NIGHT TIME
POLARIMETRY
Stefano Bagnulo
(Armagh Observatory)
(Position)
Intensity
Intensity vs. time
Intensity vs. wavelength
Intensity vs. time AND vs. wavelength…
HOW
MUCH?
POLARIZATION BY ABSORPTION
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polabs.html
http://www.olympusmicro.com/primer/lightandcolor/
polarization.html
REFLECTED LIGHT IS POLARIZED!
http://background.uchicago.e
du/~whu/intermediate/polari
zation/polar1.html
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polabs.html
http://www.getfpv.com/polarized-lens-for-layerlens-forgopro-3-1pcs.html
http://science.howstuffworks.com/3-d-glasses2.htm
http://science.howstuffworks.com/3-d-glasses2.htm
https://www.youtube.com/watch?v=Fu-aYnRkUgg
THE STOKES PARAMETERS
I (“natural” light, or “intensity”)
Q & U (“linear polarization”)
V
(“circular polarization”)
Georges Gabriel Stokes (1852)
STOKES PARAMETERS:
THE CHOICE OF A REFERENCE SYSTEM
Right handed coordinate system (x,y,z), where:
•z-axis is directed along the direction of propagation
• x-axis is directed along an “arbitrary” direction
x-axis:
celestial meridian passing through the object
OPERATIONAL DEFINITIONS OF STOKES
PARAMETERS
Q=
-
V =
Positive, right handed
U=
-
Negative, left handed
ANGLE θ
P = (Q 2 + U 2)1/2
Q = P cos2θ
U = P sin2θ
USING RELATIVE UNITS
PQ = Q/I
PU = U/I
PV = V/I
AN “IDEAL” POLARIMETER
Landi Degl’Innocenti & Landolfi
(2004)
BASIC FORMULAS FOR AN IDEAL
POLARIMETER
BASIC FORMULAS FOR AN IDEAL
POLARIMETER
BASIC FORMULAS FOR AN IDEAL
POLARIMETER
What happens if things change between the two
measurements (i.e. k is not constant)?
Use a beam splitter!
POLARIMETRIC OPTICS
α = position angle of the
fast axis
β = position angle of the
acceptance axis
γ = phase retardation
Retarder waveplate
+
V/I: γ = 90o; α = -45o, +45o, …
Q/I, U/I: γ = 180o; α = 0o, 22.5o, 45o, …
Wollaston prism
β = 0o and β = 90o
IMAGING POLARIMETRY (STOKES Q)
α=0o
I+Q
I-Q
“Parallel” beam
“Perpendicular” beam
Nucleus of 133P/Elst-Pizarro
IMAGING POLARIMETRY (STOKES U)
α=22.5
o
I+U
I-U
“Parallel” beam
“Perpendicular” beam
Nucleus of 133P/Elst-Pizarro
IMAGING POLARIMETRY (STOKES Q)
α=0o
I+Q
I-Q
“Parallel” beam
“Perpendicular” beam
Nucleus of 133P/Elst-Pizarro
IMAGING POLARIMETRY (STOKES U)
α=22.5
o
I+U
I-U
“Parallel” beam
“Perpendicular” beam
Nucleus of 133P/Elst-Pizarro
STOKES V SPECTRA FROM RCP AND LCP
I+V
(RCP)
I-V
(LCP)
IMAGING
LOW-MID RESOLUTION
SPECTROPOLARIMETRY (R<10000) (slitfed)
HIGH RESOLUTION
SPECTROPOLARIMETRY
(fiber fed)
(R= 30-100000)
FORS @ VLT
(IMAGING + LOW RESOLUTION SPECTROPOLARIMETRY)
ISIS @ WHT
(LOW - MID RESOLUTION SPECTROPOLARIMETRY)
NARVAL@TBL & ESPADONS @ CHFT
(HIGH RESOLUTION SPECTROPOLARIMETRY)
ZEEMAN EFFECT
ν0 + νL
ν0 − νL
ν0
σ
σ
ν0 + νL
σ πσ
ν0 − νL
Zeeman Effect
Zeeman Effect: “Local” case
Circular polarization
Transverse Field
Stokes I
Stokes V
B = 10 kG
Linear polarization
Stokes Q
Linear polarization
Stokes U
ZEEMAN EFFECT: “LOCAL” CASE
Circular Polarization
Longitudinal Field
B = 10 kG
Stokes I
Linear Polarization
Stokes Q
Stokes V
Linear Polarization
Stokes U
Zeeman Effect
Circular polarization
σ
π
σ
Stokes I
Linear
polarization
Stokes V
Linear polarization
B = 10 kG
Stokes Q
Stokes U
THE UNPOLARIZED SPECTRUM OF HD 96441
94600
Hε
Hγ
Hδ
Hβ
V/I = -4.67 10-13FIELD?
(1/λ2) (1/I) (dI/dλ) <Bz>
<Bz> = +2430 ± 110 G
Stokes I
σV/I
V/I
THE OBLIQUE ROTATOR MODEL
Bd = 10 kG, β=45o ; i = 90o, v sini = 10 kms-1
SOLAR AND STELLAR MAGNETISM
Session I on Monday:
Solar and Stellar Magnetic fields I
Session VII on Wednesday:
Solar and Stellar Magnetic fields II
Session V on Tuesday:
Data analysis techniques for polarimetric observations
SURFACES, DUST, ATMOSPHERES
This afternoon:
Tutorial by Michael Mischenko
Session VIII on Thursday:
Polarization diagnostic of Atmospheres and
Circumstellar Environments (including star forming
regions, Herbig Ae/Be stars, M dwarfs, Earthshine,
SNe…)
POLARIZATION OF REFLECTED LIGHT
http://background.uchicago.e
du/~whu/intermediate/polari
zation/polar1.html
POLARIZATION FROM REFLECTION
Incident light
(unpolarized)
Reflected light
(polarized)
PHASE
ANGLE
Cellino et al. (2015)
http://www.telegraph.co.uk/science/space/8494145/Giant-asteroidheading-close-to-Earth.html
POLARIZATION OF REFLECTED LIGHT
http://background.uchicago.e
du/~whu/intermediate/polari
zation/polar1.html
POLARIMETRY OF SOLAR SYSTEM
OBJECTS
Session IX on Thursday afternoon:
Polarimetry as a tool for discovery science I.
http://www.spitzer.caltech.edu/images/2666-ssc200704e-Isolating-a-Planet-s-Spectrum
I + Q spectrum
I - Q spectrum
Polarised spectrum
REFLECTANCE AND POLARIZATION FROM
EARTH-LIKE PLANETS
Stam (2008)
EXO-PLANETS
Session X on Friday morning:
Polarimetry as a tool for discovery science II.
THANK
YOU!