Session II.3.12
Part II Quantities and Measurements
Module 3 Principles of Radiation
Detection and Measurement
Session 12 Efficiency, Geometry
4/2003 Rev 2
IAEA Post Graduate Educational Course
Radiation Protection and Safe Use of Radiation Sources
II.3.12 – slide 1 of 47
Overview
 We will discuss how to convert measured
values so that they represent the actual
amount of activity present
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II.3.12 – slide 2 of 47
Surface Contamination
Removable
Fixed
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II.3.12 – slide 3 of 47
Surface Contamination
Point Source
1
2
4
8
Dispersed Source
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II.3.12 – slide 4 of 47
Surface Contamination
Factors for calculating dpm from cpm
c x 1 x 1 x 1
m
IE
GE
Y
=
d
m
where:
 IE = intrinsic efficiency of instrument (counts per hit)
 GE = geometric efficiency (hits per particle emitted)
 Y = yield of radionuclide (particles emitted per
disintegration)
NOTE: a “hit” implies that a photon or particle enters the
detector but it may or may not result in a “count”
4/2003 Rev 2
II.3.12 – slide 5 of 47
Surface Contamination
Factors for calculating dpm from cpm
c x 1 x 1 x 1
m
IE
GE
Y
4/2003 Rev 2
=
d
m
c x 1
c
m
h
x
1
h
p
x 1
p
d
=
d
m
c x h
m
c
x
p
h
x d
p
=
d
m
IE = c/h
GE = h/p
Y = p/d
II.3.12 – slide 6 of 47
Surface Contamination
Factors for calculating dpm from cpm
For the simple case of one type of radiation
(as presented on the previous slides):
1
c
m x (IE x GE x Y)
=
d
m
For the general case of several different types of radiations:
c
m x
4/2003 Rev 2
1
d
= m
{(IE1 x GE1 x Y1) + (IE2 x GE2 x Y2) + …}
II.3.12 – slide 7 of 47
Surface Contamination
Factors for calculating cpm from dpm
c = IE x GE x Y
m
x
d
m
where again:
 IE = intrinsic efficiency of instrument (counts per hit)
 GE = geometric efficiency (hits per particle emitted)
 Y = yield of radionuclide (particles emitted per
disintegration)
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II.3.12 – slide 8 of 47
Surface Contamination
Factors for calculating cpm from dpm
c = IE x GE x Y
m
c = c
m
h
4/2003 Rev 2
x
h
p
x p
d
x
x
d
m
d
m
IE = c/h
GE = h/p
Y = p/d
II.3.12 – slide 9 of 47
Surface Contamination
Factors for calculating cpm from dpm
For the simple case of one type of radiation
(as presented on the previous slides):
c = IE x GE x Y
m
x
d
m
For the general case of several different types of radiations:
c = {(IE x GE x Y ) + (IE x GE x Y ) + …} x d
1
1
1
2
2
2
m
m
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II.3.12 – slide 10 of 47
Geometric Efficiency
2
or
4
GE = h/p
If the instrument is
placed on top of the
source (e.g., a
portable survey
instrument), then the
GE = 0.5 h/p or less.
4/2003 Rev 2
However, if the detector
surrounds the source
(e.g., a “well counter”),
then the
GE = 1 h/p or less.
II.3.12 – slide 11 of 47
Geometric Efficiency
2
or
4
GE = h/p
If every particle emitted in the direction of the detector
strikes the “sensitive volume” of the detector, then we
should have a perfect geometric efficiency of 0.5 or 1.0
depending on whether it is a 2 or 4 geometry. However,
some of the particles impinging on the detector may not
interact with the sensitive volume (e.g. they are unable to
penetrate the detector faceplate or they escape through a
small gap such as exists at the entrance of a well counter)
4/2003 Rev 2
II.3.12 – slide 12 of 47
Example
A vendor of survey instruments states:
“Beta Efficiency = 35% as a percent of 2 emission rate”
 This means that the detector “counts” 35% of all the
particles emitted in the upward direction (towards the
detector)
 Its intrinsic efficiency (IE) is 35% (it counts 35 out of
every 100 particles that hit the detector)
4/2003 Rev 2
II.3.12 – slide 13 of 47
Example
A vendor of survey instruments states:
“Beta Efficiency = 35% as a percent of 2 emission rate”
c
0.35
h
h
c
x 0.5
= total efficiency = 0.175
p
p
 Remember, the ultimate goal is to detect the amount
of surface contamination (Bq or dpm), so you MUST
be able to account for ALL of the particles emitted not
just those striking the detector
 This will give you the total number of disintegrations
per minute (dpm)
4/2003 Rev 2
II.3.12 – slide 14 of 47
Example
If the detector is not in contact with the source (i.e., it is
not as close as possible to the source), then some of
the particles travelling upwards may not hit the
detector. In that case, the Geometric Efficiency (GE)
has two components:
h
GE =
p
h
= u
u
x p
where u/p is the fraction of the particles emitted
upwards (normally 0.5) and h/u is the fraction of the
upward particles that actually hit the detector which
could be any fraction from 1 to 0 depending on how
close or far the detector is from the source.
4/2003 Rev 2
II.3.12 – slide 15 of 47
Example
h
GE =
p
h
= u
u
x p
 For example, if an alpha detector is placed on top of an
alpha emitting source, the GE (h/p) would equal 0.5
(u/p = 0.5 and h/u = 1) which means that ½ of the particles
are emitted upward towards the detector and every alpha
particle traveling in that direction struck the detector
 But if the same detector were raised about 5 cm above the
source, the GE would equal 0. Even though u/p would still
be 0.5 (the same number of particles are traveling upward
towards the detector), h/u would be 0 since none of the
upward particles would reach the detector, they would be
stopped by the intervening air gap
4/2003 Rev 2
II.3.12 – slide 16 of 47
Sample Problem 1
The surface contamination limits in the United States
are given in terms of dpm per 100 cm2. You are
performing a surface contamination survey using an
alpha probe which has a scale calibrated in cpm. The
sensitive area of the probe is 60 cm2. Briefly explain
what you would do to make your measurement(s)
consistent with the limits.
ANSWER: You would have to convert cpm to dpm using
the process described in the previous slides and then
you would have to scale your measurements from 60
cm2 to 100 cm2.
4/2003 Rev 2
II.3.12 – slide 17 of 47
Sample Problem 2
A technician uses a GM pancake probe to monitor a
tabletop for beta/gamma surface contamination. The
probe has a sensitive area of 40 cm2. The technician
surveys an area measuring about 400 cm2 and obtains
an average reading of 2,300 cpm. The background is
100 cpm. The instrument has a total efficiency (intrinsic
plus geometric) of 10%. What is the contamination level
in terms of dpm per 100 cm2?
4/2003 Rev 2
II.3.12 – slide 18 of 47
Sample Problem 2
Measurement is 2,300 cpm – 100 cpm = 2,200 cpm
c x 1 x 1 x 1
m
IE
GE
Y
IE x GE = 0.1
Assume that Y = 1
=
c x 1 x
m
0.1
d
m
1
1
= d
m
c x 10 = d
m
m
dpm = 10 x 2,200 cpm = 22,000
2
22,000 dpm
55,000 dpm
100
cm
x
=
2
2
40 cm
100 cm
100 cm2
4/2003 Rev 2
II.3.12 – slide 19 of 47
Sample Survey Terms
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II.3.12 – slide 20 of 47
Sample Survey Frequencies
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II.3.12 – slide 21 of 47
Reasons for
Surveys
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II.3.12 – slide 22 of 47
Survey Requirements
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II.3.12 – slide 23 of 47
Surveys
Radiation Level Surveys
vs
Contamination Surveys
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II.3.12 – slide 24 of 47
Radiation Level Monitoring
1
2 4
1
2 4
Ionization chamber:
GM detector:
Measures exposure
rate which is what
we want
May measure cpm
but we want
exposure rate
4/2003 Rev 2
II.3.12 – slide 25 of 47
Intrinsic Efficiency (IE)
 For contamination monitoring we need to relate the
number detected to the number emitted from the
source because that relates to the activity on the
surface which is what we want to know
 For radiation level monitoring we are interested in
the “exposure rate” which is a function of how many
free electrons are produced in our detector which is
dependent on how many photons hit our detector but
independent of how many are emitted from the
source
4/2003 Rev 2
II.3.12 – slide 26 of 47
Converting cpm to mR/hr
The simplest way to convert
from cpm to mR/hr using a GM
detector is to use an instrument
with a dual scale. In this image,
1 mR/hr = 1,200 cpm
c
min
c
1
x
=
2
sec
area of detector (cm )
c
x
2
cm - sec
4/2003 Rev 2
1
IE
c
h
=
h
cm2 - sec
II.3.12 – slide 27 of 47
Converting cpm to mR/hr
photons
cm2 - sec
This quantity can be
converted to mR/hr
by using a photon
fluence graph which
tells us how many
photons per cm2 per
sec is required to
produce one R/hr
4/2003 Rev 2
II.3.12 – slide 28 of 47
Calibration of a NaI Detector
If an instrument is calibrated in
a fixed geometry and then used
in that same geometry, it can be
“taught” to provide the
information desired.
For example, here is a 13 cm
diameter sodium iodide (NaI)
detector called a FIDLER (Field
Instrument for the Detection of
Low Energy Radiation)
4/2003 Rev 2
II.3.12 – slide 29 of 47
Calibration of a NaI Detector
If we calibrate this instrument
properly, although the meter
indicates cpm, we can instantly
convert the results to Bq/m2
As this figure shows, the
detector is placed at a fixed
distance from the surface
(30 cm) both during calibration
and during use
4/2003 Rev 2
II.3.12 – slide 30 of 47
Calibration of a NaI Detector
Point Sensitivity:
If we place our detector at some height (h) and place a
source of radiation Q directly under it, we can determine
the point source sensitivity (Sp) of the detector which is
just the net counts (N) divided by the activity of the
source (Q) which yields:
Sp = N = cpm
Bq
Q
h
The point source sensitivity can be used to convert any
reading from cpm to Bq provided the height (h) doesn’t
change and the radionuclide is the same.
4/2003 Rev 2
II.3.12 – slide 31 of 47
Calibration of a NaI Detector
Area Sensitivity:
First draw some concentric rings
under a detector with the source in
the center. If we now move the
source away from the center to
one of the rings, we can determine
the sensitivity of the detector to
radiation off-center.
4/2003 Rev 2
II.3.12 – slide 32 of 47
Calibration of a NaI Detector
We can move the source along the ring and make a
measurement at each point but we should get the same
reading each time since the detector is in the center of
the ring. The sensitivity would be the total counts from
the ring divided by the total activity in the ring which is
the same as a single count divided by a single source on
the ring.
r
4/2003 Rev 2
II.3.12 – slide 33 of 47
Calibration of a NaI Detector
So we only have to make one measurement for each ring
to determine the sensitivity of the detector to a source at
that distance off center.
h
r
4/2003 Rev 2
r
II.3.12 – slide 34 of 47
Calibration of a NaI Detector
r
r
Area Sensitivity:
r+r
4/2003 Rev 2
The area of one of the rings is
equal to the area of the circle with
radius (r + r) minus the area of
the circle with radius r
II.3.12 – slide 35 of 47
Calibration of a NaI Detector
r
r+r
 (r + r)2 - r2
where r is the width of the ring
Expanding yields:
 r2 + 2rr + (r)2 - r2
which reduces to:
2r r + (r)2
however, (r)2 can be ignored since it is a small
perturbation which leaves 2rr where r is a fixed width
and r varies depending on which ring we are looking at.
4/2003 Rev 2
II.3.12 – slide 36 of 47
Calibration of a NaI Detector
Note that 2rr is the same as Dr or Cr where D is the
diameter of the circle and C is the circumference. Cr is
just the circumference times the width which is the area
of the ring.
To obtain the sensitivity of the detector to the entire area
of contamination we would have to integrate over each
ring as the radius goes to infinity. Actually, after the
radius gets to a certain point, the source will be so far
from the detector that the detector will no longer see any
of the radiation emitted.
4/2003 Rev 2
II.3.12 – slide 37 of 47
Calibration of a NaI Detector
An integral is the same as a summation so for practical
calibration we can make measurements at discrete
points and sum the results to obtain the area sensitivity
of the detector. For each ring with a new radius (r) we
will obtain a new net result (N) in cpm so that the
summation is:
(2r1r)N1 (2r2r)N2 (2r3r)N3
….
+
+
+
Q
Q
Q
4/2003 Rev 2
II.3.12 – slide 38 of 47
Calibration of a NaI Detector
However, 2, , r and Q are constant so they can be
taken out of the summation and we are left with:
2r
Q
 riNi
where the only variables are r which is the radius of the
circle (the distance from the source to the center of the
circles under the detector) and N which is the net counts
(cpm above background) obtained with the source at that
point.
4/2003 Rev 2
II.3.12 – slide 39 of 47
Calibration of a NaI Detector
If the points of measurement (r) are chosen to be 0, 5,
15, 25, 35 … 105 cm, then r is 10 cm and the equation
becomes:
20
Q
 riNi = area sensitivity =
cpm - cm2
Bq
=
cpm
Bq
cm2
(assuming Q is in Bq and r and r are in cm)
4/2003 Rev 2
II.3.12 – slide 40 of 47
Calibration of a NaI Detector
If you prefer m2 instead of cm2 then r and r (both in
cm) can be converted to meters by multiplying each by
(1 m/100 cm). We end up with 20/(100 x 100) = 2 x 10-3.
The equation then becomes:
2 x 10-3 
Q
4/2003 Rev 2
 riNi = area sensitivity =
cpm
Bq
m2
II.3.12 – slide 41 of 47
Sample Problem
end window
GM detector
moveable
shelf
sample
holder
background = 50 cpm
sample = 200 cpm
net sample =
200 cpm - 50 cpm =
150 cpm
standard = 2.2 x 105 Bq or dpm
standard = 4,440 cpm (above background)
efficiency = (4,440 cpm)/(2.2 x 105 dpm) = 0.02 c/d = 2%
contamination = 150 cpm/0.02 c/d = 7,500 dpm or Bq
4/2003 Rev 2
II.3.12 – slide 42 of 47
Contamination Summary
To evaluate the dpm on a swipe do the following:
cpm for sample - cpm for background
efficiency of the system (counts/disintigration)
To determine the efficiency of the system do the following:
cpm for a known standard - cpm for background
dpm of the known standard
4/2003 Rev 2
II.3.12 – slide 43 of 47
Good Survey Practices
 Use appropriate instrument for type of radiation
 Stabilize instrument, use check source
 Turn instrument on in background area, move up
range as necessary
 Survey slowly to accommodate slow response time
(2 to 5 cm per second), close to surface
 Use sound, the more senses, the better
 Compare readings to licensee’s surveys
 Record all information
4/2003 Rev 2
II.3.12 – slide 44 of 47
Variable Survey Conditions






Changing geometry
Partial detector irradiation (small beams)
Extreme environmental conditions
Varying energies and mixtures
Composition of contaminated surfaces
Variances in calibrations (sources, geometry, scatter,
electronic)
 Pulse versus continuous radiation
 Dose vs Exposure and counts per minute (cpm)
versus dpm
4/2003 Rev 2
II.3.12 – slide 45 of 47
Variables of Removable Wipes







Use the correct wipe materials
Wet or dry (efficiency versus self shielding)
Transportation losses
Efficiency of wipe
Geometry, detector, window, background, calibration
Interpretation of results
Your measurement techniques vs licensee’s - Let
them demonstrate
4/2003 Rev 2
II.3.12 – slide 46 of 47
Where to Get More Information
 Cember, H., Introduction to Health Physics, 3rd
Edition, McGraw-Hill, New York (2000)
 Firestone, R.B., Baglin, C.M., Frank-Chu, S.Y., Eds.,
Table of Isotopes (8th Edition, 1999 update), Wiley,
New York (1999)
 International Atomic Energy Agency, The Safe Use
of Radiation Sources, Training Course Series No. 6,
IAEA, Vienna (1995)
4/2003 Rev 2
II.3.12 – slide 47 of 47