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On waveplate polarimeters
for
high precision CMB
and
mm astronomy measurements
Maria Salatino
Physics Department “Sapienza Università di Roma”
Rencontres de Moriond, La Thuile, 13th-20th March 2010
Summary of the
presentation
cosmological +
astrophysical signals
Rotating Half Wave Plate
(HWP) + fixed polarizer
Mueller formalism
components temperatures;
non ideal parameters;
internal reflections;
reflections between components
B-POL,
SPIDER,
EBEX...
PILOT
POLARIZED
DETECTED
SIGNAL
new description of the
HWP
Assumptions
optimization
experimental setup
(temperatures of
distinct components,
bkg ...)
The HWP polarimeter:
ideal behavior
HWP
Principle of operation:
rotating HWP followed
by a fixed polarizer
polarizer
hor
Wdet ( )  D  [ M pol
 M HW P ( )]  Sin
S
det
TRAS, ideal
1
( )  [ S 0  S1 cos 4  S 2 sin 4 ]
2
with
detector
  t
Stokes + Mueller matrix formalism
SPIDER
Ongoing and future polarization experiments
QUBIC
BPOL
EBEX
LSPE
BRAIN
PILOT
The HWP polarimeter: real behavior
TBKG
1. Temperatures of
the components +
background
HWP
polarizer
TPOL
emission of
polarized radiations
If they were constant, given typical
temperatures of
CMBP experiments
optical devices,…..
detector
they would add simply an offset contribution but…
The HWP polarimeter: real behavior
TBKG
2.
HWP
ax , ay ≠ 0,1
ne(n), no(n)
polarizer
detector
TPOL
Non ideal parameters
(absorbing coefficients,
HWP refraction indeces, ...)
Spectral dependence of the
absorbing coefficients
(Savini et al., 2006)
THE MUELLER FORMALISM
rotating HWP or QWP
1

0
0

0

0
0
1
0
0 Cos()
0 Sin()





Cos() 
0
0
-Sin ()
 S0 
 
 S1 
S 
 2
S 
 3
sapphire HWP
Advantages:
simple description for the radiation detected by a polarimeter
Drawbacks:
independence by the incidence angle;
 doesn’t depend on the frequency;
assumption: 100% transmitted radiation.
THE ADACHI FORMALISM
(Adachi S. et al., 1960)
  (k e  ko ) 
j Sin(k e d)
 Cos(k e d)

 j Sin( ke d ) Cos(k d)
e

ηe

0
0

0
0


2π ν d
(ne  no )
c
0
0
Cos(k o d)
jSin(



0


jηo Sin(k o d) 

Cos(k o d) 

0
ko d
)
ηo
Advantages:
Spectral dependence of 
no (n )  3.053  4.7 104 ν  2.2 1010 ν 2  1.11012 ν 3
ne (n )  3.387  1.3 10 ν
5
(Savini G. et al., Applied Optics, 2006)
n
d
c
ne
no
frequency incidence wave;
thickness crystal;
speed of light;
extraordinary refraction index;
ordinary refraction index.
 characteristic impedence

of the medium

 Ex

Hy 


E
y


 H 
x

input and output wave
In vacuum
ηo  ηe  1
H x  Ex
H y  Ey
air
HWP
air
OPTICALLY ACTIVE
MULTIPLE REFLECTIONS
(OAMR)
Ingredients:
dielectric reflection;
optical action HWP;
spectral dependence Adachi;
Fresnel equations for an
anisotropic medium.
A new Mueller matrix for the transmitted
field by a HWP and for the reflected one;
Complicate expression, function of
ne , no , 
2 output waves from the HWP:
the reflected and transmitted
component.
(Salatino M. et al., in preparation)
1.

 0.
 0.

 0.

0. 0.
1. 0.
0. - 1 .
0. 0.
ideal HWP
0. 

0. 
0. 

- 1. 
 0.737

 0.008
 0.

 0.

0.008
0.737
0.
0.
0.
0.
- 0.737
0.028
real HWP
0.


0.

- 0.028 

- 0.737 
The HWP polarimeter: real behavior
TBKG
3. Internal reflections
HWP
ax , ay ≠ 0,1
polarizer
TPOL
birefringency +
multiple reflections
detector
OAMR
1 plate -> complete solution + new
Mueller matrix
2 or more plates -> approximate
solutions
(Salatino M. et al., in preparation)
The HWP polarimeter: real behavior
TBKG
4. Reflections between
components
HWP
ax , ay ≠ 0,1
emission of
polarized radiations
TPOL
polarizer
Normal incidence
Input: monochromatic wave
Non monochromatic waves ->
small circular polarization (few % S1)
detector
Detected signal due to CMB only
Lambda CDM model + T/S=0.1
expected signal: 10-7 K
Signal when staring at
a given pixel, while
HWP rotates
Real HWP (absorption + OAMR)
Similar signal amplitude but
different height of the peaks
(2theta component)
e=1%
150 GHz
BKG->
Cos(2 theta)
POL ->
Cos(2 theta)
Total
The radiation reflected by the HWP produces a cos(2*theta) which contaminates
the CMBP Stokes parameters.
Necessity of cooling down the polarizer and to reduce the background.
CMB
0.6 mK @ 2+4
Spurious
10 mK @ 2
Spurious
0.3 mK @ 2
Total signal
dominated
by HWP
emission
@ 2
The result of the addition of the modulated emission of BKG and
Pol depends on the relative angle between the CMBP
polarization angle and the orientation of the wire grid.
Can we
separate it
?
NON LINEARITIES
The disturbance signals at 2theta (produced by unpolarized background,
waveplate emission and reflected polarizer emission) are easily
separated from the sky signal at 4theta.
However if they are too large they challenge the linearity of the
detectors and the dynamic range of the data acquisition system.
Bolometers become non linear and start to saturate so that a pure 2
theta signal acquires a 4theta component.
2
out
in
24..
NON LINEARITIES
Greater effect on S1 with respect to S2,
limits on the bkg
HWP WITH ANTI REFLECTION COATING
Naive model
The efficiency of the polarimeter increases
by a factor > 2.
HWP
The spurious signal reflected by the HWP is
reduced by at least one order of
magnitude.
However here there could be a component
modulated at 4 theta; which would
be extremely dangerous!
Possible solution…
HWP
HWP
Reduction of the
detected emission
reflected from the HWP +
polarized emission
with different
phases
detector arrays
detector + pol arrays
1st flight Kiruna
(Sweden)
Off-axis telescope (70 cm)
He tank
polarizer
fiberglass cylinders
124 cm
Targets: cirrus clouds
at high Galactic latitudes,
Galactic plane
vapor cooled shields
Polarized Instrument for Long Wavelenght
Observation of the Tenuous interstellar
medium
?
secondary
mirror
tertiary
mirror
70 cm
The PILOT Cryogenic Waveplate Rotator
innovative MECHANICAL
SYSTEM driven by a DC
motor running
at room temperature
the control of its position
is assured by
a 3-bit optical encoder
fed by optical fibers
HWP at 4K
(Salatino et al., 2008)
CONCLUSIONS AND FUTURE DEVELOPMENTS (1/2)
A study of the sistematics introduced in a CMBP polarimeter has been done
taking into account the emission of the polarizer and the unpolarized radiative
background;
both the thermal emission of the polarizer and the unpolarized bkg
are modulated at 2;
this has been done by means of a new description of the HWP which takes
into account multiple reflections, the transmitted and reflected fields inside
an anisotropic medium, ….
the non linear behavior of the bolometers introduces a 4 component
-> constraints on the bkg;
possible dangerous signals at 4 can be reduced with 1 polarizer per bolometer;
in the PILOT experiment a DC motor running at room temperature
will rotate the HWP at 4K.
CONCLUSIONS AND FUTURE DEVELOPMENTS (2/2)
The HWP description has been done with some assumptions:
normal incidence ;
input monochromatic wave;
no ARC.
Future work:
slant incidence -> effect of the mixing of extraordinary and ordinary ray on the
incoming ray;
input non monochromatic wave;
full model ARC ;
achromatic HWP (multi-plates) with multi-layer ARCs.
-------------------------------------------------------Full simulation of a balloon/ satellite experiment ->
multi-pixel analysis of these sistematics.