1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS EN ISO 16610-21:2012Geometrical product specifications (GPS) FiltrationPart 21: Linear profile filters: Gaussian filters BS EN ISO 16610-21:2012 BRITISH STANDARDNational forew
2、ordThis British Standard is the UK implementation of EN ISO 16610-21:2012. It is identical to ISO 16610-21:2011. It supersedes BS EN ISO 11562:1997 which is withdrawn.The UK participation in its preparation was entrusted to Technical Committee TDW/4, Technical Product Realization.A list of organizat
3、ions represented on this committee can be obtained on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. The British Standards Institution 2012. Published by BSI Standards Limited 2012IS
4、BN 978 0 580 64406 1 ICS 17.040.20 Compliance with a British Standard cannot confer immunity from legal obligations.This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 August 2012.Amendments issued since publicationDate Text affectedEUROPEAN S
5、TANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-21 August 2012 ICS 17.040.20 Supersedes EN ISO 11562:1997English Version Geometrical product specifications (GPS) - Filtration - Part 21: Linear profile filters: Gaussian filters (ISO 16610-21:2011) Spcification gomtrique des produits (GPS) - Filt
6、rage - Partie 21: Filtres de profil linaires: Filtres gaussiens (ISO 16610-21:2011) Geometrische Produktspezifikation (GPS) - Filterung - Teil 21: Lineare Profilfilter: Gau-Filter (ISO 16610-21:2011) This European Standard was approved by CEN on 13 July 2012. CEN members are bound to comply with the
7、 CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC Management
8、 Centre or to any CEN member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status a
9、s the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Ne
10、therlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES KOMITEE FR NORMUNG Management Centre: Avenue Marnix 17, B-1000 Brussels 2012 CEN All rights of ex
11、ploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 16610-21:2012: EBS EN ISO 16610-21:2012EN ISO 16610-21:2012 (E) 3 Foreword The text of ISO 16610-21:2011 has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product speci
12、fications and verification” of the International Organization for Standardization (ISO) and has been taken over as EN ISO 16610-21:2012 by Technical Committee CEN/TC 290 “Dimensional and geometrical product specification and verification” the secretariat of which is held by AFNOR. This European Stan
13、dard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by February 2013, and conflicting national standards shall be withdrawn at the latest by February 2013. Attention is drawn to the possibility that some of the elements o
14、f this document may be the subject of patent rights. CEN and/or CENELEC shall not be held responsible for identifying any or all such patent rights. This document supersedes EN ISO 11562:1997. According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following co
15、untries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
16、Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 16610-21:2011 has been approved by CEN as a EN ISO 16610-21:2012 without any modification. BS EN ISO 16610-21:2012ISO 16610-21:2011(E) ISO 2011 All rights rese
17、rved iiiContents Page Foreword iv Introductionvi 1 Scope1 2 Normative references1 3 Terms and definitions .1 4 Characteristics of Gaussian profile filter for an open profile .2 4.1 Gaussian weighting function for an open profile 2 4.2 Transmission characteristics of an open profile .3 4.2.1 Transmis
18、sion characteristic of the long wave component for an open profile3 4.2.2 Transmission characteristic of the short wave component for an open profile.4 4.3 End effects .5 5 Characteristic of Gaussian profile filter for a closed profile.7 5.1 Introduction7 5.2 Gaussian weighting function for a closed
19、 profile7 5.3 Transmission characteristic of a closed profile filter9 5.3.1 Transmission characteristic of the long wave component for a closed profile .9 5.3.2 Transmission characteristic of the short wave profile component .10 Annex A (informative) Implementation errors for open and closed profile
20、s (convolution algorithm).12 Annex B (informative) Examples .19 Annex C (informative) Relationship to the filtration matrix model 21 Annex D (informative) Relation to the GPS matrix model.22 Bibliography23 BS EN ISO 16610-21:2012ISO 16610-21:2011(E) iv ISO 2011 All rights reservedForeword ISO (the I
21、nternational 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
22、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 electrotechnica
23、l 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 bod
24、ies 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
25、 or all such patent rights. ISO 16610-21 was prepared by Technical Committee ISO/TC 213, Dimensional and geometrical product specifications and verification. ISO 16610-21 cancels and replaces ISO 11562:1996, which has been technically revised. ISO 16610 consists of the following parts, under the gen
26、eral title Geometrical product specifications (GPS) Filtration: Part 1: Overview and basic concepts Technical Specification Part 20: Linear profile filters: Basic concepts Technical Specification Part 21: Linear profile filters: Gaussian filters Part 22: Linear profile filters: Spline filters Techni
27、cal Specification Part 28: Profile filters: End effects Technical Specification Part 29: Linear profile filters: Spline wavelets Technical Specification Part 30: Robust profile filters: Basic concepts Technical Specification Part 31: Robust profile filters: Gaussian regression filters Technical Spec
28、ification Part 32: Robust profile filters: Spline filters Technical Specification Part 40: Morphological profile filters: Basic concepts Technical Specification Part 41: Morphological profile filters: Disk and horizontal line-segment filters Technical Specification Part 49: Morphological profile fil
29、ters: Scale space techniques Technical Specification The following parts are planned: Part 26: Linear profile filters: Filtration on nominally orthogonal grid planar data sets Part 27: Linear profile filters: Filtration on nominally orthogonal grid cylindrical data sets BS EN ISO 16610-21:2012ISO 16
30、610-21:2011(E) ISO 2011 All rights reserved v Part 42: Morphological profile filters: Motif filters Part 60: Linear areal filters: Basic concepts Part 61: Linear areal filters: Gaussian filters Part 62: Linear areal filters: Spline filters Part 69: Linear areal filters: Spline wavelets Part 70: Robu
31、st areal filters: Basic concepts Part 71: Robust areal filters: Gaussian regression filters Part 72: Robust areal filters: Spline filters Part 80: Morphological areal filters: Basic concepts Part 81: Morphological areal filters: Sphere and horizontal planar segment filters Part 82: Morphological are
32、al filters: Motif filters Part 89: Morphological areal filters: Scale space techniques BS EN ISO 16610-21:2012ISO 16610-21:2011(E) vi ISO 2011 All rights reservedIntroduction This part of ISO 16610 is a geometrical product specification (GPS) standard and is to be regarded as a global GPS standard (
33、see ISO/TR 14638). It influences the chain links 3 and 5 of all chains of standards. The ISO/GPS masterplan given in ISO/TR 14638 gives an overview of the ISO/GPS system of which this document is a part. The fundamental rules of ISO/GPS given in ISO 8015 apply to this document and the default decisi
34、on rules given in ISO 14253-1 apply to specifications made in accordance with this document, unless otherwise indicated. For more detailed information about the relation of this part of ISO 16610 to the GPS matrix model, see Annex D. This part of ISO 16610 develops the terminology and a concept of G
35、aussian filters. It has the transmission for the cut-off wavelength as 50 % since the short wave and long wave portions of surface profile are separated and can be reconstructed without altering the surface profile. BS EN ISO 16610-21:2012INTERNATIONAL STANDARD ISO 16610-21:2011(E) ISO 2011 All righ
36、ts reserved 1Geometrical product specifications (GPS) Filtration Part 21: Linear profile filters: Gaussian filters 1 Scope This part of ISO 16610 specifies the metrological characteristics of the Gaussian filter, for the filtration of profiles. It specifies, in particular, how to separate long and s
37、hort wave components of a surface profile. 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 amen
38、dments) applies. ISO/TS 16610-1:2006, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic concepts ISO/TS 16610-20:2006, Geometrical product specifications (GPS) Filtration Part 20: Linear profile filters: Basic concepts ISO/IEC Guide 98-3:2008, Uncertainty of measurement
39、Part 3: Guide to the expression of uncertainty in measurement (GUM:1995) ISO/IEC Guide 99:2007, International vocabulary of metrology Basic and general concepts and associated terms (VIM) 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO/TS 16610-1, IS
40、O/TS 16610-20, ISO/IEC Guide 98-3 and ISO/IEC Guide 99 and the following apply. 3.1 linear profile filters profile filter to separate profiles into long wave and short wave components ISO/TS 16610-20:2006 3.1.1 open profile finite length surface profile with two ends ISO/TS 16610-1:2006 BS EN ISO 16
41、610-21:2012ISO 16610-21:2011(E) 2 ISO 2011 All rights reserved3.1.2 closed profile connected finite length surface profile without ends ISO/TS 16610-1:2006 3.1.3 cut-off wavelength wavelength of a sinusoidal profile of which 50 % of the amplitude is transmitted by the profile filter ISO/TS 16610-20:
42、2006 4 Characteristics of Gaussian profile filter for an open profile 4.1 Gaussian weighting function for an open profile The weighting function of an open profile filter (see Figure 1) has the equation of the Gaussian function with the cut-off wavelength c, where c is cut-off. The equation is given
43、 by: 2cc1() expxsx =(1) where x is the distance from the centre (maximum) of the weighting function; cis the cut-off wavelength; is a constant, to provide 50 % transmission characteristic at the cut-off c. For implementation, the weighting function equation is as follows: 2cc cccc1exp for()0 Otherwi
44、se xLxLsx =uu(2) where Lcis a truncation constant of the weighting function (see Annex A for recommended values); is given by: ln20,469 7 =(3) The graph of the weighting function is shown in Figure 1. BS EN ISO 16610-21:2012ISO 16610-21:2011(E) ISO 2011 All rights reserved 3-1 -0,5 0 0,5 100,511,522
45、,5YXKey X cx Y c()s x Figure 1 Weighting function of a Gaussian profile filter for an open profile 4.2 Transmission characteristics of an open profile 4.2.1 Transmission characteristic of the long wave component for an open profile The transmission characteristic (see Figure 2) is determined from th
46、e weighting function by means of the Fourier transformation. The transmission characteristic of the long wave component (mean line) is given by: 2c10expaa=(4) where a0is the amplitude of a sinusoidal wave profile before filtering; a1is the amplitude of this sinusoidal profile in the mean line; is th
47、e wavelength of this sinusoidal profile. BS EN ISO 16610-21:2012ISO 16610-21:2011(E) 4 ISO 2011 All rights reserved10-210-11001011020102030405060708090100YXKey X c Y amplitude transmission 10,aa in percent Figure 2 Long wave transmission function of the Gaussian filter for an open profile 4.2.2 Tran
48、smission characteristic of the short wave component for an open profile The transmission characteristic (see Figure 3) is determined from the weighting function by means of the Fourier transformation and is complementary to the transmission characteristic of the long wave profile component. The tran
49、smission characteristic of the short wave component is given by: 2c201expaa= 21001aaaa= (5) where a2is the amplitude of the short wave component of a sinusoidal wave profile. BS EN ISO 16610-21:2012ISO 16610-21:2011(E) ISO 2011 All rights reserved 510-210-11001011020102030405060708090100YXKey X c Y amplitude tran
