Diapositiva 1

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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
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Summary of the presentation
cosmological astrophysical signals

• new description of the
• HWP

Rotating Half Wave Plate (HWP) fixed polarizer
Assumptions
Mueller formalism
optimization experimental setup (temperatures
of distinct components, bkg ...)
components temperatures non ideal
parameters internal reflections reflections
between components
B-POL, SPIDER, EBEX...
PILOT
POLARIZED DETECTED SIGNAL
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The HWP polarimeter ideal behavior
HWP

• 
  Principle of operation
• 
  rotating HWP followed
• by
  a fixed polarizer

polarizer
with
Stokes Mueller matrix formalism
detector
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Ongoing and future polarization experiments
SPIDER
QUBIC
BPOL
EBEX
LSPE
BRAIN
PILOT

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The HWP polarimeter real behavior
TBKG

• Temperatures of
• the components
• background

HWP
emission of polarized radiations
polarizer
TPOL
If they were constant, given typical
temperatures of CMBP experiments optical
devices,..
detector
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they would add simply an offset contribution but
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The HWP polarimeter real behavior
TBKG

• Non ideal parameters
• (absorbing coefficients,
• HWP refraction indeces, ...)

HWP
ax , ay ? 0,1 ne(n), no(n)
Spectral dependence of the absorbing
coefficients (Savini et al., 2006)
polarizer
TPOL

detector
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THE MUELLER FORMALISM
rotating HWP or QWP
sapphire HWP

• Advantages
• simple description for the radiation detected by
  a polarimeter
• Drawbacks
• independence by the incidence angle
• f doesnt depend on the frequency
• assumption 100 transmitted radiation.

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THE ADACHI FORMALISM
(Adachi S. et al., 1960)

• frequency incidence wave
• d thickness crystal
• c speed of light
• ne extraordinary refraction index
• no ordinary refraction index.

• characteristic impedence
• of the medium

input and output wave In vacuum
Advantages Spectral dependence of f
(Savini G. et al., Applied Optics, 2006)
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OPTICALLY ACTIVE MULTIPLE REFLECTIONS
(OAMR)
air
HWP

• Ingredients
• dielectric reflection
• optical action HWP
• spectral dependence Adachi
• Fresnel equations for an
• anisotropic medium.

air
A new Mueller matrix for the transmitted field by
a HWP and for the reflected one Complicate
expression, function of ne , no , f
2 output waves from the HWP the reflected and
transmitted component.
(Salatino M. et al., in preparation)
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ideal HWP
real HWP
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The HWP polarimeter real behavior
TBKG
3. Internal reflections
HWP
ax , ay ? 0,1
polarizer
TPOL


birefringency multiple reflections
OAMR
1 plate -gt complete solution new
Mueller matrix 2 or more plates -gt
approximate
solutions
detector
(Salatino M. et al., in preparation)
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The HWP polarimeter real behavior
TBKG
4. Reflections between components
HWP
ax , ay ? 0,1
emission of polarized radiations

TPOL

Normal incidence Input monochromatic wave
polarizer
Non monochromatic waves -gt small circular
polarization (few S1)
detector
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Detected signal due to CMB only Lambda CDM model
T/S0.1 expected signal 10-7 K
Ideal HWP
Signal when staring at a given pixel, while HWP
rotates
Real HWP
Real HWP (absorption OAMR) Similar signal
amplitude but different height of the
peaks (2theta component)
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e1 150 GHz
BKG-gt Cos(2 theta)
POL -gt Cos(2 theta)
Total
The radiation reflected by the HWP produces a
cos(2theta) which contaminates the CMBP Stokes
parameters. Necessity of cooling down the
polarizer and to reduce the background.
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CMB 0.6 mK _at_ 2q4q
Spurious 10 mK _at_ 2q
Spurious 0.3 mK _at_ 2q
Total signal dominated by HWP emission _at_ 2q Can
we separate it ?
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.
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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.
2q
out
in
2q4q..
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NON LINEARITIES
Greater effect on S1 with respect to S2, limits
on the bkg
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HWP WITH ANTI REFLECTION COATING
Naive model
The efficiency of the polarimeter increases by a
factor gt 2. 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!
HWP
WORK IN PROGRESS
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Possible solution
HWP
HWP
Reduction of the detected emission reflected
from the HWP polarized emission with
different phases
detector arrays
detector pol arrays
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Polarized Instrument for Long Wavelenght
Observation of the Tenuous interstellar medium
vapor cooled shields
He tank
polarizer
124 cm
?
Targets cirrus clouds at high Galactic
latitudes, Galactic plane
fiberglass cylinders
1st flight Kiruna (Sweden)
secondary mirror
tertiary mirror
70 cm
Off-axis telescope (70 cm)
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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)
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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 2q
• 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 4q component
• -gt constraints on the bkg
• possible dangerous signals at 4q 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.

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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 -gt 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 -gt
• multi-pixel analysis of these sistematics.