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Healpy map2alm and alm2map errors

I'm studying healpy. Specifically I am interested in map2alm and alm2map: I found question where example of applying the functions "to both sides" (in answer) is provided. As we can see, we get significant errors in comparison with the original map after applying map2alm and alm2map consecutively.Therefore I want to control these errors. So my question is:

  1. Is there any way to reduce the error, without using higher nside? (For example if I want to use a certain nside)
  2. Also, maybe there is another way to get a "spectral characteristic" of a map, that wouldn't have such big errors?
Solution

  • No, there is no other way.

    Going from real space to harmonic space is like doing a Fast Fourier Transform. If you don't have enough time resolution, your FFT is not going to be very good, there is just not enough information to have an accurate representation is frequency domain.

    Here is the same, the only way you are going to have a low error at low nside is if you have a signal that is easily represented in harmonic space, for example a pure dipole, see this notebook, even at just nside 8, error is at 1/1000:

    http://nbviewer.jupyter.org/gist/zonca/2f87cb19ca8293539947b0d4aeca42b2