ISO/FDIS 11421
(Main)Optics and photonics — Uncertainty of optical transfer function (OTF) measurement
Optics and photonics — Uncertainty of optical transfer function (OTF) measurement
Optique et photonique — Incertitude de mesurage de la fonction de transfert optique (OTF)
La présente Norme internationale donne des indications générales sur l'évaluation des sources d'erreur dans un matériel de fonction de transfert optique ainsi que sur l'utilisation de cette information afin d'estimer les erreurs de mesurage de l'OTIF. Elle donne également des indications sur l'appréciation et la spécification d'un schéma de précision générale d'un matériel de mesurage spécifique, ainsi que des méthodes de recommandation d'une évaluafion de routine.Le corps principal de la présente Norme internationale traite exclusivement de la partie fonction de transfert de modulation (MTF) de l'OTF. La fonction de transfert de phase (PTF) est traitée assez brièvement dans l'annexe A.
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FINAL DRAFT
International
Standard
ISO/TC 172/SC 1
Optics and photonics — Uncertainty
Secretariat: DIN
of optical transfer function (OTF)
Voting begins on:
measurement
2025-08-14
Optique et photonique — Incertitude de mesurage de la fonction
Voting terminates on:
de transfert optique (OTF)
2025-10-09
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
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TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
Reference number
FINAL DRAFT
International
Standard
ISO/TC 172/SC 1
Optics and photonics — Uncertainty
Secretariat: DIN
of optical transfer function (OTF)
Voting begins on:
measurement
Optique et photonique — Incertitude de mesurage de la fonction
Voting terminates on:
de transfert optique (OTF)
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
© ISO 2025
IN ADDITION TO THEIR EVALUATION AS
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
or ISO’s member body in the country of the requester.
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
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Published in Switzerland Reference number
ii
Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Terms and definitions .1
3.2 Symbols .2
4 Sources of uncertainty in measuring equipment. 3
4.1 General .3
4.2 Geometry of optical bench system .4
4.2.1 General .4
4.2.2 Finite object and image distance .4
4.2.3 Infinite object distance and finite image distance .5
4.2.4 Infinite object and image distance .6
4.2.5 Suppression of image distance errors by refocusing .6
4.2.6 Mounting of test piece .6
4.3 Azimuth changing .7
4.3.1 General .7
4.3.2 Finite object and image distance .7
4.3.3 Infinite object distance and finite image distance .7
4.3.4 Infinite object and image distance .7
4.3.5 Suppression of image distance errors by refocusing .7
4.4 Alignment (orientation) of TTU and image analyser .7
4.5 Correction factors .8
4.5.1 General .8
4.5.2 Slit width errors .9
4.5.3 Correction for MTF of incoherently coupled relay lenses .9
4.5.4 Spatial frequency correction for field angle .9
4.5.5 Off-axis magnification errors due to image distortion using grating objects .10
4.6 Image distance error .10
4.7 Spatial frequency errors .11
4.8 Residual aberrations in relay optics . .11
4.9 Spectral characteristics.11
4.10 Extent of test target and/or scan and/or camera detector .11
4.11 Angular response characteristics of image analyser . 12
4.12 Polar luminance/radiation characteristics of object generator . 12
4.13 Signal and data processing . 12
4.14 Stray radiation . 12
4.15 Coherent radiation . 12
4.16 Baseline error . 12
4.17 Linearity of camera detector . 13
5 Methods of assessing measurement errors .13
5.1 General . 13
5.2 Geometry of optical bench system . 13
5.2.1 Straightness of slideways . 13
5.2.2 Parallelism of surfaces and/or perpendicularity to reference axes .16
5.2.3 Errors of rotation angles .17
5.3 Collimation error (departure from infinite object distance) .18
5.4 Image distance setting . 20
5.5 Spectral characteristics.21
5.6 Extent of target and/or scan and/or camera detector . 22
5.7 Signal and data processing . 22
5.8 Polar response to image analyser. 22
iii
6 Calculation of overall uncertainty of a measurement .23
7 Specifying a general equipment uncertainty .24
7.1 General .24
7.2 Nominal uncertainty value (NUV) .24
7.3 Standard-lens measurements (SLM) . 25
7.4 Audit-lens measurements (ALM) . 25
7.5 Slit aperture test (SAT) . 26
8 Routine performance evaluation .26
Annex A (normative) Uncertainty of PTF measurement.27
Annex B (informative) Determination of rate of change of MTF with various parameters .29
Annex C (informative) Example calculation of NUV .32
Bibliography .44
iv
...
ISO/TC 172/SC 1
Secretariat: DIN
Date: 2025-06-23xx
Optics and Photonics photonics — Uncertainty of optical transfer
function (OTF) measurement
Optique et photonique — Incertitude de mesurage de la fonction de transfert optique (OTF)
FDIS stage
© ISO 2025
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication
may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying,
or posting on the internet or an intranet, without prior written permission. Permission can be requested from either
ISO at the address below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: + 41 22 749 01 11
EmailE-mail: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
Contents
Foreword vii
Introduction viii
1 Scope 1
2 Normative references 1
3 Terms and definitions 1
3.1 Definitions 1
3.2 Symbols 2
4 Sources of uncertainty in measuring equipment 3
4.1 General 3
4.2 Geometry of optical bench system 4
4.2.1 Object and image at finite conjugates 4
4.2.2 Infinite object and finite image conjugates 5
4.2.3 Infinite object and image conjugates 5
4.2.4 Image intensifiers and other systems with physically defined object and/or image surfaces
4.2.5 Mounting of test piece 6
4.3 Azimuth changing 6
4.3.1 Object and image at finite conjugates 6
4.3.2 Infinite object and finite image conjugates 6
4.3.3 Infinite object and image conjugates 6
4.3.4 Image intensifiers and other systems with physically defined object and/or image surfaces
4.4 Alignment (orientation) of TTU and image analyser 7
4.5 Correction factors 7
4.5.1 Slit width errors 8
4.5.2 Correction for MTF of incoherently coupled relay lenses 8
4.5.3 Spatial frequency correction for field angle 8
4.5.4 Off-axis magnification errors due to image distortion using grating objects 8
4.6 Focus error 9
4.7 Spatial frequency errors 9
4.8 Residual aberrations in relay optics 9
4.9 Spectral characteristics 10
4.10 Extent of test target and/or scan and/or camera detector 10
4.11 Angular response characteristics of image analyser 10
4.12 Polar luminance/radiation characteristics of object generator 10
4.13 Signal and data processing 10
4.14 Stray radiation 10
4.15 Coherent radiation 11
4.16 Baseline error 11
4.17 Linearity of camera detector 11
5 Methods of assessing measurement errors 11
5.1 Geometry of optical bench system 11
5.1.1 Straightness of slideways 11
5.1.2 Parallelism of surfaces and/or perpendicularity to reference axes 14
5.1.3 Errors of rotation angles 15
5.2 Collimator focus (departure from infinite object distance) 16
5.3 Focus setting 17
5.4 Spectral characteristics 18
5.5 Extent of target and/or scan and/or camera detector 19
5.6 Signal and data processing 19
5.7 Polar response to image analyser 19
6 Calculation of overall uncertainty of a measurement 20
7 Specifying a general equipment uncertainty 21
7.1 Nominal uncertainty value (NUV) 22
7.2 Standard-lens measurements (SLM) 22
7.3 Audit-lens measurements (ALM) 22
7.4 Slit aperture test (SAT) 23
8 Routine performance evaluation 23
ii
Annex A (normative) Uncertainty of PTF measurement 24
Annex B (informative) Determination of rate of change of MTF with various parameters 26
Annex C (informative) Example calculation of NUV 29
Annex D (informative) Uncertainty of PTF measurement . 40
Bibliography 40
iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO 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. ISO
collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO document should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).).
ISO draws attention to the possibility that the implementation of this document may involve the use of
(a) patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed
patent rights in respect thereof. As of the date of publication of this document, ISO had not received notice
of (a) patent(s) which may be required to implement this document. However, implementers are
cautioned that this may not represent the latest information, which may be obtained from the patent
database available at www.iso.org/patents. ISO shall not be held responsible for identifying any or all
such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the World
Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 172, Optics and photonics optical
instruments, Subcommittee SC 1, Fundamental standards.
This second edition cancels and replaces the first edition (ISO 11421:1997), which has been technically
revised.
The main changes are as follows:
— — sagittal and tangential OTF were defined;
— — symbols, formulae and nomenclature have been revised
— — off-axis magnification errors due to image distortion using grating objects has been newly added;
— — the document has been revised to be in agreement with the terms and definitions of ISO/IEC
Guide 98 (GUM) and ISO/IEC Guide 99 (VIM) regarding the expression of measurement uncertainties;
— — Explanations for the calculation of measurement uncertainties have been added;
— Annex C— Annex C was revised.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
Introduction
The optical transfer function (OTF) is one of the main criteria used for objectively evaluating the image-
forming capability of optical, electro-optical and photographic systems.
The terms used in the measurement of OTF are defined in ISO 9334, whilst ISO 9335 covers the actual
principles and procedures of measurement. A further International Standard, ISO 9336 (all parts), deals
with specific applications in various optical and electro-optical fields and is in several parts, each dealing
with a particular application.
Although ISO 9335 lists the main factors which influence the uncertainty of OTF measurement and
describes procedures which are aimed at achieving accurate and repeatable results, it does not cover in
detail the techniques and procedures for evaluating the uncertainty of OTF measuring equipment and for
estimating the uncertainty in measurements made on specific imaging systems.
The present document lists the main sources of uncertainty in OTF measuring equipment and provides
guidance on how these can be assessed and how the results of these assessments can be used in
estimating the uncertainty in any measurement of OTF. One of the aims in preparing this document is to
encourage the setting of more realistic uncertainty levels for the results of OTF measurements. Another
is to encourage the use of methods of expressing the uncertainty of OTF test equipment which recognize
the fact that the uncertainty of a particular measurement is a function of both the equipment and the test
piece.
v
Optics and optical instruments photonics — Uncertainty of optical
transfer function (OTF) measurement
1 Scope
This document gives general guidance on evaluating the sources of error in optical transfer function (OTF)
equipment and in using this information to estimate errors in a measurement of OTF. It also gives guidance
on assessing and specifying a general uncertainty for a specific measuring equipment, as well as
recommending methods of routine assessment.
The main body of this document deals exclusively with the modulation transfer function (MTF) part of the
OTF. The phase transfer function (PTF) is dealt with relatively briefly in Annex Aannex A.
2 Normative references
There are no normative references in this document.
3 Terms and, definitions and symbols
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— — ISO Online browsing platform: available at https://www.iso.org/obp
— — IEC Electropedia: available at https://www.electropedia.org/
3.1 3.1Terms and definitions
3.1.1
standard lens
single- or multi-element lens which has been constructed with a level of uncertainty which is sufficient to
ensure that for precisely specified conditions of measurement the MTF is equal to that predicted from
theoretical calculations to an uncertainty of better than 0,05 (MTF units)
Note 1 to entry: In order to achieve this uncertainty, standard lenses are usually of simple construction and therefore
of limited performance. An example of a widely used lens is the 50 mm focal length piano-convex lens described in
Reference [0[3].]. This and several other standard test lenses (including afocal systems and lenses operating in the
infrared wavelength bands) are available commercially.
3.1.2 3.2
audit lens
Singlesingle- or multi-element lens of stable construction whose uncertainty of construction is not sufficient
to enable the MTF to be predicted by calculation from design data (usually as a result of the complexity of the
lens), but whose “accepted” values for the MTF under precisely defined measuring conditions have been
obtained by measurements done by a reputable authority (preferably a national standards laboratory, if such
a service is available)
3.1.3 3.3
sagittal OTF
test pattern which is constant (shows no periodic variation) in the direction parallel to a line through the
centre of the image circle
Note 1 to entry: A fixed and defined azimuthal orientation of the sample under test is required for the
terms sagittal OTF and tangential OTF to be unambiguous.
[ [6]]
Note 2 to entry: See also ISO 9334 0 and Figure 1Figure 1. An illustration can also be found in
Reference [0[9].].
Note 3 to entry: In literature, the term “sagittal” is used synonymous with “radial”.
3.1.4 3.4
tangential OTF
test pattern which is constant (shows no periodic variation) in the direction parallel to a tangent of the image
circle
Note 1 to entry: A fixed and defined azimuthal orientation of the sample under test is required for the
terms sagittal OTF and tangential OTF to be unambiguous.
[ [6]]
Note 2 to entry: See also ISO 9334 0 and Figure 1Figure 1. An illustration can also be found in
Reference [0[9].].
Note 3 to entry: In literature, the term tangential is employed synonymous with “meridional.”
11421_ed2fig1.EPS
Key
1 sagittal to image circle
2 tangential to image circle
3 image pattern vector
4 center of image field
5 image circle
Figure 1 — Sagittal and tangential OTF, excerpt from ISO 9334:2012, Figure 1
3.2 Symbols
Symbol Meaning Unit
h object height mm, mrad, degree
h′ image height mm, mrad, degree
′
𝛥ℎ error in image height mm, mrad, degree
l object distance mm
l′ image distance mm
𝛥𝑙 error in object distance, is indexed to distinguish error sources mm
Symbol Meaning Unit
Δl′ error in image distance, is indexed to distinguish error sources mm
𝑃 best focus point mm
𝑓
𝛥𝑎 angular departure of object slide from perpendicularity to rad
reference axis
′
𝛥𝑎 angular departure of image slide from perpendicularity to rad
reference axis
𝑖, 𝑖 ′ Auxiliary distance describing intermediate object distance or mm
𝑙 𝑙
intermediate image distance.
M magnification dimensionless
−1 −1 −1
r spatial frequency mm , mrad , degree
−1 −1 −1
r𝛥𝑟 error in spatial frequency mm , mrad , degree
−1
m(r,l,h) rate of change of MTF with object distance mm
−1
m′(r,l’,h′) rate of change of MTF with image distance mm
−1
p(r,l,h) rate of change of MTF with object height mm
−1 −1 −1
p′(r,l’,h′) or rate of change of MTF with image height mm , mrad , degree
p′(r,l’,ω)
ω field angle mrad, degree
ω𝛥𝜔 error in field angle mrad, degree
𝑓 focal length of collimator mm
𝑐
𝑓 focal length of sample under test mm
𝑠
ψ azimuth angle degree
ψ𝛥𝜓 error in azimuth angle between slits degree
R (test lens focal length)/(collimator focal length) or (decollimator dimensionless
focal length)/(collimator focal length)
g′ width of slit referred to image plane mm
L′ length of shorter slit referred to image plane mm
MTFC MTF of relay lens dimensionless
−1 −1 −1
r spatial frequency for zero field angle mm , mrad , degree
o
n′(r,l’,h′) rate of change of MTF with spatial frequency mm, mrad, degree
MTF𝛥MTF(r) error in MTF, is indexed to distinguish error sources dimensionless
MTFC𝛥MTFC(r) MTF error of the relay lens dimensionless
MTF 𝛥MTF (r) MTF errors resulting from aberrations of relay lens error dimensionless
rl rl
NOTE The notation m(r,l,h), m′(r,l’,h′), p′(r,l’,h′) etc. denotes that these parameters are functions of both spatial
frequency r, image or object distance l’ and l, and image or object
...
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