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1. Seongjun Park
   

   Member
   Joined: Mar '12
   Posts: 9

   Dear Dr. Treeby and Dr. Cox,

   First of all, thanks for sharing this great toolbox.

   I am trying to understand how the PA reconstruction is realized by Matlab. From the paper(Kornel P. Kostli and et.al, APPLIED OPTICS, Vol.42, no.10, 1 April 2003), the detected signal is the function of p(t, y) and its Fourier transform simply gives P(w,ky). Then, the transform w to kx by dispersion relation & interpolation gives P(kx,ky). So far, everying is clear. But, during realizing these procedures with Matlab, there are some difficulies for me to understand:
   1. From Your Matlab code (KspaceLinRecon.m), w is defined as w=c*kgrid.kx instread of w=c*(kx^2+ky^2)^1/2 which is from dispersion relation. Both are identical? Or Am I misunderstanding?

   2. Similarly, w_new which may refer to kx is defined as w_new=c*kgrid.k instead of w_new=((w/c)^2-kgrid.ky^2)^1/2. Would you explain why?

   3. From the code 'p=sf.*fftshift(fftn(fftshift(p)))', Would you let me know why fftshift(p) is used? When I run the simulation after replacing it with p=sf.*fftshift(fftn(p)) it gives odd outcome which is wrong.

   Sorry for taking away your precious time.
   Thank you.

   Kind regards,
   Seongjun Park

   Posted 11 years ago #

2. bencox
   

   Developer
   Joined: Mar '10
   Posts: 292

   Hi Seongjun,

   These two lines,

   kgrid = makeGrid(Nt, dt*c, Ny, dy);
   w = c*kgrid.kx;

   are just a way of using the machinery of the makeGrid command to calculate the vector of frequencies that the FFT returns the data at when Fourier transforming in from time to frequency. Don't read too much significance into the use of kx here. The frequencies to which the data needs to be transformed are then calculated using w_new = (c*kgrid.k); as makeGrid has already calculated kgrid.k = sqrt(kx^2+ky^2).

   So, w contains the frequencies at which the data has been recorded, which are evenly spaced, whereas w_new contains the frequencies (not evenly spaced) at which the data needs to be known if the dispersion relation it going to map the data to points evenly spaced in (kx,ky).

   I hope that's clearer!

   Ben

   Posted 11 years ago #

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