k-Wave

1. s148275
   

   Member
   Joined: Mar '20
   Posts: 15

   Hello,

   I am using a point source to determine the input phase and amplitude of elements positioned on a sphere around this point source. I want the point source to mimic a focus spot of these elements. To determine the phase and amplitudes sensors are positioned at the element locations. To extract the amplitudes and delays my idea is to do some sort of time-reversed simulation in which energy increases with distance and wherein also positive attenuation is used. So normally the sensors which are furthest away have a lower pressure amplitude than the elements close to the point source. I would like to reverse that.

   For attenuation I can simply change the sign with medium.alpha_sign so that it increases with distance, however pressure is inversely proportional to distance and this does not change if I change the alpha_sign. How can I change the input of the point source so that the pressure increases with distance instead of decreases?

   Best,
   Frank

   Posted 4 years ago #

2. bencox
   

   Developer
   Joined: Mar '10
   Posts: 292

   Hi Frank,

   I haven't quite understood what it is you want to do. Do you want to use the signals measured at the detectors on the sphere surrounding the point source to determine amplitudes and phases, so that if these detectors were then used as sources (with these amplitudes and phases) the result would be a field focussed at the position where the point source was? In that case you need to do two things. First run the simulation with a continuous wave, single frequency, point source until it is in a steady state. Then record an integer number of periods arriving at the detectors. Then use the k-Wave function `extractAmpPhase'.

   The attenuation due to geometric spreading from a point source is inherent in the wave equation, so that can't be reversed. But if you have many source points then the wavefield can, of course, constructively interfere at the focus to give a larger amplitude.

   Hope that helps.

   Ben

   Posted 4 years ago #

3. s148275
   

   Member
   Joined: Mar '20
   Posts: 15

   Hi Ben,

   Thanks for the response.

   Yes, your explanation is correct! What you describe with the extractAmpPhase function is exactly what I am doing now. In this way it is indeed possible to extract the amplitudes and phases measured at the sources/elements. The delays I can calculate from the phase and that works for both a homogeneous and heterogeneous medium.

   In my case the focus location is not positioned at the center of the sphere. So I am struggling a bit with the amplitudes. What I measure now is a small amplitude at large distances from the point source, because of intensity decrease and attenuation. It makes sense to directly use this amplitude as the input of the sources, because there are fewer elements close to the focus spot than far away from it and therefore the closest elements need the largest amplitude. This results in a nice spot which is what I want. So actually it already works quite nice!

   But I am not sure whether this method is still correct for a heterogeneous medium? Therefore my idea was to do a simulation in which the pressure grows from the point source. And then I will measure a large amplitude at the element with the largest distance to the focus point. By inversing and scaling this I could calculate the correct amplitudes (I think?).

   To get a growing amplitude I might could use a negative time series?

   Best,
   Frank

   Posted 4 years ago #

4. bencox
   

   Developer
   Joined: Mar '10
   Posts: 292

   Hi Frank,

   The wave equation gives the same behaviour whichever direction of time you use, it is invariant to switching t with minus t. The amplitude decay is due to the energy in the wave spreading out over a larger area as the wavefront grows. In 3D it spreads proportionally to 1/radius^2. To make it grow, the medium would have to give energy to the wave as it propagated (a bit like a laser medium does), but k-Wave can't model that.

   Best wishes,
   Ben

   Posted 4 years ago #

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