1、November 2010 Translation by DIN-Sprachendienst.English price group 15No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).I
2、CS 17.180.01; 37.020!$l24“1731517www.din.deDDIN ISO 15529Optics and photonics Optical transfer function Principles of measurement of modulation transfer function (MTF) ofsampled imaging systems (ISO 15529:2010)English translation of DIN ISO 15529:2010-11Optik und Photonik Optische bertragungsfunktio
3、n Messung der Modulationsbertragungsfunktion (MTF) von abtastendenAbbildungssystemen (ISO 15529:2010)Englische bersetzung von DIN ISO 15529:2010-11Optique et photonique Fonction de transfert optique Principes de mesure de la fonction de transfert de modulation (MTF) des systmes deformation dimage ch
4、antillonns (ISO 15529:2010)Traduction anglaise de DIN ISO 15529:2010-11www.beuth.deDocument comprises pagesIn case of doubt, the German-language original shall be considered authoritative.2911.10 DIN ISO 15529:2010-11 2 A comma is used as the decimal marker. Contents Page National foreword .3 Nation
5、al Annex NA (informative) Bibliography.3 Introduction .4 1 Scope 5 2 Normative references 5 3 Terms, definitions and symbols.5 3.1 Terms and definitions5 3.2 Symbols 8 4 Theoretical relationships 9 4.1 Fourier transform of the image of a (static) slit object 9 4.2 Fourier transform of the output fro
6、m a single sampling aperture for a slit object scanned across the aperture10 4.3 Fourier transform of the average LSF for different positions of the slit object 12 5 Methods of measuring the MTFs associated with sampled imaging systems12 5.1 General12 5.2 Test azimuth.13 5.3 Measurement of system MT
7、F, Tsys(r) of a sampled imaging device or complete system .13 5.4 Measurement of the MTF of the sampling aperture, Tap19 6 Method of measuring the aliasing function, the aliasing ratio and the aliasing potential .19 Annex A (informative) Background theory21 Annex B (informative) Aliasing in sampled
8、imaging systems 24 Bibliography 29 National foreword This standard has been prepared by Technical Committee ISO/TC 172 “Optics and photonics”, Subcommittee SC 1 “Fundamental standards” (Secretariat: DIN, Germany). The responsible German body involved in its preparation was the Normenausschuss Feinme
9、chanik und Optik (Optics and Precision Mechanics Standards Committee), Working Committee NA 027-01-02 AA Grundnormen der Optik. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. DIN shall not be held responsible for identifying any
10、or all such patent rights. The DIN Standards corresponding to the International Standards referred to in this document are as follows: ISO 9334 DIN ISO 9334 ISO 9335 DIN ISO 9335 ISO 11421 DIN ISO 11421 National Annex NA (informative) Bibliography DIN ISO 9334, Optics and photonics Optical transfer
11、function Definitions and mathematical relationships DIN ISO 9335, Optics and photonics Optical transfer function Principles and procedures of measurement DIN ISO 11421, Optics and optical instruments Accuracy of optical transfer function (OTF) measurement 3 DIN ISO 15529:2010-11 Introduction One of
12、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
13、 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
14、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
15、 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 p
16、osition 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 descri
17、ptive 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 i
18、n 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
19、 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
20、 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
21、 clothing) can produce 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
22、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. Optics and photonics Optical transfer function Principles of measurement
23、 of modulation transfer function (MTF) of sampled imaging systems 4 DIN ISO 15529:2010-11 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
24、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 describe
25、d, 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
26、), 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,
27、 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 a
28、nd 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, wher
29、e 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 produ
30、ced by a lens or other imaging system (e.g. when the device is a detector array). N1) National footnote: Aliasing is understood to be the overlapping of neighbouring spatial frequency bands. N1)5 DIN ISO 15529:2010-11 3.1.2 sampling period a physical distance between sampling points or sampling line
31、s 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 fu
32、nction (LSF) 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
33、 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 Lap(u) is a one-dimensional function of position u in the object plane, or equivalent position in the image. 3.1.5 optical tran
34、sfer function (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 reconstruc
35、tion 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 Drf(r) and Trf(r) respectively. 3.1.8 MTF of a sampled imaging system Tsys(r) produ
36、ct of the 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 constit
37、utes the system. 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. N2) National footnote: A “narrow line object” shall be understood to be the image of an illuminated narrow slit. N2)6 DIN ISO 15529
38、:2010-11 3.1.9 Fourier transform of the image of a narrow slit produced by the imaging 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 c
39、omplete system NOTE Limg(u) is different for different positions of the slit object relative 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 MT
40、F test slit is moved over a distance equal to, or greater than, one period of the sampling 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
41、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. 3.1.11 aliasing ratio of a sampled imaging system AR, sys(r) ratio AF,sys(r)/|Fimg(r)|av, where |Fimg(r)|avis the average of
42、 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(r)
43、|avas a measure of the signal. 3.1.12 MTF of an imaging pick-up subsystem Timp(r) product of the aperture MTF, Tap(r), with the MTF of the lens, Tlens(r), where the MTF of the lens includes the effect of any optical anti-aliasing filters that are part of the system and which form the image on the sa
44、mpling array 3.1.13 aliasing potential of a sampled imaging system AP, impratio of the area under the imaging pick-up MTF, Timp(r), from r = 0,5 to r = 1, to the area under the same curve from r = 0 to r = 0,5, where the spatial frequency (r) is normalized so that 1/a becomes unity 7 DIN ISO 15529:2
45、010-11 3.2 Symbols See Table 1. Table 1 Symbols used Symbol Parameter Units AF, sys(r) Aliasing function associated with the complete imaging system 1 AP,impAliasing potential associated with the imaging subsystem 1 AR,sys(r) Aliasing ratio associated with the complete imaging system 1 a Sampling pe
46、riod mm, mrad, degrees 1/(2a) Nyquist spatial frequency limit mm1, mrad1, degree1Dap(r) Optical transfer function of a sampling aperture 1 Dlens(r) Optical transfer function of the optical system including any anti-aliasing filters 1 Drf(r) Optical transfer function of the reconstruction function 1
47、Fav(r) Fourier transform of Lav(u) 1 Fimg(r) Fourier transform of the final image of the slit object 1 Fin(r) Fourier transform of Lin(uFslt(r) Fourier transform of the slit object 1 Lap(u) Line spread function of a sampling aperture 1 Lav(u) Line spread function obtained by averaging the LSF associ
48、ated with different positions of the slit object relative to the sampling array 1 Limg(u) Line spread function associated with the complete imaging system 1 Lin(u) Line spread function of the combination of slit object, optical system including any anti-aliasing filters and sampling aperture 1 r Spa
49、tial frequency mm1, mrad1, degree1Tap(r) Modulation transfer function of a sampling aperture 1 Timp(r) Modulation transfer function of an imaging pick-up subsystem 1 Tlens(r) Modulation transfer function of the optical system including any anti-aliasing filters 1 Trf(r) Modulation transfer function of the reconstruction function 1 Tsys(r) Modulation transfer function of a sampled imaging system 1 u Local image field coordinate mm, mrad, degrees 8 DIN ISO 15529:2010-11 4 Theoretical relationships 4.1 Fourier transform of the
