Let me get this out of the way first. Yes, my goal is to figure out how to build a 3D speaker scanner similar to Klippel's. Of course the first step is to figure out the theories.
In my post back in August, I wrote that I knew next to nothing about the mathematics of acoustics. I also wrote that reverse engineering Klippel's scanner might be too ambitious. In retrospect I think I should have said that acoustics was not my field. Mathematics is my hobby and this problem seems like a good challenge. I'd like to find out the mathematical theories behind Klippel's scanner.
I began to look for published papers on the web. (I am also aware of the thread “Klippel near field scanner on a shoestring” at DIYAudio forum.) Very soon I discovered that the technology developed for this type of applications (by the naval and noise and vibration people) is called nearfield acoustical holography (NAH). A little more reading later I decided to get a copy of Professor Sean Wu's book “The Helmholtz Equation Least Squares Methods” as his method seems most promising.
This is a report of my investigation. I am happy to say that I am revising my assessment from “too ambitious” to “likely doable”. I am including the first 3 parts in this post. They have all the important information and the 4th part is just a supplement. I also include all the Python code I used for my simulations to generate the plots in my report.
Here is a summary of the content:
Part 1: The Fundamentals of the Spherical Wave Functions
Part 2: The Helmholtz equation least squares methods
Part 3: Sound field separation
Part 4: Implementation Guide (hardware discussions started with post 34)
Code: (will come later today or tomorrow) Uploaded
Unfortunately at this moment I am unable to build a prototype robotic scanner to test. I am living in a small apartment. If and when I get to move into a house and has room for DIY projects, I would like to build a small version for testing smaller speakers. But at the meantime, I have to be content with just sharing my report.
Sorry for being longwinded in my report. Comments / critiques / corrections are appreciated. I'll try my best to answer questions. I only started reading up on acoustics a few months ago, and only the stuff that are related to this project. My understanding on this topic is very limited and I will be very surprised if I have not made plenty of noob mistakes.
Thanks.
In my post back in August, I wrote that I knew next to nothing about the mathematics of acoustics. I also wrote that reverse engineering Klippel's scanner might be too ambitious. In retrospect I think I should have said that acoustics was not my field. Mathematics is my hobby and this problem seems like a good challenge. I'd like to find out the mathematical theories behind Klippel's scanner.
I began to look for published papers on the web. (I am also aware of the thread “Klippel near field scanner on a shoestring” at DIYAudio forum.) Very soon I discovered that the technology developed for this type of applications (by the naval and noise and vibration people) is called nearfield acoustical holography (NAH). A little more reading later I decided to get a copy of Professor Sean Wu's book “The Helmholtz Equation Least Squares Methods” as his method seems most promising.
This is a report of my investigation. I am happy to say that I am revising my assessment from “too ambitious” to “likely doable”. I am including the first 3 parts in this post. They have all the important information and the 4th part is just a supplement. I also include all the Python code I used for my simulations to generate the plots in my report.
Here is a summary of the content:
Part 1: The Fundamentals of the Spherical Wave Functions
Part 2: The Helmholtz equation least squares methods
Part 3: Sound field separation
Part 4: Implementation Guide (hardware discussions started with post 34)
Code: (will come later today or tomorrow) Uploaded
Unfortunately at this moment I am unable to build a prototype robotic scanner to test. I am living in a small apartment. If and when I get to move into a house and has room for DIY projects, I would like to build a small version for testing smaller speakers. But at the meantime, I have to be content with just sharing my report.
Sorry for being longwinded in my report. Comments / critiques / corrections are appreciated. I'll try my best to answer questions. I only started reading up on acoustics a few months ago, and only the stuff that are related to this project. My understanding on this topic is very limited and I will be very surprised if I have not made plenty of noob mistakes.
Thanks.
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