ISO 15529:2010

INTERNATIONAL ISO
STANDARD 15529
Third edition
2010-08-01
Optics and photonics — Optical transfer
function — Principles of measurement of
modulation transfer function (MTF) of
sampled imaging systems
Optique et photonique — Fonction de transfert optique — Principes de
mesure de la fonction de transfert de modulation (MTF) des systèmes
de formation d'image échantillonnés

Reference number
©
ISO 2010
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.

©  ISO 2010
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2010 – All rights reserved

Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms, definitions and symbols .1
3.1 Terms and definitions .1
3.2 Symbols.4
4 Theoretical relationships.5
4.1 Fourier transform of the image of a (static) slit object.5
4.2 Fourier transform of the output from a single sampling aperture for a slit object scanned
across the aperture .6
4.3 Fourier transform of the average LSF for different positions of the slit object.8
5 Methods of measuring the MTFs associated with sampled imaging systems .8
5.1 General .8
5.2 Test azimuth.9
5.3 Measurement of T of a sampled imaging device or complete system .9
sys
5.4 Measurement of the MTF of the sampling aperture, T .15
ap
6 Method of measuring the aliasing function, the aliasing ratio and the aliasing potential.15
Annex A (informative) Background theory.17
Annex B (informative) Aliasing in sampled imaging systems.20
Bibliography.25

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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 15529 was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee SC 1,
Fundamental standards.
This third edition cancels and replaces the second edition (ISO 15529:2007) which has undergone a minor
revision to include measurement and test procedures for aliasing of sampled imaging systems.
iv © ISO 2010 – All rights reserved

Introduction
One of the most important criteria for describing the performance of an imaging system or device is its MTF.
ISO 9334 covers the conditions to be satisfied by an image system for the MTF concept. These conditions
require that the imaging system be linear and isoplanatic.
For a system to be isoplanatic, the image of a point object (i.e. the point spread function) must be independent
of its position in the object plane to within a specified accuracy. There are types of imaging systems where this
condition does not strictly apply. These are systems where the image is generated by sampling the intensity
distribution in the object at a number of discrete points, or lines, rather than at a continuum of points.
Examples of such devices or systems are: fibre optic face plates, coherent fibre bundles, cameras that use
detector arrays such as CCD arrays, line scan systems such as thermal imagers (for the direction
perpendicular to the lines), etc.
If one attempts to determine the MTF of this type of system by measuring the line spread function of a static
narrow line object and calculating the modulus of the Fourier transform, one finds that the resulting MTF curve
depends critically on the exact position and orientation of the line object relative to the array of sampling points
(see Annex A).
This International Standard specifies an “MTF” for such systems and outlines a number of suitable
measurement techniques. The specified MTF satisfies the following important criteria:
⎯ the MTF is descriptive of the quality of the system as an image-forming device;
⎯ it has a unique value that is independent of the measuring equipment (i.e. the effect of slit object widths,
etc., can be de-convolved from the measured value);
⎯ the MTF can, in principle, be used to calculate the intensity distribution in the image of a given object,
although the procedure does not follow the same rules as it does for a non-sampled imaging system.
This International Standard also specifies MTFs for the sub-units, or imaging stages, which make up such a
system. These also satisfy the above criteria.
A very important aspect of sampled imaging systems is the “aliasing” that can be associated with them. The
importance of this is that it allows spatial frequency components higher than the Nyquist frequency to be
reproduced in the final image as spurious low frequency components. This gives rise to artefacts in the final
image that can be considered as a form of noise. The extent to which this type of noise is objectionable will
depend on the characteristics of the image being sampled. For example, images with regular patterns at
spatial frequencies higher than the Nyquist frequency (e.g. the woven texture on clothing) can produce very
visible fringe patterns in the final image, usually referred to as moiré fringes. These are unacceptable in most
applications if they have sufficient contrast to be visible to the observer. Even in the absence of regular
patterns, aliasing will produce noise-like patterns that can degrade an image.
A quantitative measure of aliasing can be obtained from MTF measurements made under specified conditions.
This International Standard defines such measures and describes the conditions of measurement.

INTERNATIONAL STANDARD ISO 15529:2010(E)

Optics and photonics — Optical transfer function — Principles
of measurement of modulation transfer function (MTF) of
sampled imaging systems
1 Scope
This International Standard specifies the principal MTFs associated with a sampled imaging system, together
with related terms, and outlines a number of suitable techniques for measuring these MTFs. It also defines a
measure for the “aliasing” related to imaging with such systems.
This International Standard is particularly relevant to electronic imaging devices such as digital still and video
cameras and the detector arrays they embody.
Although a number of MTF measurement techniques are described, the intention is not to exclude other
techniques, provided they measure the correct parameter and satisfy the general definitions and guidelines for
MTF measurement as set out in ISO 9334 and ISO 9335. The use of a measurement of the edge spread
function, rather than the line spread function (LSF), is noted in particular as an alternative starting point for
determining the OTF/MTF of an imaging system.
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.
ISO 9334, Optics and photonics — Optical transfer function — Definitions and mathematical relationships
ISO 9335, Optics and photonics — Optical transfer function — Principles and procedures of measurement
ISO 11421, Optics and optical instruments — Accuracy of optical transfer function (OTF) measurement
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document the terms and definitions given in ISO 9334 and the following apply.
3.1.1
sampled imaging system
imaging system or device, where the image is generated by sampling the object at an array of discrete points,
or along a set of discrete lines, rather than a continuum of points
NOTE 1 The sampling at each point is done using a finite size sampling aperture or area.
NOTE 2 For many devices “the object” is actually an image produced by a lens or other imaging system (e.g. when the
device is a detector array).
3.1.2
sampling period
a
physical distance between sampling points or sampling lines
NOTE Sampling is usually by means of a uniform array of points or lines. The sampling period may be different in two
orthogonal directions.
3.1.3
Nyquist limit
maximum spatial frequency of sinewave that the system can generate in the image, equal to 1/(2a)
NOTE See also 3.1.9.
3.1.4
line spread function (LSF) of the sampling aperture of a sampled imaging system
L (u)
ap
variation in sampled intensity, or signal, for a single sampling aperture or line of the sampling array, as a
narrow line object is traversed across that aperture, or line and adjacent apertures or lines
NOTE 1 The direction of traverse is perpendicular to the length of the narrow line object and in the case of systems
which sample over discrete lines, is also perpendicular to these lines.
NOTE 2 L (u) is a one-dimensional function of position u in the object plane, or equivalent position in the image.
ap
3.1.5
optical transfer function (OTF) of a sampling aperture
D (r)
ap
Fourier transform of the line spread function, L (u), of the sampling aperture
ap
D rL=⋅u exp−i2πur du
() ( ) ( )
ap ap
∫
where r is the spatial frequency
3.1.6
modulation transfer function (MTF) of a sampling aperture
T (r)
ap
modulus of D (r)
ap
3.1.7
reconstruction function
function used to convert the output from each sampled point, aperture or line, to an intensity distribution in the
image
NOTE The reconstruction function has an OTF and MTF associated with it denoted by D (r) and T (r) respectively.
rf rf
3.1.8
MTF of a sampled imaging system
T (r)
sys
product of the aperture MTF, T (r), and the MTF of the reconstruction function, T (r), with the MTF of any
ap rf
additional input device (e.g. a lens) and output device (e.g. a CRT monitor) which are regarded as part of the
imaging system
NOTE When quoting a value for T it should be made clear what constitutes the system. The system could, for
sys
example, be just a detector array and associated drive/output electronics, or could be a complete digital camera and CRT
display.
2 © ISO 2010 – All rights reserved

3.1.9
Fourier transform of the image of a narrow slit produced by the i
...