If Xg and yy are the values of x and y with the applicator centered by
eye relative to the collecting electrode, it has been found that 36 current
measurements at~2-mm intervals over the ranges X9-5 <x <x +5 mm and
Yor5 < ¥ < YotS cover a large enough area so that the current drops to less
than half its maximum value in all directions. (In the Appendix A example,
the array of current measurements is plotted at the top of p. 135.) Along
each x = constant (or y = constant) line there are two values of y (or x) for
which I = Ija,/2. These two Ms, (or xa) values can be calculated by linear
interpolation, and their average is a measure of one coordinate of the center
of the distribution, y, (or x.). This may or may not coincide with the
originally estimated center coordinate y, (or x)). At the end of the mapping
measurements, an average Ve and Xe can be calculated. (In the Appendix A
example, Vy and Xy are listed on p. 135 as y* and x* » while the values of y.
and X_ are “listed “as Yay and 3.0
Xaye “the averages Yo "35.45 mn I I T
and X. = 121.88 mm, are not far
from the original yy = 36.0 mm
and xy = 121.2 mn.) I is 25
plotted as a function of
r= v(x - X,)2 + (y - ¥,)4, as
shown in figure 9 for a
particular applicator. (In
the Appendix A example, this
plot is at the bottom of
p. 135.)

»
°

a

For most applicators, the
current decreases monotonically
with increasing radius as in
figure 9. A 50% radius R can
be read directly from the
graph, and the area calculated
from this as m2. This is a
close approximation to the real
area mR2 if the chamber spacing
d, and source distance Az, are
both sufficiently small. A I I

JONIZATION CURRENT, pA

Os

rough estimate of uncertainty °6 2 4 6 8
for a given d and Az can be RADIUS,mm

obtained from the following

equation describing the Fig. 9: Currents measured with the probe
jonization current per unit electrode across the face of
mass of air as a function of SN D-402, plotted as a function
position: of radius, measured from the

center of the current distribu-
tion. The curve was drawn
freehand.

14


During measurements of both (I/d), and A, the source surface must be
raised until it touches the extrapolation chamber high-voltage-electrode foi)
(This does not produce a short circuit since only the inner foil surface is at
high voltage.) For determination of the zero-separation dial-gauge reading
go» or for source insertion and removal, the source support structure has to
be retracted by about 20 cm. These large changes in the z coordinate are
produced by releasing the three rapid retraction screws shown in figure 5 and
sliding the microscope-stage down on the three vertical steel rods shown, The
barrel micrometer is used only for fine control of Az.

Figure 7 shows both the apparatus and the measuring instruments. The
apparatus, at the right in figure 7, is surrounded on three sides by a 3/8-
inch-thick transparent plastic housing, intended for radiation protection of
the operator who sits facing the front panel. His hands can be inserted into
the housing for source and/or chamber manipulation through doors on either
side. The operator's torso and face are always protected by 3/8-inch of
plastic. The applicator shown inside the housing in figure 7 has been coverec
with a lead cap, to protect the operators fingers during source/chamber mani-
pulation. This lead cap was put in position with the tonys shown lying on the
bottom plate of the apparatus in figure 7.

The extrapolation-chamber collecting electrode is connected via low-noise
coaxial cable to the input of a Keithley 610C electrometer. This instrument
has a dial readout that is usually turned off. In its place, a Digitec 266 DC
voltmeter (DVM) provides a digital readout of the electrometer feedback
voltage. The X1 Output of the 610C is connected to the Hi terminal of the
OVM, and the Guard terminal of the 610C is connected to the Lo terminal of the
DVM. The 610C is used with the Feedback switch set to Fast, and the mode
switch set to 10-8, 10-9, or 10-12 coulombs full scale.

Underneath the electrometer in figure 7 is a locally made DVM timer,
which controls the Digitec DVM display. The timer output is connected to
terminals D6 on the DVM card-edge connector, so that the DVM displays the
instantaneous electrometer feedback voltage only when it gets a positive pulse
from the timer. The front panel of the timer contains an ERC counter, an ITC
comparator, and a Start button. When the Start button is pushed, the timer
generates a pulse, the DVM displays an initial voltage, and the counter starts
counting elapsed time. When the counter reaches the pre-set comparator
Number, it generates a second pulse, the DVM displays a final voltage, and the
counter stops counting. For the particular timer shown in figure 7, the time
unit for both counter and comparator is centiseconds. (for some of the local
DVM timers, the time unit is milliseconds.)

Underneath the Digitec DVM is a high-voltage power supply, connected
between the chamber high-voltage electrode and ground. This is a Keithley
Mode? 240A, which can provide from 0 to 1200 volts potential of either
polarity. (Although this power supply could be replaced by one delivering 0
to 100 V, both the amplitude and the stability of the 240A have proven
adequate.) The voltage is connected to the chamber high voltage electrode by
means of the brass rod shown at the upper right in figure 5, which makes a
sliding contact with a brass ring mounted on insulators above the captain's
wheel. Ihe voltage selected in any given situation depends on the electrode
separation d. During extrapolation measurements, a constant potential
gradient is maintained, since this both minimizes the corrections and exerts a


Faecay = exp (A At) (9)

where At is the time since the reference date of 1986 Jan 1, and A is the
decay constant (6.659 x 10-5 day~! for 9%Sr).

Finally, g, should be determined by fitting the corrected currents to th
equation:

T=c)+cyg (10)
and calculating:
c
0
ra (11)

1

The numbers computed for I, c), Cy, and g, should be recorded. The data
listed below represents the first three sets oF measurements made with the
configuration shown in figure 12.

Captain's wheel Current, pA
setting, g Feb 20 Mar 21 Apr 3
4.682 1.990 2.013 2.022
4.485 3.939 3.969 3.974
4.288 5.948 5.968 5.982
4.092 7.951 7.977 7.961
3.895 9.923 9.939 9.967
Cy 49.288 49.271 49.316
Cy -10.106 -10.097 -10.105
Go 4.877 4.880 4.880

The measured currents increased with time, but not enough to change the
coefficients cy and c, or the dial-gauge-zero setting gy by more than 0.1%.
It is felt that all of these measurements were valid, but the reason for the
current increase is unknown. These periodic checks will continue, and the
results considered satisfactory unless g, changes by as much as 1%. This
would correspond to a change of about 0.1 mm in the dial-gauge-zero setting.

4.4 Current per unit air gap:

Applicator SN 0258 should now be replaced by the unknown source, and the
source support structure raised until the source is near the extrapolation
chamber high-voltage electrode. Then with d = 0.5 mm, and x = X., y = Yc, the
barrel micrometer reading m, for which Az = d/2 = 0.25 mm should be found, by
decreasing Az until the current drops rapidly. Current measurements are then
made for the 5 different air gaps d = 0.5, 1, 1.5, 2, 2.5 mm, with z = d/2 +
0.01 mm, for which the barrel micrometer readings are m=m +d - 0.49. The
current measurements should be corrected by the factors feemp and f, from

eqs (4) and (5). recom

18


CONTENTS

Abstract 2. 6 ee ee ee ee ee ee we ee eee ee ee eee ne
List of Figures . . 2 we we eee we ewe er we ewe ee we wee
1. The Calibration Service 2... eee ee eee wee ween es
2. The General Approach. . 2... ewww eee ere reer wvene
3. Description of the System . 2... 2 ee wee we ee we ee we

4. Operational Procedures. ..... 22s

4.1 Current measurement and correction 2... ee ee ee ee we
4.2 Measurement of source area A «ee ee eee eee eee ene
4.3 Quality assurance measurements .... ee eee ee eevee

4.4 Current per unit air gap 2... 2.2.2. eee ee eee eee
5. Surface Absorbed-Dose Rates 2... eee eee ee ee ee eee
6. Calibration Uncertainty 2... 2 eee eee eee eee eens
References 2. ee eee ee ee ee ee ee ee ee ee ee es
Appendix A. Examples from a databook .... eee eee eee vee

Appendix B. Sample calibration report... 2... 2. ee ee eee ee

10
10
12
16
18
19
20
21
A-1

B-1


0G 8420/85 Page ? of 2
1985 JUN 24

For the source submitted, one calibration was made, to determine the average
absorbed-dose rate to water across the surface of the source. The active
source area was determined by mapping the relative dose rate across the source
surface with a l-mm diameter collecting electrode. The rate of change of cur-
rent with air-gap thickness was measured with a 28-imm diameter Conducting
plastic collecting electrode.

The water absorbed-dose rate at the surface of the source, averaged over the
active area of the source, is given in the table in SI units (grays per second)
and in special units (rads per second).

This measurement has been assigned an uncertainty of + 15%, which has the
approximate significance of a 95% confidence limit.

Information on the technical aspects of this report can be obtained from

Je S. Pruitt, Radiation Physics C206, National Bureau of Standards,
Gaithersburg, Maryland 208799. (301) 975-5587.

Calibration performed by J. S. Pruitt Ash
Report approved by R. Loevinger RL

For the Director

"Willan B One

William R. Ott

Chief, Radiation Physics Division
Center for Radiation Research
National Measurement Laboratory

Area Correction factors Water
Source Distance A Oiameter 8 U Absorbed-dose rate
(mm) (mm? j (mm) (Gy/s) (rad/s)
176 0 46 7.6 1.010 1.003 0.43 43


gaily, L+ n2 = 2 + VE + 2 (peau?) + (242)?
am = * log, 2n?2 (8)

where in terms of the coordinates of figure 1, » = r/R, n= Az/R,
r = ¥x2 + y2, and K is a constant.

This equation was derived by the author assuming that the activity is
spread uniformly over a circle of radius R on the source surface, that the
beta-particles are emitted isotropically from the source surface, that their
paths are straight, and that energy deposition is uniform along these paths.
The derivation is based on an A/r2 solid angle approximation where A is a
plane area, and consequently current per unit solid angle becomes infinite as
the distance approaches zero. If the current/volume is normalized to its
value on the central axis of the source (yp = 0), the normalized current is
well behaved for all distances (that is, for all values of n).

Figure 10 is a plot of the normalized currents for several values of n.
For each curve, the apparent radius R is the product of the true radius R and
the value of » where the curve crosses the half-value line. For n= 1,
Az = R, and mR2 exceeds mR? by a factor of about 2. For n= 0.2 (not shown)
mR2 exceeds mR2 by about 4%, and for n = 0.1, the difference is less than 1%.
In a typical case, d = 0.2 mm, Az = 0.12 mm, R = 4 mm, and n = 0.03, for which
mR2/nR2 = 1.001. :

T T Ui T T T T

10 4
‘ F 4
2
WW
ac
a
2?
Oo
a
ao 0s 4
N
a
at
=
a
9 -
S 4

°

° 05 ! 5 2

RELATIVE RADIUS /L= r/R

Fig. 10: Theoretical probe profiles for five different source distances,
n= AZ/R.

15


REFERENCES
Calibrations and Related Services, National Bureau of Standards,
Spec. Publ. 250, Gaithersburg, MD 20899 (1986).

J. S. Pruitt, "Calibration of Beta-Particle Ophthalmic Applicators at
NBS," J. Res. Nat. Bur. Stand. (U.S.), 91, 165 (1986).

R. Loevinger and N. G Trott, Int. J. Appl. Rad. Isotopes 17, 103 (1966).
J. Bohm, Physics in Med. and Biol. 21, 754 (1976).

J. S. Pruitt, Radiation Protection Dosimetry 11, 151 (1985).

ICRU Report 31, International Commission on Radiation Units and
Measurements (Washington, D.C., 1979). The value of W/e cited comes from
the value for dry air (33.85 J/C), modified by a humidity factor for
ambient air taken from Figure 5.14.

M. Berger and S. Seltzer, National Bureau of Standards Internal Report,
NBSIR 82-2550A (1983); also as ICRU Report 37 (1984). The electron
spectrum used was measured with a lithium-drifted silicon detector.

Tabata, Ito, and Okabe, Nucl. Instr. Methods 94, 509 (19/1).

al


Shield

Bottom plate

Fig. 12: Front view of extrapolation chamber (above), showing source support
structure retracted for quality assurance measurements. NBS
applicator SN 0258 is shown with its plastic shield moved towards the
source.

v7


The graph of parasitic current in figure 8 shows evidence both of
electrons coming to rest in the collecting electrode (the central peak of the
distribution), and background (the negative tails). The central peak of the
parasitic current is more symmetrical than the ion current peak, probably
because of multiple scattering of the primary beam in the plastic backing of
the electrode, which tends to round off the edges of the distribution. The
parasitic background is a current of about 10-50 fA. The ion current
background is negligible.

The ion current calculated with eq (3) must be multiplied by two
correction factors, one to correct air density inside the chamber to 22°C and
760 mmHg, and the other to correct for ion recombination and diffusion inside
the chamber. These factors are given by:

t _ 160 (T + 273.15) (4)
temp 295.15 P

Where T is the temperature in degrees Celsius and P is the pressure in mmHg;

50.5 Id

0.0044
Frecom = {CL - “axe JG -

sya = (17.24 x 10-5) E+ BBS) T (5)

Xd

where I is ion current in nA, d is electrode separation in mm, A is source
area in mm2?, and X is potential gradient, in V/mm. Equation (4) comes from
the ideal gas law, and eq (5) comes from Bohm,* with bracketed terms for
general recombination, initial recombination, and diffusion, reading from left
to right. (For the data listed on p. 136 of Appendix A, as the chamber air
gap increases from 0.5 mm to 2.5 mm, the general recombination term decreases
from 0.9996 to 0.9911, the initial recombination term holds steady at 0.9998,
and the diffusion term increases from 0.9949 to 0.9990.)

4.2 Measurement of source area A

This operation is performed with the small collecting electrode, or probe
(fig. 6), using a fixed small air gap d (fig. 3), and with az just slightly
larger than d/?. Current measurements can be made at different points in the
x-y plane over a large enough area so that the current drops to less than half
its maximum value in all directions. If the x-y plane, determined by the
microscope stage, is parallel to the plane of the chamber high-voltage
electrode, this mapping can be done with no change in Az. These planes are
seldom parallel, however, because the rapid retraction mechanism described in
section 3 (for large changes in Az) ts only a crude adjustment. With the
vertical position az set su that the applicator 1s close to but not touching
the HV electrode foil when the applicator is centered, the changes in x and y
that occur during mapping of the source may cause the applicator to run into

the electrode, diminishing the air gap in the chamber and reducing the chamber
sensitivity.

The operator can avoid this effect by simply sighting by eye to determine
when the applicator is close to the HV electrode foil, independent of the
barrel micrometer readings. A simple test can be run once, to get a feel for
what the position of the two components looks like when they are too close.

12


The particular collecting electrode shown has a diameter of about 30 mm
and is surrounded by a guard electrode with an outside diameter of 50 mm.
Both guard and collecting electrodes are made of 8-mm thick A-150 conducting
plastic, electrically isolated with 30-um plastic film held in place with
epoxy cement. The high-voltage electrode is Mylar aluminized on the inside
surface, with a diameter of 70 mm and a thickness of 0.7 mg/cm2 (about 5 um).

Figures 4 and 5 are respectively a 3/4 front view and a side view of the
apparatus, showing the extrapolation chamber above and the NBS ophthalmic
applicator SNO258 below. (The applicators in figures 4 and 5 have been
retracted from their normal position by about 3 cm for clarity.) The extrapo-
lation chamber housing is mounted on the underside of the 6-mm thick
triangular brass top plate, which is supported on three 19-mm diameter brass
posts. The lower half of this housing, including the bronze ring on which the
circumferential scale is engraved, the captain's wheel, and the mylar HV
electrode foil, can be rotated to change d, the chamber plate separation.

Each complete revolution of the captain's wheel changes d by 0.635 mm

(40 turns/inch). The internal collecting-electrode-guard-electrode unit of
figure 3 cannot be seen in figure 4, but it rests on three brass supports
rigidly attached to the top plate in figure 4,

The orientation of the captain's wheel, uniquely related to the plate
separation d, can be specified by a single number, the angle of rotation
(which may increase to many multiples of 2m radians). In practice, that angle
is broken down into two related components, 6 and g. The number 6 is one-
hundredth of the number read from the circumferential scale shown in figure 4.
This scale consists of 100 divisions, so 6 varies from 0 to 1 in one revolu-
tion. The number g is read from the dial gauge visible at the top of
figure 4. There are two scales on the dial gauge. The large scale is divided
into 100 divisions, with 0.001 inches per division. The small scale is
divided into 10 units, with 0.1 inches between units. The dial gauge reading
g is the sum of the small gauge reading, a whole number, and the large gauge
reading, a fraction between zero and unity. Its units are tenths of an inch.

The two numbers g and 6 can be related by setting @ to zero and then
rotating the dial gauge until the large needle points to a multiple of 0.25
(four revolutions of the captain's wheel are equivalent to one revolution of
the large dial gauge needle). Then the electrode separation, in mm, can be
written:

d = 2.54 (g, - 9) where 9= 9) -; (1)
and gg is the dial gauge needle reading when d = 0. g, is the closest
multiple of 0.25 larger than g (for two examples, if g = 5.173 (or 4.635),
G, = 5.25 (or 4.75), and 6 = 0.308 (or 0.460) ). Gq must be measured by
extrapolation, as described in the next section.

The collecting electrode shown in figure 3 has a much larger area than
the active area of all ordinary ophthalmic applicators, which have diameters
between 6 mm and 9 mm. This type of collecting electrode is used to determine
the ratio (I/d),, where I is the ionization current generated in the air
volume defined by the collecting area A, and the electrode separation d. The
ratio I/d is a function of both d and the applicator distance Az, and the zero
subscript refers to the limiting case where both d and az are zero. This
limiting value of I/d is a characteristic of the source and of the electrode
material and is independent of A, if A, is sufficiently large.

4


NAS 506—Analysis paper

136

901107

4 bm WM gy

dr fo sv

x/0l®

i/fe

404 235 7,71 410

1214 38.5]

194095
| 255

~_ |@.26 +0

4.70 +50



133

901-102

xlo® | oe

2 Alg Olam Wie y
we 0.2 [5.51 0.477 5.00 +4 |124.2 250)

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i fad eal al el id a nal nd de

epi iell

i

- 7 “0b | -1877



1. The Calibration Service

This service is intended to provide calibrations for 29Sr + 9°Y beta-
particle applicators used in medicine for treatment of ophthalmic conditions.
It was started in 1977. A typical ophthalmic applicator is shown in figure 1.
It is a New England Nuclear Model NB-1. The National Bureau of Standards
(NBS) owns an NB-1, serial number 0258. The quantity chosen for calibration
is the average surface absorbed-dose rate to water over the active area of the
source. If an applicator is immersed in water, or placed on a water-like
material, such as tissue, the surface absorbed dose rate to water is the rate
at which energy is absorbed by water from the beta particles, per unit mass of
water, at the surface of the applicator. The applicators accepted for
calibration generally have activities between 370 MBq (10 mCi) and 7.4 GBq
(200 mCi). (The corresponding range of surface absorbed-dose rates is from
about 0.1 Gy/s to about 2 Gy/s.) Activities less than 370 MBq are not very
useful because of the long times required to obtain biologically significant
exposures, while activities larger than 7.4 GBq would produce radiation
protection problems for the persons using and calibrating the applicator. The
stated uncertainty is + 15%, with the approximate significance of a 95%
confidence limit.

‘Welds
[2
= E
d 4
C =)
Tc 7]
A 0.08 mm thick SS foil
B_ Porous glass disc Infused with
radioactive material

C Aluminum Spacer
D 6.35 mm diameter handle
E 10cm X 10cm X 5 mm plastic shield

U

Fig. 1. NBS-owned ophthalmic applicator SN 0258.


Fig.
Fig.
Fig.

Fig.
Fig.
Fig.
Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

10.

11.

12.

LIST OF FIGURES

NBS-owned ophthalmic applicator SN 0258 .....-24-e2e-2ee-
Electron energy spectrum from a 9%Sr + 9°Y source... 2. ee

Cross section of 30-mm diameter collecting electrode unit,
showing relative position of high voltage electrode and
applicator «2 1 6 we ee we were reer rere ev enoe

Front view of extrapolation chamber and source support structure
Side view of extrapolation chamber and source support structure
Cross section of 1-mm diameter collecting electrode unit ...

Front view of extrapolation chamber housing and measuring
imstruments . 6 6 eee ee ee ee ee we ee ee wee ene

Variation of ion current and parasitic current across
applicator SN 01386 2... eee ee ew ee we ee we we we wee

Currents measured with the probe electrode across the face of
SN D-402, plotted as a function of radius, measured from the
center of the current distribution 2... 2 eee eee ewe

Theoretical probe profiles for five different source distances,

N= AZ/R cee eee eee vere vevrvrvveveessees

Measured probe profiles of applicators SN 0258 and SN 157, in
comparison with theoretical predictions for uniformly
distributed sources . 6. 1 ee ee ee ee ee eee ern

Front view of extrapolation chamber showing source support
structure retracted for quality assurance measurements ....

vi

Page
1
2

ll

14

15

16

17


With the applicator and HV-electrode foil just barely separated by eye, the
operator can measure the jon-chamber current, reduce the separation by 0.01 mm
using the barrel micrometer reading, repeat the current measurement, etc. It
will be found that the current increases slowly as Az is reduced, until the
two components touch. With further reduction of az, the current drops
rapidly.

For most ophthalmic applicators, the uppermost surface is not flat, as
shown in figure 3, but slightly convex. The orientation of the applicator
should be such that the convex surface would be first to touch the HV elec-
trode when az is reduced to d/2. In extreme cases, the head of the applicator
is cocked relative to the handle, so that the rim of the surface meets the HV
electrode first. In such cases, it may be possible to compensate for this
awkward alignment by tilting the source-support plate, depressing one or more
of the three fittings attaching it to the vertical steel rods.

In preparing for source-area measurements, it is necessary to find gy,
the d = 0 point on the dial-gauge scale. This can be done with the source in
position, but retracted by about 20 cm, In this condition, the corrected
current is a linear function of d, and the d = 0 point can be determined by
measurements with several air gaps and linear extrapolation to zero current.
The corrections required are the two listed in the preceding section, from
and fF rocoms plus a third factor that corrects for scatter from the sidewalls
of the chamber, and a fourth factor that corrects for attenuation in the air
between source and chamber. These extra factors are appreciable only when the

source-chamber distance is large. At 20 cm, the empirical formulas for these
factors are:

Fecat = 1 - 0.0094 d (6)

where d is the chamber air gap in mm, and:

+n
n

= - 2)-1
atten (1 + 0.077 h - 0.335 h2)

heil- OF eemp)7* . (7)

Equation (6) was derived by increasing the thickness of scattering material,
and eq (7) comes from experiments at reduced atmospheric pressure.> (There is
no need to determine g, each time the probe electrode is used. Its value may
change slightly when this electrode is removed and replaced, but the source
area measurement is insensitive to this change.)

The mapping itself consists of repeated measurements with different x and
y coordinates but with similar az = d/2. The air gap d should be reduced to
0.1 mm or 0.2 mm, with the chamber voltage gradient set for about 20 V/mm.
For each change of x and/or y, the applicator must first be retracted
{az > d/2) and then returned to Az = d/2 after the change, because the x-y
plane and the HV foil plane are not parallel. The theoretical description of
the chamber current given in eq (8), below, can be used to show that: small
variations in Az have a negligible effect on the measured currents.

13


The determination of average surface absorbed-dose rate is performed in
two steps using ionization chambers of different diameters, because two
quantities need to be measured. The total current per unit air gap at the
source surface, (I/d),, is measured with an ion chamber at least two
B-particle ranges larger in diameter than the active area of the source; the
active area A of the source is determined by mapping with an jon chamber much
smaller in diameter than the diameter of the active area. In practice, the
two measurements are made with the same ionization chamber, but the size of
the collecting electrode is changed. The average surface absorbed-dose rate
is directly proportional to the ratio (1/d) 9/ (pA) where p is air density.
This ratio has dimensions of current per unit mass of air (A/kg).

The general plan of the calibration is to measure ionization current per
unit mass of air with the applicator at several distances from the center of
the ionization chamber air gap, and to extrapolate to zero distance and zero
air gap to obtain a value at the surface of the applicator. Sections 3 and 4
are concerned with this determination of extrapolated current per unit mass of
air. Section 5 describes the calculation of the absorbed-dose rate, and
section 6 is a discussion of the uncertainties inherent in this calibration

method.

BRASS BACKING

GUARD ELECTRODE
COLLECTING ELECTRODE
COAXIAL CONNECTOR

3. Description of the System

The extrapolation ionization
chamber is essentially the same
as that described by Loevinger
and Trott,3 with several
collecting electrodes which can
be interchanged and a thin
aluminized-plastic-film high-
voltage electrode. The relative
position of the electrodes and an
ophthalmic applicator under study
are shown in figure 3. The T
extrapolation chamber itself is a qd 3 —- sr
parallel plate capacitor of o 4 az oO
variable plate separation, d. /
The guard electrode is grounded Cj HIGH VOLTAGE ELECTRODE
and the collecting electrode
potential is very close to }>——— OPHTHALMIC APPLICATOR
ground. In this condition, the
lines of force are perpendicular Y
to the collecting electrode, and x
the collecting electrode receives
only charged particles that have
been generated in the cylindrical
air volume defined by d and the
collecting electrode area, Ace

The extrapolation chamber has Fig. 3: Cross section of 30-mm diameter
means for both changing d and for collecting electrode unit,
measuring this change, but does showing relative position of
not provide an absolute measure high voltage electrode and

of d itself without extrapolation. applicator.

INSULATING FILMS

EIST SS OS]

Besos ese}

Lg


The corrected current per unit air gap at zero air gap, (I/d) 9, comes
from fitting the five corrected currents to the equation:

I/d = (I/d), (1+ ad + 8d?) (12)
This extrapolation is only approximate for this poor-geometry determination.
Sometimes a quadratic equation of this type | fits the data very well and
sometimes poorly. In general, a = -0.1 mm-!, and g = 0.01 mm-2

5. Surface Absorbed-Dose Rates

The average surface absorbed-dose rate in water comes from the Bragg-Gray
formula:

* 33.7 2124
1

428 (1/4) 9 x k Gy/s (18)

xd kk
197 extrap “back foil
where A is the source area in mm? and (1/4) 9 is the corrected current per unit
air gap at zero air gap, in nA/mm. In the above equation, 33.7 is the average
energy in joules, needed to produce one coulomb of ions of either sign in
air,® 1.124 is the ratio of the average collision mass stopping power of water
to that of air,” and 1.197 is the density of air at the reference temperature
and pressure, in kg/m3. The correction factors are:

Kextrap = 0.98, a correction for systematic errors in the extrapolation
technique;

kpack = 1-010, a correction for difference between backscatter from water
and backscatter from TE plastic;

keoq] = 1-003, a correction for foil attenuation in the extrapolation
chamber entrance foil.

The (I/d)) ratio from eq (12) depends on the extrapolation path to a
minor extent. For example, if the ratio Az/d had been maintained at 1 rather
than at 1/2, the measured (I/d), ratio would have been slightly smaller.
Ideally, the ratio should be measured varying only d, with az = 0 throughout.
The closest one can come to this ideal situation is to extrapolate I/d to zero
d for several fixed values of Az and then extrapolate the zero-d limits to
zero Az independently, the procedure described at the end of section 2.
However, this increases the calibration time by a large factor and has
consequently been replaced by the present techniques, where Az and d are
extrapolated to zero simul taneously. For applicator SN 0258, it was found
that the ideal (I/d), is 2% smaller than the value obtained with az/d = 1/2.
This is the origin of the correction factor Kextrap:

The backscatter factor was estimated from published formulas for back-
scatter probability as a function of atomic number and beta-particle energy.®
Using the chemical formulation for the collecting electrode material, and the
source spectrum measured with the silicon detector, figure 2, the value for
Kpack Was obtained.

The foil attenuation correction factor, Kfoit = 1.003, was determined
from measurements with extra thicknesses of 0.7 mg/cm2 aluminized foil.

19


NBS MEASUREMENT SERVICES:
CALIBRATION OF BETA-PARTICLE-
EMITTING OPHTHALMIC APPLICATORS

John S. Pruitt

Center for Radiation Research
National Measurement Laboratory
National Bureau of Standards
Gaithersburg, MD 20899

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary
NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
Issued July 1987


SN 0258
#
(

Rapid retraction screw

Bottom plate |

Fig. 5: Side view of extrapolation chamber (above) and source support

structure. NBS applicator SN 0258 is shown.


gauge

SN 0258

Shield

Fig. 4: Front view of extrapolation chamber (above) and source support
structure. NBS applicator SN 0258 is shown.


NBS 506—Anolysis paper

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This service was called 8.4K in the old SP2bu manual. The designation
has been changed to 47030C in the 1986 version of S$P250.! The latter also
contains instructions for shipping and handling the applicators.

A report entitled "Calibration of Beta-Particle Ophthalmic Applicators at
the National Bureau of Standards" has been published in the Journal of
Research of the NBS.2 It contains much of the information given in this
report. Examples from a data book are given tn Appendix A, and a sample
calibration report is given in Appendix B.

2. The General Approach

The average surface absorbed-dose rate to water is determined from
ionization-chamber measurements in air, and converted to water with Bragg-Gray
cavity-ionization theory, a routine conversion described in detail in
section 5. Water was the medium chosen for calibration because it is
universally available and its properties are close to those of tissue. The
primary alternative method of calibration uses thermoluminescent dosimeters,
but this method was rejected because these dosimeters must be calibrated with
a different radiation source. Use of the Bragg-Gray theory requires knowledge
of only a well-known constant, the eneray required to produce unit ionization
in air, and the ratio of averaye stopping powers for water and air. This
ratio can be calculated from tabulated stopping powers if the beta-particle
energy spectrum is known, Figure 2 shows a typical strontium 90-yttrium 90
energy spectrum. It was obtained with a 5-mm-deep silicon surface-barrier
detector at room temperature in air, under 0.013 mm of aluminized polyethylene
terephthalate. The measurements were made at a distance of 11 cm froma
Buchler-Amersham source, and have not been corrected for either backscatter or
self-absorption, The spectral shape need not be known with great precision,
however, Since stopping-power ratios vary slowly with beta-particle energy.

1606; r r + : T t t

Counts per Channel
s
g 8

8

05 1 15 2 25

Electron Energy, MeV

Fig. 2. Electron energy spectrum from a 29Sr + 90Y source.


Figure 11 is a plot of probe ion current vs. radius for two applicators and

matching source profiles calculated from eq (8).

The parameter Az was

assigned the approximate value 0.1 mm in the calculation, and values of

R = 3.18 mm and 4.35 mm were read from the graph. h
Equation (8) is not an accurate description of

normalized at the origin.

All four curves have been

either source profile, but the comparison with the NBS owned SN 0258 is con-

sistent with the assumption
that the activity in this
source is spread uniformly
over an area of 4.35-mm
radius. The small differ-
ences between theory and
measurement appear to be
easily explained. The
differences near r = R can be
attributed to the finite size
of the probe electrode. The
differences at larger radii
probably arise from the fact
that the activity in SN 0258
lies below the applicator
face, so that the elemental
sources cannot be treated as

1.0

0.5)

NORMALIZED CURRENT

T T T T —T T

isotropic at large angles. to)
This will cause the real
distribution to fall off more
rapidly at large radii than
the theoretical distribution.
The activity in SN 157, in
contrast, appears to be
highly peaked at the center.

Fig. 11:

RADIUS r,mm

Measured probe profiles of
applicators SN 0258 and SN 157, in
comparison with theoretical predic-
tions for uniformly distributed
sources.

4.3 Quality assurance measurements:

After measuring the source area, the probe electrode unit (fig. 6) should
be replaced by the 30-mm electrode unit (fig. 3), and the source support
structure should be retracted for a determination of g,, the d = 0 dial-gauge
reading, for this electrode. The unknown source should be replaced by the
NBS-owned SN 0258 applicator so that this g, determination can also serve as a
quality assurance test. It is necessary to mount the applicator in a position
that is independent of the vertical position of the source support structure,
which is not reproducible. This can be done as shown in figure 12. The
SN 0258 plastic shield should be pushed as close to the source end as
possible. The support structure should be retracted far enough so that the
applicator handle rests on the bottom plate in figure 10 when it is centered
in the hole as shown, but not far enough for the support structure itself to
touch bottom. In this condition, small vertical motions of the support
structure have no effect on the applicator position.

Extrapolation chamber current measurements should be made at each of the
five g settings listed below. The current measurements should be multiplied
by five correction factors, the four already described by eqs (4) to (7), as
well as a decay correction factor:

16


APPENDIX A. Examples from a data book

The examples given are four pages from data book DB863, pages 133-136.
These cover the calibrations of applicator SN176. The first three pages cover
the area determination, using probe electrode 0.5A, and the fourth page covers
the determination of (I/d),, using 30-mm-electrode 30F. There were no
determinations of gy, the a = 0 dial-gauge reading. (The quantities called g
and gy in this report have in the past been called 2 and 29.)

The values of gy used in the calibration of SN176 had been measured on
1983 Nov 11 for electrode 0.5A (do = 5,585), and on 1985 Apr 1 for electrode
30F (gq = 4.888).

The databook column headings and their meanings are:

time,n:
Real time on a 24-hour scale (i.e., 1436 is 2:36 p.m.). n is a double
number, a-b, where a is the number of initial runs not included in the
average and b is the number averaged (i.e., 1-5 means there were six
measurements, but only the latter five were averaged).

equip:
A listing of the apparatus. On page 133, for instance, the numbers
stand for:
0.5 A is the collecting electrode number
SN 176 is the applicator number
185325 is the NBS number of a Keithley 610C electrometer
103.13 pF is the measured capacitance on the scale used (10-19 coul)
168929 is the NBS number of a Fluke 412B high voltage power supply
189695 is the NBS number of the comparator on the DVM timer
25 s is the comparator setting
183047 is the NBS number of a Digitec 266 DVM
2V is the DVM scale used
gale:

A listing of the quantities necessary to calculate currents from
measured voltage changes. They are stored in the memory of an HP41C
calculator in bins:
81: d, the chamber electrode separation, in mm
82, 83 and 84: a, 8, and ko constants needed for f and Foe
85: A, either the active area of the source or the collecting
electrode area, whichever is smaller, in mn2
86: X, the extrapolation chamber potential gradient, in V/mm
87: I/I(nA), a constant defining the units of the quantity I
88: At, the number of days away from the reference date
89: A, the source decay constant, in days-}
90: C/t, the ratio of capacitance to runtime. C = Cx 1012,
t= tx 10. The exponent k is usually chosen so that C/t is
a number between unity and 10.
91: Cos the DVM calibration correction factor

A-1


ABSTRACT

This service provides calibrations for 9°Sr + 9°Y beta particle
ophthalmic applicators. The calibration determines the average
surface absorbed-dose rate to water over the active area of the
applicator. The technique used is to measure current per unit mass
of air at the active surface with an extrapolation ionization
chamber, and to convert this into absorbed-dose rate with Bragg-Gray
cavity ionization theory. The extrapolation chamber measurements
are made in three parts. In the first part, a 1 mm diameter probe
electrode is used to map the relative dose rate across the source
surface, and to determine the active area. In the second part, the
probe electrode is replaced by a 30 mm diameter electrode, and the
test applicator is replaced by an NBS-owned applicator for quality
assurance measurements. In the third part, the 30 mm electrode is
used with the test applicator to determine the extrapolation curve
slope at the source surface. The ratio of this slope to the source
area, divided by the air density, yields current per unit air mass.
The transformation to absorbed-dose rate is described. The
component uncertainties are listed and are shown to yield a total
uncertainty of + 15%, with the approximate significance of a 95%
confidence limit. Data book measurements and a calibration report
are given for one particular applicator.

Key words: absorbed dose rate; calibration service; extrapolation chambe
ophthalmic applicator; quality assurance measurements ; surfac
dose rate.

iv


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The measured current is the sum of two components, an fon current
generated in the chamber air gap by interaction between air molecules and the
incident beta-particles, and a parasitic current generated in the body of the
collecting electrode by beta-particles coming to rest. These two components
can be separated by making measurements with both positive and negative
high-voltage polarity. The ion current component will change sign when the
polarity changes, while the parasitic component will not.

If I+ and I- are currents measured with positive and negative polarity
respectively, the jon current is:

(3)

where I- is normally a regative number. The parasitic current is (I* + I-)/2
and may be either positive or negative. It has no immediate application, but
is usually recorded because abrupt changes may indicate measurement problems.
The data tabulated in Appendix A are good examples of the normal range of
variation of the parasitic current, labeled Tp. Page 136 lists data taken
with a 30-mm diameter collecting electrode such as shown in figure 3. The Tg
measurements in this case show a normal progression from about -40 pA to about
-38 pA as the chamber air gap increases from 0.5 mm to 2.5 mm. Departures
from this progression by 20% or more usually indicate that one of the system
electronic components is malfunctioning.

Figure 8 shows the

variation of both the jon
and parasitic currents
across the face of the most 1.5
asymmetric applicator that
has been studied in this
laboratory.. The measure-
ments were made with the
probe electrode, using an PARASITIC
electrode spacing, d, of Lob
0.05 mm and an applicator
distance, Az, of 0.4 mm.
The asymmetry of the fon
current is presumably
caused by an uneven distri-
bution of activity across
the applicator face. The 05
tails of the ion current
distribution are caused by

beta particles that leave

the applicator with large

velocity components perpen-

+pA

CURRENT

dicular to the beam direc- te)

tion, The tails rapidly f L ——
become more prominent as 0 10 20 30
the applicator distance az DISTANCE ACROSS SOURCE ,mm
increases.

Fig. 8: Variation of ion current and parasitic
current across applicator SN 0136.

11


PREFACE

The calibration and related measurement services of the National Bureau
of Standards are intended to assist the makers and users of precision
measuring instruments in achieving the highest possible levels of
accuracy, quality, and productivity. NBS offers over 300 different
calibration, special test, and measurement assurance services. These
services allow customers to directly link their measurement systems to
measurement systems and standards maintained by NBS. These services
are offered to the public and private organizations alike. They are
described in NBS Special Publication (SP) 250, NBS Calibration Services
Users Guide.

The Users Guide is being supplemented by a number of special
publications (designated as the "SP 250 Series") that provide a
detailed description of the important features of specific NBS
calibration services. These documents provide a description of the:
(1) specifications for the service; (2) design philosophy and theory;
(3) NBS measurement system; (4) NBS operational procedures; (5)
assessment of measurement uncertainty including random and systematic
errors and an error budget; and (6) internal quality control procedures
used by NBS. These documents will present more detail than can be
given in an NBS calibration report, or than is generally allowed in
articles in scientific journals. In the past NBS has published such
information in a variety of ways. This series will help make this type
of information more readily available to the user.

This document (SP 250-9), NBS Measurement Services: Calibration of
Bet a-Particle-Emitting Ophthalmic Applicators, by J. S. Pruitt, is the
ninth to be published in this new series of special publications. It
describes the calibration of ophthalmic applicators used in medical
dosimetry for treatment of conditions that can be corrected with the
shallow-dose exposures available from beta-particle radioactive
sources. The calibrated quantity is the surface absorbed-dose rate to
water averaged over the active area of the source (see test number
47030C in the SP 250 Users Guide). Inquiries concerning the technical
content of this document or the specifications for these services
should be directed to the author or one of the technical contacts cited
in SP 250.

The Center for Radiation Research (CRR) is in the process of publishing
21 documents in this SP 250 series, covering all of the calibration
services offered by CRR. A complete listing of these documents can be
found inside the back cover.

NBS would welcome suggestions on how publications such as these might
be made more useful. Suggestions are also welcome concerning the need
for new calibration services, special tests, and measurement assurance
programs.

George A. Uriano Chris E. Kuyatt
Director Director
Measurement Services Center for Radiation Research

iii


6. Calibration Uncertainty

There is some uncertainty associated with each term of eq (13). Those
determined by extrapolation-chamber measurements with the 30-mm-diameter
collecting electrode, such as (I/d), and keg;1, have (relative) standard
deviations of the order of 0.1%; These are much smaller than the estimated
uncertainties and are usually ignored. The estimated uncertainties are liste
in the table below. Each is intended to be comparable to a (relative)
standard deviation, in that the chance that the true value of the quantity
lies within plus or minus the stated uncertainty is intended to be about 2 ov
of 3 (or, strictly speaking, there is a 2 out of 3 chance that the confidence
interval generated in this fashion will cover the true unknown value of the
quantity).

Relative
Absorbed-dose-rate uncertainties Uncertainty
(%)
Instrumental 0.3
Average energy per ion pair 0.4
Stopping-power ratio 3
Rate of change of current, (I/d) 9 3
Extrapolation correction, kextrap 1
Backscatter correction, Keack 1
Attenuation correction, Kea <0.1
Source surface area, A 6
Combined uncertainty (quadratic sum) 7.5
Overall uncertainty (combined x 2) 15

The instrumental uncertainties include voltmeter readings, capacitance
measurements, and pressure and temperature determinations. The uncertainty in
W/e comes directly from reference 5. The stopping-power-ratio uncertainty
includes uncertainties in the stopping-powers themselves plus uncertainties in
the beta-particle spectra. The uncertainty in (I/d), is an estimate of the
reliability of a quadratic fit to an extrapolation curve with Az = d/2. The
uncertainties in the three k factors are all estimates based on the size of
the corrections and on how carefully they were measured. The uncertainty in
surface area is a (relative) standard deviation, based on repeated measure-
ments for several sources, using the normal 2-mm grid.

When the uncertainties are combined in quadrature to obtain a combined
uncertainty, the result is + 7.5%. This number is an approximate (relative)
standard deviation. Doubling it gives an overall uncertainty of + 15% which
can be interpreted as having the approximate significance of a 95% confidence
limit.

The surface area uncertainty is dominant in table 1 and is the only one
that can be appreciably reduced at present. It can be reduced to about 1% by
mapping a normal source with a 1-mm grid, but this step is so much more time-
consuming that it is not offered as an NBS calibration service. In this case,
however, the combined uncertainty would be about + 4%. This would lead to a
stated overall uncertainty of + 8% with the approximate significance of a 95%
confidence limit. :

20


Library of Congress Catalog Card Number: 87-619844

National Bureau of Standards Special Publication 250-9
Natl. Bur. Stand. (U.S.), Spec. Publ. 250-9, 36 pages (July 1987)
CODEN: XNBSAV

Commercial products—materials and instruments —are identified in this document for the sole pur-
pose of adequately describing experimental or test procedures. In no event does such identification
imply recommendation or endorsement by the National Bureau of Standards of a particular product;
nor does it imply that a named material or instrument is necessarily the best available for the purpose
it serves.

U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON: 1987

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325


APPENDIX B

0G 8420/85 Page lof 2
0B 863/133
TFN 235324
1985 JUN 24

U.S. DEPARTMENT OF COMMERCE
NATIONAL BUREAU OF STANDARDS
GAITHERSBURG, MD 20899

REPORT OF CALIBRATION

90s Beta-particle Source Technical Operations Source No. 176
RS #85-0879
Submitted by

Received at NBS on 1985 JUN 28
Calibration date 1985 JUL 10

Beta-particle sources are calibrated in terms of the absorbed-dose rate to
water. Absorbed-dose rate is determined from current measurements with an
extrapolation ionization chamber that has a tissue-equivalent-plastic collect-
ing electrode. The water absorbed-dose rate is given by

4
b= telo7 x A (AD), Gy/s

where (41/4d), is the rate of change of current (normalized to a reference
temperature and pressure) with extrapolation chamber air-gap thickness as the
thickness approaches zero, 33.7 is the mean energy expended per unit charge in air,
1,124 is the ratio of the mean mass stopping power of water to that of air, 1.197
is the density of air at the reference temperature and pressure (22°C and 1
standard atmosphere), 8 is a correction for reduced backscatter from the collecting
electrode, U is a correction for attenuation by the high-voltage electrode, and A
is an area. For calibrations at the surface of the source, A is the active area of
the source, defined as the area within the 50% isodose line at the source surface.
The listed diameter is 2VA/i.


zd:

Source distance and electrode separation, respectively, both in mm.

2,0 (or g,6):

The extrapolation chamber coordinates needed to obtain the electrode
separation d. & (or g) is measured in tenths of an inch and 6 in
fractions of a revolution.

m,HV:
m is the reading of the barrel micrometer used for fine adjustments of
the vertical position of the applicator, in mm. HV is the extrapolation
chamber potential difference in volts.

ay?
The applicator horizontal and vertical coordinates on the microscope
stage, in mm.

The correction factors feemp and Taecay

If V is a voltage read from the DVM, V = V x 109, where j is chosen to
eliminate decimal points in recording the data. “BV is the average
change in V during a run. o, is the standard deviation per run of this
average.

Ti,

—— Normalized ton current and parasitic current, respectively. From the
definitions of j and k, I=I x 10 Jtle- » and is usually recorded without
decimal points.

foofp:

The correction f .
on factors fscat and F recom

A-2


For measurements of the source
area A, the collecting-electrode-
guard-electrode unit of figure 3 can
be lifted out of the extrapolation
chamber and replaced by a unit with
approximately the same outline but
with a much smaller collecting elec-
trode, shown in cross section in the
upper diagram in figure 6. This
probe electrode is a 0.6-mm-diameter
pencil lead, shown as a solid black
vertical strip in both upper and
lower parts of figure 6. It is
surrounded by a 0.4-mm-thick insula-
ting ring of epoxy resin, giving an
effective probe diameter of about
1mm. The probe is surrounded by a
graphite guard ring, 19 mm in
diameter. This in turn is sur-
rounded by a 50-mm-diameter acrylic
ring that is recessed from the
surface of the graphite by about
0.4 mm. The graphite guard ring is
grounded through a graphite coating
on the acrylic ring.

The probe electrode is more
complex than the 30-mm electrode
because of the special precautions
taken to make the 0.4-mm epoxy ring
of uniform thickness. The lower
diagram in figure 6 shows how this Fig. 6: Cross section of 1-mm diameter

was achieved with alignment holes collecting electrode unit (top)
which were eventually removed. The and the technique used to
alignment holes are in graphite, center pencil-lead collecting
outside the two Finish Planes, electrode (bottom). After
completely filled by the pencil machining, only the material
lead. After the epoxy has dried, between the two finish planes
the unit is machined until it looks remains.

like the graphite-epoxy insert in
the upper diagram. It was necessary to use a slow-drying epoxy for the

insulator, from which the bubbles had been removed by spinning in a
centrifuge.

The ophthalmic applicator can be moved in three perpendicular directions.
The x and y motions (along axes shown in fig. 3) are provided by the micro-
scope stage, and are controlled by two horizontal rods with knurled knobs at
the ends. These rods are a safety measure, allowing the x and y positions to
be set to within + 0.05 mm without excessive radiation exposure to the
fingers. Motion along the z axis (perpendicular to the x-y plane) is con-
trolled by the vertical barrel micrometer shown just to the right of the
applicator in figure 4, While changing Az, the operator's fingers are
protected both by the brass plate on which the microscope stage is mounted and
by the 1/4-inch-thick plastic shield attached to the applicator handle.


constant force on the flexible high voltage electrode. It has been found that
electrode flexure is negligible if the voltage gradient does not exceed

40 V/mm. Measurements have been made successfully with gradients between

10 V/mm and 40 V/mm. Corrections have to be applied in all cases, as
explained in a later section.

The two instruments at the extreme left-hand side of figure 7 are for
determining the relative air density inside the chamber. The lower instrument
ts a Wallace and Tiernan Model FA139 aneroid barometer, which reads ambient
air pressure in units of millimeters of mercury (mmHg). The upper instrument
is a Yellow Springs Instrument Co. Tele-Thermometer, to which is attached a
long cable with a temperature probe at the end. This probe usually sits in
the chamber well, immediately above the brass backing of the collecting-
electrode-guard-electrode unit, and gives an approximate measure of the
chamber air temperature.

4. Operational Procedures

This section contains descriptions of the measurement procedures for both
current per unit air gap, (1/d) 9, and source area, A, as well as correction
formulas and quality assurance measurements. An example of data collection
and analysis is given in Appendix A, taken directly from databook 863.
Appendix B shows the report issued for this particular ophthalmic applicator.

4.1 Current measurement and correction

The extrapolation chamber current measured in amperes during a run is:

(2)

where: C is the electrometer capacitance, in farads,

vy and Ve are initial and final DVM voltage measurements, in volts,

At is the run time, in seconds, determined by the DVM timer.

The value of the capacitance C must be determined for each electrometer
scale by independent measurements. For the particular electrometer shown in
figure 3, NBS #184539, the capacitances measured in March 1982 were:

Full-scale (C) Capacitance (pF)
10-8 10,000.
10-9 1,011.9
10-10 103.94

(These numbers have changed by several tenths of 1% from earlier measurements
in 1979.) Each voltage determination is the product of a DVM reading and a
DVM correction factor. For the DVM of figure 7, NBS #183047, the correction
factor measured on 86 Feb 21 for the 2-V (or 20-V) scale is 0.9977 (0.9991).
(These havé changed by 0.1% (0.1%) over the course of 3 years).

10