Example of generating a Gaussian beam in spherical harmonics space

Generate \(b_{lm}\) representation of a Gaussian beam

import healpy as hp
import numpy as np
import matplotlib.pyplot as plt
from astropy import units as u

Configure parameters of the transformation

lmax = 32
pol = True
nside = 64
beam_width = 10 * u.degree

Generate the \(b_{lm}\)

The shape is \((1, \ell_{max})\) for temperature only, \((3, \ell_{max})\) for a polarized beam.

blm=hp.blm_gauss(beam_width.to_value(u.radian), lmax=lmax, pol=pol)

blm.shape

(3, 96)

Plot

Plot the beam, rotate inside mollview for better visualization

m = hp.alm2map(blm, lmax=lmax, mmax=2 if pol else 0, nside=nside, pol=pol)

for each_m, label in zip(m, "IQU"):
    hp.mollview(each_m, rot=[0, 90], title=f"Beam map, {label}")