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6.1 Introduction

Chapter 6 Measurement of Ionizing Radiation

In the early days of x-ray usage, skin erythema was used as a measure of radiation effects.

In the orthovoltage era, the skin was the limiting organ to the delivered dose. This is no longer true after megavoltage machines were introduced with its skin-sparring properties.

In 1928, the roentgen (denoted by R) was adopted as the unit of measuring x and radiation exposure.

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6.2 The Roentgen

The roentgen is a unit of exposure.

The exposure is defined as: ,

where dQ is the amount of charges (either + or , but not both) produced in air when all the electrons liberated by photons in air of mass dm are completely stopped in air.

dm

dQX

source

+ + + +

----

e-

+

++

___

e-+

++ ___e-

+++

___

airkgCR /1058.21 4

Electron equilibrium:in a volume,ionization loss = ionization gain

or,electrons entering the volume = electrons leaving the volume

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6.3 Free-Air Ionization Chamber

(R)41058.21

LA

Qp p

X

To electrometerguard

electrodecollecting electrode

L

collecting volume

source

Lead-lined box

diaphragm+ + + +

----

e-

+

++

___

PD

Ap

(R)41058.21

LA

QD D

X

Used in primary national labs (NIST) to measure exposure according to its definition.

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6.4 Thimble Chamber

Air shell

Air cavity Air cavity

Solid air shell

Thimble wall (air-equivalent)

Air cavity

Central electrode (graphite or aluminium)

insulator

Most of the ionization produced in the cavity air arises from electrons liberated in the wall.

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6.4 Thimble Chamber (effective atomic number)

The effective atomic number of the wall material and the central electrode should be such that the system as a whole behaves like a free-air chamber. Most commonly used wall material is graphite and electrode is either graphite or aluminum.

The effective atomic number of a mixture is the atomic number of an element with which photons interact the same way.

Z

94.2/194.294.222

94.211 nnZaZaZaZ

Where a1, a2, …, an are the fractional contribution of each element to the total number of electrons in the mixture.

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6.4 Thimble Chamber (effective atomic number)

Example: calculation of for air:Z

Composition by weight - N: 75.5%, O:23.2%, Ar:1.3%

Number of electrons/g of air: (fraction by weight) w

A

A

ZN

2323

107.0232.0999.15

81002.6

O

2323

1027.2755.0007.14

71002.6

N

2323

1004.0013.094.39

181002.6

Ar

Number of electrons/g of air: 3.011023

a1 = 2.27/3.01 = 0.754

a2 = 0.70/3.01 = 0.233

a3 = 0.04/3.01 = 0.013

67.718013.08233.07754.094.2/194.294.294.2 airZ

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6.4 Thimble Chamber (chamber calibration)

A thimble chamber can be used directly to measure exposure if (a) it were air equivalent, (b) its cavity volume were accurately known, and (c) its wall thickness was sufficient to provide electronic equilibrium.

Av

QX

1

The exposure X is given by:

Q is the ionization charge liberated in the cavity air of density and volume v;

A is a correction factor accounting for the attenuation in the wall.

wall thickness

cham

ber

resp

onse

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6.4 Thimble Chamber (chamber calibration)

In practice, however, a chamber is calibrated against the free-air chamber for x-rays up to a few hundred kilovolts, and against a standard cavity chamber for higher energies. This is because:

1. The chamber is not exactly air-equivalent.

2. The cavity volume is not precisely known.

The chamber calibration factor provided by the standard laboratory already includes the wall correction factor and other perturbation factors.

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6.4 Thimble Chamber (desirable chamber characteristics)

1. Minimal variation in sensitivity or exposure calibration factor with photon energies.

2. Suitable volume to allow expected range of exposures.

3. Minimal variation in sensitivity with the direction of incident radiation.

4. Minimal ‘stem’ leakage.

5. Calibrated for exposure against a standard instrument for all radiation qualities of interest.

6. Minimal ion recombination loss (sufficient voltage, typically 300 V).

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6.5 Practical Thimble Chambers (condenser)

+ + + + + + + + + ++ + + + + + + + + + + + + + +

+ + + + +

– – – – –

– – – – –

– – – – – – – – – – –

– – – – – – – – – – –

Air equivalent wall

air

insulator

Metal shield

The chamber is initially fully charged. When it is exposed to radiation, ions are produced in the air cavity and collected, leading to a reduction of charge on the electrodes. The reduction in charge is proportional to the exposure.

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6.5 Practical Thimble Chambers (condenser)

CQV /

Chamber sensitivity is defined as voltage drop per roentgen, it is proportional to the air cavity volume v, and inversely proportional to the capacitance C.

Charge Q produced in chamber volume v due to exposure X:

Voltage dropoff V over chamber capacitance C:

Chamber sensitivity: CvXV air /

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6.6 Electrometers (string electrometer)

The string electrometer is used together with the condenser type chamber.

First, the chamber is fully charged in the electrometer, the shadow of the string is at the fully charged position (zero position).

Second, the chamber is removed from the electrometer and exposed to radiation. Ions collected on the electrode reduces the charge.

Third, the chamber is placed back in the electrometer, the position of the string now moves away from the zero position, depending on the reduction in charge on the electrode.

conductive fiber

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6.5 Practical Thimble Chambers (condenser)

Stem leakage caused by ionization produced in the stem, rather than in the air cavity. Its effect depends on the field size and can be corrected.

source

collimator

radiation beam

point of measurement

chamberprotective

cap

radiation beam

determination of stem effect

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6.5 Practical Thimble Chambers (Farmer)

electrode (Al)

graphite air

insulator

Commercially available, provides better (flatter) energy response characteristics. Air cavity volume is typically 0.6 cm3

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6.6 Electrometers (other electrometer)

The electrometer is connected to the chamber during the entire time of exposure and readout. (Unlike condenser chamber/string electrometer, in which the chamber is attached to the electrometer during reading, but detached during exposure.)

It can be used to measure the charge (integration mode, nC), current (rate mode, nA), or direct exposure-reading (direct reading dosimeter mode).

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6.7 Special Chambers

To electrometer

Build-up slab

Air cavity

Collecting electrode

Thin window

Parallel-plate chambers: fixed spacing (typically 2mm) between 2 parallel-plate electrodes. Suitable for shallow depths and electron beams.

Extrapolation chambers: similar to parallel-plate chambers, except that the electrode spacing is variable. By varying the spacing, one can estimate the surface dose by extrapolating to zero electrode spacing.

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6.8 Ion Collection (saturation)

Chamber voltage

Ion

curr

ent

Saturation region

Incomplete collection due to ion recombination in the chamber

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Collection efficiency can be measured using the ‘two voltage’ method in which one voltage is set at the operating voltage (typically V1=300 V), and the second voltage half of its value (e.g. V2=150 V).

The recombination correction factor, Pion, can be obtained from the ratio of the charges (Q1/Q2) collected at the 2 voltages.

The voltage on the chamber should be chosen so that the collection efficiency (1/Pion) is at least 99%.

6.8 Ion Collection (collection efficiency)

producedionsofnumber

collectedionsofnumberefficiencycollection

Q1/Q2

Pio

n at V

1

continuous radiation

pulsed radiation

scanning pulsed radiation

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6.9 Chamber Polarity Effects

Polarity effect: the charge collected by an ion chamber changes in magnitude when the polarity of the collecting voltage is reversed.

This effect can be minimized by taking the average of the 2 readings with reversed polarity.

The polarity effect is more severe for electron beams than for photon beams.

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6.10 Environmental Conditions

Chamber calibration factor is stated under standard conditions (P=760 mm Hg, T=22°C). In normal use, chamber is unsealed and communicated to the outside atmosphere. The density (and the mass) of air in the air cavity is affected by the temperature and pressure, and therefore need to be corrected.

295

273760,

T

PC PT

P is the pressure in mm of Hg, and T is the temperature in degrees of Celsius (adding 273 converts Celsius to absolute temperature in degrees of Kelvin).

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Example: A chamber was calibrated under the standard conditions: T=22°C, P=760 mm Hg. When the chamber is used under the room conditions: T=25°C, P=750 mm Hg, and reads a charge of M=3×10-8 Coulomb, what is the corrected reading Mcorr?

Coulomb

MM corr

8

8

1007.3

750

760

295

298103

750

760

22273

25273

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6.11 Measurement of Exposure

X = M • CT,P • Cs • Cst • NC

X is the exposure in Roentgen.

M is the chamber reading.

Nc is the chamber exposure calibration factor traceable to NIST.

CT,P is the temperature, pressure correction factor.

Cs is the correction factor for recombination loss.

Cst is correction factor for stem leakage.