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]}
instrument = maria.get_instrument(array=array)
instrument.arrays
[1]:
| n | FOV | baseline | bands | polarized | |
|---|---|---|---|---|---|
| array1 | 652 | 28.68’ | 0 m | [f090,f150] | 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 652 28.68’ 0 m [f090,f150] 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√s 49.13 uK√s 1.458’
1 f150 150 GHz 30 GHz 0.5 12.25 aW√s 60 uK√s 104 uK√s 0.8748’
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]:
from maria.io import fetch
input_map = maria.map.load(fetch("maps/einstein.h5"))
input_map.plot(stokes=[["I", "Q"],
["U", "V"]])
Downloading https://github.com/thomaswmorris/maria-data/raw/master/maps/einstein.h5: 100%|██████████| 931k/931k [00:00<00:00, 95.7MB/s]
[4]:
plan = maria.Plan(
start_time="2024-08-06T03:00:00",
scan_pattern="daisy",
scan_options={"radius": 0.5, "speed": 0.1}, # in degrees
duration=900, # in seconds
sample_rate=50, # in Hz
scan_center=(0, -23),
frame="ra_dec")
print(plan)
plan.plot()
Plan:
start_time: 2024-08-06 03:00:00.000 +00:00
duration: 900 s
sample_rate: 50 Hz
center:
ra: 00ʰ00ᵐ0.00ˢ
dec: -23°00’0.00”
scan_pattern: daisy
scan_radius: 0.9989°
scan_kwargs: {'radius': 0.5, 'speed': 0.1}
[5]:
sim = maria.Simulation(
instrument,
plan=plan,
site="llano_de_chajnantor",
atmosphere="2d",
atmosphere_kwargs={"weather": {"pwv": 0.5}},
map=input_map
)
print(sim)
Constructing atmosphere: 100%|██████████| 10/10 [00:33<00:00, 3.37s/it]
Simulation
├ Instrument(1 array)
│ ├ arrays:
│ │ n FOV baseline bands polarized
│ │ array1 652 28.68’ 0 m [f090,f150] 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√s 49.13 uK√s 1.458’
│ 1 f150 150 GHz 30 GHz 0.5 12.25 aW√s 60 uK√s 104 uK√s 0.8748’
├ Site:
│ region: chajnantor
│ location: 23°01’45.84”S 67°45’17.28”W
│ altitude: 5.064 km
│ seasonal: True
│ diurnal: True
├ Plan:
│ start_time: 2024-08-06 03:00:00.000 +00:00
│ duration: 900 s
│ sample_rate: 50 Hz
│ center:
│ ra: 00ʰ00ᵐ0.00ˢ
│ dec: -23°00’0.00”
│ scan_pattern: daisy
│ scan_radius: 0.9989°
│ scan_kwargs: {'radius': 0.5, 'speed': 0.1}
├ Atmosphere(10 processes with 10 layers):
│ ├ spectrum:
│ │ region: chajnantor
│ └ weather:
│ region: chajnantor
│ altitude: 5.064 km
│ time: Aug 5 23:07:29 -04:00
│ pwv[mean, rms]: (0.5 mm, 15 um)
└ ProjectedMap:
shape(stokes, nu, y, x): (4, 1, 685, 685)
stokes: IQUV
nu: [90.] GHz
t: naive
z: naive
quantity: rayleigh_jeans_temperature
units: K_RJ
min: -1.000e-02
max: 2.540e-01
center:
ra: 00ʰ00ᵐ0.00ˢ
dec: -23°00’0.00”
size(y, x): (1°, 1°)
resolution(y, x): (5.255”, 5.255”)
beam(maj, min, psi): (91.73 marcsec, 91.73 marcsec, 0°)
memory: 30.03 MB
[6]:
tod = sim.run()
print(tod)
tod.plot()
Generating turbulence: 100%|██████████| 10/10 [00:01<00:00, 7.81it/s]
Sampling turbulence: 100%|██████████| 10/10 [00:08<00:00, 1.23it/s]
Computing atmospheric emission: 100%|██████████| 2/2 [00:05<00:00, 2.78s/it, band=f150]
Sampling map: 100%|██████████| 2/2 [00:10<00:00, 5.49s/it, channel=[ 0. inf] Hz]
Generating noise: 100%|██████████| 2/2 [00:01<00:00, 1.78it/s, band=f150]
TOD(shape=(652, 45000), fields=['atmosphere', 'map', 'noise'], units='pW', start=2024-08-06 03:14:59.979 +00:00, duration=900.0s, sample_rate=50.0Hz, metadata={'atmosphere': True, 'sim_time': <Arrow [2025-05-30T18:53:24.796257+00:00]>, 'altitude': 5064.0, 'region': 'chajnantor', 'pwv': 0.5, 'base_temperature': 272.523})
[7]:
from maria.mappers import BinMapper
mapper = BinMapper(
center=(0, -23),
stokes="IQU",
frame="ra_dec",
width=1.0,
height=1.0,
resolution=1.0 / 256,
tod_preprocessing={
"window": {"name": "tukey", "kwargs": {"alpha": 0.1}},
"remove_spline": {"knot_spacing": 30, "remove_el_gradient": True},
"remove_modes": {"modes_to_remove": [0]},
},
map_postprocessing={
"gaussian_filter": {"sigma": 1},
# "median_filter": {"size": 1},
},
units="mK_RJ",
)
mapper.add_tods(tod)
output_map = mapper.run()
print(output_map)
Mapping band f090: 100%|██████████| 3/3 [00:00<00:00, 7.48it/s, band=f090, stokes=U]
2025-05-30 18:53:36.035 INFO: Ran mapper for band f090 in 6.912 s.
Mapping band f150: 100%|██████████| 3/3 [00:00<00:00, 7.37it/s, band=f150, stokes=U]
2025-05-30 18:53:42.937 INFO: Ran mapper for band f150 in 6.898 s.
ProjectedMap:
shape(stokes, nu, y, x): (3, 2, 256, 256)
stokes: IQU
nu: [ 90. 150.] GHz
t: naive
z: naive
quantity: rayleigh_jeans_temperature
units: mK_RJ
min: -1.184e+02
max: 1.202e+02
center:
ra: 00ʰ00ᵐ0.00ˢ
dec: -23°00’0.00”
size(y, x): (1°, 1°)
resolution(y, x): (14.06”, 14.06”)
beam(maj, min, psi): (14.06”, 14.06”, 0°)
memory: 6.291 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"], nu_index=[[0], [1]])
[ ]: