1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS ISO 15529:2010Optics and photonics Opticaltransfer function Principlesof measurement of modulationtransfer function (MTF) ofsampled imaging systemsBS ISO 15529:2010 BRITISH ST
2、ANDARDNational forewordThis British Standard is the UK implementation of ISO 15529:2010. Itsupersedes BS ISO 15529:2007 which is withdrawn.The UK participation in its preparation was entrusted to TechnicalCommittee CPW/172/1, Optics and Photonics - FundamentalStandards.A list of organizations repres
3、ented on this committee can beobtained on request to its secretary.This publication does not purport to include all the necessaryprovisions of a contract. Users are responsible for its correctapplication. BSI 2010ISBN 978 0 580 70687 5ICS 17.180.01Compliance with a British Standard cannot confer imm
4、unity fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strategy Committee on 31 October 2010.Amendments issued since publicationDate Text affectedBS ISO 15529:2010Reference numberISO 15529:2010(E)ISO 2010INTERNATIONAL STANDARD ISO15529Third edi
5、tion2010-08-01Optics 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 systmes de formation dim
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9、ntral Secretariat at the address given below. COPYRIGHT PROTECTED DOCUMENT 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 permissi
10、on in writing from either ISO at the address below or ISOs 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 copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2010 All rights reserved
11、BS ISO 15529:2010ISO 15529:2010(E) ISO 2010 All rights reserved iiiContents Page Foreword iv Introduction.v 1 Scope1 2 Normative references1 3 Terms, definitions and symbols 1 3.1 Terms and definitions .1 3.2 Symbols4 4 Theoretical relationships5 4.1 Fourier transform of the image of a (static) slit
12、 object5 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 object8 5 Methods of measuring the MTFs associated with sampled imaging systems .8 5.1 General .8
13、 5.2 Test azimuth.9 5.3 Measurement of Tsysof a sampled imaging device or complete system 9 5.4 Measurement of the MTF of the sampling aperture, Tap15 6 Method of measuring the aliasing function, the aliasing ratio and the aliasing potential.15 Annex A (informative) Background theory.17 Annex B (inf
14、ormative) Aliasing in sampled imaging systems20 Bibliography25 BS ISO 15529:2010ISO 15529:2010(E) iv ISO 2010 All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing Interna
15、tional 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
16、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
17、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 t
18、he 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. Th
19、is 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. BS ISO 15529:2010ISO 15529:2010(E) ISO 2010 All rights reserved vIntroduction One of the most important c
20、riteria 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 ob
21、ject (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
22、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 perpendic
23、ular 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 orientat
24、ion 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
25、 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 giv
26、en 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 i
27、maging 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 ca
28、n 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 produ
29、ce very visible fringe patterns in the final image, usually referred to as moir 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
30、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. BS ISO 15529:2010BS ISO 15529:2010INTERNATIONAL STANDARD ISO 15529:2010(E) ISO 2010 All righ
31、ts reserved 1Optics 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
32、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.
33、 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 ed
34、ge 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 refere
35、nces, 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
36、 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
37、. 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. NO
38、TE 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). BS ISO 15529:2010ISO 15529:2010(E) 2 ISO 2010 All rights reserved3.1.2 sampling period a physical distance between sampling points or sampling lines NOTE Sam
39、pling 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 (LS
40、F) of the sampling aperture of a sampled imaging system Lap(u) 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
41、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 Lap(u) is a one-dimensional function of position u in the object plane, or equivalent position in the image. 3.1.5 optical transfer funct
42、ion (OTF) of a sampling aperture Dap(r) Fourier transform of the line spread function, Lap(u), of the sampling aperture () () ( )ap apexp i2 dD rLu uru=where r is the spatial frequency 3.1.6 modulation transfer function (MTF) of a sampling aperture Tap(r) modulus of Dap(r) 3.1.7 reconstruction funct
43、ion 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 Drf(r) and Trf(r) respectively. 3.1.8 MTF of a sampled imaging system Tsys(r) product of the
44、aperture MTF, Tap(r), and the MTF of the reconstruction function, Trf(r), with the MTF of any 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 Tsysit should be made clear what constitutes the s
45、ystem. The system could, for example, be just a detector array and associated drive/output electronics, or could be a complete digital camera and CRT display. BS ISO 15529:2010ISO 15529:2010(E) ISO 2010 All rights reserved 33.1.9 Fourier transform of the image of a narrow slit produced by the imagin
46、g system Fimg(r) () () ( )img imgexp i2 dF rLu uru=where the line spread function of the system, Limg(u), is the variation in sampled intensity, or signal, across the image of a narrow slit object generated by the complete system NOTE Limg(u) is different for different positions of the slit object r
47、elative to the sampling array. 3.1.10 aliasing function of a sampled imaging system AF, sys(r) half the difference between the highest and lowest value of |Fimg(r)| i.e. the modulus of Fimg(r) as the image of the MTF test slit is moved over a distance equal to, or greater than, one period of the sam
48、pling array ()() ()img imgmax minF,sys2Fr FrAr= NOTE 1 It is the limiting value of this difference as the width of the test slit approaches zero (i.e. its Fourier transform approaches unity). NOTE 2 AF, sys(r) is a measure of the degree to which the system will respond to spatial frequencies higher
49、than the Nyquist frequency and as a result generate spurious low frequencies in the image. 3.1.11 aliasing ratio of a sampled imaging system AR, sys(r) ratio AF,sys(r)/|Fimg(r)|av, where |Fimg(r)|avis the average of the highest and lowest value of |Fimg(r)| as the image of the MTF test slit is moved over a distance equal to, or greater than, one period of the sampling array NOTE AR, sys(r) can be considered as a measure of the noise/signal ratio where AF, sys(r) is a measure of the noise component and |Fimg(
