CODEWITHSUNDEEP
pythonhealpy
Girish Kulkarni
Girish Kulkarni

Reputation: 53

Spherical harmonic transform of complex-valued map?

Can healpy compute the spherical harmonic transform of a complex-valued map?

When I try this using healpy.sphtfunc.map2alm, there is no warning, but the function gives a_{l,m} only for m>0. This makes sense for real-valued maps, for which a_{l,-m} = (-1)^m * a_{l,m}^*. But for complex-valued functions, this symmetry does not exist.

Thanks!

Upvotes: 3

Views: 250

Answers (1)

Andrea Zonca
Andrea Zonca

Reputation: 8773

Asked Martin Reinecke, developer of HEALPix C++, here his answer:

What you can do is to run map2alm separately on the real and imaginary parts of your map; the resulting a_lm coefficients are then simply a_lm,real + i*a_lm,imag. If you want the coefficients with negative m as well, you need to use the symmetry relation separately on a_lm,real and a_lm, imag first and then combine them as described. The reason why there is no direct support for complex-valued maps is that this would make a_lm handling and spherical harmonic transforms much more complicated, just to cover a case that is rarely needed (at least in the area where healpy was originally used) and that can be emulated by the workaround above if really needed.

All a_lm objects in Healpix and healpy are designed in a way that there is the mentioned symmetry between +m and -m. For quantities with spin!=0 this symmetry doesn't exist either, so we introduce the linear combinations alm_E and alm_B, for which it exists again.

Upvotes: 3

Related Questions