.
https://www.researchgate.net/public..._separation_method_application_to_a_car_trunk

Thanks, a read for this afternoon- 42 C and not far away is on fire so an ideal chance to stay indoors.

BTW, the equi-distance points on a sphere...performed better...

That makes sense, optimisation of the measurement points was an issue I raised in the DIYaudio thread but never received much response.
And I never felt I understood it well myself.

Best wishes
David

I found...robotics rotary axes with center pass...

They look nice, I expected they probably existed, any idea what these cost, approximately?

 

[NTK]

They look nice, I expected they probably existed, any idea what these cost, approximately?

The link I provided in post 64 takes you to the Igus product page, and some of the models have US pricing (don't know if they show if your IP address is not in North America). But anyway, here are 2 snips from the Igus product pages.

[Edit - added after initial post] Yes. You have good point. Sound field separation is needed only at the lower frequencies. I believe we can use a coarse double spherical grid, and combine it with a fine single grid.

 

[Dave Zan]

The link I provided...(don't know if they show if your IP address is not in North America).

Thanks, I followed the link and saw they looked nice but no price showed so I presumed, like you, it was because I'm not in USA.

Sound field separation is needed only at the lower frequencies. I believe we can use a coarse double spherical grid, and combine it...

Seems reasonable to me. I still don't have an intuitive feel for the optimum way to place the measurement points but I suspect it's not very sensitive, within reason.
I expect the least squares fit will take care of most details but I haven't read your Sean Wu reference yet, need to check if I can find a library copy.

Best wishes
David

 

[somebodyelse]

Thanks, I followed the link and saw they looked nice but no price showed so I presumed, like you, it was because I'm not in USA.

Almost all of them show prices here (UK), although most are on 2-6 week delivery. Prices take a massive jump when adding a motor.

 

[NTK]

Almost all of them show prices here (UK), although most are on 2-6 week delivery. Prices take a massive jump when adding a motor.

Thank you very much for checking. The Igus ones are the most reasonably priced hollow rotary actuators I am able to find so far. There are other ones I have found too, but much more costly (examples here and here).

I wouldn't recommend getting motors from Igus as there are more economical options. We'll need the coupling housing and a flexible coupling to attach a standard size stepper motor (NEMA 17 or 23), and we can use whichever stepper drive controller we want.

@Dave Zan
My goal for this week is to test out sound field separation using double spherical measurements. I think it is actually not bad. For the higher frequencies when we don't need sound field separation, if we measure with one single spherical surface (i.e. same r for all points), the spherical Hankel and Bessel functions become independent of r (since r is the same) and will be combined into one constant (for each spherical harmonics order n). Therefore, we don't need to solve for 2 coefficients but only 1, and thus halves the number of measurement points required. We shall see.

I have no experience with actual speaker testing. Do you know at what frequencies time-gated measurements become good enough?

For moving the mic in the r direction, especially if we need only 2 positions, I think the simple school kid DIY method of using two syringes as (manual) hydraulic actuator may be OK?

Cheers!

 

[somebodyelse]

I'm all for keeping the price low, and the Igus price without motors looks surprisingly reasonable. The coupling's 'price on request' so I half expect a nasty surprise. It also looks like a trivial job for a 3d printer. I was wondering about a (partially) 3d printed rotary actuator too. It might make things more widely applicable if the Igus ones are hard to find in some parts of the world. Motors, couplers etc. are widely available cheaply for hobby CNC, 3d printing etc. so I don't see them as a problem.

You can get ~50mm out of the stepper and slides in an old CD/DVD drive if the syringes won't do.

 

[No. 5]

Do you know at what frequencies time-gated measurements become good enough?

I'll throw in my own two cents and say that in my experience, you really start losing fine details pretty quickly below 1kHz with a gate in the low single digits. For reference, most DIY'ers make due with a 6ms gate window or less, some really dedicated ones can do 10-12ms with towering outdoor contraptions and get better resolution down to ~700Hz, but if this project is going to work in a typical living space or garage, I'm guessing a 3ms window would be needed, and then your looking at a 1-2kHz cut off.

 

[NTK]

I'll throw in my own two cents and say that in my experience, you really start losing fine details pretty quickly below 1kHz with a gate in the low single digits. For reference, most DIY'ers make due with a 6ms gate window or less, some really dedicated ones can do 10-12ms with towering outdoor contraptions and get better resolution down to ~700Hz, but if this project is going to work in a typical living space or garage, I'm guessing a 3ms window would be needed, and then your looking at a 1-2kHz cut off.

Thanks very much for the info. That gives me some idea on what the highest order spherical harmonics I'll need, and therefore the number of measurement points for the concentric grid. The second thing is that in order to avoid aliasing, the separation distance of the concentric grid needs to be less than 1/2 the wavelength of the highest frequency. At 1500 Hz, it will be about 114 mm.

Cheers!

 

[somebodyelse]

Isn't the size of our machine going to be the limiting factor for gate window, since parts of the machine will be the first to reflect? 3ms gives us ~3ft path from speaker to nearest part of machine and back to mic. That seems plausible for moderately sized speakers and an uncluttered single garage in this part of the world.

Is there a lower limit on the change in r? And do you know yet what positioning accuracy we need?

 

[Dave Zan]

...since parts of the machine will be the first to reflect?

Yes, this is why my proposed mechanical structure was fairly skeletal and intended to minimise reflections.
Even with time windows and field separation any reduction in reflections can only help, especially early reflections.
Hence the radially mounted mike boom, as shown in post #53.

Is there a lower limit on the change in r?

More is better for low frequency resolution, subject to alias limit.
BRÜEL & KJÆR make a sound intensity measurement system with two spaced microphones and that can provide us with some hints of what's realistic.
Even with B&K's best, very expensive, mics it's not very accurate at low frequencies because the spacers are less than 100 mm.
I have the data somewhere- I will check the details.
One possibility is to sample at more than two radii for practical reasons, even if not theoretically needed.
The increased separation improves the low frequency accuracy and the intermediate samples stop alias problems.

Best wishes
David

 

[NTK]

And do you know yet what positioning accuracy we need?

Klippel says their NFS has a positioning accuracy of 3 mm. Simulation with errors (both in positioning and sound pressure) to assess the robustness of the method is on my to-do list. I'll start on it after the concentric surfaces sound field separation simulations.

 

[No. 5]

Isn't the size of our machine going to be the limiting factor for gate window, since parts of the machine will be the first to reflect? 3ms gives us ~3ft path from speaker to nearest part of machine and back to mic. That seems plausible for moderately sized speakers and an uncluttered single garage in this part of the world.

When it gets to be time to hammer out the details of the hardware design, I can do a 3D CAD layout in SolidWorks to help get every inch (or centimeter) that can be had between the Scanner and the speaker and microphone.

It is my suspicion that Klippel chose a cylindrical scan surface so as to more easily accommodate larger speakers in a typical room environment since most speakers have a taller profile.