IEC 61745:1998

INTERNATIONAL
IEC
STANDARD
First edition
1998-08
End-face image analysis procedure
for the calibration of optical fibre
geometry test sets
Reference number
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Terminology, graphical and letter symbols
For general terminology, readers are referred to IEC 60050: International
Electrotechnical Vocabulary (IEV).
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used in electrical technology, IEC 60417: Graphical symbols for use on equipment.
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* See web site address on title page.

INTERNATIONAL
IEC
STANDARD
First edition
1998-08
End-face image analysis procedure
for the calibration of optical fibre
geometry test sets
 IEC 1998  Copyright - all rights reserved
No part of this publication may be reproduced or utilized in any form or by any means, electronic or
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– 2 – 61745 © IEC:1998(E)
CONTENTS
Page
FOREWORD . 3
Clause
1 General . 4
1.1 Scope and object . 4
1.2 Definitions . 4
1.3 Geometrical parameters of optical fibres . 7
1.4 Description of geometry test sets . 7
1.5 Calibration standard requirements. 7
2 Calibration . 8
2.1 Introductory remark. 8
2.2 Rationale for calibration of geometry test sets . 8
2.3 Calibration procedure. 9
2.4 Check calibration procedure. 11
2.5 Spatial linearity . 12
2.6 Calibration of core/cladding concentricity error measurement . 12
2.7 Calibration of non-circularity measurement. 12
3 Evaluation of uncertainties . 12
3.1 Introductory remark. 12
3.2 Evaluation of uncertainty in test set calibration . 12
3.3 Evaluation of uncertainty in fibre measurement. 15
3.4 Evaluation of uncertainty in chromium mask measurement . 16
3.5 Summary . 16
4 Documentation . 17
4.1 Records. 17
4.2 Certificate of calibration . 17
4.3 Sample calibration certificate . 18
Figure 1 – Example of a calibration chain and the accumulation of uncertainties. 19
Annex A (informative) Derivation of calibration factors . 20
Annex B (informative) Worked examples for the determination of calibration factors . 23
Annex C (normative) Calculation of uncertainties . 24
Annex D (informative) Worked examples for the determination of uncertainties . 27
Annex E (informative) Generation of working standards . 29
Annex F (informative) Estimation of uncertainty in the measurement of core/cladding
concentricity error . 30
Annex G (informative) Estimation of uncertainty in the measurement of non-circularity . 33

61745 © IEC:1998(E) – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
__________
END-FACE IMAGE ANALYSIS PROCEDURE FOR THE CALIBRATION
OF OPTICAL FIBRE GEOMETRY TEST SETS
FOREWORD
1) The IEC (International Electrotechnical Commission) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of the 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, the IEC publishes International Standards. 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. The 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 the 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 National Committees.
3) The documents produced have the form of recommendations for international use and are published in the form
of standards, technical reports or guides and they are accepted by the National Committees in that sense.
4) In order to promote international unification, IEC National Committees undertake to apply IEC International
Standards transparently to the maximum extent possible in their national and regional standards. Any
divergence between the IEC Standard and the corresponding national or regional standard shall be clearly
indicated in the latter.
5) The IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with one of its standards.
6) Attention is drawn to the possibility that some of the elements of this International Standard may be the subject
of patent rights. The IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 61745 has been prepared by IEC technical committee 86: Fibre
optics.
The text of this standard is based on the following documents:
FDIS Report on voting
86/125/FDIS 86/134/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.
Annex C forms an integral part of this standard.
Annexes A, B, D, E, F and G are for information only.
A bilingual version of this standard may be issued at a later date.

– 4 – 61745 © IEC:1998(E)
END-FACE IMAGE ANALYSIS PROCEDURE FOR THE CALIBRATION
OF OPTICAL FIBRE GEOMETRY TEST SETS
1 General
1.1 Scope and object
In the research and production environments there exists a range of test methods for
characterizing the geometry of optical fibres. Furthermore, each test method may determine
one or more of the many parameters required for complete geometrical characterization. This
International Standard describes the calibration of test sets which perform end-face image
analysis, also known as near-field or grey-scale analysis. The principles, however, may be
applied to test sets of a different type.
This standard addresses the calibration of measurements made on single-mode fibres only;
however, this type of test set may also be used to measure the geometrical parameters of the
cores of multimode fibres, but the evaluation of uncertainties associated with these
measurements is beyond the scope of this standard.
The procedures outlined are to be performed by calibration laboratories and by the
manufacturers or users of geometry test sets, for the purpose of calibrating geometry test sets
and for evaluating the uncertainties in measurements made on calibrated test sets. The
calibration of fibre coating or cable measurement test sets is not covered by this standard. The
object of this standard is to define a standard procedure for the calibration of test sets for
measuring the glass geometry of optical fibres.
1.2 Definitions
For the purpose of this International Standard, the following definitions apply.
1.2.1
accredited calibration laboratory
calibration laboratory authorised by the appropriate National Standards laboratory to issue
calibration certificates with a specified uncertainty, which demonstrate traceability to national
standards
1.2.2
artefact
any object that is measured on or used to calibrate a geometry test set. An artefact may be, for
example, an optical fibre or a chromium-on-glass pattern
1.2.3
calibration
process by which the relationship between the values indicated by the geometry test set under
calibration and the known values of the calibration standard is established. The purpose of
calibration is to bring all geometry test sets into substantial agreement with a national
standards laboratory. This may be performed either by adjustment of the geometry test set or
by documentation of a calibration factor(s) in a calibration certificate. The pertaining
environment and instrument conditions at the time of calibration are usually recorded.
Calibration includes estimation of all uncertainties.
1.2.4
calibration chain
chain of transfers from a national standard to the geometry test set through intermediate or
working standards (see figure 1)

61745 © IEC:1998(E) – 5 –
1.2.5
calibration checking
establishing that a geometry test set that has been previously calibrated but has reached its
calibration due date remains within specified uncertainty limits. If the geometry test set has
drifted outside these limits, then re-calibration is required. Otherwise, the re-checking period
can be extended for a stated period. The test set may be checked using a working standard
1.2.6
calibration standard
artefact that is calibrated against a reference standard and is used to calibrate test sets. The
artefact may be a fibre or a chromium-on-glass pattern. Proper use of a calibration standard
ensures traceability. The term includes the reference standard, the transfer standard and the
working standard(s), in descending order of metrological uncertainty
1.2.7
combined standard uncertainty
combination of a number of individual standard uncertainties.
The term "accuracy" should be avoided in this context.
In calibration reports and technical data sheets, the combined standard uncertainty in the
geometry test set measurement is reported as an overall expanded uncertainty with the
applicable confidence level, for example 95,5% or 99,7%.
1.2.8
confidence level
estimation of the probability that the true value of a measured parameter lies within a given
range (expanded uncertainty)
1.2.9
correction offset
number that is added to or subtracted from the measurement result of a test set to correct for a
known physical effect
1.2.10
coverage factor, k
factor used to calculate the expanded uncertainty U from the standard uncertainty
1.2.11
expanded uncertainty, U
range of values within which the true value of the measured parameter, at the stated
confidence level, can be expected to lie. It is also called the confidence interval and is equal to
the coverage factor k times the standard uncertainty u:
U = k ⋅ u
The measurement uncertainty of a geometry test set should be specified in the form of
expanded uncertainty.
NOTE – When the distribution of uncertainties is assumed to be normal and a large number of measurements are
made, then confidence levels of 68,3 %, 95,5 % and 99,7 % correspond to values for k of 1, 2, and 3 respectively
(see clause C.3 ).
1.2.12
geometry test set
instrument used to measure the geometrical parameters of an optical fibre. The parameters
measured will depend on the type of geometry test set

– 6 – 61745 © IEC:1998(E)
1.2.13
infant fibre
fibre whose geometry is to be measured on a calibrated geometry test set
1.2.14
instrument state
description of the measurement conditions of the geometry test set during calibration and
measurement, for instance form-fits used, data filtering schemes employed and other important
information concerning the test set such as warm-up time and date of calibration
1.2.15
national standard
standard whose measurement is traceable to fundamental quantities, such as the wavelength
of light, and which is used as the basis for fixing the value, in a country, of all other standards
of the quantity concerned
1.2.16
national standards laboratory
body or laboratory that maintains and operates the national standard
1.2.17
operating range
range of conditions under which the geometry test set is designed to perform within the stated
expanded uncertainty; for example diameter of the fibre being measured and environmental
conditions, such as temperature
1.2.18
reference standard
artefact measured at a calibration laboratory, with the measurement traceable to national
standards
1.2.19
scaling factor
ratio of the known standard values for a calibration standard to the values indicated by the
geometry test set when no correction offsets are applied
1.2.20
standard uncertainty
standard uncertainty may be evaluated either by statistical methods, termed type A evaluation,
or by other means, termed type B evaluation (see annex C for a more detailed description).
A type A evaluation of uncertainty consists of a statistical analysis of a series of measure-
ments, such as when evaluating certain random effects of measurement.
A type B evaluation of uncertainty is used when a statistical analysis is not appropriate. It
consists of an estimation of the probable sources of uncertainty, such as when evaluating
certain systematic effects of measurement.
NOTE – In order to combine standard uncertainties from different sources it is important that they all be stated at
the same confidence level. This may be achieved by use of the coverage factor k, which is determined with
reference to Student's t distribution for each individual uncertainty component.
1.2.21
traceability
ability to demonstrate, for a measurement result or a geometry test set, a calibration chain
originating from a national standard
Geometry test sets calibrated by the procedures in this standard are traceable. Direct
traceability of the measurement result to either a national standards laboratory or to an
accredited calibration laboratory needs to be demonstrated. Such traceability includes the
calibration schedules of all artefacts in the calibration chain and detailed calculations of all

61745 © IEC:1998(E) – 7 –
(cumulative) transfer uncertainties in the calibration chain. The use of a working standard alone
to compare or monitor geometry test set calibration cannot establish or re-establish traceability,
but can only extend the duration of the traceability certification if no change is found.
1.2.22
transfer standard
standard that is calibrated against a reference standard and is used for calibrating geometry
test sets
1.2.23
transfer uncertainty
estimate characterizing the uncertainty of a measurement caused by uncertainties in the
transfer process, at the given confidence level (such as changes in environmental conditions).
These uncertainties may arise from the calibration standards used as well as from the
geometry test set.
1.2.24
working standard
standard that is usually calibrated against a transfer standard or a reference standard and is
used on a routine basis to check geometry test sets
1.3 Geometrical parameters of optical fibres
It is necessary to characterize the geometrical properties of optical fibres in order to ensure
satisfactory mechanical and optical performance. The geometrical parameters measured by the
types of test sets consist of the following:
a) cladding (reference surface) diameter;
b) cladding non-circularity;
c) core/cladding concentricity error.
NOTE – Geometry measurements on a single-mode fibre are usually performed at a wavelength other than that
corresponding to single-mode operation of the fibre. It is, however, generally assumed that the value of mode-field
concentricity error of a single-mode fibre is the same as that of core/cladding concentricity error, but this is beyond
the scope of this standard.
1.4 Description of geometry test sets
End face image, or grey-scale, test sets usually comprise an optical microscope, an illumina-
tion source, an electronic image recording device, such as a camera, and a means of storing
image data for processing by digital computer. A second illumination source is usually
employed to launch light into the other end of the fibre. This enables the position of the fibre
core also to be measured. A typical measurement sequence is as follows: a cleaved fibre end
is positioned in the measurement port of the instrument and an image of the fibre end is
formed on the camera. The image of the fibre is focused, usually under automatic computer
control, digitized, and then transferred to a computer which determines the geometrical
parameters of the fibre.
The quality of the fibre end is critical in this method, and the presence of cleave damage, such
as chips or edge roughness, can seriously affect the measurement. It is thus usual to employ
data-filtering methods to reduce the sensitivity of the measured result to the presence of cleave
damage.
1.5 Calibration standard requirements
The calibration procedure detailed in this standard requires the use of traceable calibration
artefacts. These artefacts consist of a calibrated fibre end and a chromium-on-glass mask.
Their nominal dimensions are discussed in 2.3.3 and 2.5.

– 8 – 61745 © IEC:1998(E)
2 Calibration
2.1 Introductory remark
The calibration procedure comprises the following two operations.
a) The magnification, or scaling factor, of the imaging system is calibrated. This is a similar
process to conventional calibration methods for optical microscopes, except that, in this
case, a two-dimensional calibration is required.
b) A correction offset is determined. This offset is required to correct for systematic effects
such as diffraction at the fibre edge, differences between the way the calibration artefact is
calibrated and the method of measurement in the test set, and distortion of the image of the
fibre edge by camera sampling.
Worked examples for the determination of calibration factors are given in annex B.
NOTE 1 – The calibration will be valid when applied to measurements in the following way:
– the scaling factors are applied multiplicatively to the raw data from the camera, before applying form-fits and
computing the cladding diameter of the fibre under test;
– the correction offset is applied additively to the computed cladding diameter of the fibre under test.
NOTE 2 – The choice of an edge-setting criterion defining the position of the cladding edge is important and
calibration applies only to measurements using the same criterion as that used at the time of calibration.
NOTE 3 – In certain circumstances it has been found sufficient to calibrate only the scaling factor, using a fibre or
chromium-on-glass standard. This approach, however, may lead to increased uncertainties when measuring fibres
which are of significantly different diameter from the calibration standard used.
2.2 Rationale for calibration of geometry test sets
The measurement of cladding diameter is common to most types of geometry test sets, so
calibration of this parameter is very important in comparing test sets of different types. This
standard, however, details only the calibration of test sets which perform end-face image
analysis.
Basically, calibration is achieved by exposing the test set to independent geometrical
calibration standards. It is these standards that form the calibration chain and, therefore,
contribute to the transfer uncertainty.
The procedure is detailed in 2.3. The complete calibration chain is illustrated in figure 1.
Calibration of the core/cladding concentricity error and non-circularity measurement is not des-
cribed as there are no suitable standard reference materials available at the time of writing.
However, procedures enabling estimation of the uncertainties obtained in the measurement of
these parameters are given in 2.6 and 2.7 respectively.
2.2.1 Verification of calibration state
For routine verification, such as may frequently be carried out on geometry test sets in use, it is
sufficient to check (but not to reset) the state of calibration of the geometry test sets using a
working standard. The working standard may be a fibre or a chrome-on-glass mask.
A procedure for generation of a working standard is given in annex E.
The distinction between checking the state of calibration and the calibration itself must be
clearly made. While it is sufficient to establish stability of the geometry test set using the
working standard, this is not a substitute for full calibration.
The use of a working standard allows continued traceability to national standards to be
claimed, if it can be satisfactorily established that the existing instrument state, correction

61745 © IEC:1998(E) – 9 –
factors, and so on, are sufficient to provide geometry results within a specified uncertainty and
without alteration. This simply means that the geometry test set has remained stable since the
last calibration.
Continued traceability can be claimed on a calibrated test set provided that the measured
values for the working standard agree with its calibrated values within the uncertainties.
Calibration is essential in the commissioning of geometry test sets, whereas a working
standard is used for routine calibration checking.
The procedure for calibration checking is described in 2.4.
2.3 Calibration procedure
2.3.1 General advice and organization
Ensure that the environmental conditions are commensurate with the working environment as
specified by the manufacturer. Employ good metrological practices at all times.
Ensure that all calibration standards used in the calibration are calibrated according to a
documented programme with traceability to national standards laboratories or to accredited
standards laboratories. If possible maintain more than one standard on each hierarchical level
of the calibration chain, so that the performance of standards can be verified by comparisons
on the same level.
Develop a documented measurement procedure for each type of calibration performed, giving
step-by-step operating instructions and equipment to be used. Use pro-forma result sheets,
uncertainty budgets and calibration certificates (see clause 4).
Operate a quality system appropriate to the range of measurements. Ensure that there is
independent scrutiny of measurement results, intermediate calculations and calibration
certificates are prepared.
2.3.2 Test requirements
a) Perform all tests at a temperature and relative humidity that are within the  manufacturer’s
specification for the test set.
b) Allow sufficient time for the geometry test set and test equipment to reach thermal
equilibrium with the environment in accordance with the manufacturer's recommendations
for the test set and the calibration standards used, before commencing the calibration
procedure.
c) Set up the geometry test set to the appropriate settings for calibration procedures, as
recommended by the manufacturer.
d) Ensure, where possible, that all accessible optical surfaces and calibration standards are
clean before measurement.
2.3.3 Calibration standard requirements
The use of calibration standards which are traceable to national standards laboratories is
mandatory. The calibration procedure requires the use of the following:
a) A fibre end with calibrated cladding diameter. The fibre should be of similar material to and
within 5,0 μm of the nominal cladding diameter of the fibres to be measured by the test set
and have a non-circularity of less than 0,5 %.
NOTE 1 – The calibrated fibre end must not be re-cleaved. This is due to variations of diameter along the length of
the fibre.
– 10 – 61745 © IEC:1998(E)
NOTE 2 – If the fibre end becomes damaged or cannot be cleaned sufficiently, it should not be used for the
purpose of calibration.
b) A calibrated measurement scale. This is a chromium-on-glass mask with a pattern,
typically, of dots, lines, circles or annuli.
For calibration checking (see 2.4), the standard may be either a fibre or a chromium-on-glass
pattern with traceable geometry values.
2.3.4 Determination of calibration factors
A derivation of the calibration factors used is given in annex A.
2.3.4.1 Scaling factor
To calibrate the scaling factor use a chromium-on-glass mask. This may comprise an array of
dots or lines, or an annular structure. The principle of calibration is to measure the distance
between graduations.
NOTE – The uniformity of the scaling factor over the field of view of the imaging system (known as spatial linearity)
will affect the uncertainty that can be transferred to measurements on fibres and also to measurements of
core/cladding concentricity error. A method for estimating spatial linearity is described in 2.5.
The scaling factors for the x and y axes of the camera are given by:
Dx
c
S = (1)
x
Dx
m
Dy
c
S = (2)
y
Dy
m
where
Dx is the measured spacing of graduations along the x-axis;
m
Dy is the measured spacing of graduations along the y-axis;
m
Dx is the calibrated spacing of graduations along the x-axis;
c
Dy is the calibrated spacing of graduations along the y-axis.
c
The procedure to measure the distance between graduations will depend on the type of chrome
mask used, as follows:
a) Regular array of dots or lines
Form an image of the array in a manner consistent with normal operation of the test set.
Measure the distances between graduations in two orthogonal directions, these being
parallel to the scan axes of the camera.
NOTE 1 – The distance over which calibration is effected should be within 5 μm of the nominal diameter of the
fibres to be measured by the test set.
NOTE 2 – It is desirable to align the axes of the array to be parallel to the scan axes of the camera. However, if
they are not so aligned, compensation for the angular misalignment needs to be applied.
b) Annulus
Form an image of the annulus in a manner consistent with normal operation of the test set.
Apply elliptical form fits to the inner and outer edges of the annulus. Determine the
measured diameters Dx and Dy along the x and y axes as follows:
m m
DDxx+
inner outer
Dx = (3)
m
61745 © IEC:1998(E) – 11 –
DDyy+
inner outer
and Dy = (4)
m
where
Dx is the measured diameter of the inner annulus along the x-axis;
inner
Dy is the measured diameter of the inner annulus along the y-axis;
inner
Dx is the measured diameter of the outer annulus along the x-axis;
outer
Dy is the measured diameter of the outer annulus along the y-axis.
outer
NOTE 1 – The diameter of the annulus should be within 5 μm of the nominal diameter of the fibres to be measured
by the test set.
NOTE 2 – If, for convenience of use, it is assumed that Dx equals Dy , any non-circularity in the annulus will
m m
affect the determination of the uncertainty in subsequent fibre non-circularity measurements, see 2.7.
Calculate the uncertainty in the determination of the scaling factors using clause 3.
2.3.4.2 Correction offset
To calibrate the correction offset a calibrated fibre is required. Form an image of the fibre end
in a manner consistent with normal operation of the test set and apply a form-fitting algorithm
to the fibre edge. Determine the correction offset O as follows:
O = D – D′ ⋅ S (5)
P,F P,F
where
D is the calibrated diameter of the fibre;
P,F
D′ is the measured diameter of the fibre (scaling factor not applied);
P,F
SS+
xy
P stands for parent, F stands for fibre and S = (mean scaling factor).
Thus D′ ⋅ S is equal to the measured diameter of the fibre, in micrometres.
P,F
Calculate the uncertainty in the determination of the correction offset using clause 3.
2.4 Check calibration procedure
This procedure is used for checking the calibration of a geometry test set. The procedure is not
used for determining calibration factors but may be used to check for test set stability since the
last calibration was performed.
As long as the geometry test set has already been calibrated and measurement of a working
standard does not reveal a geometry uncertainty greater than the permitted total uncertainty,
the claim of traceability may be extended.
a) Ensure that the test requirements given in 2.3.2 have been met.
b) Present the working standard to the geometry test set under consideration.
c) In the case where the working standard is
– a fibre: measure the mean cladding diameter;
– a chromium-on-glass mask: measure the distance between graduations.
Compare the measured values with the reference values and record any differences. It is
necessary to repeat the measurement several times to statistically reduce uncertainty in the
mean measured value.
– 12 – 61745 © IEC:1998(E)
2.5 Spatial linearity
The uncertainty in the measurement of fibres the diameter of which differs by more than 5 μm
from that of the fibre used for calibration may be estimated in one of two ways.
a) Measure a chromium-on-glass artefact at different positions within the field of view.
b) Measure the spacing between graduations of an array of lines or dots over the whole field
of view.
NOTE – In either case, the linear dimension of the artefact or the interval must be less than one-quarter of the
diameter of the calibration fibre used. If method a) is used, only a nominal calibration of the artefact is necessary. If
method b) is used, it is necessary to use an artefact that has each interval calibrated.
A variation in the scaling factor over the field of view indicates a source of uncertainty in the
calibration of the test set scaling factor. The importance of this uncertainty will depend on the
range of fibre diameters to be measured on the calibrated test set. Estimate the magnitude of
the uncertainty and add it to the total scaling factor uncertainty u , derived in 3.2.1.
S
2.6 Calibration of core/cladding concentricity error measurement
Core/cladding concentricity error is defined as the distance between the centres of the core
and cladding of a fibre.
At the time of writing there are no standard reference materials (SRM) available from standards
laboratories for direct calibration of this parameter. A procedure is given in annex F describing
how to estimate the uncertainty obtained in a concentricity error measurement.
2.7 Calibration of non-circularity measurement
Non-circularity is defined as the difference in radial distance of edge points that are
respectively furthest from and closest to the fitted centre, divided by the fitted radius. In the
case of an ellipse form-fit, non-circularity is the difference between the major and minor axes,
divided by their mean.
At the time of writing there are no standard reference materials (SRM) available from standards
laboratories for direct calibration of this parameter. A procedure is given in annex G describing
how to estimate the uncertainty obtained in a non-circularity measurement.
3 Evaluation of uncertainties
3.1 Introductory remark
In this clause, the reporting of uncertainties in the calibration of a test set and also in
subsequent measurements is discussed. The analysis is based on the statistical mathematics
given in annex C. It is important to choose a confidence level at which to calculate uncertain-
ties and use the appropriate values for the coverage factor in each calculation (see definition
1.2.11 and clause C.3).
The uncertainty of calibration of the test set is discussed in 3.2. The uncertainty in the
measurement of a fibre is discussed in 3.3. The uncertainty in the measurement of a
chromium-on-glass mask is discussed in 3.4.
Worked examples for the determination of uncertainties are given in annex D.
3.2 Evaluation of uncertainty in test set calibration
The calibration procedure (see 2.3.4) comprises two operations. First a scaling factor is
determined and then a correction offset factor is determined. Sources of uncertainty in both of
these parameters must be evaluated to estimate the calibration uncertainty of the test set.

61745 © IEC:1998(E) – 13 –
3.2.1 Uncertainty in scaling factor
The following terms are used:
S = scaling factor
D = calibrated spacing of graduations of parent chromium standard
P,C
u = uncertainty in calibration of parent chromium standard
P,C
D′ = measured spacing of graduations of parent chromium standard (raw data)
P,C
u′ = statistical uncertainty in measurement of parent chromium standard (raw data)
P,C
u = transfer uncertainty of parent chromium standard
Tr,P,C
n = number of measurements
C
where P stands for parent and C for chromium.
The determination of the scaling factor is described in 2.3.4.1 and is given in terms of two
scaling factors, one for each of the two camera axes. For the purpose of estimating the
uncertainty in the scaling factor, the two scaling factors may be combined to give the following
expression:
D
P,C
S = (6)
D′
P,C
The uncertainty u in the scaling factor consists of the calibration uncertainty u of the
S P,C
parent chromium standard, any changes u that may have occurred in the parent
Tr,P,C
chromium standard since its calibration, and the statistical uncertainty u′ in the
P,C
measurement of the parent chromium standard on the test set .
The relative uncertainty u in the scaling factor is given by:
S
 
uS′⋅
P, C
2 2
 
uu++
Tr,P,C P,C
 
n
 
C
u = (7)
S
D
P,C
3.2.1.1 Determination of u
P,C
The uncertainty u in the calibration of the parent standard may be determined from the
P,C
parent's calibration certificate or data sheet. Using the expanded uncertainty U of the
P,C
parent, calculate u as follows:
P,C
U
P,C
=
u (8)
P,C
k
where k is the coverage factor.
Determine k from the parent's calibration certificate.
3.2.1.2 Determination of u
Tr,P,C
The transfer uncertainty may be due to factors affecting the calibration of the parent chromium
standard, for example ageing, temperature-induced changes and cleanliness. Estimate the
transfer uncertainty using equation (C.2).

– 14 – 61745 © IEC:1998(E)
3.2.1.3 Determination of u′′
P,C
Determine the statistical uncertainty in measurement of the parent chromium standard using
equation (C.1).
3.2.2 Uncertainty in offset correction factor
The following terms are used:
S = scaling factor
D = calibrated diameter of parent fibre standard
P,F
u = calibration uncertainty of parent fibre standard
P,F
u′ = statistical uncertainty in measurement of parent fibre standard (raw data)
P,F
u = transfer uncertainty of parent fibre standard
Tr,P,F
n = number of measurements
F
where P stands for parent and F for fibre.
The determination of the offset correction factor is described in 2.3.4.2. The offset O is given
by:
OD=−D′ ⋅S (9)
P,F P,F
The uncertainty u in the offset factor consists of the uncertainty u in the calibration of the
O P,F
parent fibre standard, any changes u that may have occurred in the fibre standard since
Tr,P,F
its calibration and the statistical uncertainty u′ in the measurement of the parent fibre
P,F
standard on the test set.
The uncertainty u in the offset is given by:

 
uS′ ⋅
P,F
 
=+ +
uu u (10)
O
P,F Tr,P,F
 
n
 F 
NOTE – The uncertainty u in the scaling factor is not included in the derivation of equation (10). This is because
S
error in the scaling factor is compensated for in the determination of the correction offset factor, according to
equation (9). It will, however, contribute to the uncertainty in fibre diameter measurement when the diameter of the
fibre being measured is different from the diameter of the calibration fibre that was used in the determination of the
offset correction factor (see 3.3).
3.2.2.1 Determination of u
P,F
The uncertainty u of the parent may be determined from the expanded uncertainty U
P,F P,F
quoted on the parent's calibration certificate or data sheet. Express this as a standard
uncertainty u as follows:
P,F
U
P,F
u = (11)
P,F
k
where k is the coverage factor.
Determine k from the parent's calibration certificate.

61745 © IEC:1998(E) – 15 –
3.2.2.2 Determination of u
Tr,P,F
The transfer uncertainty may be due to factors affecting the calibration of the parent fibre
standard, for example ageing, temperature induced changes, and cleanliness. Estimate the
transfer uncertainty using C.2.
3.2.2.3 Determination of u′′
P,F
Determine the statistical uncertainty in measurement of the parent fibre standard using C.1.
3.3 Evaluation of uncertainty in fibre measurement
The following terms are used:
D = calibrated diameter of parent fibre standard used in offset determination
P,F
D = diameter of infant fibre (to be determined)
I,F
D′ = measured diameter of infant fibre (raw data)
I,F
u′ = statistical uncertainty in measurement of infant fibre (raw data)
I,F
u = operational uncertainty of infant fibre
Op,I,F
n = number of measurements
F
where I stands for infant and F for fibre.
The measured diameter of the infant fibre after calibration is given by:
= ′ ⋅+
DD SO (12)
I,F I,F
The uncertainty u in the measurement consists of the uncertainty u in the scaling factor, the
I,F S
uncertainty u in the offset factor and the statistical uncertainty u′ in the measurement of
O I,F
the infant fibre on the test set. Further, if the measurement depends on changes in operating
conditions from those existing at the time of calibration, these changes must be taken into
account in the form of an operational uncertainty u . Uncertainty in the determination of the
Op,I,F
scaling factor contributes to the uncertainty in the determination of the fibre diameter when
the diameter of the fibre under test is different from the diameter of the calibration fibre that
was used in the determination of the correction offset factor (see 3.2.2). This is included as the
final term in the following expression.
The uncertainty u in the measured diameter of the infant fibre is given by:
I,F
 
′ ⋅
uS
I,F
2 2 2 2
 
′
uu=+u + +(SDD⋅− ) ⋅u (13)
I,F I,F P,F
O Op,I,F S
 
n
 
F
3.3.1 Determination of u
Op,I,F
The operational uncertainty is due to operating conditions that are different from those existing
at the time of calibration, for example cleave quality, cleanliness and operating temperature.
Estimate the operational uncertainty using C.2.
3.3.2 Determination of u'
I,F
Determine the statistical uncertainty in measurement of the infant fibre using C.1.

– 16 – 61745 © IEC:1998(E)
3.4 Evaluation of uncertainty in chromium mask measurement
The following terms are used:
D = spacing of graduations of infant chromium mask (to be determined)
I,C
D′ = measured spacing of graduations of infant chromium mask (raw data)
I,C
u′ = statistical uncertainty in measurement of infant chromium mask (raw data)
I,C
u = operational uncertainty of infant chromium mask
Op,I,C
n = number of measurements
C
where I stands for infant and C for chromium.
The measured diameter of the infant chromium mask after calibration is given by:
DD= ′ ⋅S (14)
I,C I,C
The uncertainty u in the measured diameter consists of the relative uncertainty u in the
I,C S
scaling factor and the statistical uncertainty u′ in the measurement of the infant chromium
I,C
mask on the test set. Further, if the measurement depends on changes in operating conditions
from those existing at the time of calibration, these changes must be taken into account in the
form of an operational uncertainty u .
Op,I,C
The uncertainty u in the measured diameter of the infant chromium mask is:
I,C
 
′
uS ⋅ 2
I,C
 
uu=+ +Du′ ⋅ (15)
()
I,C Op,I,C I,C S
 
n
 
C
3.4.1 Determination of u
Op,I,C
The operational uncertainty is due to operating conditions that are different from those existing
at the time of calibration, for example cleave quality, cleanliness and operating temperature.
Estimate the operational uncertainty using C.2.
3.4.2 Determination of u′′
I,C
Determine the statistical uncertainty in measurement of the infant chromium mask using C.1.
3.5 Summary
The uncertainty in the calibration of the test set has been evaluated in terms of the scaling
factor uncertainty and the offset factor uncertainty, in 3.2.1 and 3.2.2 respectively.
The uncertainties in the measurement of a test fibre and a chromium-on-glass mask are
evaluated in 3.3 and 3.4 respectively.
The statement of uncertainty in the measurement on a fibre or chromium mask includes the
uncertainties of the calibration standards used to calibrate the test set, the statistical measure-
ment uncertainties and any other additional measurement uncertainties.

61745 © IEC:1998(E) – 17 –
4 Documentation
4.1 Records
Proper records shall be kept when a geometry test set is calibrated according to this pro-
cedure. These records shall include the following:
a) description of the test set and unique identification (serial number);
b) date on which the calibration was performed;
c) results obtained from the calibration process (see clause 3);
d) re-calibration interval;
e) identification of the calibration procedure followed;
f) unique identification of all calibration standards used and certification demonstrating
traceability;
g) identification of personnel performing the calibration;
h) statement of uncertainties involved in calibrating the test set and of their cumulative effect
on the uncertainties in the scaling and offset factors (see clause 3);
i) instrument state, such as threshold levels for edge point select
...