1、BRITISH STANDARD BS ISO 11421:1997 Optics and optical instruments Accuracy of optical transfer function (OTF) measurement ICS 37.020BSISO11421:1997 This British Standard, having been prepared under the directionof the Consumer Products and Services Sector Board, was published under the authority of
2、the Standards Board and comes intoeffect on 15 December 1997 BSI 04-1999 ISBN 0 580 28842 0 National foreword This British Standard reproduces verbatim ISO11421:1997 and implements it as the UK national standard. The UK participation in its preparation was entrusted to Technical Committee CPW/172, O
3、ptics and optical instruments, which has the responsibility to: aid enquirers to understand the text; present to the responsible international/European committee any enquiries on the interpretation, or proposals for change, and keep the UK interests informed; monitor related international and Europe
4、an developments and promulgate them in the UK. A list of organizations represented on this committee can be obtained on request to its secretary. Cross-references The British Standards which implement international or European publications referred to in this document may be found in the BSI Standar
5、ds Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Find” facility of the BSI Standards Electronic Catalogue. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for
6、 their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, theISOtitlepage, pagesiitoiv, pages1 to26, aninside back cover and abackcover. This
7、 standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover. Amendments issued since publication Amd. No. Date CommentsBSISO11421:1997 BSI 04-1999 i Contents Page National foreword Inside front cove
8、r Foreword ii Text of ISO 11421 1ii blankBSISO11421:1997 ii BSI 04-1999 Contents Page Foreword iii 1 Scope 1 2 Normative reference 1 3 Definitions and symbols 1 4 Sources of inaccuracy in measuring equipment 3 5 Methods of assessing levels of accuracy 9 6 Calculation of overall accuracy of a measure
9、ment 17 7 Specifying a general equipment accuracy 17 8 Routine performance evaluation 21 Annex A (normative) Accuracy of PTF measurement 22 Annex B (informative) Determination of rate of change of MTF various parameters 22 Annex C (informative) Example calculation of NAV 24 Annex D (informative) Bib
10、liography Inside back cover Figure 1 Errors from alignment of analysing slit with respect to object pattern 6 Figure 2 Mechanical bench errors 10 Figure 3 Straightness and parallelism using distance transducer 11 Figure 4 Use of autocollimator for alignment of surfaces 12 Figure 5 Calibration of ang
11、ular rotation 13 Figure 6 Checking collimator focus 14 Figure 7 Determination of systematic focus errors 15 Figure 8 Testing image analyser off-axis 18 Figure 9 Through-focus diffraction-limited MTF curves as specified for generating NAV 19 Figure B.1 Determination of rate of change of MTF with focu
12、s 23 Figure B.2 Determination of rate of change of MTF with spatial frequency 24 Table 1 Preferred parameter values for calculating NAV 20 Descriptors: Optics, optical equipment, image quality indicators, measurement, optical measurements, accuracy, estimation, errors.BSISO11421:1997 BSI 04-1999 iii
13、 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
14、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 matter
15、s of electrotechnical standardization. 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 least75% of the member bodies casting a vote. International Standard ISO11421 was
16、prepared by Technical Committee ISO/TC172, Optics and optical instruments, Subcommittee SC1 Fundamental standards. Annex A forms an integral part of this International Standard. Annex B, Annex C and Annex D are for information only.iv blankBSISO11421:1997 BSI 04-1999 1 Introduction The optical trans
17、fer 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 ISO9334, whilst ISO9335 covers the actual principles and procedures of measurement
18、. Afurther International Standard, ISO9336, deals with specific applications in various optical and electro-optical fields and is in several parts, each dealing with a particular application. Although ISO9335 lists the main factors which influence the accuracy of OTF measurement and describes proced
19、ures which are aimed at achieving accurate and repeatable results, it does not cover in detail the techniques and procedures for evaluating the accuracy of OTF measuring equipment and for estimating the uncertainty in measurements made on specific imaging systems. The present International Standard
20、lists the main sources of inaccuracy 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 error band in any measurement of OTF. One of the aims in preparing this International Standard is to encourage the
21、 setting of more realistic uncertainty levels for the results of OTF measurements. Another is to encourage the use of methods of expressing the accuracy of OTF test equipment which recognize the fact that the accuracy of a particular measurement is a function of both the equipment and the test piece
22、. 1 Scope This International Standard 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 ofOTF. It also gives guidance on assessing and specifying a general accuracy value for a spec
23、ific measuring equipment, as well as recommending methods of routine assessment. The main body of this International Standard deals exclusively with the modulation transfer function (MTF) part of the OTF. The phase transfer function (PTF) is dealt with relatively briefly inAnnex A. 2 Normative refer
24、ence The following standard contains provisions which, through reference in this text, constitute provisions of this International Standard. At the time of publication, the edition indicated was valid. All standards are subject to revision, and parties to agreements based on this International Stand
25、ard are encouraged to investigate the possibility of applying the most recent edition of the standard indicated below. Members of IEC and ISO maintain registers of currently valid International Standards. ISO 9334:1995, Optics and optical instruments Optical transfer function Definitions and mathema
26、tical relationships. 3 Definitions and symbols 3.1 Definitions For the purposes of this International Standard, the following definitions apply. 3.1.1 standard lens single- or multi-element lens which has been constructed with a level of accuracy which is sufficient to ensure that for precisely spec
27、ified conditions of measurement the MTF will be equal to that predicted from theoretical calculations to an accuracy of better than0,05 (MTFunits) NOTEIn order to achieve this accuracy, standard lenses are usually of simple construction and therefore of limited performance. An example of a widely us
28、ed lens is the50mm focal length plano-convex lens described in reference 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 audit lens single- or multi-element lens of stable construction w
29、hose accuracy 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 rep
30、utable authority (preferably a national standards laboratory, if such a service is available)BS ISO 11421:1997 2 BSI 04-1999 3.2 Symbols Symbol Meaning Unit h h9 %h9 l l9 %l9 %z %z9 %a %a9 %Z %Z9 M r %r m(r,h) m9(r,h9) or m9(r,) p9(r,h9) or p9(r,) q9(r,h9) % f % R g9 L9 MTF c r o n9(r,h9) %MTF(r) %M
31、TF c (r) %MTF rl %l %MTF(random) %MTF (systematic) %MTF(total) %MTF(rand) n %MTF(syst) n object height image height error in image height object conjugate image conjugate error in image distance departures from straightness of object slide departures from straightness of image slide angular departur
32、e of object slide from perpendicularity to reference axis angular departure of image slide from perpendicularity to reference axis total departure from ideal object plane total departure from ideal image plane magnification spatial frequency error in spatial frequency rate of change of MTF with obje
33、ct focus (for image intensifier and similar systems) rate of change of MTF with image focus rate of change of MTF with image height rate of change of MTF with image distance field angle error in field angle focal length azimuth angle error in azimuth angle between slits (test lens focal length)/(col
34、limator focal length) or (decollimator focal length)/(collimator focal length) width of slit referred to image plane length of shorter slit referred to image plane MTF of relay lens spatial frequency for zero field angle rate of change of MTF with spatial frequency error in MTF MTF error of the rela
35、y lens MTF errors resulting from aberrations of relay lens error error in setting collimator focus total error in MTF random sources total error in MTF systematic sources total error in MTF from all sources error in MTF from nth source of random error error in MTF from nth source of systematic error
36、s mm, mrad, degree mm, mrad, degree mm, mrad, degree mm mm mm mm mm rad rad mm mm dimensionless mm 1 , mrad 1 , degree 1 mm 1 , mrad 1 , degree 1 mm 1 mm 1 mm 1 , mrad 1 , degree 1 mm 1 mrad, degree mrad, degree mm degree degree dimensionless mm mm dimensionless mm 1 , mrad 1 , degree 1 mm, mrad, de
37、gree dimensionless dimensionless dimensionless mm dimensionless dimensionless dimensionless dimensionless dimensionless NOTEThe notation m(r,h), m9(r,h9), p9(r,h9) etc. denotes that these parameters are functions of both spatial frequency r and image height h9 or h (i.e. the value of the parameter w
38、ill be different for different frequencies and different image heights).BSISO11421:1997 BSI 04-1999 3 4 Sources of inaccuracy in measuring equipment In this clause the main sources of inaccuracy in OTF measuring equipment are listed and the effects on a measurement of MTF described (brief comments o
39、n the measurement of PTF will be found inAnnex A). 4.1 Geometry of optical bench system The function of the optical bench is to provide a means for supporting the “test target unit”, the “test specimen” and the “image analyser” in the correct geometrical relationship (i.e. that defined by the chosen
40、 I-state, in accordance with ISO9334). To achieve this one normally relies on such things as the straightness of slideways, their parallelism to each other and/or to the surface to which the test specimen is referenced, the accuracy of angle scales etc. Departures from the assumed geometry result in
41、 deviations from the ideal I-state and therefore errors in the measured OTF. The important bench parameters depend on the test arrangement being used (note that for bench arrangements such as “nodal slide benches” which are not covered by this International Standard, the user must make his own asses
42、sment of errors). For the arrangements recommended in ISO9335, the main sources of inaccuracy and the resulting MTF errors are as follows. 4.1.1 Object and image at finite conjugates Both the test target unit (TTU) and image analyser slideways shall be straight and perpendicular to the “reference ax
43、is”. Departures from straightness and perpendicularity will produce departures from the ideal focal planes given by: for the TTU and for the image analyser, where h and h9 are object and image heights, %z and %z9 are departures from straightness and %a and %a9 angular (radian) departures from perpen
44、dicularity to the reference axis, for the TTU and image analyser slideways respectively. The combined effect is given by: where is the magnification. If m9(r,h9) is the rate of change of MTF(r) with focus, then the error in MTF is given by: Two further possible sources of error are in the accuracy w
45、ith which the image height h9 is set and the accuracy with which the object and/or image distances are set. The error in MTF is in this case given by (assuming image height and image distance are the parameters set): where %h9 and %l9 are the errors in image height and image distance respectively an
46、d p9 and q9 are the corresponding rates of change in MTF. Usually p9 and q9 are small and this source of error may be ignored (i.e. errors will be less than0,01 in MTF units). 4.1.2 Infinite object and finite image conjugates Similar considerations as for4.1.1 apply except that there is only a singl
47、e slideway. Departures from the ideal focal plane are given in this instance by: and the corresponding error in MTF is given once again by: M h h - =BS ISO 11421:1997 4 BSI 04-1999 Errors may also arise from errors in setting image height or field angle (whichever is used in defining the I-state) an
48、d in setting the object distance to be infinity. These give MTF errors as previously, i.e.: or, if field angle rather than image height is specified: In the above equations h9, %l9, p9 and q9 are as defined in4.1.1, is the field angle and % is the error in the field angle. The value of %l9 shall be
49、determined from the known departure of the object conjugate from infinity. The relevant equation is: where f is the focal length of the lens and l is the actual object conjugate. Usually errors in MTF from these latter two sources are small and may be ignored except where, instead of using a collimator, a very long object conjugate is used on the assumption that it provides a sufficiently close approximation to an infinite conjugate. 4.1.3 Infinite object and image conjugates With the recommended bench arrang
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