angular resolution when computing uv coverage

[dprelogo]

In function telescope_functions.get_uv_coverage, could you explain why is Nb = Nbase*theta_max/2 and not only Nbase*theta_max?

I'm using your code for applying thermal noise to the 21cmfast lightcones, found this as final-checking, not sure if it is a mistake or I don't see something...

Thanks :)

[sambit-giri]

Sorry for such a late reply. I must have missed the notification for this issue.

Nbase*theta_max/2 has no physical meaning. This 1/2 factor cancels out in the condition statements (e.g. Nb[:,0]<ncells/2) following that part of the code. In the current form of the code to calculate the uv coverage, the baselines were counted twice when this 1/2 factor is removed from both Nbase*theta_max/2 and Nb[:,0]<ncells/2.

[dprelogo]

Thank you for a reply!

In the meantime I made a simple equivalent function, you can look at it here. I'm just creating uv frequency map with np.fft.fftfreq and then creating a histogram of baselines with np.histogram2d. The overall effect is that I get zoomed-in uv coverage by the factor of two in each dimension, which should be consistent with this 1/2.

As you said, factors cancel out, so if multiply by theta_max/2 and take conditions in range <-ncells/2, ncells/2>, that's effectively <-1/theta_max, 1/theta_max> so 2/theta_max interval in total in fourier space. If I multiply with theta_max, and take the same range, that will sum to 1/theta_max.

For the double counting, I think the final uv_map can be divided by two, but I can't see where this comes from.

[sambit-giri]

This factor of 2 comes from the way one takes care of mirror baselines.

[steven-murray]

Just to weigh in on this:

The size of a cell in fourier space (in inverse radians) should simply be D_c(z)/boxsize. In inverse Mpc, its 2pi/boxsize. Placing a cut-off at B (metres) means placing a cutoff at u = B/lambda. This should be at the n=u*boxsize / D_c(z) pixel from the centre.

So, the lines

theta_max = boxsize/cm.z_to_cdist(z)
Nb  = np.round(Nbase*theta_max/2)

are getting the baselines, Nb, almost in units of their cell-number, except for that divide-by-2.

Say we have a simulation box of size 100 Mpc, with 100 cells. Then the size of a Fourier-cell (in inverse radians) is D_c / 100, and we have 100 cells, from -D_c/2 to D_c/2.

We should expect a baseline with u=D_c/2 to be included in the last cell. In the code, we'd get Nb = u * 50 / D_c = 25 for this baseline. This passes all the cuts (which are that it has to be <50 and >-50. But it really should be in the 100th cell, not the 25th cell!

This doesn't seem correct, and I'm not sure it has much to do with the mirror baselines?

[sambit-giri]

Thanks @steven-murray and @dprelogo for pointing out the mistake. I have modified the code. Now the map should match with the one @dprelogo gets with their version of telescope_functions.get_uv_coverage (when mirror baselines are not included).

[steven-murray]

Awesome!