IEC 61217:2011

IEC 61217 ®
Edition 2.0 2011-12
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Radiotherapy equipment – Coordinates, movements and scales

Appareils utilisés en radiothérapie – Coordonnées, mouvements et échelles
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IEC 61217 ®
Edition 2.0 2011-12
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Radiotherapy equipment – Coordinates, movements and scales

Appareils utilisés en radiothérapie – Coordonnées, mouvements et échelles

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX XB
ICS 11.040.50; 13.280 ISBN 978-2-88912-824-2

– 2 – 61217 © IEC:2011
CONTENTS
FOREWORD . 6
INTRODUCTION . 8
1 Scope and object . 10
2 Normative references . 10
3 Coordinate systems . 10
3.1 General . 10
3.2 General rules . 11
3.3 Fixed reference system ("f") (Figure 1a) . 12
3.4 GANTRY coordinate system ("g") (Figure 4) . 12
3.5 BEAM LIMITING DEVICE or DELINEATOR coordinate system ("b") (Figure 5) . 13
3.6 WEDGE FILTER coordinate system ("w") (Figure 7) . 13
3.7 X-RAY IMAGE RECEPTOR coordinate system ("r") (Figures 6 and 8) . 14
3.8 PATIENT SUPPORT coordinate system ("s") (Figure 9) . 14
3.9 Table top eccentric rotation coordinate system ("e") (Figures 10 and 11) . 15
3.10 Table top coordinate system ("t") (Figures 10, 11, 18 and 19). 15
3.11 PATIENT coordinate system ("p") (Figures 17a and 17b) . 16
3.12 Imager coordinate system ("i") and focus coordinate system ("o") . 17
3.12.1 General . 17
3.12.2 The imager coordinate system ("i") . 17
3.12.3 Focus coordinate system ("o") . 18
4 Identification of scales and digital DISPLAYS . 18
5 Designation of ME EQUIPMENT movements . 19
6 ME EQUIPMENT zero positions. 19
7 List of scales, graduations, directions and DISPLAYS . 20
7.1 General . 20
7.2 Rotation of the GANTRY (Figures 14a and 14b) . 20
7.3 Rotation of the BEAM LIMITING DEVICE or DELINEATOR (Figures 15a and 15b) . 20
7.4 Rotation of the WEDGE FILTER (Figures 7 and 14a) . 20
7.5 RADIATION FIELD or DELINEATED RADIATION FIELD . 21
7.5.1 General . 21
7.5.2 Edges of RADIATION FIELD or DELINEATED RADIATION FIELD (Figure 16a) . 21
7.5.3 DISPLAY of RADIATION FIELD or DELINEATED RADIATION FIELD
(Figures 16a to 16k) . 22
7.6 PATIENT SUPPORT isocentric rotation . 23
7.7 Table top eccentric rotation . 23
7.8 Table top linear and angular movements . 24
7.8.1 Vertical displacement of the table top . 24
7.8.2 Longitudinal displacement of the table top . 24
7.8.3 Lateral displacement of the table top . 24
7.8.4 Pitch of the table top . 24
7.8.5 Roll of the table top . 24
7.9 X-RAY IMAGE RECEPTOR movements . 24
7.9.1 X-RAY IMAGE RECEPTOR rotation . 24
7.9.2 X-RAY IMAGE RECEPTOR radial displacement from RADIATION SOURCE
(SID) . 25
7.9.3 X-RAY IMAGE RECEPTOR radial displacement from ISOCENTRE . 25

61217 © IEC:2011 – 3 –
7.9.4 X-RAY IMAGE RECEPTOR longitudinal displacement . 25
7.9.5 X-RAY IMAGE RECEPTOR lateral displacement . 25
7.10 Other scales . 25
Annex A (informative) Examples of coordinate transformations between individual
coordinate systems . 57
Annex B (informative) Coordinate transformations between IEC and DICOM PATIENT
coordinates . 64
Bibliography . 65
Index of defined terms . 66

Figure 1a – Coordinate systems for an isocentric RADIOTHERAPY EQUIPMENT (see 3.1)
with all angular positions set to zero . 27
Figure 1b – Translation of origin Id along Xm, Ym, Zm and rotation around axis Zd
parallel to Zm (see 3.2d)) . 28
Figure 1c – Translation of origin Id along Xm, Ym, Zm and rotation around axis Yd
parallel to Ym (see 3.2d)) . 28
Figure 2 – X Y Z right-hand coordinate mother system (isometric drawing) showing ψ,
ϕ, θ directions of positive rotation for daughter system (see 3.2a)) . 29
Figure 3 – Hierarchical structure among coordinate systems (see 3.2c) and 3.2e)) . 30
Figure 4 – Rotation (ϕg = 15°) of GANTRY coordinate system Xg, Yg, Zg in fixed
coordinate system Xf, Yf, Zf (see 3.4) . 31
Figure 5 – Rotation (θb = 15°) of BEAM LIMITING DEVICE or DELINEATOR coordinate
system Xb, Yb, Zb in GANTRY coordinate system Xg, Yg, Zg, and resultant rotation of
RADIATION FIELD or DELINEATED RADIATION FIELD of dimensions FX and FY (see 3.5) . 32
Figure 6 – Displacement of image intensifier type X-RAY IMAGE RECEPTOR coordinate
system origin, Ir, in GANTRY coordinate system, by Rx = –8, Ry = +10, Rz = –40
(see 3.7) . 33
Figure 7 – Rotation (θw = 270°) and translation of WEDGE FILTER coordinate system Xw,
Yw, Zw in BEAM LIMITING DEVICE coordinate system Xb, Yb, Zb, the BEAM LIMITING DEVICE
coordinate system having a rotation θb = 345° (see 3.6) . 34
Figure 8 – Rotation (θr = 90°) and displacement of X-RAYIMAGE RECEPTOR coordinate
system Xr, Yr, Zr in GANTRY coordinate system Xg, Yg, Zg (see 3.7) . 35
Figure 9 – Rotation (θs = 345°) of PATIENT SUPPORT coordinate system Xs, Ys, Zs in
fixed coordinate system Xf, Yf, Zf (see 3.8) . 36
Figure 10 – Table top eccentric coordinate system rotation θe in PATIENT SUPPORT
coordinate system which has been rotated by θs in the fixed coordinate system with
θe = 360° – θs (see 3.9 and 3.10) . 37
Figure 11a – Table top displaced below ISOCENTRE by Tz = –20 cm (see 3.9 and 3.10) . 37
Figure 11b – Table top coordinate system displacement Tx = + 5, Ty = Le + 10 in
PATIENT SUPPORT coordinate system Xs, Ys, Zs rotation (θs = 330°) in fixed coordinate
system Xf, Yf, Zf (see 3.9 and 3.10) . 38
Figure 11c – Table top coordinate system rotation (θe = 30°) about table top eccentric
system. PATIENT SUPPORT rotation (θs = 330°) in fixed coordinate system Tx = 0, Ty =
Le (see 3.9 and 3.10) . 38
Figure 12a – Example of BEAM LIMITING DEVICE scale, pointer on mother system
(GANTRY), scale on daughter system (BEAM LIMITING DEVICE), viewed from ISOCENTRE
(see 3.2f)2) and Clause 4) . 39
Figure 12b – Example of BEAM LIMITING DEVICE scale, pointer on daughter system (BEAM
LIMITING DEVICE), scale on mother system (GANTRY), viewed from ISOCENTRE (see
3.2f)2) and Clause 4) . 40

– 4 – 61217 © IEC:2011
Figure 12c – Examples of scales (see Clause 4) . 40
Figure 13a – Rotary GANTRY (adapted from IEC 60601-2-1) with identification of axes 1
to 8, directions 9 to 13, and dimensions 14 and 15 (see Clause 5) . 41
Figure 13b − ISOCENTRIC RADIOTHERAPY SIMULATOR or TELERADIOTHERAPY EQUIPMENT,
with identification of axes 1; 4 to 6; 19, of directions 9 to 12; 16 to 18 and of
dimensions 14; 15 (see Clause 5) . 42
Figure 13c – View from radiation source of teleradiotherapy radiation field or radio-
therapy simulator delineated radiation field (see Clause 5) . 43
Figure 14a – Example of ISOCENTRIC TELERADIOTHERAPY EQUIPMENT (see 7.2 and 7.4) . 44
Figure 14b – Example of ISOCENTRIC RADIOTHERAPY SIMULATOR equipment (see 7.2) . 45
Figure 15a – Rotated (θb = 30°) symmetrical rectangular RADIATION FIELD (FX × FY) at
NORMAL TREATMENT DISTANCE, viewed from ISOCENTRE looking toward RADIATION SOURCE
(see 7.3) . 46
Figure 15b – Same rotated (θb = 30°) symmetrical rectangular RADIATION FIELD (FX ×
FY) at NORMAL TREATMENT DISTANCE, viewed from RADIATION SOURCE (see 7.3) . 46
Figure 16a – Rectangular and symmetrical RADIATION FIELD or DELINEATED RADIATION
FIELD, viewed from RADIATION SOURCE (see 7.5) . 47
Figure 16b – Rectangular and asymmetrical in Yb RADIATION FIELD or DELINEATED
RADIATION FIELD, viewed from RADIATION SOURCE (see 7.5) . 47
Figure 16c – Rectangular and asymmetrical in Xb RADIATION FIELD or DELINEATED
RADIATION FIELD, viewed from RADIATION SOURCE (see 7.5) . 48
Figure 16d – Rectangular and asymmetrical in Xb and Yb RADIATION FIELD or
DELINEATED RADIATION FIELD, viewed from RADIATION SOURCE (see 7.5) . 48
Figure 16e – Rectangular and symmetrical RADIATION FIELD, rotated by θb = 30°,
viewed from RADIATION SOURCE (see 7.5) . 49
Figure 16f – Rectangular and asymmetrical in Yb RADIATION FIELD, rotated by θb = 30°,
viewed from RADIATION SOURCE (see 7.5) . 49
Figure 16g – Rectangular and asymmetrical in Xb RADIATION FIELD, rotated by θb = 30°,
viewed from RADIATION SOURCE (see 7.5) . 50
Figure 16h – Rectangular and asymmetrical in Xb and Yb RADIATION FIELD, rotated by
θb = 30°, viewed from RADIATION SOURCE (see 7.5) . 51
Figure 16i – Irregular multi-element (multileaf) contiguous RADIATION FIELD, viewed from
RADIATION SOURCE, with element motion in Xb direction (see 7.5) . 52
Figure 16j – Irregular multi-element (multileaf) two-part RADIATION FIELD, viewed from
RADIATION SOURCE, with element motion in Xb direction (see 7.5) . 53
Figure 16k – Irregular multi-element (multileaf) contiguous RADIATION FIELD, viewed
from RADIATION SOURCE, with element motion in Yb direction (see 7.5) . 54
Figure 17a – PATIENT coordinate system (PATIENT is supine) . 55
Figure 17b – Rotation of PATIENT coordinate system . 55
Figure 18 – Table top pitch rotation of table top coordinate system Xt, Yt, Zt (see 3.10
and 7.8.4) . 56
Figure 19 – Table top roll rotation of table top coordinate system Xt, Yt, Zt (see 3.10.
and 7.8.5) . 56
Figure B.1 – Coordinate transformations between IEC and DICOM PATIENT coordinates . 64

61217 © IEC:2011 – 5 –
Table 1 – ME EQUIPMENT movements and designations . 19
Table 2 – Individual coordinate systems. 26
Table A.1 − Rotation matrices . 58

– 6 – 61217 © IEC:2011
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
RADIOTHERAPY EQUIPMENT –
COORDINATES, MOVEMENTS AND SCALES

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
in the subject dealt with may participate in this preparatory work. International, governmental and non-
governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International standard IEC 61217 has been prepared by subcommittee 62C: Equipment for
radiotherapy, nuclear medicine and radiation dosimetry, of IEC technical committee 62:
Electrical equipment in medical practice.
This second edition cancels and replaces the first edition, published in 1996, amendment 1,
published in 2000 and amendment 2, published in 2007. This edition constitutes a technical
revision to include imager and focus coordinate systems in Subclause 3.12. Beyond this
Subclause, changes were only introduced where needed to include the above coordinate
systems.
The text of this particular standard is based on the following documents:
FDIS Report on voting
62C/530/FDIS 62C/539/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.

61217 © IEC:2011 – 7 –
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
In this standard, the following print types are used:
– Requirements and definitions: roman type.
– Test specifications: italic type.
– Informative material appearing outside of tables, such as notes, examples and references: in smaller type.
Normative text of tables is also in a smaller type.
– TERMS USED THROUGHOUT THIS STANDARD THAT HAVE BEEN LISTED IN THE INDEX OF DEFINED
TERMS: SMALL CAPITALS.
The verbal forms used in this standard conform to usage described in Annex H of the ISO/IEC
Directives, Part 2. For the purposes of this standard, the auxiliary verb:
– “shall” means that compliance with a requirement or a test is mandatory for compliance
with this standard;
– “should” means that compliance with a requirement or a test is recommended but is not
mandatory for compliance with this standard;
– “may” is used to describe a permissible way to achieve compliance with a requirement or
test.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
– 8 – 61217 © IEC:2011
INTRODUCTION
RADIOTHERAPY is performed in medical centres where a variety of ME EQUIPMENT from different
MANUFACTURERS is usually concentrated in the RADIOTHERAPY department. In order to plan and
simulate the TREATMENT, set up the PATIENT and direct the RADIATION BEAM, such ME
EQUIPMENT can be put in different angular and linear positions and, in the case of MOVING
BEAM RADIOTHERAPY, can be rotated and translated during the IRRADIATION of the PATIENT. It is
essential that the position of the PATIENT, and the dimensions, directions, and qualities of the
RADIATION BEAM prescribed in the treatment plan, be set up or varied by programmes on the
radiotherapy EQUIPMENT with accuracy and without misunderstanding. Standard identification
and scaling of coordinates is required for ME used in RADIOTHERAPY, including RADIOTHERAPY
SIMULATORS and ME EQUIPMENT used to take images during or in connection with
RADIOTHERAPY, because differences in the marking and scaling of similar movements on the
various types of ME EQUIPMENT used in the same department may increase the probability of
error. In addition, data from ME EQUIPMENT used to evaluate the tumour region, such as
ultrasound, X-ray, CT and MRI should be presented to the treatment planning system in a
form which is consistent with the RADIOTHERAPY coordinate system. Coordinate systems for
individual geometrical parameters are required in order to facilitate the mathematical
transformation of points and vectors from one coordinate system to another.
A goal of this standard is to avoid ambiguity, confusion, and errors which could be caused
when using different types of ME EQUIPMENT. Hence, its scope applies to all types of
TELERADIOTHERAPY ME EQUIPMENT, RADIOTHERAPY SIMULATORS, information from diagnostic ME
EQUIPMENT when used for RADIOTHERAPY, recording and verification equipment, and to data
input for the TREATMENT PLANNING process.
Movement nomenclature is classified as defined terms according to IEC/TR 60788:2004 as
well as terms defined in IEC 60601-2-1 and IEC 60601-2-29 (see index of defined terms).
This standard is issued as a publication separate from the IEC 60601 series of safety
standards. It is not a safety code and does not contain performance requirements. Thus, the
present requirements will not appear in future editions of the IEC 60601-2 series, which deals
exclusively with safety requirements.
IEC 60601-2-1, IEC 60601-2-11, IEC 60601-2-29, IEC 60976, IEC 60977, IEC 61168 and
IEC 61170 include ME EQUIPMENT movements and scale conventions. A number of changes
and additions have been made in this standard.
A major value of a standard coordinate system is its contribution to safety in RADIOTHERAPY
TREATMENT PLANNING. The scales that are demonstrated in this standard are consistent with
the coordinate systems described herein. USERS may use other scale conventions. It is
anticipated that MANUFACTURERS will normally employ the scale conventions of this standard
for new ME EQUIPMENT.
It is anticipated that future amendments may address the following:
– three-dimensional RADIOTHERAPY SIMULATORS;
– CT type RADIOTHERAPY SIMULATORS.
Amendment 2, published in 2007, had extended the rotation of the PATIENT support devices
around the Z-axis in the IEC fixed coordinate system to two additional rotations – rolling
around the PATIENT’S longitudinal axis and pitching around the patient’s transversal axis.
The use of the two new additional degrees of freedom (pitch and roll) generalizes the
coordinate systems to include systematically 3 rotations and 3 translations, therefore
supporting 6 degrees of freedom in a systematic way. Modern patient support devices with 6
degrees of freedom can use a combined translation and rotation to get the same result as the
eccentric table top rotation. When changing table position data using the new IEC systems,

61217 © IEC:2011 – 9 –
the definition of isocentric rotations is sufficient to transfer all treatment-related information.
The eccentric table top coordinate system is however maintained for backward compatibility.
NOTE It is quite common in proton therapy to use a treatment chair, where the PATIENT can be rotated and tilted,
while the beam line has a fixed direction.

– 10 – 61217 © IEC:2011
RADIOTHERAPY EQUIPMENT –
COORDINATES, MOVEMENTS AND SCALES

1 Scope and object
This International Standard applies to equipment and data related to the process of
TELERADIOTHERAPY, including PATIENT image data used in relation with RADIOTHERAPY
, RADIOTHERAPY SIMULATORS, isocentric GAMMA BEAM THERAPY
TREATMENT PLANNING SYSTEMS
EQUIPMENT, isocentric medical ELECTRON ACCELERATORS, and non-isocentric equipment when
relevant.
The object of this standard is to define a consistent set of coordinate systems for use
throughout the process of TELERADIOTHERAPY, to define the marking of scales (where
provided), to define the movements of ME EQUIPMENT used in this process, and to facilitate
computer control when used.
2 Normative references
The following referenced documents are indispensable for the application of this document.
For dated references, only the edition cited applies. For undated references, the latest edition
of the referenced document (including any amendments) applies.
IEC 60601-1:2005, Medical electrical equipment – Part 1: General requirements for basic
safety and essential performance
IEC 60601-1-3:2008, Medical electrical equipment – Part 1-3: General requirements for basic
safety and essential performance – Collateral Standard: Radiation protection in diagnostic X-
ray equipment
IEC 60601-2-1:2009, Medical electrical equipment – Part 2-1: Particular requirements for the
basic safety and essential performance of electron accelerators in the range 1 MeV to 50 MeV
IEC 60601-2-11:1997, Medical electrical equipment – Part 2: Particular requirements for the
safety of gamma beam therapy equipment
IEC 60601-2-29:2008, Medical electrical equipment – Part 2-29: Particular requirements for
the basic safety and essential performance of radiotherapy simulators
IEC 60788:2004, Medical electrical equipment – Glossary of defined terms
IEC 62083:2009, Medical electrical equipment – Requirements for the safety of radiotherapy
treatment planning systems
3 Coordinate systems
3.1 General
An individual coordinate system is assigned to each major part of the ME EQUIPMENT which can
potentially be moved in relation to another part, as illustrated in Figure 1a and summarized in
Table 1. Furthermore a fixed reference system is defined. Each major part (e.g. GANTRY,
RADIATION HEAD) is always stationary with respect to its own coordinate system.

61217 © IEC:2011 – 11 –
Perspective views of an ISOCENTRIC medical ELECTRON ACCELERATOR and a RADIOTHERAPY
SIMULATOR are shown in Figures 1a, 14a and 14b. Isometric projection drawings of coordinate
systems are shown in several Figures 1a, 14a and 14b. In the figures, an elliptic (isometric
projection) arrow around an axis of a coordinate system always shows clockwise rotation of
that coordinate system about that axis when viewed from its origin and in the positive
direction.
NOTE In the following description of individual coordinate systems, counter-clockwise (ccw) rotations are
sometimes described in which the axis of rotation is not viewed from the origin of the individual coordinate system.
The definitions of coordinate systems, as stated in the following subclauses, allow
mathematical transformations (rotation and/or translation) of the coordinates from one system
to any other coordinate system. See Annex A for examples of coordinate transformations.
3.2 General rules
Following requirements apply:
a) All coordinate systems are Cartesian right-handed. The positive parameter directions of
linear and angular movements between systems are identified in Figure 2. With all
coordinate system angles set to zero, all coordinate system Z axes are vertically upward.
b) Coordinate axes are identified by a capital letter followed by a lower-case letter,
representing coordinate system identification.
c) Coordinate systems have a hierarchical structure (mother-daughter relation) in the sense
that each system is derived from another system. The common mother system is the
fixed reference system. Figure 3 and Table 2 show the hierarchical structure which is
divided into two sub-hierarchical structures, one in relation to the GANTRY, the second in
relation to the PATIENT SUPPORT.
d) The position and orientation of each daughter coordinate system (d) is derived from its
mother coordinate system (m) by translation of its origin Id along one, two or three axes
of its mother system and then by rotation of the daughter system about one of the
daughter translated system axes.
NOTE 1 The mechanical motions of parts of the ME EQUIPMENT may follow a different sequence, as long as
the ME EQUIPMENT ends up in the same position and orientation as it would have done if the indicated
sequence had been followed.
Figures 1b and 1c show examples of translation of the daughter system origin Id along
the mother system coordinate axes Xm, Ym, Zm.
Figure 1b shows translation of origin Id along Xm, Ym, Zm and rotation about axis Zd
which is parallel to Zm.
Figure 1c shows translation of origin Id along Xm, Ym, Zm and rotation about axis Yd
which is parallel to Ym.
EXAMPLE The BEAM LIMITING DEVICE coordinate system is derived from the GANTRY system and the latter
from the fixed system. Thus, a rotation of the GANTRY system causes an analogous rotation of the coordinate
axes of the BEAM LIMITING DEVICE coordinate system in the fixed system and the origin of the BEAM LIMITING
DEVICE system (position of the RADIATION SOURCE) is displaced in the fixed system (in space).
e) A point defined in one system can be defined in the coordinates of the next higher system
(its mother) or the next lower system (its daughter) by applying a coordinate
transformation, see Figure 3 and Annex A. Thus, it is possible to calculate, for a point
defined in the BEAM LIMITING DEVICE system, its coordinates in the table top system by
application of successive coordinate transformations (rotations and translations of the
origin, as defined in 3.2d)), going first from the BEAM LIMITING DEVICE system upwards to
the fixed system (i.e. BEAM LIMITING DEVICE system to GANTRY system to fixed system) and
from this downwards to the table top system (i.e. fixed system to PATIENT SUPPORT system
to table top eccentric rotation system, if available, to table top system). Such a coordinate
transformation may considerably facilitate the solution of complex geometrical problems

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encountered in treatment planning, as well as minimize errors in the positioning of ME
EQUIPMENT.
f) Notations
1) Capital letters are used for coordinate axis identification and lower-case letters are
used for coordinate system identification.
EXAMPLE Yg means y axis of the GANTRY system.
2) The rotation of one coordinate system with respect to its mother system about one
particular axis of its own system is designated by the rotation angle which identifies
the axis about which it rotates (ψ about X, ϕ about Y, and θ about Z), and by a lower-
case letter identifying the system involved.
EXAMPLE θb = 30° means rotation of the "b" system with respect to the “g” system by an angle of
30° (clockwise as viewed from ISOCENTRE) around axis Zb of the "b" system (see Figures 12a, 12b and
also Figure 5, where θb = 15°).
3) The linear position of the origin of a coordinate system within its mother system is
designated by capital letters identifying the daughter coordinate system and by the
designation of the coordinate axis of the mother system along which it is translated.
EXAMPLE Ry = (numerical value) means position of the origin of the X-RAY IMAGE RECEPTOR
coordinate system along coordinate axis Yg (of its mother system).
4) For a movable component part which does not have its own coordinate system, its
position within the system in which it moves is designated by a capital letter
identifying the device in movement and a lower-case letter identifying the coordinate
axis of the coordinate system along which it moves.
EXAMPLE X1 [Xb] = (numerical value) means position of RADIATION FIELD or DELINEATED RADIATION
FIELD edge X1 along axis Xb of the BEAM LIMITING DEVICE system.
NOTE 2 When a component part position can be displaced along only one coordinate axis, then the
designation of this coordinate axis can be omitted. Thus, for the above example, X1 = (numerical value)
is sufficient.
5) The position of a point within a coordinate system is given by the numerical values of
its coordinates in that system.
EXAMPLE Coordinate values of a point in the X-RAY IMAGE RECEPTOR system
xr = +20 cm
yr = −10 cm
zr = 0 cm
g) For rotational transformations involving more than one rotation the sequence of the
rotations must be kept consistent. If the rotational sequence varies, the resulting
transformation matrix and the orientation of the axes will be different.
The sequence in which the rotations shall be applied is the sequence in which these
rotations are described in Clause 3 of this standard.
–1
NOTE 3 M = M (see A.1).
ab ba
3.3 Fixed reference system ("f") (Figure 1a)
The fixed coordinate system "f" is stationary in space. It is defined by a horizontal coordinate
axis Yf directed from the ISOCENTRE toward the GANTRY, by a coordinate axis Zf directed
vertically upward and by a coordinate axis Xf, normal to Yf and Zf and directed to the viewer's
right when facing the GANTRY. For ISOCENTRIC EQUIPMENT the origin If is the ISOCENTRE Io and,
therefore, Yf is the rotation axis of the GANTRY.
3.4 GANTRY coordinate system ("g") (Figure 4)
The "g" coordinate system is stationary with respect to the GANTRY and its mother system is
the "f" system. Its origin Ig is the ISOCENTRE. Its coordinate axis Zg passes through and is
directed towards the RADIATION SOURCE. Coordinate axes Yg and Yf coincide.

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The "g" system is in the zero angular position when it coincides with the "f" system.
The rotation of the "g" system is defined by the rotation of coordinate axes Xg, Zg by an angle
ϕg about axis Yg (therefore about Yf of the "f" system).
An increase in the value of ϕg corresponds to a clockwise rotation of the GANTRY as viewed
along the horizontal axis Yf from the ISOCENTRE towards the GANTRY.
3.5 BEAM LIMITING DEVICE or DELINEATOR coordinate system ("b") (Figure 5)
The "b" coordinate system is stationary with respect to the BEAM LIMITING DEVICE or
DELINEATOR system and its mother system is the "g" system. Its origin Ib is the RADIATION
SOURCE. Its coordinate axis Zb coincides with and points in the same direction as axis Zg. The
coordinate axes Xb and Yb are perpendicular to the corresponding edges X1, X2, Y1 and Y2
RADIATION FIELD or DELINEATED RADIATION FIELD (see 7.5).
of the
NOTE The positions of the RADIATION FIELD edges are defined by the coordinate system. The coordinate system is
not defined by the RADIATION FIELD edges.
For ME EQUIPMENT which allows varying the distance from the ISOCENTRE to the RADIATION
SOURCE (e.g. some RADIOTHERAPY SIMULATORS), this SAD-movement corresponds to a linear
displacement of the "b" coordinate system along the Zg axis of its mother system (“g”
system).
The "b" system is in the zero angular position when the coordinate axes Xb, Yb are parallel to
and in the same directions as the corresponding axes Xg, Yg.
The rotation of the "b" system is defined by the rotation of the coordinate axes Xb, Yb about
axis Zb (therefore about axis Zg of the "g" system) by an angle θb.
An increase in the value of angle θb corresponds to the clockwise rotation of the RADIATION
FIELD or DELINEATED RADIATION FIELD as viewed from the ISOCENTRE towards the RADIATION
SOURCE (see Figures 15a, 15b).
3.6 WEDGE FILTER coordinate system ("w") (Figure 7)
The "w" coordinate system is stationary with respect to the WEDGE FILTER and its mother
system is the "b" system. Its origin, Iw, is a defined point such that the coordinate axis Yw is
directed towards the thin edge of the WEDGE FILTER and in its zero position axis Zw passes
through the RADIATION SOURCE, coincides with axis Zb and points in the same direction as Zb.
NOTE 1 The MANUFACTURER or USER may choose the location of Iw to suit the design of the WEDGE FILTER DEVICE.
For example it is possible to define Iw as the point of intersection of axis Zw with a particular surface of the WEDGE
FILTER.
In the zero angular position of the "w" system (θw = 0) and of the "b" system (θb = 0) the thin
edge of the WEDGE FILTER (end, along Yw, with highest transmission) is toward the GANTRY
and the coordinate axes Xw, Yw are parallel to the corresponding axes Xb, Yb.
The rotation of the "w" system is defined by the rotation of coordinate axes Xw, Yw about axis
Zw (parallel to axis Zb of the "b" system) by an angle θw.
An increase in the value of angle θw corresponds to the counter-clockwise rotation of the
WEDGE FILTER about Zw (parallel to axis Zb) as viewed from the RADIATION SOURCE.
At the zero angular position of the "w", "b" and "g" coordinate systems, a positive longitudinal
displacement of the origin Iw corresponds to the movement of the WEDGE FILTER thin edge
toward the GANTRY, along Yb and a positive lateral displacement corresponds to the
movement along Xb to the viewer's right when facing the GANTRY.

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NOTE 2 For convenience of access, mechanical WEDGE FILTERS may be inserted transversely. In such cases,
WEDGE FILTER orientation angles also apply. If, for example, with the "b" and "g" systems in zero angular positions
(θb = 0 and ϕg = 0), the WEDGE FILTER is inserted with the thin edge directed to the viewer's left when facing the
GANTRY, the angle θw corresponds to 90°. In the same conditions, when the WEDGE FILTER is inserted with the thin
edge directed to the viewer’s right when facing the GANTRY, the angle θw corresponds to 270°.
...