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1、A Reference number ISO 15529:1999(E) INTERNATIONAL STANDARD ISO 15529 First edition 1999-08-01 Optics and optical instruments Optical transfer function Principles of measurement of modulation transfer function (MTF) of sampled imaging systems Optique et instruments doptique Fonction de transfert opt
2、ique Principes de mesurage de la fonction de transfert de modulation (MTF) des systmes de formation dimage chantillonns Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/19/2007 04:52:34 M
3、DTNo reproduction or networking permitted without license from IHS -,-,- ISO 15529:1999(E) ISO 1999 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,
4、without permission in writing from the publisher. International Organization for Standardization Case postale 56 CH-1211 Genve 20 Switzerland Internetisoiso.ch Printed in Switzerland ii Contents 1 Scope1 2 Normative references1 3 Terms, definitions and symbols.1 4 Theoretical relationships 4 5 Measu
5、rement of MTF associated with sampled imaging systems.6 6 Measurement of aliasing function13 Annex A (informative) Background theory.14 Bibliography17 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not fo
6、r Resale, 04/19/2007 04:52:34 MDTNo reproduction or networking permitted without license from IHS -,-,- ISOISO 15529:1999(E) iii Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing Interna
7、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
8、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 3. Draft International Standar
9、ds 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. International Standard ISO 15529 was prepared by Technical Committee ISO/TC 172, Optics and optical
10、instruments, Subcommittee SC 1, Fundamental standards. Annex A of this International Standard is for information only. Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/19/2007 04:52:34 MD
11、TNo reproduction or networking permitted without license from IHS -,-,- ISO 15529:1999(E) ISO iv Introduction One of the most important criteria for describing the performance of an imaging system or device is its modulation transfer function (MTF). The conditions that must be satisfied by an imagin
12、g system for the MTF concept to apply are specified in ISO 9334. They are that the imaging system must 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
13、 accuracy. There are types of imaging systems where this condition does not strictly apply. These are systems in which 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 o
14、r systems are: fibre-optic faceplates, 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
15、function (LSF) 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). The present International Sta
16、ndard 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 which is independent of the measurin
17、g equipment (i.e. the effect of object slit widths, etc. can be deconvolved 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 nonsampled imaging sys
18、tem. This International Standard also specifies MTFs for the subunits, or imaging stages, which make up such a system. These also satisfy the above criteria. Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001
19、 Not for Resale, 04/19/2007 04:52:34 MDTNo reproduction or networking permitted without license from IHS -,-,- INTERNATIONAL STANDARD ISOISO 15529:1999(E) 1 Optics and optical instruments Optical transfer function Principles of measurement of modulation transfer function (MTF) of sampled imaging sys
20、tems 1 Scope This International Standard specifies the principal modulation transfer function (MTF) associated with a sampled imaging system, together with related terms. It also outlines a number of suitable techniques for measuring these MTFs. This International Standard is particularly relevant t
21、o electronic imaging devices, such as CCD cameras and the CCD arrays themselves. Although a number of 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 measure
22、ment as set out in ISO 9334 and ISO 9335. The use of a measurement of the edge spread function (ESF), 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 normative d
23、ocuments contain provisions which, through reference in this text, constitute provisions of this International Standard. For dated references, subsequent amendments to, or revisions of, any of these publications do not apply. However, parties to agreements based on this International Standard are en
24、couraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. For undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain registers of currently valid International Standards. ISO
25、 9334:1995, Optics and optical instruments Optical transfer function Definitions and mathematical relationships ISO 9335:1995, Optics and optical instruments Optical transfer function Principles and procedures of measurement ISO 11421:1997, Optics and optical instruments Accuracy of optical transfer
26、 function (OTF) measurement 3 Terms, definitions and symbols 3.1 Terms and definitions For the purposes of this International Standard, the following terms and definitions apply. 3.1.1 sampled imaging system imaging system or device with which the image is generated by sampling the object at an arra
27、y 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 sampling aperture or area of finite size. Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technica
28、l Standards 1/9972545001 Not for Resale, 04/19/2007 04:52:34 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO 15529:1999(E) ISO 2 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 arr
29、ay). 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 spatial frequency equal to 1/(2a) cf. 3.1.9. NOTE I
30、t is the maximum spatial frequency of sinewave that the system can generate in the image. 3.1.4 line spread function of the sampling aperture of a sampled imaging system LSFap(u) variation in sampled intensity, or signal, for a single sampling aperture or line of the sampling array, as a narrow-line
31、 object is traversed across that aperture or line and adjacent apertures or lines NOTE 1The direction of traverse is perpendicular to the length of the narrow-line object and, in the case of systems which sample over discrete lines, it is also perpendicular to these lines. NOTE 2 LSFap(u) is a one-d
32、imensional function of position u in the object plane, or equivalent position in the image. 3.1.5 optical transfer function of a sampling aperture OTFap(r) Fourier transform of the line spread function, LSFap(u), of the sampling aperture OTF( )LSF( ).exp( i)d apap ruu ru= . . . . 2 p where r is the
33、spatial frequency. 3.1.6 modulation transfer function of a sampling aperture MTFap(r) modulus of OTFap(r) 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
34、 and an MTF associated with it, denoted by OTFrf(r) and MTFrf(r) respectively. 3.1.8 MTF of a sampled imaging system MTFsys(r) product of MTFap(r) and MTFrf(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 s
35、ystem Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/19/2007 04:52:34 MDTNo reproduction or networking permitted without license from IHS -,-,- ISOISO 15529:1999(E) 3 NOTE When quoting
36、a value for MTFsys it should be made clear what constitutes the system. The system could, for example, be just a CCD detector array and associated drive/output electronics, or could be a complete CCD camera and CRT display. 3.1.9 aliasing function of a sampled imaging system AFsys(r) difference betw
37、een the highest and lowest values of MTFsys(r) as the image of the MTF test slit is moved over a distance equal to, or greater, than one period of the array NOTE 1 It is the limiting value of this difference as the width of the test slit approaches zero (i.e. as its Fourier transform approaches unit
38、y). NOTE 2 AFsys(r) is a measure of the degree to which the system will respond to spatial frequencies higher than the Nyquist frequency and as a result generate spurious low frequencies in the image. 3.2 Symbols SymbolParameterUnits aSampling periodmm, mrad, degrees 1/(2a)Nyquist spatial frequency
39、limitmm-1, mrad-1, degree-1 uLocal image field coordinatemm, mrad, degrees rSpatial frequencymm-1, mrad-1, degree-1 LSFap(u)Line spread function of a sampling aperturedimensionless OTFap(r)Optical transfer function of a sampling aperturedimensionless MTFap(r)Modulation transfer function of a samplin
40、g aperture dimensionless OTFrf(r)Optical transfer function of the reconstruction function dimensionless MTFrf(r)Modulation transfer function of the reconstruction function dimensionless MTFsys(r)Modulation transfer function of a sampled imaging system dimensionless FTslt(r)Fourier transform of the s
41、lit objectdimensionless OTFlns(r)Optical transfer function of the relay lensdimensionless MTFlns(r)Modulation transfer function of the relay lensdimensionless FTimg(r)Fourier transform of the final image of the slit object dimensionless AFsys(r)Aliasing function of the system under testdimensionless
42、 LSFin(u)Line spread function of the combination of slit object, relay lens and sampling aperture dimensionless FTin(r)Fourier transform of LSFin(u)dimensionless LSFav(u)Line spread function obtained by averaging the LSF associated with different positions of the object slit relative to the sampling
43、 array dimensionless FTav(r)Fourier transform of LSFav(u)dimensionless Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/19/2007 04:52:34 MDTNo reproduction or networking permitted without
44、 license from IHS -,-,- ISO 15529:1999(E) ISO 4 4 Theoretical relationships 4.1 Fourier transform of the image of a (static) slit object 4.1.1 General case The stages of image formation in a generalized sampled imaging system are illustrated in Figure 1. The values of the relevant parameters used he
45、re are specified in clause 3. Key 1Object slit FTslt(r) 2Lens OTFlns(r) / MTFlns(r) 3Sampling apertures OTFap(r) / MTFap(r) 4Reconstruction function OTFrf(r) / MTFrf(r) Figure 1 Image formation by a sampled imaging system For a sampled imaging system we have: FTimg(r) = k FTin (r 2 k/a)exp (i2(k/a)O
46、TFrf (r)(1) where FTin(r) = FTslt (r)OTFlns (r)OTFap (r)(2) and where k is an integer (i.e. k = 0, 1, 2, 3 ) and is a phase term describing the position of the slit relative to the sampling array. NOTE More information on the mathematical relationships involved in imaging with sampled systems can be
47、 found in 1 (see Bibliography) and in most textbooks dealing with Fourier transform methods. 4.1.2 Special cases The relationships listed in this clause are given without derivation (a brief explanation of their derivation can be found in annex A). 4.1.2.1 Cut-off spatial frequency of FTin(r) is les
48、s than or equal to the Nyquist frequency 1/(2a) For this condition and for spatial frequencies less than the Nyquist frequency, the system behaves as a non- sampled system and we have: FTimg(r) = FTin(r)MTFrf(r)(3) where FTin(r) = FTslt(r)MTFlns(r)MTFap(r)(4) Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/19/2007 04:52:34 MDTNo reproduction or networking permitte