Calibration of CMB instruments
• One of the most difficult steps in the measurement of CMB spectrum, anisotropy and polarization, is the calibration of the instrument.
• 20% errors (in temperature units) are still normal for these experiments. A 5% measurement is considered high accuracy.
• The problem is due to
– The lack of suitable laboratory standards: the best available source producing known brightness at mm-waves is a cryogenic blackbody – a source diffucilt to operate and to use.
– The lack of well known Galactic sources as celestial standards.
Planets are small and can have atmospheric features; AGNs are variable; HII regions are contaminated by surrounding diffuse emission.
Calibration of CMB instruments
• Let’s pose the problem in rigorous terms:
• We call B(α,δ) the brightness of the sky in W/m2/sr (we will deal with spectral dependance later; here we consider the signal integrated over the instrument spectral bandwidth)
• A generic photometer observing the direction αο,δο, will detect a signal
• For a point source located in α,δ , the fluxF(W/m2) produces a signal
• The responsivity (gain) (V/W) must be calibrated, and the angular response R(θ) as well. This is the response of the system to off-axis radiation as a function of the off-axis angle θ, normalized to the on- axis response to the same source.
• The calibration can be performed observing a source with known brightness or known flux.
[ ]
Ωℜ
= A
∫
B R dV o o o o
π α δ ϑ α δ α δ
δ
α , ) 4 ( , ) ( , , , )
(
ℜ
[
( , , , )]
) ,
(
α
oδ
o AF Rϑ α
oδ
oα δ
V =ℜ
The CMB dipole as a calibrator
• The dipole anisotropy of the CMB is the best responsivity (gain) calibration source, for several reasons:
A. Its amplitude is well known, and derived from astrometric, non- photometric data.
B. Its spectrum is exactly the same as the spectrum of the CMB anisotropy. No color correction needed.
C. It is unpolarized.
D. Its signal is only about 10 times larger than the signal of CMB anisotropy: detector non linearities are avoided.
E. The Dipole brightness is present everywhere in the sky
• The disadvantage is that the dipole is a large-scale signal.
Significant sky coverage is needed to detect it with an accuracy sufficient for instrument calibration. Moreover, foreground contamination and 1/f noise effects increase as larger sky areas are explored.
Derivation of the CMB dipole
• We are moving with a velocity v with respect to the CMB Last Scattering Surface.
• The CMB is isotropic in the reference frame O’ of the LSS, but is not isotropic in the restframe O of the observer, which is in motion.
• The distribution function f of particles with momentum p is a Lorentz invariant: In fact
where dN is a scalar, so is invariant, and the phase space volume dxidpi can also be shown to be a Lorentz invariant. So
i idp dx f(p)= dN
) ( ) (p f p f′ ′ =
Derivation of the CMB dipole
• The Lorentz transformation for the momentum p is
• Applying this eq. to the Planck distribution function for photons we get
• This formula was first derived by Mosengheil (1907), and rederived by Peebles and Wilkinson (1968), Heer and Kohl (1968), Forman (1970).
• For smallβ :
p c c p
c r
r
r r ′
×
−
= −
/c n v 1
/ v
1 2 2
T c T
T p T
T p ′
−
= −
× ′
−
= −
⇒
′ ′
= 1 cos( )
1 /c
n v 1
/ v
1 2 2 2
θ β r β
r
⎥⎦
⎢ ⎤
⎣
⎡ + +
≅ cos(2 )
) 2 cos(
1 ) (
2
β θ θ β θ To
T
kinematic term
light aberration term
O’
p p nr =r/
vr O
pr
β
• The motion of the Earth with respect to the CMB is the combination of
– The motion of the Earth around the Sun (well known) – The motion of the Sun in the Galaxy (well known) – The motion of the Galaxy in the Local Group (known) – The bulk motion of the Local Group (not well known) due to the
gravitational acceleration generated by all other large masses present in the Universe
• The annual revolution of the Earth around the Sun is known extremely well ( v ~ 30 km/s), and produces an annual modulation in the CMB dipole. This is the main signal used in COBE and WMAP for the Dipole calibration, since it is known from astrometric measurements much better than the total motion of the earth.
• This effect produces a modulation of the order of βTo, i.e.
about 300μK, on a total dipole of the order of 3.5 mK.
CMB dipole signal
• The CMB temperature fluctuation corresponds to a CMB brightness fluctuation, which can be found by deriving the Planck formula with respect to T:
• This conversion from Temperature to Brightness is the same for the dipole and for any smaller scale temperature or polarization anisotropy. For this reason the Dipole spectrum is the same as the spectrum of CMB anisotropy. The maximum of this spectrum is at 271 GHz.
CMB x CMB
x
kT x h T T e B
I xe ν Δ = ν
= −
Δ ( , ) ;
1
0.1 1 10
10-16 10-15 10-14
Brightness (W/cm2 /sr/cm-1 )
wavenumbers (cm-1)
30 GHz 300 GHz
3 GHz
10 cm 1 cm 1 mm
Cosmic Dipoles
• If the isotropic source spectrum is not a BlackBody, the dipole formula is different.
• A typical example is the cosmic X-Ray background, whose specific brightness is basically a power law with slope
• In general the dipole anisotropy of the specific brightness induced by our speedβ with respect to the cosmic matter emitting the background can be derived as
• This is very sensitive to steep features in the spectrum (α large) which can compensate the smallness of β.
ν α ν
d dI I v d
I
d =
= ln ln
...}
) cos(
) 3 ( 1 { )
(
θ
=Io + −α β θ
+ ICMB dipole signal
• The signal produced by the CMB dipole temperature fluctuation is
• Since the dipole signal is almost constant within the beam of the instrument
• So from a scatter plot of the measured signal vs. the expected CMB Dipole the slope a can be estimated:
[ ]
∫
∫
= −
Ω Δ
ℜ
= Δ
ν ν ν
δ α δ α ϑ δ α δ
α
d E T e B
xe K T
d R
T AK V
x CMB x
CMB
o o DIP
o o DIP
) ( ) , 1 ( 1
) , , , ( ) , ( )
, (
[ ]
Ω Δℜ
≅
ΔVDIP(αo,δo) AK TDIP(αo,δo)
∫
Rϑ d[ ]
Ωℜ
=
+ Δ
= Δ
∫
R dAK a
b T
a
VDIP o o DIP o o ϑ
δ α δ
α , ) ( , )
(
calibration constant (V/K)
[ ]
Ω ⇒ Δℜ
=
ΔVDIP A
∫
IDIPRϑdCMB dipole signal
• The CMB map obtained from the same instrument in voltage units (uncalibrated) is
where
• The conversion constant from voltage units to
Temperature units is the same we have obtained from the Dipole calibration:
[ ]
{ [ ] }
( , )( , )) , (
) , , , ( ) , ( )
, (
o o
T d R AK V
d R
T AK V
o o
o o o
o
δ
δ α
α ϑ
δ α
δ α δ α ϑ δ α δ
α
Δ Ω ℜ
= Δ
Ω Δ
ℜ
= Δ
∫
∫
a
T V o o
o o
) , ) (
,
( ( , ) α δ
δ
α α δ =Δ Δ
[ ]
[ ]Ω Ω
= Δ
Δ
∫ ∫
d R
d R
T
T o o
o
o ϑ
δ α δ α ϑ δ δ α
α αδ
) , , , ( ) , ( )
, ( ( , )
calibrated T map:
uncalibrated V map:
calibration constant (V/K)
CMB dipole signal
• Notice that
– since we have defined the calibrated temperature map as the intrinsic CMB map weighted with the angular response, and – since we have used the CMB dipole as a calibrator …
• the calibrated temperature map does not depend on the detailed angular response, and does not depend on the spectral response of the instrument:
• Where
a
T V o o
o o
) , ) (
,
( ( , )
α δ
δ
α
α δ =Δ Δ[ ]
b T
a V
in d R AK a
o o DIP o
o
DIP = Δ +
Δ
Ω ℜ
=
∫
) , ( )
,
(α δ α δ
ϑ
Sample CMB dipole signals:
• COBE map
Sample CMB dipole signals:
• COBE map
Gal. Eq.
apex of motion (WMAP) l=(263.85+0.1)o b=(48.25+0.04)o (close to the ecliptic…)
Amplitude (WMAP)
ΔT=(3.346+0.017)mK
Dipole signal in the B98 region (filtered in the same way as B98 data) Detected signal at 150 GHz (detector B150A)
-1,0 -0,5 0,0 0,5 1,0 1,5
-0,008 -0,006 -0,004 -0,002 0,000 0,002 0,004
Preliminary Calibration BOOMERanG LDB 1998/99
55' pixels (1610)
Signal B150A (mV)
COBE dipole (mK)
Slope : a = (4.0+0.4) nV/μK
Point Sources
• A point source must be observed anyway to measure the Angular Response R(θ). This is needed for estimates of the instrinsic power spectrum of the map.
• The point source will inevitably have a spectrum different from the spectrum of the CMB.
• The signal from the source will be:
• where F(ν) is the specific flux of the source (W/m2/Hz).
• If the source flux is known, and the instrument makes a map of the region surrounding the source, the observation can be used to estimate the calibration constant a as follows:
[ ] ∫
ℜ
=
ϑ α δ α δ ν ν ν
δ
α
AR F E dV( o, o) ( o, o, , ) ( ) ( )
Point Sources
• So the calibration constant a , needed to convert the uncalibrated map into a calibrated CMB map , can be estimated from:
– The uncalibrated map of the source V(α,δ) – The flux of the source F(ν)
– The relative spectral response of the instrument E(ν)
[ ] [ ]
∫
∫ ∫
∫
∫ ∫ ∫
Ω −
=
= Ω ℜ
=
⇒ Ω ℜ
Ω=
ν ν ν
ν ν δ ν
α ϑ ν ϑ ν ν
δ α
d E F T
d E T e B
xe d V
d R K A a
d RA A d E F
d V
CMB x CMB
x
o o
o o
) ( ) (
) ( ) , 1 ( )
, (
) ( ) (
) , (
Point Sources
• CMB anisotropy/polarization experiment have a typical resolution of a few arcmin.
• Known sources much smaller than this typical size can be considered point-sources and can be used to measure the angular response and the gain.
• Several kinds can be used:
– Planets
– Compact HII regions – AGNs
• All kinds have their own peculiarities.
Gaseous Planets :
•The size is in the sub-arcmin range.
•Atmospheric features can be important.
• Has a tenuous atmosphere, and no sub-mm features. Its
Mars
emitting surface is basically a blackbody at 180 K.
• The typical size is 6” (check the ephemeres for the time of the observation).
• The typical signal expected from Mars is equivalent to a CMB temperature fluctuation. This can be found as follows:
{
[ ]} {
[ ]Ω}
=Ω Δ
⇒
⎪⎩ ⇒
⎪⎨
⎧
Δ Ω ℜ
= Δ
Ω ℜ
= Δ
∫ ∫
∫ ∫
d R K
d E T T B
T d R AK V
d E T B A V
Mars Mars Mars
Mars Mars
Mars Mars Mars
ϑ ν ν ν ϑ
ν ν ν
) ( ) , (
) ( ) , (
) , , ( )
( ) , 1 (
) ( ) , (
c CMB Mars Beam Mars CMB CMB
x x
Mars Beam Mars CMB
Mars T fT T
d E T e B
xe
d E T T B
T ν
ν ν ν
ν ν ν
Ω
= Ω
− Ω
= Ω
Δ
∫
∫
10 100
10 100 1000
ΔT (mKCMB)
frequency (GHz)
Signal from Mars (6”) in CMB units in a 5’ FWHM beam : About 1000 times the rms CMB anisotropy in the same beam.
More than enough to measure the angular response.
But what about linearity ? Is there a saturation risk ?
Beam Mars
TMars
Ω Ω
Degree-scale anisotropy as a calibrator
• Many experiments focus on a small sky patch, in order to obtain maximum S/N per pixel, to study CMB anisotropy/polarization at intermediate and small scales.
• Large scale signals are not measured and are filtered out to remove the effect of 1/f noise and detector instability.
• The Dipole is not a suitable calibrator for these experiments.
• A possibility is to use the WMAP data in the selected region. WMAP has detected CMB anisotropy with S/N~1 for 15’ pixels, and 0.5% calibration accuracy.
• A scatter plot of experiment data vs. WMAP can provide the gain calibration. Point sources (AGN) should be removed first, since their effect is strongly frequency dependent.
b (deg) b (deg) b (deg)b (deg)
l (deg) 90GHz l (deg)
b (deg)
220GHz
WMAP 1st yrBOOMERanG 98
b (deg)
l (deg) 150GHz
41GHz l (deg) 60GHzl (deg) 94GHzl (deg)
b (deg) b (deg) b (deg)b (deg)
l (deg) 90GHz l (deg)
b (deg)
220GHz
b (deg)
l (deg) 150GHz
41GHz l (deg) 60GHzl (deg) 94GHzl (deg) PKS0537-441
BOOMERanG 98WMAP 1st yr
b (deg) b (deg) b (deg)b (deg)
l (deg) 90GHz l (deg)
b (deg)
220GHz
b (deg)
l (deg) 150GHz
41GHz l (deg) 60GHzl (deg) 94GHzl (deg) PMNJ0519-4546
BOOMERanG 98WMAP 1st yr b (deg) b (deg) b (deg)b (deg)
l (deg) 90GHz l (deg)
b (deg)
220GHz
b (deg)
l (deg) 150GHz
41GHz l (deg) 60GHzl (deg) 94GHzl (deg) PKS0454-46
WMAP 1st yrBOOMERanG 98
10 100 100 1000 10000
200 30
CMB rms
PKS0537-441 PMNJ0519-4546 PKS0454-46
μKCMB in a 20' beam
frequency (GHz)
55 . 2 '
20
430100
/ −
⎟⎠
⎜ ⎞
⎝
= ⎛
⎟⎟⎠
⎜⎜ ⎞
⎝
⎛ Ω
GHz K
F
CMB
ν μ
• There are additional AGNs lost in the confusion of the CMB fluctuations.
• The WOMBAT catalogue and tools predict quite well the flux observed for the 3 detected AGN, and can be used to estimate the contamination due to unresolved AGNs.
• In the 3% of the sky mapped by B98 the contamination of the PS at 150 GHz is less than 0.3% at l=200, and less than 8% at l=600.
• This is reduced by 50% if the resolved sources (at 150 GHz) are removed, and by 80% if are removed those resolved at 41 GHz.
0.0 0.5 1.0 1.5 2.0 2.5 3.0 1
10 100
Flux (Jy) @ 150 GHz
counts
WOMBAT catalog
http://astron.berkeley.edu/wombat/foregrounds/radio.html
0 200 400 600 800 1000 1200 1400 0
1000 2000 3000 4000 5000
6000 CMB
all sources
resolved @150GHz removed resolved @40GHz removed
l(l+1)cl/2π (μK2 )
multipole l
150GHz
b (deg) b (deg) b (deg)b (deg)
l (deg) 90GHz l (deg)
b (deg)
220GHz
WMAP 1st yrBOOMERanG 98
b (deg)
l (deg) 150GHz
41GHz l (deg) 60GHzl (deg) 94GHzl (deg)
Scatter Plot
• Once point sources have been removed, one can scatter-plot the experiment data (in V) vs. the WMAP data (in KCMB), and obtain the calibration constant (in V/K) from the slope of the best fit line.
• Problems of this approach:
a) The experiment beam is different from the WMAP beam (see next slide).
b) The experiment response to large scales can be different from the WMAP response
c) The noise level of the two experiments is different: this biases the best fit slope.
• A solution for a) is to re-bin the maps in pixels larger than the beams.
• Problem b)&c) can be corrected carrying out detailed simulations to estimate the bias.
B98-150GHz
WMAP 94GHz
B98 150 GHz
WMAP 94GHz
11’Gaussian 13’Gauss
ian
13’G auss
ian 11’G
aus sian
a)
b) b)
b)
• Experiment data = yi ; WMAP data = xi• In the case of BOOMERanG 98 and WMAP, in 7’
pixels, σ(yi) ~30μK, σ(xi) ~80μK .
• Best slope estimate :
1) Remove averages from data setsyiandxi, so thaty=ax 2) Find the value of a which minimizes χ2 :
3) Make simulations of best fit lines for correlated data with different levels of noise forxiand yi. To understand if - for the noises of the experiment and of WMAP - there is a bias.
( ) ( )
( ) ( )
∑ + −
=
i i i
i i
x a y
ax
a
2y
2 22 2
σ χ σ
230.0 240.0 -20.0 -10.0 1380. 0.116 7.700 240.0 250.0 -20.0 -10.0 7332. 0.296 2.900 250.0 260.0 -20.0 -10.0 7353. 0.381 2.300 260.0 270.0 -20.0 -10.0 7289. 0.246 2.400 270.0 280.0 -20.0 -10.0 885. 0.221 2.900 230.0 240.0 -30.0 -20.0 3940. 0.305 3.200 240.0 250.0 -30.0 -20.0 6954. 0.305 2.500 250.0 260.0 -30.0 -20.0 6954. 0.285 2.700 260.0 270.0 -30.0 -20.0 6869. 0.279 2.500 270.0 280.0 -30.0 -20.0 143. 0.154 7.100 230.0 240.0 -40.0 -30.0 5518. 0.178 4.600 240.0 250.0 -40.0 -30.0 6213. 0.270 2.800 250.0 260.0 -40.0 -30.0 6213. 0.337 3.000 260.0 270.0 -40.0 -30.0 6158. 0.288 2.200 270.0 280.0 -40.0 -30.0 520. 0.227 2.600 230.0 240.0 -50.0 -40.0 5117. 0.188 4.200 240.0 250.0 -50.0 -40.0 5416. 0.285 3.100 250.0 260.0 -50.0 -40.0 5417. 0.291 2.900 260.0 270.0 -50.0 -40.0 5200. 0.245 3.000 270.0 280.0 -50.0 -40.0 1196. 0.243 2.500 230.0 240.0 -60.0 -50.0 230. 0.262 3.200 240.0 250.0 -60.0 -50.0 3415. 0.171 3.600 250.0 260.0 -60.0 -50.0 2583. 0.164 3.800
l(o) b(o) N R amin
• Results for several regions:
• First 4 columns define the region, in Galactic coordinates; 5th column is the number of pixels observed by both experiments; 6th column is Pearson’s correlation coefficient; 7th column is the best fit calibration constant.
• Resulting average calibration:
(3.5+0.3)ADU/μK
A variant of this correlation method is based on the cross-power spectrum:
– Compute the Angular Power Spectrum of the uncalibrated experiment, XX(l), and the Cross Power Spectrum between the uncalibrated experiment and WMAP, XW(l):
1/a(l)[V/K]= XW(l)/XX(l)
– Using the same region, cosmic variance is not effective
– The method is computationally more costly – Beam and low multipoles response differences can
be taken into account easily:
– 1/a(l)[V/K]= [XW(l)/(BX(l)BW(l))]/[XX(l)/BX2(l)]
where B2are the spherical harmonic transforms of the beams/responses (Hivon E. et al. 2003, Polenta et al. 2004).
100 200 300 400 500 600
0.7 0.8 0.9 1.0 1.1 1.2 1.3
B98 - 150 GHz A+A1+A2+B1 raw
cl[WMAPxB98]/cl[B98*B98]
multipole
No obvious trend vs multipole: beam calibration OK Gain calibration: to be multiplied by 0.95 + 0.01
Hivon E. et al. 2003 All cl corrected for beam and finite sky coverage
WMAP/B98 (gain recalibration)
0.95 +/- 0.01 0.95 +/-0.03 Sum
0.97 +/- 0.03 0.96 +/- 0.03 B150B2
0.95 +/- 0.02 0.97 +/- 0.03 B150A2
0.85 +/- 0.02 0.89 +/- 0.03 B150A1
0.96 +/- 0.02 0.95 +/- 0.03 B150A
C(l) based Pixel based Channel
Raw maps on 1.8% of the sky (Netterfield et al. cut)
0.95 +/- 0.01 0.95 +/-0.03 Sum
0.95 +/- 0.02 0.95 +/- 0.03 B150B2
0.98 +/- 0.02 0.98 +/- 0.03 B150A2
0.92 +/- 0.03 0.91 +/- 0.03 B150A1
0.96 +/- 0.02 0.95 +/- 0.03 B150A
C(l) based Pixel based Channel
Destriped maps on 1.8% of the sky (Netterfield et al. cut)
Hivon E. et al. 2003
• The nominal calibration of the 150 GHz map was off by 5% (well within the published 10% error)
• The new calibration is accurate to 1%, which is very good news for the calibration of B2K
Beam pattern calibration
• We have seen before why beam calibration is so important.
• For example it affects directly the estimates of the angular power spectrum at high multipoles:
• Where B is the spherical harmonics transform of the beam, a steeply decreasing function at high multipoles
!
2 ,
l l
l
B
c = c
measuredB98-150GHz
WMAP 94GHz
B98 150 GHz
WMAP 94GHz
11’Gaussian 13’Gaussian
13’G aussian
11’G aus
sian
R( θ ) B
l2 SHTBOOM98: 150 GHz window function
Combination of:
Pixelization (14’ healpix) Effective beam (including estimated 2’ rms pointing jitter)
Freq. FWHM 90GHz 18’+2’
150GHz 10’+1’
240GHz 14’+1’
410GHz 13’+1’
Pointing jitter
• As an example of how important can be the estimate of the instrument beam and of systematic errors, let’s consider what happened for the first release of the BOOMERanG data (B98 Nature paper).
• The effective beam is the convolution of the telescope beam [(9.2+0.5)’FWHM @ 150 GHz]with the telescope pointing jitter.
• The results in Nature were based on a jitter estimate of (2+1)’rms from a few scans of RCW38 done in CMB mode. This is, however, on the edge of the area surveyed for CMB measurements. We understand now that this result is not representative of all the data in CMB mode.
• With the improved pointing solution it is possible to infer the effective beam (and the jitter) from many more measurements of 3 AGN in the center of the CMB area. We see that the old pointing solution had a jitter of (4+2)’ rms-> Nature results should be corrected: the effective beam was(12.7+1.4)’FWHMinstead of the assumed (10+1)’FWHM.
• The new pointing solution has a jitter of (2.5+2.0)’ rms. The effective beam for the new data with new pointing solution is
(10.9+1.4)’FWHM.
Corresponding Effect on the PS
• Original data, as published in Nature, with published random and systematic errors
0 100 200 300 400 500 600
0 1000 2000 3000 4000 5000 6000 7000
original Nature data Nature +1σ gain Nature -1σ gain Nature +1σ gain +1σ beam Nature -1σ gain -1σ beam
l(l+1)cl/2π (μK2)
multipole
Corresponding Effect on the PS
Original data and data correctedfor jitter underestimate
Correction substantial at l=600 (+35%, but still within published
errors)
0 100 200 300 400 500 600
0 1000 2000 3000 4000 5000 6000 7000
original Nature data jitter underestimate corrected Nature +1σ gain Nature -1σ gain Nature +1σ gain +1σ beam Nature -1σ gain -1σ beam
l(l+1)cl/2π (μK2)
multipole
Also Calibration Correction
• We also found a better treatment of the effect of high pass filters in the Dipole calibration
• 10% (1σ) decrease of gain i.e. additional 20% coherent increase of the PS values
0 100 200 300 400 500 600
0 1000 2000 3000 4000 5000 6000 7000
original Nature data jitter underestimate and gain corrected Nature +1σ gain Nature -1σ gain Nature +1σ gain +1σ beam Nature -1σ gain -1σ beam
l(l+1)cl/2π (μK2)
multipole
0 100 200 300 400 500 600 0
1000 2000 3000 4000 5000 6000 7000
B98 data corrected
l(l+1)cl/2π (μK2)
multipole
Corrected data : the 2nd peak is not evident yet
• After the correction, there is a hint of a 2nd peak, but it is not statistically significant.
• the data (from a single bolometer) are still not sensitive enough.
192 196 200 204 208
location of peak lp (multipole)
4500 4600 4700 4800 4900 5000
peak amplitude lp(lp+1)clp/2π (μK2)
6 8 10 12 14
0.26 0.28 0.30 0.32
beam FWHM (arcmin) (l>320 average)/ (peak amplitude)
Effect of jitter underestimate in preliminary results: 10’ –> 12.7’
1%
4%
4%
Old beam New beam
Effects of jitter underestimate and calibration correction on science
• Cosmological parameters extraction from the corrected B98 together with the COBE-DMR PS data:
• Ωoremains the same – (1% effect is negligible)
• Ωbh2changes from 0.036+0.006 to 0.027+0.006 (same weak priors, l<625):
• (cfr. BBN: Ωbh2= 0.020+0.002)
• We are comparing the density of baryons 3 minutes after the big-bang (assuming it is the same as at z=3) to the density of baryons 300000 yrs after the Big Bang.
• Different physics (nuclear reactions vs acoustic waves in a plasma), different experimental methods and systematic effects!
Artificial Planet Diam = 20, 40 cm Dist. 2 km (4, 8 arcmin) Telescope BEAM Calibration At ground calibration with artificial planet(tethered blackbody + CCD monitor)
Telescope Beam Calibration : scans on RCW38
For BOOMERanG this is a point source, very useful to get our beam size. We have hundreds of scans for each detector, so we can obtain both the telescope beam and the pointing jitter
2.5’
P.de Bernardis Oct.2000
Compact HII region in an area free from Galactic confusion Acbar data at 1.4 mm = 2.5’ diam.
