Support additional cylindrical (aka equiangular) sampling schemes

[Magwos]

In CMB data analysis (aiming at probing small angular scales), an interest has been growing towards cylindrical griding, named CAR in https://phy-act1.princeton.edu/public/saiola/act_dr4_C20.pdf or ECP in https://www.aanda.org/articles/aa/full_html/2013/08/aa21575-13/aa21575-13.html. It corresponds to a rectangular projection, equi-spaced in latitude, and not equal-area projection, but with the same number of pixels per ring, and relies on Clenshaw-Curtis quadrature weightings for the associated transforms.

This sampling scheme is the baseline one used for the ACT (Atacama Cosmology Telescope) collaboration and central in many tools developed for the LAT analysis in the Simons Observatory collaboration (in which I am part of).

I wanted to ask if it would be possible to have s2fft support for such sampling scheme.

[jasonmcewen]

Thanks @Magwos, sounds like a very useful feature. We can certainly add this. Note that MW/DH equiangular sampling is already supported but I appreciate you probably want exactly the same sampling as used elsewhere.

Do you have a reference (paper and/or code) with the precise details of the sampling? I had a super quick look at the references you posted but didn't immediately see the details there.

[Magwos]

Thanks a lot for your positive answer!

So, currently the implementation that is most used is done through the package https://github.com/simonsobs/pixell (in particular https://github.com/simonsobs/pixell/blob/master/pixell/curvedsky.py), which itself calls the ducc package (https://mtr.pages.mpcdf.de/ducc/sht.html#module-ducc0.sht) for their transforms.

An example of CMB-science oriented package calling pixell is this one: https://github.com/simonsobs/pspy
Pspy is mostly used towards small-scale science, and it is usually applied to partial sky maps with very high resolution (typically nside=4096, the SO LAT will have a resolution of 1 arcmin), storing only the relevant pixels and not the 0 of the unobserved area (and of course the coordinates of the patch observed).

If you need more details about all of this, please let me know.

[jasonmcewen]

Thanks @Magwos !

Adding further details from your email that you sent separately so we have everything here in one place.

there is no paper detailing this CAR pixelisation which was adopted by ACT (named after the Plate-Carré projection, or Equirectangular one), as it corresponds in fact to the ECP (equidistant cylindrical projection) grid also detailed here: https://www.aanda.org/articles/aa/pdf/2013/06/aa21494-13.pdf (4.4.1)