Detection and (Linear) Data Model

Detection and (Linear) Data Model

Jörn WilmsRemeis-Sternwarte & ECAP

Universität Erlangen-Nürnberg

http://pulsar.sternwarte.uni-erlangen.de/wilms/

[email protected]

http://pulsar.sternwarte.uni-erlangen.de/wilms/

[email protected]

Part 1: Why is X-ray and Gamma-Ray AstronomyInteresting?

Part 2: Tools of the Trade: Satellites

Earth’s Atmosphere

CXC

Earth’s atmosphere isopaque for all types of EMradiation except for opti-cal light and radio.

Major contributer at highenergies: photoabsorption(∝ E−3), esp. from Oxygen(edge at ∼500 eV).=⇒ If one wants to look at

the sky in other wave-bands, one has to go tospace!

The Present

XMM-Newton (ESA): launched 1999 Dec 10 Chandra (NASA): launched 1999 Jul 23

Currently Active Missions: X-ray Multiple-Mirror Mission (XMM-Newton; ESA),Chandra (USA), Suzaku (Japan, USA), Swift (USA),

International Gamma-Ray Laboratory (INTEGRAL; ESA), Fermi (USA), AGILE (Italy),MAXI (Japan), ASTROSAT (India), NICER (USA), Spectrum-X-Gamma (RU/D)

We are living in the “golden age” of X-ray and Gamma-Ray Astronomy

The Present

IceCube/PINGU

KAGRAAdvanced LIGO/Virgo

H.E.S.S.

VLTAPEXALMA

IRAM/NOEMAFAST

MEERKATASKAP/MWA

LOFAR

Lomonosov/MVL-300

DAMPEFermi

AGILEINTEGRAL

Spectrum-X-GammaKanazawa-Sat3HaloSatMVN

Insight-HXMTNICER

XPNAV-1POLAR

ASTROSATNuSTAR

MAXISwift

ChandraXMM-Newton

Solar OrbiterTESS

GaiaKepler/K2

HST

SofiaSpitzer

Queqiao/NCLELongjiang-1/2

RadioAstron

20322030202820262024202220202018Year

The Present

KM3NeTIceCube/PINGU

Einstein TelescopeLIGO-India

KAGRAAdvanced LIGO/Virgo

CTAH.E.S.S.

E-ELTLSST

VLTAPEXALMA

SKAIRAM/NOEMA

FASTMEERKAT

ASKAP/MWALOFAR

M5

Lomonosov/MVL-300Glowbug

DAMPEFermi

AGILEINTEGRAL

AthenaEinstein Probe

XRISMSVOM

IXPEASO-S

Spectrum-X-GammaKanazawa-Sat3HaloSatMVN

Insight-HXMTNICER

XPNAV-1POLAR

ASTROSATNuSTAR

MAXISwift

ChandraXMM-Newton

ArielPLATO

EuclidWSO-UV

CHEOPSSolar OrbiterTESS

GaiaKepler/K2

HSTWFIRST

SPHERExJWST

SofiaSpitzer

Queqiao/NCLELongjiang-1/2

RadioAstron

20322030202820262024202220202018Year

Part 3: Tools of the Trade: Mirrors and Detectors

IntroductionHow is X-ray astronomy done?

Detection process:

Imaging Detection Data reduction Data analysis


Imaging:

• Wolter telescopes (soft X-rays up to ∼15 keV)

• Coded Mask telescopes (above that)

• Collimators


Detectors:

• Non-imaging detectorsDetectors capable of detecting photons from a source, but without any spatial resolution

=⇒ Require, e.g., collimators to limit field of view.

Example: Proportional Counters, Scintillators

• Imaging detectorsDetectors with a spatial resolution, typically used in the IR, optical, UV or for soft X-rays.Generally behind some type of focusing optics.

Example: Charge coupled devices (CCDs), Position Sensitive Proportional Counters(PSPCs)

X-ray Imaging

Cassegrain telescope, after WikipediaReminder: Optical telescopes are usually reflectors:primary mirror→ secondary mirror→ detectorMain characteristics of a telescope:• collecting area (i.e., open area of telescope, ∼ πd2/4, where d: telescope diameter)• angular resolution,

θ = 1.22λ

d(1)

if surface roughness and alignment can be ignored

X-ray ImagingOptical telescopes are based on principle that reflection “just works” withmetallic surfaces. For X-rays, things are more complicated. . .

1α

2α

1θ

n2

n1

n1

<

Snell’s law of refraction:sinα1

sinα2=n2

n1= n (2)

where n index of refraction, and α1,2 angle wrt.surface normal. If n � 1: Total internal reflec-tionTotal reflection occurs for α2 = 90◦, i.e. for

sinα1,c = n ⇐⇒ cos θc = n (3)

with the critical angle θc = π/2 − α1,c.Clearly, total reflection is only possible for n <1

Light in glass at glass/air interface: n = 1/1.6 =⇒ θc ∼ 50◦ =⇒ principle behind optical fibers.

X-ray ImagingIn general, the index of refraction is given by Maxwell’s relation,

n =√εµ (4)

where ε: dielectricity constant, µ ∼ 1: permeability of the material.For free electrons (e.g., in a metal), (Jackson, 1981, eqs. 7.59, 7.60) showsthat

ε = 1 −(ωp

ω

)2with ω2

p =4πnZe2

me(5)

where ωp: plasma frequency, n: number density of atoms, Z: nuclearcharge.(i.e., nZ: number density of electrons)

With ω = 2πν = 2πc/λ, Eq. (5) becomes

ε = 1 −nZe2

πmec2λ2 = 1 −

nZre

πλ2 (6)

re = e2/mec

2 ∼ 2.8× 10−13 cm is the classical electron radius.

X-ray Imaging

n =

√1 −

nZre

πλ2 ∼ 1 −

nZre

2πλ2 = 1 −

ρ

(A/Z)mu

re

2πλ2 =: 1 − δ (7)

Z: atomic number, A: atomic weight (Z/A ∼ 0.5), ρ: density, mu = 1 amu = 1.66× 10−24 g

Critical angle for X-ray reflection:

cos θc = n = 1 − δ (8)

Since δ� 1, Taylor (cos x ∼ 1 − x2/2):

θc =√

2δ = 5.6 ′(

ρ

1 g cm−3

)1/2λ

1 nm(9)

So for λ ∼ 1 nm: θc ∼ 1◦.

X-ray ImagingTypical parameters for selected elements

Z ρ nZ

g cm−3 e− Å−3

C 6 2.26 0.680Si 14 2.33 0.699Ag 47 10.50 2.755W 74 19.30 4.678Au 79 19.32 4.666

After Als-Nielsen & McMorrow (2004, Tab. 3.1)

To increase θc: need material with high ρ=⇒ gold (XMM-Newton) or iridium (Chandra).

For more information on mirrors etc., see, e.g., Aschenbach (1985), Als-Nielsen & McMorrow (2004),or Gorenstein (2012)

X-ray Imaging

0 5 10 15 20

Photon Energy [keV]

0.0

0.2

0.4

0.6

0.8

1.0

Reflectivity 0.5deg

0.4deg

0.2deg

1deg

Reflectivity for Gold

X-rays: Total reflec-tion only works inthe soft X-rays andonly under grazingincidence=⇒ grazing inci-dence optics.

Wolter Telescopes

Incident

paraxial

radiation

Hyperboloid

Paraboloid

HyperboloidFocus

after ESA

To obtain manageable focal lengths (∼10 m), use two reflections on aparabolic and a hyperboloidal mirror (“Wolter type I”)(Wolter 1952 for X-ray microscopes, Giacconi & Rossi 1960 for UV- and X-rays).

But: small collecting area (A ∼ πr2l/f where f: focal length)

Wolter Telescopes

−+

Ni Electroforming

Cleaning

Gold Deposition

MirrorAu

Ni

Separation

(cooled)

IntegrationProduction

Metrology

Integration

on Spider

Hole Drilling

Handling

Mandrel

Super Polished Mandrel

Recycle Mandrel

(after ESA)Recipe for making an X-ray mirror:1. Produce mirror negative (“Mandrels”): Al coated with Kanigen nickel (Ni+10% phos-

phorus), super-polished [0.4 nm roughness]).2. Deposit ∼50 nm Au onto Mandrel3. Deposit 0.2 mm–0.6 mm Ni onto mandrel (“electro-forming”, 10µm/h)4. Cool Mandrel with liquid N. Au sticks to Nickel5. Verify mirror on optical bench.

numbers for eROSITA (Arcangeli et al., 2017)

Wolter Telescopes

Wolter Telescopes

Characterization of mir-ror quality: Half EnergyWidth, i.e., circle within50% of the detected en-ergy are found. Note:energy dependent!for XMM-Newton: 20 ′′ at1.5 keV, 40 ′′ at 8 keV.for eROSITA: 16 ′′ at 1.5 keV,15.5 ′′ at 8 keV

Ground calibration, e.g., at PANTER

Detection of X-rays

Space

Ener

gy

EFermi

Semiconductors: separa-tion of valence band andconduction band ∼1 eV(=energy of visible light).

Absorption of photon in Si:Energy of photon releasedphoto electron(s) + scattering off e−+ phonons. . .

Number of electron-hole pairs produced: Problem: normal semiconductor:e−-hole pairs recombine immediately

Detection of X-rays

Space

Ener

gy

EFermi

Acceptors

Donors

n-type p-type

“Doping”: moves valence-and conduction bands.Connecting “n-type” anda “p-type” semiconductor:pn-junction.

In pn junction: electron-hole pairs created by ab-sorption of an X-ray areseparated by field gradient

=⇒electrons can then be collected in potential well away from the junc-tion and read out.

Detection of X-raysMaterial Z Band gap E/pair

(eV) (eV)Si 14 1.12 3.61Ge 32 0.74 2.98

CdTe 48–52 1.47 4.43HgI2 80–53 2.13 6.5GaAs 31–33 1.43 5.2

Number of electron-hole pairs produced determined by band gap + “dirteffects”(“dirt effects”: e.g., energy loss going into bulk motion of the detector crystal [“phonons”])

Npair ∼Ephoton

Epair(10)

• optical photons (E: few eV): ∼1 e−-hole-pair per absorption event• X-ray photons: ∼1000 e−-hole-pairs per photonBut: Since band gap small: thermal noise =⇒ need cooling(ground based: liquid nitrogen, −200◦C, in space: more complicated. . . )

Detection of X-rays

e_

e_

e_

e_

photoelectrons

Atom

Photoelectron

trackp−type

(undepleted)

Potential energy

for an electron

p−type (−) silicon

(depleted)

n−type (+) silicon

(depleted)

SiO insulator

0.1 m deep

Polysilicon electrodes

11

1 2 3

1 pixel

(~15 m)

~2 m

~10 m

~250 m

3 1 2 3 1 2 3 2 3

µ

µ

µµ

µ

Photon

µconductors; ~0.5 m deep

2

After Bradt

Two-Dimensional imaging is possible with more complicated semiconduc-tor structures: Charge Coupled Devices (CCDs).

CCDs

−PulseΦ

1Φ

2Φ

3Φ

− − − −−−

3Φ

2Φ

1Φ

Transfer

− − −

− − −

− − −

0V 0V 0V

0V0V

0V 0V 0V

+V

+V +V

+V

(after McLean, 1997, Fig. 6.9)

Principle of the readout of a CCD with Φ-pulses.

CCDs

Gate strips

p−

sto

ps

Read−

out e

lectro

nic

s

combine several readoutstripes gives a two dimen-sional detector.Separation of individual columnswith p-stops (highly doped Si) toprevent charge diffusion betweencolumns.

Read out:• move charge to corner• preamplify• digitize in Analog-

Digital-Converter (ADC)Fast CCDs: one read out electronics per columnExpensive, consumes more power =⇒ only done in the fastest X-ray CCDs (< µs resolution).

CCDs

+ + + + + +

+

− − − −

−

−

preamp

on−chip

n−

p p p p p p

p

285 µ

m12 µ

m

Phi−Pulses to transfer electrons

Depletion voltagePotential for electrons

Anode

Transfer direction

Schematic structure of the XMM-Newton EPIC pn CCD.

Problem: Infalling photons have to pass through structure on CCD surface =⇒ loss of lowenergy response, also danger through destruction of CCD structure by cosmic rays. . .Solution: Irradiate back side of chip. Deplete whole CCD-volume, transport electrons topixels via adequate electric field (“backside illuminated CCDs”)Note: solution works mainly for X-rays

Grades

Charge cloud in Si has roughly 2D Gaussian distribution=⇒ Distribution of clouds on adjacent pixels: “eventgrades”Total E:

∑pixels Ei

ESA: single events, double events,. . . ; US: grade 0 for singles,grade 1–4 for doubles, etc.; other grading schemes are possible.

C. Schmid

Background

M. WilleBackground in CCDs:• cosmic rays (e.g., muons), leaving long tracks on detector• low E (<MeV) protons, focused via mirrors onto CCDs. Especially during solar flares

In principle also electrons: charged “net” over mirror deflects them; this not possible for protonsdue to higher mass; back-illuminated CCDs can usually cope with this and are not damaged.

Typically background reduction on board through thresholding events, e.g., >15 keV wheremirror is non-reflective

Optical Loading

F. Krauss

Optical loading: like all CCDs, X-ray sensitive CCDs are sensitive to opticallightMitigation: optical filter, either on chip or via filter wheelBlocks out light to 8 mag or so =⇒ brighter stars are problem

Part 5: Analyzing Data – Theory

Formal Data AnalysisIn order to analyze X-ray data, we need to understand how the measuredsignal is produced:

1. Sensitivity of the detector: “how much signal do we have?”=⇒ modeled as energy-dependent collecting areaoften called the “ARF” (ancilliary response function)

2. Energy resolution of the detector: “where is the signal detected?”=⇒ modeled as convolution of signal with energy resolutionoften called the “detector response”

Linear Model

Summarizing the previous information mathematically:

nph(c) =

∫∞0R(c,E) ·A(E) · F(E)dE+ nbackground(c) (11)

Linear Model


nph(c) =


count rate inchannel c

(counts s−1)

Linear Model


nph(c) =



(counts s−1)

photon flux density(ph cm2 s−1 keV−1),

Linear Model


nph(c) =



(counts s−1)


We measure this

Linear Model


nph(c) =



(counts s−1)


We measure this Astrophysics is here

Linear Model


nph(c) =



(counts s−1)

detector response(∝ probability todetect photon of

energy E inchannel c).


We measure this Astrophysics is here

Linear Model


nph(c) =



(counts s−1)

detector response(∝ probability todetect photon of

energy E inchannel c).

effective area(cm2)


We measure this Astrophysics is hereCalibration

(“response” / “rsp”)

Effective Area

Mirror

IrM

4,5

IrM

3

IrM

2Ir

M1

IrL3

IrL1

1010.1

10+4

10+3

10+2

Energy [keV]

Area[cm

2]

Effective area for an Athena-like mission with a simplified Si-based detector

Effective Area

Mirror+45nm polyamide+70nm Al

AlK

OK

NK

CK

IrM

4,5

IrM

3

IrM

2Ir

M1

IrL3

IrL1

1010.1

10+4

10+3

10+2

Energy [keV]

Area[cm

2]


Effective Area

Mirror+45nm polyamide+70nm Al

+Si QE

AlK

OK

NK

CK

SiK

IrM

4,5

IrM

3

IrM

2Ir

M1

IrL3

IrL1

1010.1

10+4

10+3

10+2

Energy [keV]

Area[cm

2]


Effective areas of the most important currentX-ray satellites

(Hanke, 2011)

Response Matrixoptical:1 pair/photon =⇒ collected charge ∝ intensity


X-ray: many pairs/photon =⇒ collected charge ∝ energyNpairs ∝ Ephoton



=⇒ imaging spectroscopy!requires very fast readout (� arrival rate of photons)

bright sources: several 1000 photons per second =⇒ readout in µs!





Poisson statistics of relative collected charge:

∆Npair

Npair






∆Npair

Npair=

√Npair

Npair






∆Npair

Npair=

√Npair

Npair=

1√Npair






∆Npair

Npair=

√Npair

Npair=

1√Npair

∼∆E

E

(∆E/E ∝ E−1/2 because of Poisson!)






∆Npair

Npair=

√Npair

Npair=

1√Npair

∼∆E

E=

exact eq.= 2.355

√3.65 eV · F

E

(∆E/E ∝ E−1/2 because of Poisson!)

F ∼ 0.1 =⇒ ∼2% at 5.9 keVF is called the Fano factor

Response Matrix

(Fürst, 2011)

Monoenergetic photons get “smeared” in energy by the detector response.Width of peak given by Eq. on previous slidenote: RMF is not required to be normalized to unity! Some missions include some quantum efficiencyterms in it.

Response Matrix

(Treis et al., 2009)

Mn Kα (5.9 keV), Mn Kβ (6.5 keV), Si escape (4.2 keV), Al fluorescence(1.5 keV) from housing [background]

Response Matrix

Response Matrix of the RXTE-PCA, log scaleSecondary “escape” peaks: response caused by Xe Kβ and Xe Lα photons escaping the de-tector.

Pile Up

some invalid patterns

Pile up: Arrival rate of photons > readouttimescale of CCD =⇒ get wrong energyassignment

• energy pileup: multiple photons insame pixel

• pattern pileup: multiple photons inadjacent pixelssome produce invalid patterns, butsome mimic normal photons

nonlinear effect!

figures by C. Schmid (PhD thesis Remeis-Observatory & ECAP, 2012)

Pile Up

Pile up: Arrival rate of photons > readouttimescale of CCD =⇒ get wrong energyassignment

• energy pileup: multiple photons insame pixel

• pattern pileup: multiple photons inadjacent pixelssome produce invalid patterns, butsome mimic normal photons

nonlinear effect!

figures by C. Schmid (PhD thesis Remeis-Observatory & ECAP, 2012)

χ2-minimizationWe had

nph(c) =


where• nph(c): source count rate in channel c (counts s−1),• F(E): photon flux density (ph cm2 s−1 keV−1),• A(E): effective area (units: cm2),• R(c,E): detector response (probability to detect photon of energy E in

channel c).

We measure nph(c), but the astrophysics is contained in F(E). Inver-sion of Eq. (12) is not possible!

=⇒ Data analysis:1. guess F(E) from astrophysics2. predict nph(c) from Eq. (12)3. compare prediction and measurement4. modify guess. . .

χ2-minimizationTo analyze data: discretize Eq. (12):

Sph(c) = ∆T ·nch∑i=0

A(Ei) · R(c, i) · F(Ei) · ∆Ei ∀c ∈ {1, 2, . . . ,nen} (13)

where Sph(c): total source counts in channel c, ∆T : exposure time (s),A(Ei): effective area in energy band i (“ancilliary response file”, ARF),R(c, i): response matrix (RMF), F(Ei): source flux in band (Ei,Ei+i), ∆Ei:width of energy band.Because of background B(c) (counts), what is measured is

Nph(c) = Sph(c) + B(c) (14)

So estimated source count rate is

S̃ph(c) = Nph(c) − B(c) (15)

with uncertainty (Poisson!)

σS̃ph(c) =√σNph(c)2 + σB(c)2 =

√Nph(c) + B(c) (16)

χ2-minimizationTo get physics out of measurement, need to find F(Ei).

Big problem: In general, Eq. (13) is not invertible.

=⇒ χ2-minimization approachUse a model for the source spectrum, F(E; x), where x vector of parameters(e.g., source flux, power law index, absorbing column,. . . ), and calculatepredicted model counts, M(c; x), using Eq. 13).Then form χ2-sum:

χ2(x) =∑c

(S̃ph(c) −M(c; x)

)2

σS̃ph(c)2(17)

Then vary x until χ2 is minimal and perform statistical test based on χ2

whether model F(E; x) describes data.

Programs used: XSPEC, ISIS, SPEX

In practice, background is not subtracted from measurement, but added on model prediction.

Part 4: Further Reading

Literature

LONGAIR, M.S., 1992, High Energy Astrophysics, Vol. 1: Particles, Photons,and their Detection, Cambridge: Cambridge Univ. Press, ∼50eGood introduction to high energy astrophysics, the 1st volume deals extensively withhigh energy procsses, the 2nd with stars and the Galaxy. The announced 3rd volume hasnever appeared. Unfortunately, everything is in SI units.

TRÜMPER, J., HASINGER, G. (eds.), 2007, The Universe in X-rays, Heidel-berg: Springer, 96.25eBook giving an overview of X-ray astronomy written by a group of experts (mainly) fromMax Planck Institut für extraterrestrische Physik, the central institute in this area in Ger-many.

BRADT, H., 2004, Astronomy Methods: A Physical Approach to Astronomi-cal Observations, Cambridge: Cambridge Univ. Press, $50Good general overview book on astronomical observations at all wavelengths.

Literature

CHARLES, P., SEWARD, F., 1995, Exploring the X-ray Universe, Cambridge:Cambridge Univ. Press, out of printSummary of X-ray astronomy, roughly presenting the state of the early 1990s.

SCHLEGEL, E.M., 2002, The restless universe, Oxford: Oxford Univ. Press,32ePopular X-ray astronomy book summarizing results from XMM-Newton and Chandra.

ASCHENBACH, B. et al., 1998, The invisible sky, New York: CopernicusPopular “table top” book summarizing the results of the ROSAT satellite, with many

beautiful pictures.

KNOLL, G.F., 2000, Radiation Detection and Measurement, 3rd edition,New York: Wiley, 126eThe bible on radiation detection. If you want one book on detectors, this is it.

WWW-Pages• http://pulsar.sternwarte.uni-erlangen.de/wilms/teach

My lectures. Including a 2 semester long course on X-ray astronomy (with exercises) anda 1 semester long course on radiation processes. Currently offline, but soon to be onlineagain, but I provide slides upon request.

• http://heasrc.gsfc.nasa.govMain www page of NASA’s satellite missions, including the data archive interface athttp://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3browse.pl

• http://cxc.harvard.edu

Chandra data center (and analysis info)

• http://xmm.esac.esa.int

XMM-Newton data center (and analysis info)

• http://ledas-www.star.le.ac.uk

Univ. Leicester data archive (many missions)

• http://www.isdc.unige.ch/heavens/

Interface to prereduced INTEGRAL and RXTE data

http://pulsar.sternwarte.uni-erlangen.de/wilms/teach

http://heasrc.gsfc.nasa.gov

http://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3browse.pl

http://cxc.harvard.edu

http://xmm.esac.esa.int

http://ledas-www.star.le.ac.uk

http://www.isdc.unige.ch/heavens/

X-ray Data Analysis 65a

Bibliography

Als-Nielsen, J., & McMorrow, D. 2004, Elements of Modern X-ray Physics, (New York: Wiley)Arcangeli, L., Borghi, G., Bräuninger, H., et al. 2017, in Internat. Conf. on Space Optics, ed. E. Armandillo, B. Cugny, N. Karafolas, Vol. 10565, SPIE Conf. Ser.,

1056558Aschenbach, B., 1985, Rep. Prog. Phys., 48, 579Fürst, F., 2011, Ph.D. thesis, Universität Erlangen-Nürnberg, ErlangenGiacconi, R., & Rossi, B. 1960, J. Geophys. Res., 65, 773Gorenstein, P., 2012, Opt. Eng., 51, 011010Hanke, M., 2011, Ph.D. thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg, ErlangenJackson, J. D., 1981, Klassische Elektrodynamik, (Berlin, New York: de Gruyter), 2 editionMcLean, I., 1997, Electronic imaging in astronomy: detectors and instrumentation, Wiley)Treis, J., Andritschke, R., Hartmann, R., et al. 2009, J. Instrumentation, 03, 03012Wolter, H., 1952, Annalen der Physik, 445, 94

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Detection and (Linear) Data Model