ISO 15571:1998

INTERNATIONAL
IS0
STANDARD
15571
First edition
1998-l 2-15
Practice for dosimetry in a gamma
irradiation facility for radiation processing
Pra tique de la dosim6 trie dans une ins talla tion de traitemen t par irradiation
gamma
Reference number
IS0 15571:1998(E)

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IS0 15571 :I 998(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide federation of national standards bodies
(IS0 member bodies). The work of preparing International Standards is normally carried out through IS0 technical
committees. Each member body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, governmental and non-governmental, in
liaison with ISO, also take part in the work. IS0 collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.
International Standard IS0 15571 was prepared by the American Society for Testing and Materials (ASTM)
Subcommittee E10.01 (as E 1702-95) and was adopted, under a special “fast-track procedure ”, by Technical
Committee lSO/TC 85, Nuclear energy, in parallel with its approval by the IS0 member bodies.
A new ISOITC 85 Working Group WG 3, High-level dosimetry for radiation processing, was formed to review the
and to maintain these standards. The USA holds the
voting comments from the IS0 “Fast-track procedure”
convenership of this working group.
International Standard IS0 15571 is one of 20 standards developed and published by ASTM. The 20 fast-tracked
standards and their associated ASTM designations are listed below:
IS0 Designation ASTM Designation Title
15554 E 1204-93 Practice for dosimetry in ga mma irra dia tion facilities for food
processing
15555 E 1205-93 Practice for use of a ceric-cerous sulfate dosimetry system
15556 E 1261-94 Guide for selection and calibration of dosimetry systems for
radiation processing
15557 E 1275-93 Practice for use of a radiochromic film dosimetry system
15558 E 1276-96 Practice for use of a polymethylmethacrylate dosimetry system
E 1310-94 Practice for use of a radiochromic optical waveguide dosimetry
15559
system
E 1400-95a Practice for characterization and performance of a high-dose
15560
radiation dosime try calibration labora tory
E 1401-96 Practice for use of a dichromate dosimetry system
15561
0 IS0 1998
All rights reserved. Unless otherwise specified, no pa r-t of this publication be reproduced or utilized in any form or by any means, electronic
may
mechanical, incl uding photocopying and mic rofilm, without permission in wr .iting from the publisher.
01
International Organization for Standardization
Case postale 56 l CH-1211 Get-t&e 20 l Switzerland
Internet iso @ isoch
Printed in Switzerland
ii

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@ IS0 IS0 15571:1998(E)
15562 E 1431-91 Practice for dosimetry in electron and bremsstrahlung irradiation
facilities for food processing
15563 E 1538-93 Practice for use of the ethanol-chlorobenzene dosimetry system
E 1539-93
15564 Guide for use of radiation-sensitive indicators
15565 E 1540-93 Practice for use of a radiochromic liquid dosimetry system
E 1607-94
15566 Practice for use of the alanine-EPR dosimetry system
15567 E 1608-94 Practice for dosimetry in an X-ray (bremsstrahlung) facility for
radiation processing
E 1631-96 Practice for use of calorimetric dosimetry systems for electron
15568
beam dose measurements and dosimeter calibrations
E 1649-94 Practice for dosimetry in an electron-beam facility for radiation
15569
processing at energies between 300 keV and 25 MeV
Practice for use of cellulose acetate dosimetry system
15570 E 1650-94
E 1702-95 Practice for dosimetry in a gamma irradiation facility for radiation
15571
processing
15572 E 1707-95 Guide for estimating uncertainties in dosimetry for radiation
processrng
15573 E 1818-96 Practice for dosimetry in an electron-beam facility for radiation
processing at energies between 80 keV and 300 keV
For the purposes of this International Standard, the following amendments to the ASTM text apply.
Page I, subclause 1. I, note I, and subclause 1.2
Replace note 1 and subclause 1.2 by the following.
1.2 Dosimetry is only one component of a total quality assurance program for an irradiation facility. Other
controls besides dosimetry may be required for specific applications such as medical device sterilization and
food preservation.
1.3 For the irradiation of food and the radiation sterilization of health care products, other specific IS0
standards exist. For food irradiation, see IS0 15554:1998, Practice for dosimetry in gamma irradiation facilities
for food processing (ASTM Practice E 1204). For the radiation sterilization of health care products, see
IS0 11137:1995, Sterilization of health care products - Requirements for validation and routine control -
Radiation sterilization. In those areas covered by IS0 11137, that standard takes precedence.
Page I, subclauses 1.3and 1.4
Renumber these subclauses as 1.4 and 1.5 respectively.
. . .
III

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IS0 15571:1998(E)
0 IS0
AMERICAN SOCIETY FOR TESTING AND MATERIALS
Designation: E 1702 - 95
100 Barr Harbor Dr., West Conshohocken, PA 19428
#Tb
Reprinted from the Annual Book of ASTM Standards. Copyright ASTM
If not listed in the current combined index, will appear in the next edition.
Standard Practice for
Dosimetry in a Gamma Irradiation Facility for Radiation
Processing’
This standard is issued under the fixed designation E 1702; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (t) indicates an editorial change since the last revision or reapproval.
170 Terminology Relating to Radiation Measurements
1. Scope
and Dosimetry3
1 .l This practice outlines dosimetric procedures to be
177 Practice for Use of the Terms Precision and Bias in
followed in irradiator characterization, process qualification,
ASTM Test Methods4
and routine processing in a gamma irradiation facility. These
456 Terminology Relating to Quality and Statistics4
procedures ensure that all product processed with ionizing
666 Practice for Calculating Absorbed Dose from
radiation from isotopic gamma sources receive absorbed
Gamma or X Radiation3
doses within a predetermined range. Other procedures re-
668 Practice for Application of Thermoluminescence-
lated to irradiator characterization, process qualification, and
Dosimetry (TLD) Systems for Determining Absorbed
routine processing that may influence absorbed dose in the
Dose in Radiation Hardness Testing of Electronic
product are also discussed. Information about effective or
Devices3
regulatory dose limits is not within the scope of this
E 1026 Practice for Using the Fricke Reference Standard
document.
Dosimetry System3
NOTE I-Dosimetry is one component of a total quality assurance
E 1204 Practice for Dosimetry in Gamma Irradiation
program for adherence to good manufacturing practices. Specific
Facilities for Food Processing3
applications of gamma radiation processing may require additional
E 1205 Practice for Use of a Ceric-Cerous Sulfate Dosim-
controls.
etry System3
I .2 This practice describes general procedures applicable E 126 1 Guide for Selection and Calibration of Dosimetry
to all gamma radiation processing requiring absorbed doses
Systems for Radiation Processing3
within a predetermined range. For procedures specific to
E 1275 Practice for Use of a Radiochromic Film Dosim-
food irradiation, see Practice E 1204. The sterilization of
etry System3
medical devices is a regulated irradiation process with
E 1276 Practice for Use of a Polymethylmethacrylate
specific process control requirements. These requirements,
Dosimetry System3
including specific dosimetry requirements for medical device
13 10 Practice for Use of a Radiochromic Optical
E
sterilization, are given in Refs (1) and (2).2 Guidelines for
Waveguide Dosimetry System3
medical device sterilization are given in Refs (3) and (4).
E 1400 Practice for Characterization and Performance of a
1.3 For guidance in the selection, calibration, and use of
High-Dose Radiation Dosimetry Calibration Labora-
specific dosimeters, and interpretation of absorbed dose in
tory3
the product from dosimetry measurements, see Guide
E 140 1 Practice for Use of a Dichromate Dosimetry
E 126 1 and Practices E 666, E 668, E 1026, E 1205, E 1275,
System3
E 1276, E 1310, E 1400, E 1401, E 1538, E 1540, E 1607,
E 143 1 Practice for Dosimetry in Electron and Brems-
and E 1650. For discussion of radiation dosimetry for
strahlung Irradiation Facilities for Food Processing’
gamma rays, see ICRU Report 14.
1538 Practice for Use of the Ethanol-Chlorobenzene
E
1.4 This standard does not purport to address all of the
Dosimetry System3
sajtity concerns, ij’ any, associated with its use. It ii the
E 1539 Guide for Use of Radiation-Sensitive Indicators3
responsibility of the user of this standard to establish appro-
E 1540 Practice for Use of a Radiochromic Liquid Dosim-
priate safety and health practices and determine the applica-
etry System3
bility o/*;egulatory limitations prior to use.
.
E 1607 Practice for Use of the Alanine-EPR Dosimetry
System3
E 1650 Practice for Use of a Cellulose Acetate Dosimetry
2. Referenced Documents
System
2.1 ASTM Standards:
E 1707 Guide for Estimating Uncertainties in Dosimetry
for Radiation Processing
2.2 ICRCJ Reports.
1 This practice is under the jurisdiction of ASTM Committee E-IO on Nuclear
Technology and Applications and is the direct responsibility of Subcommittee
El0.01 on Dosimetry for Radiation Processing.
Current edition approved Sept. IO, 1995. Published November 1995.
3 Anma/ Book oJASTIU Standards, Vol 12.02.
2 The boldface numbers in parentheses rcfcr to a list of references at the end of
4 Annrra~ Book oJASTM Standards, Vol 14.02.
this practice.
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ISO15571:1998(E) @ IS0
ICRU Report 14 Radiation Dosimetry: X-Rays and 4.15 Polymerization of monomers and grafting of mono-
Gamma Rays with Maximum Photon Energies Between mers onto polymers;
4.1.6 Control of pathogens in liquid or solid waste;
0.6 and 50 MeV
4.1.7 Enhancement of color in gemstones and other
ICRU Report 33 Radiation Quantities and Units
materials;
4.1.8 Modification of characteristics of semiconductor
3. Terminology
devices; and
3.1 Definitions- Other terms used in this practice are
4.1.9 Research on materials effects.
defined in Terminology E 170 and ICRU Report 33.
NOTE 2-Dosimetry is required for regulated irradiation processes
3.1.1 absorbed dose-quantity of radiation energy im-
such as the sterilization of medical devices and the treatment of food. It
parted per unit mass of a specified material. The unit of
may be less important for other industrial processes, for example,
absorbed dose is the gray (Gy), where 1 Gy is equivalent to
polymer modification, which can be evaluated by changes in the
the absorption of 1 J per kg (= 100 rad). The mathematical
physical and chemical properties of the irradiated materials.
relationship is the quotient of dZ by dm, where dZ is the mean
4.2 Dosimeters are used as a means of quality control of
energy imparted by ionizing radiation to matter of mass dm
the process by relating the measured response of the dosim-
(see ICRU 33).
eter to radiation to the absorbed dose in the product or in a
D = &f&n
specified material such as water.
3.1.2 absorbed-dose mapping-measurement of the ab-
4.3 An irradiation process usually requires a minimum
sorbed-dose distribution within an irradiation unit through
absorbed dose to achieve the desired effect. There also may
the use of dosimeters placed at specified locations.
be a maximum absorbed dose that the product can tolerate
3.1.3 compensating dummy-simulated product used and still meet its functional specifications. Dosimetry is
during routine production runs with irradiation units con- essential to the irradiation process since it is used both to
taining less product than specified in the product loading
determine these limits and to confirm that the product is
configuration or used at the beginning or end of a production
irradiated within these limits.
run to compensate for the absence of product.
4.4 The absorbed-dose distribution within the product
3.1.4 dosimeter set-one or more dosimeters used to
depends on the overall product dimensions and weight,
measure the absorbed dose at a location to a desired
irradiation geometry, and source activity distribution. The
confidence level and whose average reading is used as the operating parameter that determines the absorbed dose is the
absorbed dose measurement at that location.
timer setting. The timer setting must be controlled to obtain
3.1.5 dosimetry system- a system used for determining
reproducible results.
absorbed dose, consisting of dosimeters, measurement in-
4.5 Before an irradiation process can be used, the irradi-
struments and their associated reference standards, and
ator must be qualified to determine its effectiveness in
procedures for the system ’s use.
reproducibly delivering known, controllable absorbed doses.
3.1.6 irradiation unit-a volume of material with a spec-
This involves testing the process equipment, calibrating the
ified loading configuration irradiated as a single entity.
equipment and dosimetry system, and characterizing the
3.1.7 production run (continuous-flow irradiation)-a se-
magnitude, distribution, and reproducibility of the absorbed
ries of irradiation units consisting of materials or products
dose delivered by the irradiator to a reference material.
having similar radiation-absorption characteristics that are
4.6 To ensure consistent and reproducible dose delivery in
irradiated sequentially to a specified range of absorbed dose.
a qualified process, routine process control requires docu-
3.1.8 simulated product-a mass of material with attenu-
mented product handling procedures before and after the
ation and scattering properties similar to those of a particular
irradiation, consistent product loading configurations, mon-
material or combination of materials. This term is some-
itoring of critical processing parameters, routine product
times referred to as dummy product.
dosimetry, and documentation of the required activities and
3.1.9 timer setting-parameter varied to control the time
functions.
during which an irradiation unit is exposed to radiation.
5. Radiation Source Characteristics
4. Significance and Use
5.1 The radiation source used in a facility considered in
this practice consists of sealed linear elements (rods or
4.1 Various products and materials routinely are irradi-
“pencils ”) of cobalt-60 or cesium-137 arranged in one or
ated at predetermined doses at gamma irradiation facilities
more planar or cylindrical arrays. Cobalt-60 and cesium-137
to reduce their microbial population or to modify their
sources decay at known rates, emitting photons with known
characteristics. Dosimetry requirements may vary depending
energies. Between source additions, removals, or redistribu-
upon the irradiation application and end use of the product,
tions, the only variation in the source output is the steady
Some examples of irradiation applications where dosimetry
reduction in the activity due to the radioactive decay.
may be used are:
4.1.1 Sterilization of medical devices;
6. Types of Facilities and Modes of Operation
4.1.2 Treatment of food for the purpose of parasite and
pathogen control, insect disinfestation, and shelf life exten- 6.1 Radiation processing facilities may be categorized by
sion; irradiator type (for example, container or bulk flow), con-
4.1.3 Disinfection of consumer products; veyor system (for example, shume-dwell or continuous), and
4.1.4 Cross-linking or degradation of polymers and operating mode (for example, batch or continuous). Product
elastomers; may be moved to the location in the facility where the
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IS0 15571 :1998(E)
0 IS0
0 E 1702
irradiation will take place either while the source is shielded 8.2.1 Establish and document the irradiator qualification
(batch operation), or while the source is exposed (continuous
program that demonstrates that the irradiator, operating
operation). Product may be transported in irradiation con-
within specified limits, will consistently produce an ab-
tainers past the source at a uniform controlled speed ;
sorbed-dose distribution in a given product to predetermined
(continuous conveyance), or instead may undergo a series of
specification. Such documentation shall be retained for the
discrete controlled movements separated by controlled time
life of the irradiator, and shall include:
periods during which the irradiation container is stationary
8.2.1.1 A description of the instrumentation and equip-
(shuffle-dwell), The source may extend above and below the
ment for ensuring the reproducibility, within specified limits,
product (overlapping source) or the product may extend
of the source-to-product geometry and of the time the
above and below the source (overlapping product). For the
product spends at different locations in the irradiation zone.
overlapping product configuration, the irradiation unit is
8.3 Equipment Testing and Calibration:
moved past the source at two or more different levels. For
8.3.1 Processing Equipment-The absorbed dose in the
irradiators with rectangular source arrays, the irradiation
product in an irradiation container depends on the operating
container generally makes one or more passes on each side of
parameters of the irradiation facility, which are controlled by
the source. In bulk-flow irradiators, products such as grain or
the processing equipment and instrumentation.
flour flow in loose form past the source.
8.3.1.1 Test all processing equipment and instrumenta-
6.2 For low absorbed-dose applications that may require
tion that may influence absorbed dose in order to verify
particularly high mechanical speed, various techniques are
satisfactory operation of the irradiator within the design
used to reduce the absorbed-dose rates. These may include
specifications.
use of only a portion of the source, use of attenuators, and
8.3.1.2 Implement a documented calibration program to
irradiation at greater distances from the source.
ensure that all processing equipment and instrumentation
6.3 The details of a particular irradiator design and the
that may influence absorbed dose are calibrated periodically.
mode of operation affect the delivery of absorbed dose to a
8.3.2 Analytical Equipment-The accuracy of the ab-
product. They therefore should be considered when per-
sorbed-dose measurement depends on the correct operation
forming the absorbed-dose measurements required in Sec-
and calibration of the analytical equipment used in the
tions 8, 9, and 10.
analysis of the dosimeters.
8.3.2.1 Check the performance of the analytical equip-
7. Dosimetry Systems
ment periodically to ensure that the equipment is func-
7.1 Dosimetry systems used to determine absorbed dose
tioning in accordance with performance specifications. Re-
shall cover the absorbed dose range of interest and shall be
peat this check following equipment modification or
calibrated before use.
servicing and prior to the use of the equipment for a
7.2 Dosimetry System Selection-It is important that the
dosimetry system calibration. This check can be accom-
dosimetry system be evaluated for those parameters associ-
plished by using standards such as calibrated optical density
ated with gamma irradiation facilities that may influence the
filters, wavelength standards, or calibrated thickness gages
dosimeter response, for example, gamma-ray energy, ab-
supplied by the manufacturer or national or accredited
sorbed-dose rate, and environmental conditions such as
standards laboratories. The correct performance of
temperature, humidity, and light. Guidance as to desirable
dosimetry analysis equipment also can be demonstrated by
characteristics and selection criteria can be found in Guide
showing that the analysis results from dosimeters, given
E 126 1. Details for individual dosimetry systems are given in
known absorbed doses, are in agreement with the expected
Practices E 1026, E 1205, E 1275, E 1276, E 1310, E 1401,
results within the limits of the dosimetry system uncertainty.
E 1538, E 1540, E 1607, and E 1650.
However, this method is only applicable to reference stan-
7.3 Dosimetry System Calibration-It is important that
dard dosimetry systems where the long-term stability of the
the dosimetry system used is properly calibrated with calibra-
response has been demonstrated and documented.
tion traceable to a recognized national or international
8.3.2.2 Implement a documented calibration program to
standard. Guidance for calibration can be found in Guide
ensure that all analytical equipment used in the analysis of
E 1261.
dosimeters is calibrated periodically.
8. Installation Qualification 8.3.2.3 Prior to each use of an analytical instrument,
check the zero setting and, if applicable, the full scale
8.1 Objective:
reading.
8.1.1 The purpose of dosimetry in qualifying a gamma
8.4 Irradiator Characterization:
irradiation facility is to establish baseline data for evaluating
8.4.1 The absorbed dose received by any portion of
the effectiveness, predictability, and reproducibility of the
product in an irradiation unit depends on facility parameters
system under the range of conditions over which the facility
such as the activity and geometry of the source, the source-
will operate. For example, dosimetry shall be used (I) to
to-product distance, and the irradiation geometry, and on
establish relationships between absorbed dose in a reproduc-
processing parameters such as the irradiation time, the
ible geometry and the operating parameters of the facility,
product composition and density, and the product loading
(2) to characterize dose variations when these conditions
configuration.
fluctuate statistically and through normal operations, and (3)
8.4.2 The absorbed-dose rate and absorbed-dose distribu-
to measure absorbed dose distributions in reference mate-
tion in the product will change during movement of the
rials.
irradiation unit, Therefore, changing from one absorbed dose
8.2 Equipment Documentation:
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@ IS0
IS0 15571: 1998(E)
to another by direct scaling of the time setting may or may the product through the irradiation zone. Enough dosimeters
should be used to obtain statistically significant results.
not be valid (see 9.3.3).
Calculation of the minimum and maximum absorbed doses
8.4.3 To ensure that product near the source is processed
may be an appropriate alternative (10, 13).
within specifications, additions to the absorbed dose re-
sulting from the movement of the source to and from the
irradiation position should be considered and quantified.
9. Process Qualification
8.4.4 The irradiator characterization process includes
9.1 Objective:
mapping the absorbed-dose distributions in irradiation units
9.1.1 Absorbed-dose requirements vary depending upon
containing actual or simulated product. Dosimetry data
the application and type of product being irradiated. Irradi-
from previously characterized irradiators of the same design
ation application is usually associated with a minimum
or theoretical calculations may provide useful information
absorbed-dose requirement and sometimes a maximum
for determining the number and location of dosimeters for
absorbed-dose requirement. For a given application, one or
this characterization process.
both of these limits may be prescribed by regulations.
Therefore, the objective of process qualification is to ensure
NOTE 3-Theoretical calculations may be performed using an ana-
lytical method such as the point-kernel method (5) or the Monte Carlo
that absorbed dose requirements are satisfied. This is accom-
method (6). In the point-kernel method, the radiation source is
plished by absorbed-dose mapping of specific products and
approximated by differential isotropic point sources. The total absorbed
product loading configurations to determine the minimum
dose at each dose point is obtained by summing the absorbed-dose
and maximum absorbed doses, the locations of the min-
contribution from each isotropic source point. The absorbed dose at a
imum and maximum absorbed-dose regions, and the timer
dose point is dependent mainly upon the energy of the gamma radiation
setting necessary to achieve absorbed dose within the set
and the effective atomic number, density, and thickness of the materials
located between the source point and dose point (for example, source
requirements.
encapsulation material, product, and metal containers or supports). In
9.2 Determination of Product Loading Configuration:
the Monte Carlo method, the total absorbed dose at a dose point is
9.2.1 A product loading configuration for irradiation shall
determined from the energy distribution at that point by modelling the
be established for each product type. The documentation for
trajectories of photons and electrons through the absorbing media. In
this loading configuration shall include specifications for
order to obtain a good statistical representation of their interactions (for
parameters that influence the radiation processing such as
example, scattering or absorption) within the media, the paths of a
sufficiently large number of photons and electrons are followed until the
product size, product mass, or product density.
dose point is reached. Like the point-kernel method, the Monte Carlo
9.3 Product A bsorbed-Dose Mapping.
method requires a knowledge of relevant properties of all materials
9.3.1 Establish the locations of the regions of minimum
between the source and dose points.
and maximum absorbed dose for the selected product and
8.4.4.1 Map the absorbed-dose distribution by a three- product loading pattern. This is accomplished by placing
dimensional placement of dosimeters throughout the actual dosimeters throughout the volume of interest for one or
or simulated product. For this general characterization, the more irradiation units. Select placement patterns that can
amount of product in the irradiation units should be the most probably identify the locations of the absorbed dose
extremes using data obtained from other absorbed-dose
amount expected during typical irradiation runs. Select
placement patterns that can most probably identify the mapping studies or from theoretical calculations. Concen-
locations of the absorbed-dose maxima and minima. Place trate dosimeters in regions of minimum and maximum
more dosimeters in these locations, and fewer dosimeters in absorbed dose with fewer dosimeters placed in areas likely to
locations likely’ to receive intermediate absorbed doses. For receive intermediate absorbed dose. Dosimeter films in
further information on the use and placement of dosimeters, sheets or strips also may be employed to obtain useful
see Refs (7-13). information.
8.4.4.2 For a given process irradiation time or product
9.3.2 Consideration should be given to possible variations
dwell time, an increase in the product density generally in the absorbed doses measured in similar locations in
results in a decrease in the minimum absorbed dose. The different irradiation units caused by variations in the product
maximum absorbed dose may not change appreciably or it
or product distributions, Timer settings chosen for routine
may decrease, but to a lesser degree than the minimum
processing should take this variation into account.
absorbed dose; therefore, the dose uniformity ratio increases.
9.3.3 Ensure that the absorbed dose received during
8.4.5 Changes in the source loading, source geometry, or
movement of the source or irradiation units during the
product transport system can affect the absorbed-dose distri-
absorbed-dose mapping is small compared to the total
bution. If such a change is made, perform sufficient
absorbed dose. If this requirement is met, the absorbed dose
dosimetry to confirm that the change has not affected the will be related directly to the timer setting, and changes to
absorbed-dose distribution, or to determine the new ab- the absorbed dose can be obtained by adjustment of the
sorbed-dose distribution. timer setting. If this requirement cannot be met, the ab-
8.4.6 Use the results of the irradiator characterization as a sorbed-dose mapping shall be performed using the timer
guide for dosimeter placement for process qualification as setting estimated to be required for the routine production
discussed in Section 9. runs and repeated if there is a significant change in the timer
8.4.7 The procedures for absorbed-dose mapping outlined
setting.
in this section may not be feasible for some types of 9.3.4 If changes that could affect the magnitude or loca-
bulk-flow irradiators. In this case, minimum and maximum
tion of the absor
...