General Characteristics of Detectors
§
Sensitivity
capability of producing an usable signal for a given type of radiation
mass of the detector, noise level, …
§
Energy resolution
§
Response Function
§
Timing
§
Efficiency
§
Dead Time
Energy Resolution
d
R = FWHM / E = ΔE / E
for
E = 1 MeV
NaI
HpGe
R ∼ 8-9 %
R ∼ 0.1 %
• Two peaks are considered as resolved when d > FWHM
• R is a function of E: it improves with higher energy (Poisson statistics)
E = n w, with w = average energy per ionization, n = # ionization
Partial deposition of energy
Poisson
σ2 =n
R = FWHM / E
= 2.35σ / E
= 2.35
2
[independent
charge carriers
Formation]
n
1
w
= 2.35
= 2.35
n
E
n
2
det
(ΔE ) = (ΔE )
2
elect
+ (ΔE )
+ ...
Full deposition of energy
σ 2 = Fn
Not fully Poisson
R = FWHM / E
= 2.35σ / E
= 2.35
F< 1
Fano Factor
Fn
Fw
= 2.35
n
E
F ≡ observed variance in n
Poisson predicted variance
Detector Response
HpGe
NaI
Compton
Edge only !
Eγ = 661 keV
S ( E) = ∫ S ( E' ) f ( E, E' )dE '
DETECTOR response function
Best Response:
f ( E, E ' ) = δ ( E − E ' )
Response Time
Time taken to form the signal after arrival of radiation
GOOD timing: signal quickly formed in a sharp pulse
almost vertical rising flank
⇒ precise moment in time
marked by the signal
Duration of the signal: No second event can be fully accepted
(insensitive detector or pile up)
Dead Time:
it is strongly related
to the efficiency
Methods to estimate
dead time
Methods to estimate dead time
m = true count rate
K = number o counts registered in interval T
τ = dead time due to a single event
à mkτ = lost counts
à mT = true number of counts
More Difficult
only counts arriving at t > τ are recorded
Distribution of time interval
between events decaying at a rate m
Efficiency
events registered
ε TOT =
= ε int × ε geom
events emitted by source
events registered
depends on radiation, material, …
ε int =
events impinging
dΩ
ε geom =
fraction of solid angle: pure geometry
4π
cos θ
dA
r2
⎛
⎞
d
⎟
= 2π ⎜⎜1 −
2
2 ⎟
d + a ⎠
⎝
A
= 2
for d >> a
d
dΩ = ∫
a
A
MonteCarlo simulations are needed for complex geometry …
Simplified Detector Model
τ = RC
Current output
R=input resistance
C=input capacitance+
detector capacitance +
cables …
τ = RC << tc
τ = RC >> tc
operation mode
for time information,
high rates, …
operation mode
for energy information
Vmax ~ Q
tc
charge collection
time ~100 ns
Ge
τ =RC
decay time
~ 50 µs
⇒ output is a string
mainly due to
preamplifier
Current flowing through the
load resistance R
is equal to
current flowing in detector
Little Current flowing through the
load resistance R
during collection time
à
Detector Current
momentarily integrated on C
of pulses
each one resulting from interaction of
single quantum of radiation
Preamplifier
τ = RC
R=input resistance
C=input capacitance+
detector capacitance +
cables …
Amplifier
(RC-CR shaping)
RC-integrator (low-pass filter)
Ein = iR + Eout
...
Eout = E (1 − e −t /τ )
operation mode
for time information,
high rates, …
CR-differentiator (high-pass filter)
operation mode
for energy information
Ein =
Q
+ Eout
C
...
Eout = Ee −t /τ
tc
charge collection
time ~100 ns
τ =RC
decay time
~ 50 µs
for Ge
Pulse shaping (in Ge)
FET
energy
Preamplifier : FET (at 130 K,
to minimize noise)
Amplifier:
CR-RC shaping circuit
time
if C1R1=C2R2=τ
true pulses
from preamp
mV
τ ~ 50µs
t
Eout = E e
t
−τ
τ
pile-up
after shaping
V
τ ~ 15 µs
τ ~ 15 µs is a good compromise
between reduced pile-up
and good energy resolution
(depending on large charge collection)