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Astronomical Techniques ILecture 14

Yogesh Wadadekar

Jan-Feb 2015

IUCAA-NCRA Grad School 1 / 21

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Focussing hard X-rays

hard because grazing angles are too small - telescopes areimpracticably long and have a small field of view. Effectivecollecting area also decreases.Can one make the effective refractive index lower so that θcincreases?

Yes, in principle. By using Bragg reflection from depth-gradedmultilayers. Alternate layers of a high Z (like W, Mb, Ni) and a lowZ (C, Si) materials with high and low refractive indices, and withbilayer thickness varying over a wide range have to be used.NuStar uses this technology.this technology is under further development.

IUCAA-NCRA Grad School 2 / 21

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Focussing hard X-rays

hard because grazing angles are too small - telescopes areimpracticably long and have a small field of view. Effectivecollecting area also decreases.Can one make the effective refractive index lower so that θcincreases?Yes, in principle. By using Bragg reflection from depth-gradedmultilayers. Alternate layers of a high Z (like W, Mb, Ni) and a lowZ (C, Si) materials with high and low refractive indices, and withbilayer thickness varying over a wide range have to be used.NuStar uses this technology.this technology is under further development.

IUCAA-NCRA Grad School 2 / 21

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Hard X-ray detector technologies

CZT - CdZnTe crystals used as detectors. useful above 10 keV. CZTimager on Astrosat is one such. NuSTAR also uses CZT detectors.These are not CCDs. But they have readout on each pixel like CMOSdevices. Current generation CZT detectors have small number ofpixels e.g. 64× 64 on NuSTAR.

IUCAA-NCRA Grad School 3 / 21

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Coded masks for Gamma ray imaging

Two of the four X-ray instruments aboard ASTROSAT use codedmasks(i) Scanning Sky Monitor (SSM) (ii) Cadmium Zinc TellurideImager (CZTI)

IUCAA-NCRA Grad School 4 / 21

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For more details read

Arnaud et al. Handbook of X-ray astronomy

IUCAA-NCRA Grad School 5 / 21

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Polarisation indicates anisotropy

studied mostly in the optical and the radio, although other wavebandsare catching up.

geometry (not everything is spherically symmetric)temperature gradientsmagnetic fieldselectrical fields

IUCAA-NCRA Grad School 6 / 21

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Polarised astronomical sources

planets (scattering by atmospheric clouds in Jupiter and Saturn)interstellar dust (possibly aligned by a magnetic field)Zeeman effect in stars with magnetic fieldsupernova asymmetriesquasars and radio jetsCMB

IUCAA-NCRA Grad School 7 / 21

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Plane Vector Wave Ansatz

~E = ~E0ei(~k ·~x−ωt)

spatially, temporally constant vector ~E0 lays in a planeperpendicular to propagation direction ~krepresent ~E0 in 2-D basis, unit vectors ~e1 and ~e2, bothperpendicular to ~k

~E0 = E1 ~e1 + E2 ~e2

E1, E2: arbitrary complex scalarsIf E1 and E2 have identical phases, ~E oscillates in fixed plane

IUCAA-NCRA Grad School 8 / 21

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Plane Vector Wave Ansatz

~E = ~E0ei(~k ·~x−ωt)

spatially, temporally constant vector ~E0 lays in a planeperpendicular to propagation direction ~k

represent ~E0 in 2-D basis, unit vectors ~e1 and ~e2, bothperpendicular to ~k

~E0 = E1 ~e1 + E2 ~e2

E1, E2: arbitrary complex scalarsIf E1 and E2 have identical phases, ~E oscillates in fixed plane

IUCAA-NCRA Grad School 8 / 21

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Plane Vector Wave Ansatz

~E = ~E0ei(~k ·~x−ωt)

spatially, temporally constant vector ~E0 lays in a planeperpendicular to propagation direction ~krepresent ~E0 in 2-D basis, unit vectors ~e1 and ~e2, bothperpendicular to ~k

~E0 = E1 ~e1 + E2 ~e2

E1, E2: arbitrary complex scalars

If E1 and E2 have identical phases, ~E oscillates in fixed plane

IUCAA-NCRA Grad School 8 / 21

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Plane Vector Wave Ansatz

~E = ~E0ei(~k ·~x−ωt)

spatially, temporally constant vector ~E0 lays in a planeperpendicular to propagation direction ~krepresent ~E0 in 2-D basis, unit vectors ~e1 and ~e2, bothperpendicular to ~k

~E0 = E1 ~e1 + E2 ~e2

E1, E2: arbitrary complex scalarsIf E1 and E2 have identical phases, ~E oscillates in fixed plane

IUCAA-NCRA Grad School 8 / 21

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Polarisation ellipse - time variation of ~E at fixed ~x

~E = ~E0ei(~k ·~x−ωt)E0 = E1eiδ1 ~ex + E2eiδ2 ~ey

IUCAA-NCRA Grad School 9 / 21

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Quasi monochromatic light

monochromatic light: purely theoretical conceptmonochromatic light wave always fully polarizedreal life: light includes range of wavelengths⇒ quasi-chromaticlightquasi-monochromatic: superposition of mutually incoherentmonochromatic light beams whose wavelengths vary in narrowrange δλ around central wavelength λ

δλ

λ� 1

measurement of quasi-monochromatic light: integral overmeasurement time tmamplitude, phase (slow) functions of time for given spatial locationslow: variations occur on time scales much longer than the meanperiod of the wave

IUCAA-NCRA Grad School 10 / 21

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Polarisation of quasi-monochromatic light

electric field vector for quasi-monochromatic plane wave is sum ofelectric field vectors of all monochromatic beams that comprise it.

IUCAA-NCRA Grad School 11 / 21

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Polychromatic or white light

wavelength range comparable to wavelengthincoherent sum of quasi-monochromatic beams that have largevariations in wavelengthcannot write electric field vector for the whole wave in aplane-wave formmust take into account frequency-dependent materialcharacteristics eg. refraction changes with wavelength.intensity of polychromatic light is given by sum of intensities ofconstituting quasi-monochromatic beams

IUCAA-NCRA Grad School 12 / 21

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Stokes formalism for quasi-monochromatic light

~I =

IQUV

=

E2

1 + E22

E21 − E2

22E1E2 cos δ2E1E2 sin δ

where δ = δ1 − δ2 and

I2 ≥ Q2 + U2 + V 2

IUCAA-NCRA Grad School 13 / 21

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Interpreting the Stokes Vectors

~I =

IQUV

=

intensity

linear 0− 90 degreeslinear 45− 135 degrees

circular left or right

degree of polarization

P =

√Q2 + U2 + V 2

I

equals 1 for fully polarised light, 0 for unpolarised lightsumming of Stokes vectors = incoherent adding ofquasi-monochromatic light waves

IUCAA-NCRA Grad School 14 / 21

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Percentage of polarised light

45 degree reflection off aluminum mirror: 5%clear blue sky: up to 75%45 degree reflection off glass: 90%LCD screen: 100%exoplanet signal: 0.001%

IUCAA-NCRA Grad School 15 / 21

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Polarisers - linear polarisers are the most common

IUCAA-NCRA Grad School 16 / 21

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Wire grid polariser

polarization perpendicular to wires (d . λ) is transmitted becauseelectric field parallel to wires induces electrical currents in wires, whichstrongly attenuates transmitted electric field parallel to wires inducedelectrical current reflects polarization parallel to wires.

IUCAA-NCRA Grad School 17 / 21

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Polaroid Polariser

sheet polarizers: stretched polyvinyl alcohol (PVA) sheet, laminated tosheet of cellulose acetate butyrate, treated with iodine. PVA-iodinecomplex analogous to short, conducting wire

IUCAA-NCRA Grad School 18 / 21

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IMPOL - A imaging polarimeter made at IUCAA

Rotating half-wave plate by angle α turns the light through 2α. Thusboth Q and U can be measured.

IUCAA-NCRA Grad School 19 / 21

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for more details

Astronomical polarimetry by Jaap Tinbergen

IUCAA-NCRA Grad School 20 / 21

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Closing

Assignment 2 to be given later today. - includes questions on noise,CCDs, photometry, spectroscopy, X-ray astronomy.Seminar talks scheduled for 2 pm - 6 pm on Thursday 26 Feb and 9am - 11 am Friday 27 Feb.Any questions or feedback regarding this course?

IUCAA-NCRA Grad School 21 / 21