def test_beam2bl(self):
""" Test beam2bl against analytical transform of Gaussian beam. """
theta = np.linspace(0, np.radians(1.), 1000)
sigma = np.radians(10. / 60.) / np.sqrt(8. * np.log(2.))
gaussian_beam = np.exp(-.5 * (theta / sigma) ** 2) / (2 * np.pi * sigma ** 2)
ell = np.arange(512 + 1.)
gaussian_window = np.exp(-.5 * ell * (ell + 1) * sigma ** 2)
bl = hp.beam2bl(gaussian_beam, theta, 512)
np.testing.assert_allclose(gaussian_window, bl, rtol=1e-5)
def test_beam2bl(self):
""" Test beam2bl against analytical transform of Gaussian beam. """
theta = np.linspace(0, np.radians(1.0), 1000)
sigma = np.radians(10.0 / 60.0) / np.sqrt(8.0 * np.log(2.0))
gaussian_beam = np.exp(-0.5 * (theta / sigma) ** 2) / (2 * np.pi * sigma ** 2)
ell = np.arange(512 + 1.0)
gaussian_window = np.exp(-0.5 * ell * (ell + 1) * sigma ** 2)
bl = hp.beam2bl(gaussian_beam, theta, 512)
np.testing.assert_allclose(gaussian_window, bl, rtol=1e-5)
def __call__(self, frequencies):
"""
Create Realistic beam models
"""
lmax = 5 * self.nside - 1
self.nfreqs = len(frequencies)
nsamples = 2048
self.model = np.zeros((self.nfreqs, nsamples))
self.tfunc = np.zeros((self.nfreqs, lmax + 1))
self.fwhm = np.zeros(self.nfreqs)
self.fwhm_frequencies = frequencies * 1.
# setup
wls = self.c / frequencies / 1e6
r = np.linspace(0, self.dish_diameter / 2., 1000) # m
# First create beam model, then the equivalent transfer function
for i, wl in enumerate(tqdm(wls)):
# self.clats in degrees
self.model[i, :], self.clats = self.BeamFunction(
self.ApertureFunc,
r,
self.aperture_taper_width,
wl,
thetamax=self.thetamax,
nsamples=self.nsamples)
good = self.model[i, :] > 0.4
pmdl = interp1d(self.model[i, good], self.clats[good])
self.fwhm[i] = pmdl(0.5) * 2
self.tfunc[i, :] = hp.beam2bl(self.model[i, :],
self.clats * np.pi / 180.,
lmax=lmax)
self.tfunc[i, :] /= self.tfunc[i, 1]
self.diffraction_constant = np.polyfit(
wls / self.dish_diameter * 180. / np.pi, self.fwhm, 1)[1]
self.data['model'] = self.model
self.data['theta'] = self.clats
self.data['beam_cl'] = self.tfunc
self.info['theta'] = {'Unit': 'degrees'}
self.data['diffraction_constant'] = (self.diffraction_constant, )
self.data['FWHM'] = self.fwhm
def __call__(self, frequencies, fwhm=None):
"""
Create the gaussian beam models
"""
gauss = lambda x, sigma: np.exp(-0.5 * (x / sigma)**2)
lmax = 5 * self.nside
self.nfreqs = len(frequencies)
nsamples = 2048
thetamax = 5
self.model = np.zeros((self.nfreqs, nsamples))
self.tfunc = np.zeros((self.nfreqs, lmax + 1))
wls = self.c / frequencies / 1e6
if isinstance(fwhm, type(None)):
fwhm = wls / self.dish_diameter * self.diffraction_constant * 180. / np.pi
else:
self.diffraction_constant = np.polyfit(
wls / self.dish_diameter * 180. / np.pi, fwhm, 1)[1]
self.clats = np.linspace(0, thetamax, nsamples)
# First create beam model, then the equivalent transfer function
for i, wl in enumerate(tqdm(wls)):
# self.clats are calculate by BeamFunction in degrees, thus FWHM in degrees
self.model[i, :] = gauss(self.clats, fwhm[i] / 2.355)
self.tfunc[i, :] = hp.beam2bl(self.model[i, :],
self.clats * np.pi / 180.,
lmax=lmax)
self.tfunc[i, :] /= self.tfunc[i, 1]
self.data['model'] = self.model
self.data['theta'] = self.clats
self.data['beam_cl'] = self.tfunc
self.data['FWHM'] = fwhm
self.info['theta'] = {'Unit': 'degrees'}
self.data['diffraction_constant'] = (self.diffraction_constant, )