{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example of generating a Gaussian beam in spherical harmonics space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate $b_{lm}$ representation of a Gaussian beam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import healpy as hp\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from astropy import units as u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Configure parameters of the transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lmax = 32\n",
    "pol = True\n",
    "nside = 64\n",
    "beam_width = 10 * u.degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate the $b_{lm}$\n",
    "\n",
    "The shape is $(1, \\ell_{max})$ for temperature only, $(3, \\ell_{max})$ for a polarized beam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "blm=hp.blm_gauss(beam_width.to_value(u.radian), lmax=lmax, pol=pol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "blm.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot\n",
    "\n",
    "Plot the beam, rotate inside `mollview` for better visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = hp.alm2map(blm, lmax=lmax, mmax=2 if pol else 0, nside=nside, pol=pol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for each_m, label in zip(m, \"IQU\"):\n",
    "    hp.mollview(each_m, rot=[0, 90], title=f\"Beam map, {label}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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