ORTEC Spectrometer Application Note

ORTEC
®
AN56
Application Note
Loss Free Counting with Uncertainty Analysis Using ORTEC’s
Innovative Zero Dead Time Technique
Objective
Show that the ORTEC loss free counting method with estimation of the uncertainty associated
with the collected data is accurate for rapidly changing count rate applications.
Intended Audience
Users of High Purity Germanium (HPGe) detectors,
hardware, and analysis software in applications
where count rates change fast enough during the
acquisition period that Live Time correction
techniques may be statistically inaccurate. Such
applications include: neutron activation analysis, real
time monitoring of effluents, and other sample
counting procedures where the half life of one or
more nuclides is significantly less than the counting
time.
Definitions
Live Time The period of data collection during which
the electronics, such as a Multichannel Analyzer
(MCA), are available to collect and process pulses
from the detector, in this case an HPGe detector,
typically measured in seconds.
Real Time The actual time expired during data
acquisition, typically measured in seconds.
Dead Time The percentage of real time that the
detector is not available for counting pulses. Dead
time is calculated by the following formula:
DT = 1 – LT
RT
Live Time Clock (LTC) A method for determining the
live time during a given real time counting period in
an MCA.
Loss Free Counting A method for correcting the
number of counts in an MCA for the dead time
exhibited during the real time counting period.
Problem
All MCA’s exhibit counting losses due to the dead
time required to process pulses from any given
source of radioactivity. Many algorithms, both
electronic and computational, are available to
determine the amount of time during which those
losses occur. When count rates of the samples being
measured are constant over the counting period (i.e.
the dead time is constant ± a few percent), then the
standard method for calculating this time is by use of
Live Time Clocks. At ORTEC, the Gedcke-Hale1 Live
Time Clock has been employed for many years in the
MCAs to provide the live time of the electronics
during any given counting period. Because of its
innovative design, the Gedcke-Hale LTC has the best
accuracy for measuring the Live Time of an MCA
during acquisition of constant count rate samples.
The dead time for any measurement is then
calculated per the equation above and displayed with
the spectral data along with the actual real time and
live time.
Accurate knowledge of the live time of the count
allows the analysis calculations to yield statistically
valid results in terms of count rates. In simplest
form, the count rate for any given peak is given by
the following equation:
P=
Area
Live Time
with the uncertainty in the Peak Count Rate given by
(in simplest form):
σP =
√
Area
Live Time
because the events recorded in the peak areas
follow normal Poisson statistical relationships.
It has been shown that when the counting rates vary
greatly during the counting period, the Live Time
Clock methods for estimating the live time become
inaccurate. Loss Free Counting methods have been
developed to correct this problem.
Unlike Live Time Clocks, loss free counting does not
try to predict and record the actual time that the
electronics are available for counting. Instead, these
methods record the actual number of counts that
would have been present had there been no dead
time in the electronics. In these methods, there is
only a real time displayed with the spectral data. The
fundamental drawback to loss free counting up until
now, is the loss of Poisson statistics and thus the
ability to determine the uncertainty with the number
of counts in the spectrum.
Solution
In April of 2000, ORTEC introduced an upgrade to its
DSPEC PLUS hardware with ZDT correction
technique along with analysis algorithms in its
GammaVision-32 software which simultaneously
solve the problem of performing loss free counting
while calculating the uncertainty in the corrected
spectrum.2 This innovative technique has been
shown to be accurate for constant counting rates up
to 90% dead time.3 The remainder of this Application
Note describes how ORTEC’s loss free counting
method with error correction was tested under
conditions of rapidly changing count rates during the
acquisition time.
Setting Up ZDT Modes
Before performing the ZDT test, a few moments will
be spent on how to set up the DSPEC PLUS in its
various ZDT modes. The DSPEC PLUS has two
memory buffers in which to store spectral data
simultaneously: Buffer 0 and Buffer 1. There are
three (3) modes in which the DSPEC PLUS
operates: LTC Only, LTC with ZDT Spectrum, and
ZDT with Variance Spectrum. Depending on which
mode is selected, the DSPEC PLUS will collect the
required spectrum. The modes and which memory
buffer contains which data is summarized in Table 1
below.
Mode Contents of Buffer 0
Contents of Buffer 1
–*
LTC Spectrum (will display normal spectrum with
Live Time, Real Time and Percent Dead Time)
Empty
0
LTC Spectrum (will display normal spectrum with
Live Time, Real Time and Percent Dead Time)
ZDT Spectrum (will display spectral counts
corrected for the dead time losses with
Real Time display only)
1
Variance Spectrum (will display the data associated
with the variance in the ZDT-corrected spectrum
with Real Time display only)
ZDT Spectrum (will display spectral counts
corrected for the dead time losses with
Real Time display only)
*ZDT Mode Disabled.
2
AN56
Loss Free Counting with Uncertainty Analysis
Results of ORTEC Experiments
Experiment No. 1: Loss Free Counting with Varying
Count Rates during the Acquisition
Tables 1 and 2 below summarize the results of the
experiments done using the strong 137Cs and 57Co
sources on the rotating disk. The results in Table 1
clearly show that for varying count rates the loss
free counting mode in the DSPEC PLUS accurately
corrects for the lost pulses in the spectrometer using
the ZDT correction method. The counting
uncertainty (1-sigma) for each test, as well as the
input count rate are also shown. The difference in
the net peak count rates with the variable sources
present compared to those without the sources are
less than 1.0%.
Similar results are shown in Table 2 using the strong
Co source to generate the dead time in the
spectrometer. In this case, all net area count rates
had a difference from the known value of less than
1.8% despite input count rates varying a factor of 6
during acquisition.
57
Table 1. Varying Count Rate During the Measurement Using Strong
ICR*
Net Rate
1173 keV
1σ
Known
1900
33.8
0.5%
–
38.3
0.5%
–
30.0
0.6%
–
Test 1
7200
33.8
0.2%
–0.2%
38.1
0.1%
0.6%
29.8
0.7%
0.6%
Test 2
8000
34.0
0.2%
–0.6%
38.3
0.4%
0.0%
30.2
3.2%
–0.8%
Δ
Net Rate
1275 keV
1σ
Cs Source on Rotating Disk.
137
Δ
Net Rate
1332 keV
1σ
Δ
Table 2. Varying Count Rate During the Measurement Using Strong 57Co Source on Rotating Disk.
Known
ICR*
Net Rate
1173 keV
1σ
Δ
Net Rate
1275 keV
1σ
Δ
Net Rate
1332 keV
1σ
Δ
1900
33.8
0.4%
–
38.3
0.5%
–
30.1
0.5%
–
Test 1
7000
33.6
0.4%
0.6%
37.8
0.1%
1.2%
29.9
0.2%
0.5%
Test 2
8100
33.2
0.5%
1.8%
38.3
0.5%
–0.2%
30.2
0.5%
–0.3%
Test 3
11000
33.8
0.5%
–0.1%
38.2
0.4%
0.1%
30.0
0.5%
0.1%
*ICR: Average Input Count Rate during the acquisition.
3
Experiment No. 2: Estimation of Uncertainty in
Loss Free Counting System
Tables 3 and 4 show the results of the Gross and
Net Peak Area uncertainties as predicted by both
the standard deviation of the counts in the peaks
and the variance spectrum in the DSPEC PLUS. As
can be clearly seen, all values have a variance less
than 4.5% and most have a variance less than 2%.
This shows that the DSPEC PLUS with ZDT and
Error Estimation Algorithms properly calculates the
uncertainty associated with additional counts in the
ZDT spectrum.
Table 3. Comparison of Predicted Uncertainties in the Gross Peak Area of ZDT-Corrected
Spectra under Varying Count Rate Conditions
511 keV (Na-22)
Input
Count
Rate (cps)*
Std Dev
of Gross
Counts (1σ)
Avg Error from
Uncertainty
Spectra
3500
35.3
4900
6900
1173 keV (C0-60)
Δ of
Variance
Std Dev
of Gross
Counts (1σ)
Avg Error from
Uncertainty
Spectra
35.1
–0.5%
15.3
15.4
29.9
29.5
–1.3%
29.8
38.0
37.9
–0.2%
16.7
7250
31.1
31.0
–0.3%
8550
32.2
32.0
–0.7%
11700
43.8
44.5
1.5%
1332 keV (C0-60)
Δ of
Variance
Std Dev
of Gross
Counts (1σ)
Avg Error from
Uncertainty
Spectra
Δ of
Variance
0.6%
15.7
15.4
–1.3%
30.5
2.6%
12.3
12.5
1.3%
16.6
–0.1%
16.4
16.6
1.3%
32.1
32.1
–0.1%
13.2
13.1
–0.8%
33.2
32.7
–1.5%
13.5
13.5
–0.1%
18.8
19.6
4.2%
18.8
19.6
4.2%
Table 4. Comparison of Predicted Uncertainties in the Net Peak Area of ZDT-Corrected
Spectra under Varying Count Rate Conditions
511 keV (Na-22)
Input
Count
Rate (cps)*
Std Dev
of Net
Counts (1σ)
Avg Error from
Uncertainty
Spectra
3500
37.0
4900
6900
Δ of
Variance
Avg Error from
Uncertainty
Spectra
36.7
–0.9%
17.0
16.9
32.9
32.6
–1.0%
32.2
39.8
39.6
–0.6%
18.4
7250
34.7
34.3
–1.2%
34.4
8550
36.8
36.3
–1.4%
35.3
11700
45.5
46.7
2.7%
21.0
*Average input count rate during the acquisition.
4
1173 keV (C0-60)
Std Dev
of Net
Counts (1σ)
1332 keV (C0-60)
Δ of
Variance
Std Dev
of Net
Counts (1σ)
Avg Error from
Uncertainty
Spectra
–0.4%
14.5
14.6
0.2%
32.8
2.1%
27.8
27.9
0.5%
18.2
–1.0%
15.4
15.6
0.7%
34.5
0.2%
30.1
29.5
–2.0%
34.8
–1.3%
30.9
30.2
–2.2%
21.5
2.4%
18.3
18.3
0.0%
Δ of
Variance
AN56
Loss Free Counting with Uncertainty Analysis
A Brief Note on the Contents of the Buffers
If both memory buffers are used, they will always
have the same number of channels (512 to 16,384).
When using Mode 1, the variance spectrum contains
the data associated with the uncertainty of every
corresponding channel in the ZDT spectrum.
Therefore, the uncertainty associated with the
number of counts in Channel 5328 in the ZDT
spectrum is equal to the square root of the number
of counts in Channel 5328 in the variance spectrum.
It is important to note that the data stored in the
DSPEC PLUS is the variance of the spectral data
rather than the actual uncertainty. It follows that to
calculate the uncertainty for a given peak, which is
either an integer or fractional number of channels in
the ZDT spectrum, the uncertainty is the square root
of the counts in the same channels or fraction
thereof. This is what GammaVision-32 does during
its analysis of these spectra.
When saving the data in either Mode 0 or Mode 1,
the ORTEC SPC format will contain the data from
both memory buffers as well as the mode selected
by the hardware so that the files can be recalled and
analyzed at a later time. The format of the data in
the SPC files is given in the File Structures Manual
which accompanies the manual for GammaVision32.
Time in each mode (see GammaVision-32 Manual
for complete set of JOB commands).
The final method for setting the ZDT modes is
through the MCB Diagnostics program that installs
with ORTEC application software.
1. Select "Start|Run…" from the Windows taskbar
2. Type "C:\User\Program Files\Common
Files\ORTEC Shared\UMCBI\MFCDiag.EXE" and
click OK
Selecting the Mode for the DSPEC PLUS
The DSPEC PLUS can be placed into any of the
three ZDT modes in a number of ways. The simplest
method is to use the control panels
SET_PRESET_TRUE 1000
in the application software such as
CLEAR
GammaVision-32 (Acquire|MCB
SEND_MESSAGE "DISABLE_ZDT"
START
Properties from the menu).
Alternatively, a JOB file can be
created that will set the DSPEC
PLUS into the proper mode before
any measurement is made. The
following JOB file contents set the
DSPEC PLUS into each of the
three modes and collects a
spectrum for 1000 seconds Real
REM Sets LTC Only mode
WAIT
SAVE "C:\User\NoZDT.SPC"
CLEAR
SEND_MESSAGE "ENABLE_ZDT"
REM Enables ZDT Modes
SEND_MESSAGE "SET_MODE_ZDT 0" REM Sets LTC and ZDT mode
START
WAIT
SAVE "C:\User\Mode0.SPC"
REM Saves both spectra in single file
CLEAR
SEND_MESSAGE "SET_MODE_ZDT 1" REM Sets ZDT with Error mode
START
WAIT
SAVE "C:\User\Mode1.SPC"
REM Saves both spectra in single file
5
3. From the Drop Down list at the top of the screen,
select the DSPEC PLUS
4. In the "Command" bar, type in the command
"ENABLE_ZDT" to enable the ZDT Modes (or
"DISABLE_ZDT" to use LTC only)
5. If in ZDT modes, in the "Command" bar, type in
the command "SET_MODE_ZDT n" where n is
either 0 or 1 depending on the mode desired
Demonstrating the ZDT with Uncertainty
Analysis
The following section describes the experimental
setup used to determine the accuracy of ORTEC’s
new ZDT method and the uncertainty analysis and
the subsequent test results.
Demonstration of ORTEC’s Loss Free Counting
System using the ZDT Method
Two sources, 60Co and 22Na, are positioned at a fixed
location from the detector. 1800 acquisitions are
made of the two sources in the absence of any
other sources to determine their "true" counting
rates. A high count rate 57Co source is then attached
to a rotating disk. The rotating disk gives rise to
variable dead times between 11% and 85% during
acquisition. The input count rate is increased by
adding additional sources to the rotating disk. Each
"test" corresponds to a different input count rate. The
net areas for the 1173, 1275, and 1332 keV peaks
are then calculated and divided by the recorded real
time to give the count rates (in cps) in the peak
areas. The net area count rates with the rotating
sources are then compared to those without the
sources present and the difference should be 0%.
The experiment is then repeated using a high count
rate 137Cs source.
Demonstration of the Uncertainty Estimation as
Determined through the Collection of the
Variance Spectra with the ZDT-corrected Counts
Spectra
Two sources, 60Co and 22Na, are positioned at a fixed
location from the detector. A high count rate 57Co
source is then attached to a rotating disk. The
rotating disk gives rise to variable dead times
between 11% and 55–85% during acquisition. 1800
spectra are then collected and stored to disk with
the DSPEC PLUS in Mode 1. The input count rate is
increased by adding additional 60Co and 22Na
sources and the 1800 dual-spectra collected again.
The average input count rate is calculated for each
of the series of spectra. The set up for this
experiment is shown graphically below.
The gross and net peak areas of 60Co and 22Na are
then determined and a standard deviation of the
1800 ZDT-corrected spectra calculated for each of
the count rates. The same peak areas (gross and
net) are calculated and averaged for the 1800
variance spectra collected at the same time as the
ZDT-corrected spectra. This average value is then
compared to the standard deviation of the ZDT
spectra. The input count rate is calculated at each of
the disk rotation speeds. The ratio of the variance
spectra and ZDT-predicted uncertainties is then
plotted against the input count rate and ideally
should be equal to 1.00.
Variable count rate setup using strong source attached
to rotating disc.
6
AN56
Loss Free Counting with Uncertainty Analysis
Conclusions
The changing count rate experiments demonstrate that the use of ORTEC’s new ZDT method for loss free
counting using the DSPEC PLUS (a) accurately corrects the spectrum for lost counts due to dead time in the
spectrometer, and (b) predicts the uncertainty associated with the counts in the spectrum added by the loss
free counting method. By incorporation of the innovative ZDT technique along with the analysis capabilities of
ORTEC's GammaVision-32 software, the spectroscopy counting laboratory and real-time monitoring
applications have one complete solution for collecting, correcting, and analyzing any sample with no dead
time losses and obtaining quantitative results with an accurate uncertainty estimation.
Acknowledgements
ORTEC would like to thank Dr. Stefaan Pomme for providing data for the experiments performed in this
application note.
1
Jenkins, Ron; Gould, R. W.; Gedcke, Dale; Quantitative X-ray Spectrometry; Marcel Dekker, New York, 1981.
2
Patent applied for.
3
Upp, Daniel L. et al; An Innovative Method for Dead Time Correction in Nuclear Spectroscopy; MARC V Conference Proceedings; April 2000.
7
AN56
Loss Free Counting with Uncertainty Analysis
Specifications subject to change
092707
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