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The United States Nuclear Regulatory Commission and Duke University

Present: Regulatory and Radiation Protection Issues in Radionuclide Therapy

Copyright 2008 Duke Radiation Safety and Duke University. All Rights Reserved.

Welcome!

This is the Eleventh of a series of training

modules in Radiation Physics.

These modules provide a basic introduction

to h matter.

Sponsored by the United States Nuclear

Regulatory Commission and Duke University

Author: Dr. Rathnayaka Gunasingha, PhD

Your Instructor

Dr. Rathnayaka Gunasingha is an

Accelerator Physicist with

background in High Energy physics.

Dr. Gunasingha is a physicist in the

Radiation Safety division and

member of the Faculty of the Duke

Medical Physics Graduate Program.

Contact:

[email protected]

Goals of the Course

Upon completing these instructional

modules, you should be able to:

understand the Basic Interaction of Radiation with

Matter

apply the knowledge in various calculations used

in Medical and Health Physics

understand the basic principles behind various

instrumentation used in Medical and Health

Physics

This Module Will Cover

The General properties of Detectors such as,

1. Modes of operation

2. Methods of recording data

3. Energy resolution

4. Efficiency of detectors

5. Dead time and dead time measurements

General properties of Detectors

• There are two types of detectors

1. Active detectors

2. Passive detectors.


1. Active detectors:

provide immediate results (“signal”), usually by

means of electric current or current pulses

2. Passive detectors:

Radiation effects of these detectors are read

after eradiation. Signal consist of changes of

diverse nature – electrical, mechanical, optical,

chemical.


• Simple detector model:

Radiation undergo some interactions and deposit the

energy. Net result is the appearance of charge Q

created by ionization within the detector volume and

producing a


• collection time tC is the time required to collect

charge Q

• Figure shows the charge accumulation in the time tc

for an interaction inside the detector.

i(t)

tct0

Q = ∫ i(t) dt

tc

0


• A pulse is due to one interaction.

• Assume the rate of irradiation is low so that we can

identify individual pulses as shown in figure.

• The size and duration of each current pulse depends

on type of interaction.

t

i(t)

Modes of operations

There are three modes of detector operations:

(1) Current mode

(2) Pulse mode

(3) Mean square voltage (MSV ) mode

Current mode

• In current mode, detector response time T is greater

than the time between individual pulses

• Recorded signal is time-dependent current due to a

sequence of events

• Detector records the average current which depends

on interaction rate and charge per interaction(Q)

t

i(t)

I(t)

Detector A

Current mode

• Average current I0 is given by the product of event

rate r and the charge Q per event

C.e

E

e

W

Qr

e

W

ErrQI

-19

0

1061 chargeelectron

eventeach per depositedenergy average

pairelectron -ionan produce torequiredenergy average

eventper charge rateevent where,

Then,

×=

=

=

==

==•


Figure shows the

fluctuations of current with

time

σ σ σ

σ

+

′= − ⇒ =

•

=

∫

I(t) = fluctuating current

Standard deviation for recorder events are

given by

If each pulse contribute the same charge

functional standard deviati

2t T2 2

I 0 I I

t

n

1(t ) I(t ') I dt (t) (t)

T

rT

σ σ= =

on of the measured

signal is

I n

0

(t) 1

I n rT

I0

I(t)

t

σi(t)

Mean Square Voltage Mode(MSV)

( )

( )

This mode is called the "Campbell mode"

Since

This mode is useful to measure mixed fields

(neutron vs. gamma fields).

Circuit measures the current fluctuations

and computes the

2 2

i

i

t Q

t

σ

σ

•

• ∝

•

square of their time average

Pulse mode

• Current mode is good when event rates are very high.

• MSV mode is good for large amplitude events

• Event rate or time information is needed pulse mode

is used.

Pulse mode

• In this mode, detector records the charge from

individual event interaction

• Usually more desirable for getting information on

amplitude and timing of individual pulses

• Not suitable for very high event rates – time between

adjacent events are too short for analysis

• Energy deposited ~ Q – enables particle spectroscopy

Pulse mode

• Output from an event depends on the counting circuit

( detector + preamplifier)

• R = input resistance of circuit

• C = equivalent capacitance of detector system

• Signal voltage V(t) depends on time constant

τ = RC

V(t)=V0(1-e-t/RC)Detector = V(t)C R

preamplifier

Pulse mode

Figure shows current output and voltage output for two cases.

tC= charge collection time

1. When RC<< tC

Current through R is instantaneous value in the detector.

Equivalent signal is shown in figure (b)

V(t) = Ri(t)

it can collect charge for a single

event with tc.

i(t)

tc

t0

Q = ∫ i(t) dt

tc

0

Pulse mode

If time between pulses are longer,

capacitor discharge through R

Output voltage V(t) is shown in

figure ( c ).

When RC >> tC

Very little current flows through R

during tC.

Detector current is integrated on

capacitor

V(t)

0t

RC << tcV(t) = Ri(t)

V(t)

t0

RC >> tcVmax = Q/C

Vmax

Pulse mode

• This is the most common means of pulse type operation.

The reasons are

1. tC determines the time required for a signal to reach to maximum ( it does not depend on the external circuit)

2. Since Vmax = Q/C

The amplitude of the output pulse is directly proportional to the energy of the radiation

Pulse mode

Advantages in pulse mode:

1. Sensitivity is greater than when using current or MSV mode.

2. Lower limit is set by the background radiation

3. Pulse amplitude carries some information on charge generated by event

- in other modes ( current or MSV) this information is lost.

- all interactions contribute to the average value of the output current

Pulse Height Spectra

• When detector is operated in pulse mode, the pulse amplitudes carry information regarding charges generated

• Amplitudes of the pulses are not the same, due to the differences in radiation energy or fluctuations of the detector

• We get a differential pulse height distribution dN/dH

• dN is the number of counts in dH energy bin

• This can be obtained using a multi-channel analyzer (MCA)


Common way to display pulses is through a

differential pulse height distribution

The number of pulses between and

is given by 2

1

1 2

H

0

H

H H

dNdH N

dH

•

•

=∫

0H (volt)

Differential pulse height spectrumdN/dH

(volt)-

1

H1 H2

maximum H

Pulse height (H)


• Another method of displaying pulse height is

Integrated pulse height distribution

X axis ( abscissa) is the same

pulse height as before.

Ordiante ( y axis ) represents

the number of pulses whose

amplitude exceeds that of a

given value of H.

At the origin, the value of y, is

N0

0H (volt)

N0

num

ber

of

puls

es

N

exceedin

g H

H3 H4

plateau

Energy Resolution

• Spectroscopy: response to mono-energetic sources

such as gamma ray or alpha particles

• Pulse height distribution from a detector is called

“response function”

•If all the pulses are

around H0, good

resolution means

little fluctuation in

pulse height. 0H (volt)

dN/dH

(volt)-

1

H0

good resolution

pulse height (H)

poor resolution

Energy Resolution

• Energy Resolution of a detector is defined as

Rule of thumb is,

one can separate two

energies H2, H1, if

H2 – H1 > FWHM

Smaller the value of R, the

better the detector will be able

to resolve energies lying

closer

Where =Full width at Half Maximum

0

FWHMR

H

FWHM

=

0H (volt)

dN/dH

H0

R = FWHM / H0h

h/2 FWHM

σ

Energy Resolution

• There are number of Sources of fluctuations:

a) Drift of detector operating characteristics ( HV,

gain ..)

b) random noise in detector & electronics

c) statistical noise intrinsic to nature of signal

(discrete number of charge carriers, fluctuations

in energy deposition in detector)

• C) will dominate because it is always in a detector

system

Energy Resolution

( )

Estimation for fluctuation, can be given by

assuming a Poisson's distribution of events

Standard deviation is

is usually large, Then the response function

is a Gaussian shape

N.

N

N

AG H e

2σ π

•

•

•

=

( )

2

0

2

H H

2

FWHM 2.35

σ

σ

− −

• =

Energy Resolution

Average pulse where constant

standard deviation = and

Energy resolution

0

Posisson Limit

0

H KN K

K N

FWHM 2.35K N

FWHMR

H

2.35K N 2.35R

KN N

σ

• = =

=

=

= =

Energy Resolution

It was found that better resolution than Poisson's

limit can be achieved. Ionization events are not

fully independent and Poisson statistics is not

applicable.

The departure of the observed s

•

• tatistical fluctuations

in the number of charge carriers from pure Poisson's

statistics is defined by Fano factor, F

observed variance in =

Poisson predicted variance

NF

Energy Resolution

Because variance is the equivalent equation

for semiconductor detectors and propotional

counters, for scintillators

Adding all sources of fluctuations ( Ga

2

limit

,

2.35K N F FR 2.35

KN N

F 1

F 1

σ•

= =

• <

≈

•

( ) ( ) ( ) ( )

uss)

2 2 2 2

Total stat noise driftFWHM FWHM FWHM FWHM .....= + +

Detection Efficiency

• Charged particles or ions immediately interact within

the detector volume as soon as they enter the detector

Every pulse can be recorded and detector is almost

100% efficient.

• Gamma and neutron travel a large distance before

they interact within the detector. Therefore, the

efficiency for uncharged particles is less than 100%


There are two classes of efficiency

1. Absolute efficiency

2. Intrinsic efficiency

Absolute efficiency is defined as

number of particles recorded

number of part

abs

int

det ected

abs

( N )

η

η

η

•

•

=icles emitted by source(

depends on the detector properties and geometry

emitted

abs

N )

η•


Intrinsic efficiency is defined as

number of pulses recorded( )

number of radiation incident on detector( )

depends on detector properties only

Taking ratio of and

det

int

inci

int

abs int

N

N

,

η

η

η η

•

=

•

•

abs inci

int emitted

N

N

η

η=


From the diagram,

inci

emitted

abs int

N

N 4

4

π

η ηπ

•

Ω=

Ω • =

• Usually not all the pulses are of interest. For instance, in

spectroscopy, only the pulses around peak are desired.

Peak efficiency εpeak is determined considering

pulses around the peak.

Ω

a

Ω = A/l2 = πa2/l2

A

l

πa2/4πl2 = Ω/4π

S


is calculated counting all interactions.

peak-to-total ratio is defined by

Figure shows peak area and total area.

total

peak

total

r

ε

ε

ε

•

•

=

•

Intrinsic peak efficiency

most commonly tabulated

for gamma detectors

0H (volt)

dN/dH

Full energy peak

Dead Time

• A detector that responds sequentially for individual

events, requires a minimum amount of time that

should separate two events in order that events be

recorded as two separate events.

• This minimum time is called the “Dead Time”

• Dead time may be due to:

a. processes in the detector

b. counting electronics

Dead Time

• In a random sample, two events may occur very close in time, and some true events may be lost due to the dead time

• There are two methods to determine the true number of events

1. paralyzable detector method

2. nonparalyzable detector method

• Dead time τ is set after each true event that occurred during the “live period”

Dead Time

• Paralyzable detector method:

Any event occurred during dead period not recorded as

counts, but it extends the dead period t following the lost

event.

• Non paralyzable detector method:

it just ignore the other event occurred during dead period

t

Following example shows the difference between

paralyzable and nonparalyzable events

Dead Time

The middle line represents 10 events along the time axis as they come.

Assume events 3,4 and 6,7,8 come very close in time (i.e. within the

dead time of previous event)

Five events in

paralyzable method

Seven events in

nonparalyzable method

1 3 4 75 6 8 92 10

events in the detectorTime

nonparalyzable

paralyzableτ

Dead

Live

Dead

Live

Dead Time

Events 1,9 and 10 are recorded by both detectors.

After event 2 is registered, event 3 and 4 restart the dead

period for paralyzable detector which misses both event 3

and 4.

In non paralyzable method, after event 2 is registered, it

recovers to register event 4. ( event 3 is lost since it is

within dead time of event 2 and event 4 is outside the

dead time of 2)

Dead Time

• After event 5 is recorded, paralyzable detector extends the

dead period from events 6,7, and 8. As a result, all events

6,7,8 are lost.

• In non-paralyzable detector, after event 5 is recorded, it

recovers to record the event 7. Only event 6 and 8 are lost

as they are within dead time of event 5 and 7 respectively.

Nonparalyzable Detector Method

Let us obtain an expression for true interaction

rate. Dead time is a fixed value for each event

in this method.

assume n= rate of true interactions

m= rate of measured events

•

= dead time for one event

Then,

fraction of time detector is dead = m

fraction of time detector is sensitive = 1-m

τ

τ

τ

Nonparalyzable Detector Method

Fraction of true events recorded =

Using , appropriate correction can be made to

measured data .

m

n

m1 m

n

mn

1 m

n

m

τ

τ

•

= −

=−

•

Paralyzable Detector Method

• The dead τ is not fixed in this method. As you saw in the example, dead time depends on how close the events are.

• In this method, only intervals longer than τ are registered. We need to find the distribution of time intervals between consecutive random events.


Let us assume, true events rates to be

Then, the average number of events occur in time

if first event occur at

probability that no event occur in time , after

first event(Poisson ter

n

t nt

t 0,

t

•

=

=

m)

Probability that an event occurs in next time

interval

nt

0P e

dt ndt

−=

=


After first event at ,

The probability that the next event occur

between and

Where = probability of observing an interval

whose length lies between

nt

t 0

t t dt p( t )dt ne dt

p( t )dt

dt

−

=

+ → =

about

The probability of intervals larger than

nt n

t

p( ) p( t )dt ne dt e τ

τ τ

τ

τ∞ ∞

− −= = =∫ ∫


Then, observed count rate is

For low event rate or slow dead time

Here, the true rate , can not be solved explicitly.

If and are known,

n

m

m ne

( n 1)

m n(1- n )

n

m

τ

τ

τ

τ

−=

<<

=

can be solved iteratively.n


Figure shows the plot of measured count rate m, as a

function of true rate n for both models

m

n1/τ

1/τ

0

1/eτ

paralyzable

nonparalyzable

m =

n


• In non-paralyzable model m can not exceed the value

. When n increases m approaches an asymptotic value.

• For paralyzable model, (using calculus) m has a maximum value (1/eτ) at n=1/τ. After that m decreases to zero with increasing n.

• Also, in this model, there could be two possible event rates n, for one measured rate m.

1

τ

Dead Time

( )

( )

Low rates or slow dead time i.e.

For non paralyzable model

For paralyzable model

So, both model agree in the limit of low rate or

slow dead time

n

n n 1

nm n 1 n

1 n

m ne n 1 n

n

τ

τ

ττ

τ

τ

−

•

= = −+

= = −

Dead Time Measurements

In order to make dead time correction for

observed events, we should know

There are two methods to measure

1. two source method

2. decay source method

m τ

τ

•

•


two source method

In this method, counting rate is observed individually

and in combination.

Assume,

and be true counting rates for sources 1, 2 and

combined

and

1 2 12

1 2

n ,n n

m ,m

•

m be observed counting rates for

sources 1, 2 and combined

n and m are the background rates for true and

observed

12

b b


( ) ( ) Then,

Using non-paralizable model value for each

12 b 1 2 bb

12 b 1 2

b12 1 2

12 b 1 2

n n n n n n

n n n n

n

mm m m

1 m 1 m 1 m 1 mτ τ τ τ

• − = − + −

+ = +

+ = +− − − −


( )( )

Solve for ,

=1 2 1 2 12 1 12 2

1 2 12

m m m m m m m m

m m m

τ

τ

•

− − −


Decay method:

A short lived source is used.

Assume is the true rate at and is the decay

constant

Assume, background is very small

Assume non-paralyzable method

0

b

t

0

n t 0

n n

n n eλ

λ

−

•

=

=

t

0 0

mn

1 m

me n m nλ

τ

τ

=−

= − +


plot of

and intercept

slope

intercept

t

0 0

me vs. m

slope - n n

λ

τ

τ

•

=

=

intercept = n0

slope = -n0τ

n0

me

λt

m


For paralyzable method,

insert into

we get

slope =

is calculated from intercept =

slope

intercept

t n

0

t

0 0

0

0 0

n n e m ne

t ln m n e ln n

- n

n ln n

λ τ

λλ τ

τ

τ

− −

−

•

= =

+ = − +

=

intercept = ln n0

slope = -n0τ

ln n0

λt

+ ln

m

e-λt

Dead Time Losses

• In all of the previous methods, we assumed radiation

from steady state sources. For these sources,

probability of an event occurring per unit time is a

constant (Poisson’s statistics)

• Some events are lost due to dead time and distribution

intervals are modified and it may deviate from

Poisson’s behavior.

Dead Time Losses from non-continuous

sources

• Radiation sources such as electron accelerators used

to generate X-rays are operated in pulse mode

• As shown in figure, it can have pulse duration T with

few microseconds and repetition frequency f with few

kW.

1/f

T

Dead Time Losses from Pulsed Source

If , source is pulsed has little effect

steady state source results can be applied

If only a small number counts may be

recorded by the detector. This is more

complicated and not cons

T

T

τ

τ

•

• ≤

ider here

If and only one count

per source pulse and detector will be recovered

before next pulse.

1T T ,

fτ τ

• < −


Assume =observed count rate

=true count rate

Since there is a single count per pulse

Probability of an observed count per

source pulse =

Average number of true events per pulse =

m

n

m

f

•

Probability that at least one true event occur per source pulse

(using Poisson distribution)

=

x

n

f

n

f

p 1- p(0 ) 1 e

1 e−

•

= = −

−


Then,

A plot of vs is shown in

figure

when

maximum observable count rate is

n

f

n

f

m1 e

f

m f 1 e

m n

n , m f

f

−

−

• = −

= −

•

• → ∞ →n

m

f

0


Solving for for

Expanding in first order

f 1n, n f ln T T

f m f

mn

m1

2 f

τ

• = < < − −

•

=

−

Credits and References

Tsoulfanidis. N, Measurement and Detection

of Radiation, McGraw-Hill, New York(1983)

G.F.Knoll, Radiation Detection and

Measurement, 3rd ed. , John Wiley & Sons

https www.safety.duke.edu radsafety drdl modules rp 12 rp

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