def offset_beam_ghost(az_off=0,
el_off=0,
polang=0,
lmax=100,
fwhm=200,
hwp_freq=25.,
pol_only=True):
'''
Script that scans LCDM realization of sky with a detector
on the boresight that has no main beam but a full-amplitude
ghost at the specified offset eam. The signal is then binned
using the boresight pointing and compared to a map made by
a symmetric Gaussian beam that has been rotated away from
the boresight. Results should agree.
Keyword arguments
---------
az_off : float,
Azimuthal location of detector relative to boresight
(default : 0.)
el_off : float,
Elevation location of detector relative to boresight
(default : 0.)
polang : float,
Detector polarization angle in degrees (defined for
unrotated detector as offset from meridian)
(default : 0)
lmax : int,
Maximum multipole number, (default : 200)
fwhm : float,
The beam FWHM used in this analysis in arcmin
(default : 100)
hwp_freq : float,
HWP spin frequency (continuous mode) (default : 25.)
pol_only : bool,
Set unpolarized sky signal to zero (default : True)
'''
# Load up alm and blm
ell, cls = get_cls()
np.random.seed(30)
alm = hp.synalm(cls, lmax=lmax, new=True, verbose=True) # uK
if pol_only:
alm = (alm[0] * 0., alm[1], alm[2])
# init scan strategy and instrument
mlen = 240 # mission length
ss = ScanStrategy(
mlen, # mission duration in sec.
sample_rate=1, # sample rate in Hz
location='spole') # South pole instrument
# create single detector on boresight
ss.create_focal_plane(nrow=1,
ncol=1,
fov=0,
no_pairs=True,
polang=polang,
lmax=lmax,
fwhm=fwhm,
scatter=True)
try:
beam = ss.beams[0][0]
# set main beam to zero
beam.amplitude = 0.
# create Gaussian beam (would be done by code anyway otherwise)
beam.gen_gaussian_blm()
#explicitely set offset to zero
beam.az = 0.
beam.el = 0.
beam.polang = 0.
# create full-amplitude ghost
beam.create_ghost(az=az_off, el=el_off, polang=polang, amplitude=1.)
ghost = beam.ghosts[0]
ghost.gen_gaussian_blm()
except IndexError as e:
if ss.mpi_rank != 0:
pass
else:
raise e
# Start instrument rotated (just to make things complicated)
rot_period = ss.mlen
ss.set_instr_rot(period=rot_period, start_ang=45)
# Set HWP rotation
ss.set_hwp_mod(mode='stepped',
freq=1 / 20.,
start_ang=45,
angles=[34, 12, 67])
# calculate tod in one go (beam is symmetric so mmax=2 suffices)
ss.partition_mission()
ss.scan_instrument_mpi(alm,
binning=False,
nside_spin=512,
max_spin=2,
verbose=2)
# Store the tod and pixel indices made with ghost
try:
tod_ghost = ss.tod.copy()
pix_ghost = ss.pix.copy()
except AttributeError as e:
if ss.mpi_rank != 0:
pass
else:
raise e
# now repeat with asymmetric beam and no detector offset
# set offsets to zero such that tods are generated using
# only the boresight pointing.
try:
beam = ss.beams[0][0]
beam.amplitude = 1.
beam.gen_gaussian_blm()
# Convert beam spin modes to E and B modes and rotate them
blm = beam.blm
blmI = blm[0].copy()
blmE, blmB = tools.spin2eb(blm[1], blm[2])
# Rotate blm to match centroid.
# Note that rotate_alm uses the ZYZ euler convention.
# Note that we include polang here as first rotation.
q_off = ss.det_offset(az_off, el_off, polang)
ra, dec, pa = ss.quat2radecpa(q_off)
# convert between healpy and math angle conventions
phi = np.radians(ra)
theta = np.radians(90 - dec)
psi = np.radians(-pa)
# rotate blm
hp.rotate_alm([blmI, blmE, blmB],
psi,
theta,
phi,
lmax=lmax,
mmax=lmax)
# convert beam coeff. back to spin representation.
blmm2, blmp2 = tools.eb2spin(blmE, blmB)
beam.blm = (blmI, blmm2, blmp2)
# kill ghost
ghost.dead = True
# spinmaps will still be created, so make as painless as possible
ghost.lmax = 1
ghost.mmax = 0
except IndexError as e:
if ss.mpi_rank != 0:
pass
else:
raise e
# reset instr. rot and hwp modulation
ss.reset_instr_rot()
ss.reset_hwp_mod()
ss.scan_instrument_mpi(alm,
binning=False,
nside_spin=512,
verbose=2,
max_spin=lmax) # now we use all spin modes
# Figure comparing the raw detector timelines for the two versions
# For subpixel offsets, the bottom plot shows you that sudden shifts
# in the differenced tods are due to the pointing for the symmetric
# case hitting a different pixel than the boresight pointing.
if ss.mpi_rank == 0:
plt.figure()
gs = gridspec.GridSpec(5, 9)
ax1 = plt.subplot(gs[:2, :6])
ax2 = plt.subplot(gs[2:4, :6])
ax3 = plt.subplot(gs[-1, :6])
ax4 = plt.subplot(gs[:, 6:])
samples = np.arange(tod_ghost.size)
ax1.plot(samples, ss.tod, label='Asymmetric Gaussian', linewidth=0.7)
ax1.plot(samples, tod_ghost, label='Ghost', linewidth=0.7, alpha=0.5)
ax1.legend()
ax1.tick_params(labelbottom='off')
sigdiff = ss.tod - tod_ghost
ax2.plot(samples, sigdiff, ls='None', marker='.', markersize=2.)
ax2.tick_params(labelbottom='off')
ax3.plot(samples, (pix_ghost - ss.pix).astype(bool).astype(int),
ls='None',
marker='.',
markersize=2.)
ax1.set_ylabel(r'Signal [$\mu K_{\mathrm{CMB}}$]')
ax2.set_ylabel(r'asym-sym. [$\mu K_{\mathrm{CMB}}$]')
ax3.set_xlabel('Sample number')
ax3.set_ylabel('different pixel?')
ax3.set_ylim([-0.25, 1.25])
ax3.set_yticks([0, 1])
ax4.hist(sigdiff, 128, label='Difference')
ax4.set_xlabel(r'Difference [$\mu K_{\mathrm{CMB}}$]')
ax4.tick_params(labelleft='off')
plt.savefig('../scratch/img/tods_ghost.png')
plt.close()
def offset_beam_interp(az_off=0, el_off=0, polang=0, lmax=100,
fwhm=200, hwp_freq=25., pol_only=True):
'''
Script that scans LCDM realization of sky with a symmetric
Gaussian beam that has been rotated away from the boresight.
This means that the beam is highly asymmetric. Scanning using
interpolation.
Keyword arguments
-----------------
az_off : float,
Azimuthal location of detector relative to boresight
(default : 0.)
el_off : float,
Elevation location of detector relative to boresight
(default : 0.)
polang : float,
Detector polarization angle in degrees (defined for
unrotated detector as offset from meridian)
(default : 0)
lmax : int,
Maximum multipole number, (default : 200)
fwhm : float,
The beam FWHM used in this analysis [arcmin]
(default : 100)
hwp_freq : float,
HWP spin frequency (continuous mode) (default : 25.)
pol_only : bool,
Set unpolarized sky signal to zero (default : True)
'''
# Load up alm and blm
ell, cls = get_cls()
np.random.seed(30)
alm = hp.synalm(cls, lmax=lmax, new=True, verbose=True) # uK
if pol_only:
alm = (alm[0]*0., alm[1], alm[2])
# init scan strategy and instrument
mlen = 240 # mission length
ss = ScanStrategy(mlen, # mission duration in sec.
sample_rate=1, # sample rate in Hz
location='spole') # South pole instrument
# create single detector
ss.create_focal_plane(nrow=1, ncol=1, fov=0, no_pairs=True,
polang=polang, lmax=lmax, fwhm=fwhm,
scatter=True)
# move detector away from boresight
try:
ss.beams[0][0].az = az_off
ss.beams[0][0].el = el_off
except IndexError as e:
if ss.mpi_rank != 0:
pass
else:
raise e
# Start instrument rotated (just to make things complicated)
rot_period = ss.mlen
ss.set_instr_rot(period=rot_period, start_ang=45)
# Set HWP rotation
ss.set_hwp_mod(mode='stepped', freq=1/20., start_ang=45,
angles=[34, 12, 67])
# calculate tod in one go (beam is symmetric so mmax=2 suffices)
ss.partition_mission()
ss.scan_instrument_mpi(alm, binning=False, nside_spin=512,
max_spin=2, interp=True)
# Store the tod made with symmetric beam
try:
tod_sym = ss.tod.copy()
except AttributeError as e:
if ss.mpi_rank != 0:
pass
else:
raise e
# now repeat with asymmetric beam and no detector offset
# set offsets to zero such that tods are generated using
# only the boresight pointing.
try:
ss.beams[0][0].az = 0
ss.beams[0][0].el = 0
ss.beams[0][0].polang = 0
# Convert beam spin modes to E and B modes and rotate them
# create blm again, scan_instrument_mpi detetes blms when done
ss.beams[0][0].gen_gaussian_blm()
blm = ss.beams[0][0].blm
blmI = blm[0].copy()
blmE, blmB = tools.spin2eb(blm[1], blm[2])
# Rotate blm to match centroid.
# Note that rotate_alm uses the ZYZ euler convention.
# Note that we include polang here as first rotation.
q_off = ss.det_offset(az_off, el_off, polang)
ra, dec, pa = ss.quat2radecpa(q_off)
# convert between healpy and math angle conventions
phi = np.radians(ra)
theta = np.radians(90 - dec)
psi = np.radians(-pa)
# rotate blm
hp.rotate_alm([blmI, blmE, blmB], psi, theta, phi, lmax=lmax, mmax=lmax)
# convert beam coeff. back to spin representation.
blmm2, blmp2 = tools.eb2spin(blmE, blmB)
ss.beams[0][0].blm = (blmI, blmm2, blmp2)
except IndexError as e:
if ss.mpi_rank != 0:
pass
else:
raise e
ss.reset_instr_rot()
ss.reset_hwp_mod()
# Now we use all spin modes.
ss.scan_instrument_mpi(alm, binning=False, nside_spin=512,
max_spin=lmax, interp=True)
if ss.mpi_rank == 0:
plt.figure()
gs = gridspec.GridSpec(5, 9)
ax1 = plt.subplot(gs[:2, :6])
ax2 = plt.subplot(gs[2:4, :6])
ax4 = plt.subplot(gs[:, 6:])
samples = np.arange(tod_sym.size)
ax1.plot(samples, ss.tod, label='Asymmetric Gaussian', linewidth=0.7)
ax1.plot(samples, tod_sym, label='Symmetric Gaussian', linewidth=0.7,
alpha=0.5)
ax1.legend()
ax1.tick_params(labelbottom='off')
sigdiff = ss.tod - tod_sym
ax2.plot(samples, sigdiff,ls='None', marker='.', markersize=2.)
ax2.tick_params(labelbottom='off')
ax1.set_ylabel(r'Signal [$\mu K_{\mathrm{CMB}}$]')
ax2.set_ylabel(r'asym-sym. [$\mu K_{\mathrm{CMB}}$]')
ax2.set_xlabel('Sample number')
ax4.hist(sigdiff, 128, label='Difference')
ax4.set_xlabel(r'Difference [$\mu K_{\mathrm{CMB}}$]')
ax4.tick_params(labelleft='off')
plt.savefig('../scratch/img/tods_interp.png', dpi=250)
plt.close()