1. Elettra Sincrotrone Trieste
Introduction to Basics on radiation probing and imaging using x-ray detectors
Ralf Hendrik Menk
Elettra Sincrotrone Trieste
INFN Trieste
Part 3

2. We want to detect the deposed energy with a generic detector
DQE
What is the DQE?
We want to detect the deposed energy with a generic detector

3. Generic detector: quantum efficiency
Mean number of incident photons
Absorption
Conclusion to course, lecture, et al.
Back plane
Transmission
Detection volume
Technically: Energy carried by photons generates free charges
Mean number of interacting photons deposing energy
Pixels

4. Photoelectric effect Nobel price 1921 Observation:
Energy of emitted photo electrons depends on photon energy only not on the intensity of the incident light
Postulation: light is also a particle (photon or quanta) with an energy
h is Planck’s quanta of action

5. Atomic levels (Bohr) X-rays are also particles Angular momentum
Coulomb force
Centripetal force
a0 = Å
Electron radius

6. Atomic levels
Electrostatic potential
13.6 eV

7. Generic detector: energy to charge conversion
Photo effect
Back plane
Ion /hole +
Conclusion to course, lecture, et al. -
photo electron
1023 Atoms /mol => P(x) ~ : rare events => Poisson statistics
bias
Pixels

8. Generic detector working principle
Photo effect 10 4 3 10 Kr
µ[gr/cm2] Si + 10 2 Ar Xe - 10 1 10
Conclusion to course, lecture, et al. 10 -1
Transmission
dead space
Photon energy [keV]
Transmission
window
absorption

9. Generic detector working principle
Photoeffect dominant

10. Generic detector working principle
Photo effect
Conclusion to course, lecture, et al.

11. Detector working principle
Electron collision induced ionization
Back plane
Ion /hole + + + + + + + - - +
Conclusion to course, lecture, et al. - - - - - + + + - - -
Wion is at least the energy required to generate an electron ion/hole pair
Thermalized photo electron - + + - -
bias
Pixels

12. Charge collection and collection efficiencySi
C (diamond)
GaAs ~1.0

13. Detector working principle
Photo electron range
Spatial and temporal impact
Ion /hole + + + + + +
Range of photo electrons
Conclusion to course, lecture, et al. + - - + - - - - - + + + - - - -
Thermalized photo electron + + - -

14. Detector working principle
Fluorescence: spatial and temporal impact.
Stopped fluorescence photon + -
Ion /hole
Conclusion to course, lecture, et al. + + + + + + + - - + - - - - - +
is the energy missing once the the fluorescence escapes from the detection volume. +
Escaped fluorescence photon + - - - - +
Thermalized photo electron + - -

15. Atomic levels
Electrostatic potential
13.6 eV

16. Atomic levels

17. Detector working principle
Auger effect
Stopped fluorescence photon
Auger electron - + -
Ion /hole
Conclusion to course, lecture, et al. + + + + + + + - - + - - - - - + + + - - - -
For Auger effect on the L shell. Normally low energy electrons with limited range . +
Thermalized photo electron + - -

18. Fluorescence and Auger yield

19. Detector working principle
Recombination & drift
Drift of charges in external electric field Si
µ electrons ≤1400 cm2 V-1s-1
µ holes ≤450 cm2 V-1s-1 - + - + + + + + + + - - +
Conclusion to course, lecture, et al. - - - - - + +
α recombination coefficient + - - - - + + - -
Ions in gas : ~ 10m/s (100 m runners)
electrons in gas : ~ 10000m/s

20. Detector working principle
Diffusion - - - - - - - - - - - - - - - - - - - - - - - - - -
Conclusion to course, lecture, et al. Si
Diffusion coefficient electrons ≤36 cm2/s
Diffusion coefficient holes ≤12 cm2/s -
t = 0
t = t1
t = t2

21. Detector working principle
Deposed energy - + - + + + + + + + - - +
Conclusion to course, lecture, et al. - - - - -
Thermal charge + + + - - - - +
Leakage current : doubles every 7°C in Si + - -

22. Detector working principle
Deposed energy - + - + + + + + + + - - +
Conclusion to course, lecture, et al. - - - - -
Thermal charge + + + - - - - +
Leakage current : doubles every 7°C in Si + - -

23. Detector working principle
Charge collection
Ion/hole tail
Collected charge - + -
electrons
~ ms for gases + + + + + + + - - +
Time t
Conclusion to course, lecture, et al. - - - - -
I(t) = dQ/dt + + + - - - - + + - -
Time t

24. Fano factor (correlation)
Total energy
Stopped fluorescence photon Ep
Energy E
Auger electron - + P - N
Ion /hole
Energy absorption step p + + +
Expected no of ionization in p + + + + - - + - - - -
Expected mean no of generated charges - + + + - - -
Error in the energy - +
Thermalized photo electron + -
F = Fano factor
F < 1 -

25. Charge generation (single photon)
Material Fano
Ar 0.2 Xe
Si:
Ge:
GaAs:
Diamond:
For a 55Fe (6.4 keV) photons in Si and 10 e- noise
Single event resolution
FWHM
Fano limit 120 eV FWHM

26. Escape peak
Peak to valley ratio

27. Continues radiation - + - + + + + + + + - - + - - - - - + + + - - - -
Collected charge Q(t)
Time t
~ ms
I(t) = dQ(t)/dt = const
Q(t) - + - + + + + + + + - - + - - - - - + + + - - - - + + - -

28. Gaseous Ionisation detector regions
Geiger region
Ion chamber region
Proportional counter region
Continuous discharge
Charge collected
recombination
Not used
Not used
Applied voltage

29. Generic detector working principle
Frame trigger
Dead time
threshold
i(t)
ADC
u(t)
noise
leakage
Conclusion to course, lecture, et al.
q(t)
ADC
u(t)
i(t)
Discr.
u(t)

30. Dead time X-ray Events Non paralyzed dead alive paralyzed dead alive
m = measured rate
n = real rate
= dead time

31. Dead time

32. DQE counting& integrating
Zero spatial frequency DQE for non -paralyzed counting detectors
Zero spatial frequency DQE for integrating detectors

33. Detective Quantum Efficiency

34. Spatial resolution
Bottom line: connect each pixel /strip to an amplifier and collect charges released
Pixel size
b/2
-b/2
Periodic repetition of pixels in real detector
Segmentation is a convolution of g(x) with Dirac comb

35. Spatial resolution Contribution to the spatial resolution
pixel size of the segmentation (g1)
range of photo electrons (g2)
diffusion of the drifting charges (g3)
range of the fluorescence (g4)
electronics cross talk (g5)
etc

36. Detective Quantum Efficiency
Integrating detectors
Counting detectors
noise: 10 photons
Dead time 10-6 s
DQE = ε 1 4b
Spatial frequency
Spatial frequency 1 2b
Photon flux
Photon flux
DQE = 0

37. Radiation dose For biomedical applications DQE should be ~ 1
Direct imaging
C: object contrast
w: detail size
Scatter imaging
For biomedical applications DQE should be ~ 1