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Polarimetry in astronomy Experimental Astrophysics December 8, 2014 Giorgos Leloudas Based on lectures/slides by N. Patat, C. Keller, C. Wheeler

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Outline General (and fun) facts about polarization Polarization in astronomy Mathematical background Measuring polarization – Dual-beam polarimeter Observations & relevant considerations (Very little on) spectropolarimetry

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Some basics Light is a transverse wave In most cases we have random superposition of many photons giving 0 net polarization No preferred direction

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But in some cases … There is preferred direction. Light is polarized Trivia: an ideal polarizer lets 50% of the light intensity through.

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Polarization is common in nature

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Examples What light is polarized in this picture ? Blue sky Rainbow Clouds ✗ ✔ ✔ (not so much)

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Everyday applications Photography Sunglasses Visit polarization.com for more fun facts (octopus, bees, Vikings, etc)!

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Experiment: sunglasses & LCD screen Warning: do try this at home !

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By electron scattering (Thomson. E.g. Solar Corona) By molecules scattering (Rayleigh. E.g. Earth ’ s atmosphere) By scattering small particles (Mie. E.g. Light Echoes) By resonant scattering (affects spectral lines only. E.g. SN) By dichroic absorption of aligned particles (IS polarization) Polarized emission in the presence of magnetic fields (Zeeman effect) Scattering produces linear polarization perpendicular to the scattering plane CIRCULAR Sources of Polarization in the Astrophysical context

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Examples - CMB BICEP2 B-mode polarization Planck Dust polarization

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Planets Starlight is unpolarized but light reflected from planets is very polarized First light from SPHERE imaging the dust ring around HR 4796A personally reminds me of:

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Supernovae A powerful tool to study the asymmetries of unresolved objects Symmetric. Not polarized Asymmetric. Polarized !

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Do not expect spectacular numbers P = 0.4% for an ellipticity E = 0.9 (so 10% asymmetry)

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Other examples AGNs – Jets, magnetic fields, sychnotron Scattering in Ly-a blobs the Sun – Zeeman effect – …

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Some typical values 45 deg reflection off aluminum mirror: 5% Clear blue sky: up to 75% 45 deg reflection off glass: 90% LCD screen: 100% Solar scattered polarization 1% to 0.001% Exoplanet signal: 0.001%

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The polarization Ellipse The tip of the electric vector draws an ellipse in the plane perpendicular to the direction of wave propagation Real electric field given by real part of Ē Intensity ~ E 2

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Let’s get quantitative λ E0yE0y E0xE0x Monochromatic Plane Wave Φ2-Φ1Φ2-Φ1 Maxwell Equations Solution: According to classical Wave Theory (oh yes, they are linear)

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Which can be rewritten as: Which is equivalent to From which one gets

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Since…after a bit of algebra one gets i.e. an ellipse

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Linear Polarization

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Circular Polarization

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Elliptical Polarization

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With the following coordinate rotation One can bring it to the canonical form: where ab RH

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One can easily show that: Which imply Together with These relations define all ellipsometric parameters and lead to the Stokes Parameters. + Right Handed – Left Handed RH

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The Stokes Parameters and Stokes Vector All Stokes parameters have the dimensions of intensity.

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Stokes parameters fully describe the polarization state of a light beam, regardless of partial/total polarization; Stokes parameters describe the polarization state of the light irrespective of its spectrum (monochromatic vs. polychromatic); Stokes vectors are additive. The polarization status of a beam resulting from the sum of two beams is described by the sum of Stokes vectors. This is true only if there is no phase relation between incoming beams. (Otherwise use Jones vectors). I Intensity Q Horizontal preference U +45º preference V Right Circ. preference

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Back to the equations… = I = V/I = U/Q Intensity Azimuth Shape handedness

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Visualization

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Stokes Vectors for some totally polarized ideal cases Pattern χ b/a Φ2-Φ1Φ2-Φ1 Normalized Stokes Vectors 00-{1,1,0,0} 900-{1,-1,0,0} 4500{1,0,1,0} -450±180{1,0,-1,0} LinearAny (0-180)Any (>0)0 or ±180{1,cos 2X, sin 2X, 0} -1,R90{1,0,0,1} 00.5,R90{1,0.6,0,0.8} 900.5,R90{1,-0.6,0,0.8}

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In general, and especially in the astrophysical context, light is only partially polarized. In this case, the Stokes Parameters still give a correct representation of the polarization state, but So that one can introduce the polarization degree P as Which can be separated into Linear and Circular:

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In all real cases, Stokes Parameters are time averages on time ranges which are much larger than the Electric field oscillation periods: A totally unpolarized beam can be imagined as the superposition of two perpendicular plane waves, with intensities and phases randomly changing on time scales larger than the oscillation period.

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Summing up Stokes Q: – The difference between the amount of photons whose electric field oscillates along the reference direction and the direction perpendicular to it Stokes U: – The difference between the amount of photons whose electric field oscillates at 45 and 135 deg wrt the reference direction Stokes V: – right handed minus left handed circular polarization

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Measuring Polarization This means measuring flux differences along different electric field oscillation planes In principle one would be able to measure linear polarization simply rotating a linear polarizer and measuring the light intensity as a function of rotation angle. In the presence of polarization this would produce an intensity modulation, with a period of 180º In practice we can do this for a limited number of rotation angles

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It can be shown that computing the I component of the S vector transformed by a linear polarizer one obtains: Or, in other words: Therefore, fitting this law to the observed f ’ s, one can immediately get I, P and χ.

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Why do we use dual-beam polarimeters Sky transparency and seeing variations hinder this method; This problem is reduced modulating the incoming beam with timescales faster than the atmospheric fluctuations; This also implies that the detector has to be read out very fast. Typically the detector is a photon-counter. All these things make this kind of instruments usable only when the photon shot noise of the source+sky is much larger than the read-out noise. In most of the cases this means bright stars only. Remarkable exceptions are polarimeters in space, where there are no transparency fluctuations. For example WFPC2 on HST. But…

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William Wollaston The magic Wollaston Prism The Wollaston Prims offers the possibility of measuring the intensity along two perpendicular directions simultaneously.

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The two beams are called Ordinary and Extraordinary and are separated by an angle which is usually referred to as throw. For astronomical polarimeters this is of the order of 10-20 arcsec. This means that the image on the telescope focal plane is splitted in two identical images (they differ for the polarization state), which are shifted by an amount equal to the throw. This would generate a complete mess… unless one uses a mask, on the Focal plane, with alternated opaque and transparent strips with a width equal to the throw. This solves the problem of overposition between O and E images,but effectively covers half of the field of view. Therefore, for panoramic polarimetry, two telescope pointings are required to cover the whole field of view. Of course, this is not a problem for single object studies (as in the case of Supernovae).

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A mask is used to avoid overlap

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An example from VLT-FORS1- M83 – V band throw=22" O E

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(The real galaxy)

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To measure intensities along different planes, there are two possibilities. Either you rotate the whole instrument(*) or… You use a half-wave retarder. VLT-FORS1 Half Wave Plate (*) This would change the FOV, and requires mask/slit re-acquisition

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Waveplate - from Wikipedia Constructed out of birefringent material Refraction index differs with light orientation Can choose width to control phase shift of polarization components of light wave A half-wave plate shifts the polarization direction of linearly polarized light Similarly, a quarter-wave plate converts Linearly to circularly polarized light (and vice versa)

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Going back to the f’s Need at least N = 2 retarder angles to solve for all unknowns. By introducing the normalized flux differences F : It can be shown that N = 4 and π/8 is the optimal Choice. We thus obtain the following solution:

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An example with a SN Ordinary beam Extraordinary beam θ = 0 θ = π/8 θ = π/4 θ = 3π/8

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Error analysis and time budgets involved It turns out that To probe a polarization of 0.3% at the 3σ level one needs a signal with SNR of 500 ! To probe a 20mag target, FORS2 on a 8m telescope just needs 1 sec for SNR = 28 But for SNR = 500 one needs 350s ( x 4)! Spectropolarimetry even more time- consuming

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ESO-172 Boomerang Nebula FORS1 P~50% ! An extreme example

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A few words on spectropolarimetry It is simply the same thing only that we study the evolution of polarization at different wavelengths

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Examples from SNe The Q-U plane

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