Polarized observations¶
This tutorial covers working with polarized instrument and maps, and recovering polarized maps from observations.
We start with a normal instrument, and create two orthogonally polarized copies of each detector by setting polarized: True in the Array config:
[1]:
import maria
from maria.instrument import Band
f090 = Band(
center=90e9, # in Hz
width=20e9, # in Hz
NET_RJ=40e-6, # in K sqrt(s)
knee=1e0, # in Hz
gain_error=5e-2)
f150 = Band(
center=150e9,
width=30e9,
NET_RJ=60e-6,
knee=1e0,
gain_error=5e-2)
array = {"field_of_view": 0.5,
"shape": "circle",
"beam_spacing": 1.5,
"primary_size": 10,
"polarized": True,
"bands": [f090, f150][:1]}
instrument = maria.get_instrument(array=array)
print(instrument.arrays)
n FOV baseline bands polarized
array1 326 28.68’ 0 m [f090] True
We can see the resulting polarization footprint in the instrument plot:
[2]:
print(instrument)
instrument.plot()
Instrument(1 array)
├ arrays:
│ n FOV baseline bands polarized
│ array1 326 28.68’ 0 m [f090] True
│
└ bands:
name center width η NEP NET_RJ NET_CMB FWHM
0 f090 90 GHz 20 GHz 0.5 5.445 aW√s 40 uK_RJ√s 49.13 uK_CMB√s 1.458’
Let’s observe the use the Einstein map, which has a faint polarization signature underneath the unpolarized signal of Einstein’s face. Remember that all maps are five dimensional (stokes, frequency, time, y, x); this map has four channels in the stokes dimensions (the I, Q, U, and V Stokes parameters). We can plot all the channels by giving plot a shaped set of stokes parameters.
[3]:
input_map = maria.map.get("maps/einstein.h5")
print(input_map)
input_map.plot(stokes=[["I", "Q"],
["U", "V"]])
2026-04-26 20:18:56.979 INFO: Fetching https://github.com/thomaswmorris/maria-data/raw/master/maps/einstein.h5
Downloading: 100%|██████████| 931k/931k [00:00<00:00, 47.0MB/s]
ProjectionMap:
data(4, 1, 685, 685):
min: -1.000e-02
max: 2.540e-01
units: K_RJ
quantity: rayleigh_jeans_temperature
stokes(4):
components: IQUV
nu(1):
values: [90.] GHz
y(685):
height: 1°
res: 5.255”
x(685):
width: 1°
res: 5.255”
frame: ra/dec
center:
ra: 00ʰ00ᵐ0.00ˢ
dec: -23°00’0.00”
beam(maj, min, psi): (0 rad, 0 rad, 0 rad)
memory: 15.02 MB
[4]:
from maria import Planner
planner = Planner(target=input_map, site="llano_de_chajnantor", constraints={"el": (60, 90)})
plans = planner.generate_plans(total_duration=600, # in seconds
sample_rate=50) # in Hz
plans[0].plot()
print(plans)
PlanList(1 plans, 600 s):
start_time duration target(ra,dec) center(az,el)
chunk
0 2026-04-27 12:00:16.152 +00:00 600 s (360°, -23.01°) (95.9°, 61.25°)
[5]:
sim = maria.Simulation(
instrument,
plans=plans,
site="llano_de_chajnantor",
atmosphere="2d",
atmosphere_kwargs={"weather": {"pwv": 0.5}},
map=input_map,
map_kwargs={"bilinear_sampling": True},
)
print(sim)
Simulation
├ Instrument(1 array)
│ ├ arrays:
│ │ n FOV baseline bands polarized
│ │ array1 326 28.68’ 0 m [f090] True
│ │
│ └ bands:
│ name center width η NEP NET_RJ NET_CMB FWHM
│ 0 f090 90 GHz 20 GHz 0.5 5.445 aW√s 40 uK_RJ√s 49.13 uK_CMB√s 1.458’
├ Site:
│ region: chajnantor
│ timezone: America/Santiago
│ location:
│ longitude: 67°45’17.28” W
│ latitude: 23°01’45.84” S
│ altitude: 5.064 km
│ seasonal: True
│ diurnal: True
├ PlanList(1 plans, 600 s):
│ start_time duration target(ra,dec) center(az,el)
│ chunk
│ 0 2026-04-27 12:00:16.152 +00:00 600 s (360°, -23.01°) (95.9°, 61.25°)
├ '2d'
└ ProjectionMap:
data(4, 1, 1, 685, 685):
min: -1.000e-02
max: 2.540e-01
units: K_RJ
quantity: rayleigh_jeans_temperature
stokes(4):
components: IQUV
nu(1):
values: [90.] GHz
t(1):
values: [1.77723474e+09] s
y(685):
height: 1°
res: 5.255”
x(685):
width: 1°
res: 5.255”
frame: ra/dec
center:
ra: 00ʰ00ᵐ0.00ˢ
dec: -23°00’0.00”
beam(maj, min, psi): (0 rad, 0 rad, 0 rad)
memory: 15.02 MB
[6]:
tods = sim.run()
print(tods)
tods[0].plot()
2026-04-26 20:19:08.879 INFO: Simulating observation 1 of 1
Constructing atmosphere: 100%|██████████| 8/8 [00:10<00:00, 1.36s/it]
Generating turbulence: 100%|██████████| 8/8 [00:01<00:00, 5.02it/s]
Sampling turbulence: 100%|██████████| 8/8 [00:05<00:00, 1.46it/s]
Computing atmospheric emission: 100%|██████████| 1/1 [00:01<00:00, 1.14s/it, band=f090]
Sampling map: 100%|██████████| 1/1 [00:09<00:00, 9.55s/it, band=f090, channel=(0 Hz, inf Hz)]
Generating noise: 100%|██████████| 1/1 [00:00<00:00, 1.68it/s, band=f090]
2026-04-26 20:19:46.530 INFO: Simulated observation 1 of 1 in 37.63 s
[TOD(shape=(326, 30000), fields=['atmosphere', 'map', 'noise'], units='K_RJ', start=2026-04-27 12:10:16.131 +00:00, duration=600.0s, sample_rate=50.0Hz, metadata={'atmosphere': True, 'sim_time': <Arrow [2026-04-26T20:19:40.378471+00:00]>, 'altitude': 5064.0, 'region': 'chajnantor', 'pwv': 0.5, 'base_temperature': 274.556})]
[7]:
from maria.mappers import BinMapper
mapper = BinMapper(
stokes="IQU",
frame="ra/dec",
width=input_map.width.deg,
height=input_map.height.deg,
resolution=2 * input_map.resolution.deg,
tod_preprocessing={
"remove_spline": {"knot_spacing": 60, "remove_el_gradient": True},
"remove_modes": {"modes_to_remove": 1},
},
map_postprocessing={
"gaussian_filter": {"sigma": 1},
},
units="mK_RJ",
tods=tods,
)
output_map = mapper.run()
print(output_map)
2026-04-26 20:19:52.347 INFO: Inferring center {'ra': '23ʰ59ᵐ59.30ˢ', 'dec': '-23°00’22.76”'} for mapper.
Preprocessing TODs: 100%|██████████| 1/1 [00:01<00:00, 1.11s/it]
Mapping: 100%|██████████| 1/1 [00:03<00:00, 3.85s/it, tod=1/1]
ProjectionMap:
data(3, 1, 1, 342, 342):
min: -1.164e+02
max: 1.350e+02
units: mK_RJ
quantity: rayleigh_jeans_temperature
stokes(3):
components: IQU
nu(1):
values: [90.] GHz
t(1):
values: [1.77729152e+09] s
y(342):
height: 59.91’
res: 10.51”
x(342):
width: 59.91’
res: 10.51”
frame: ra/dec
center:
ra: 23ʰ59ᵐ59.30ˢ
dec: -23°00’22.76”
beam(maj, min, psi): (1.458’, 1.458’, 0 rad)
memory: 2.807 MB
Note that we can’t see any of the circular polarization, since our instrument isn’t sensitive to it.
[8]:
output_map.plot(stokes=["I", "Q", "U"])
