1D radial power spectrum issue

[alexandrefortin]

Thank you very much for providing this free library.

I tried to apply the code provided on Noise Power Pylinac documentation to some simple synthetic 2D signals including 4 spatial frequencies of equal amplitude A :

• noise_cartesian(X,Y) = A cos(2π* f1 * X) + A cos(2π* f2 * Y) + A cos(2π* f3 * X) + A cos(2π* f4 * Y)

• noise_radial(R) = A cos(2π* f1 * R) + A cos(2π* f2 * R) + A cos(2π* f3 * R) + A cos(2π* f4 * R)

  f1 = 0.18 mm-1
  f2 = 0.32 mm-1
  f3 = 0.45 mm-1
  f4 = 0.61 mm-1

I was expecting to find 4 peaks of equal power on the corresponding 1D radial power spectrum :

However I had two issues :

1. The peaks power are not equal (it seems to decrease as 1/f)
2. The peaks frequencies are shifted from the input values

Am I missing something ? By definition the power spectrum is expected to give a power proportional to the squared amplitude, am I wrong ?

Here is my modified code : PyLinac_SelfGeneratedNoise.txt

Thank you for your reply.

[alexandrefortin]

Complement to my previous post

I tried to slightly modify the core/nsp.py file by removing the common normalization over the number of pixels bin in the radial_average. By doing so, I got the expected power for the peaks (however their frequency still seems shifted downward on the 1D spectrum, whereas the values measured on the 2D spectrum are correct).

[alexandrefortin]

I think I found the issue origin for the frequency shift.

It seems to be a simple scaling problem, as the highest frequency bin is located in the image diagonal, so a √2 factor is to be applied to the axis and to the average power values :
scalingFactor = 1. / mmPixel_Size / math.sqrt(2)
x_vals = np.arange(len(nps1d_1))/len(nps1d_1) * scalingFactor

With this, the output frequencies match the input :