SIST EN ISO 16610-21:2012
(Main)Geometrical product specifications (GPS) - Filtration - Part 21: Linear profile filters: Gaussian filters (ISO 16610-21:2011)
Geometrical product specifications (GPS) - Filtration - Part 21: Linear profile filters: Gaussian filters (ISO 16610-21:2011)
ISO 16610-21:2011 specifies the metrological characteristics of the Gaussian filter, for the filtration of profiles. It specifies, in particular, how to separate long and short wave components of a surface profile.
Geometrische Produktspezifikation (GPS) - Filterung - Teil 21: Lineare Profilfilter: Gauß-Filter (ISO 16610-21:2011)
Dieser Teil von ISO 16610 legt die messtechnischen Eigenschaften des Gauß-Filters für die Filterung von Profilen fest. Er legt insbesondere fest, wie langwellige und kurzwellige Komponenten eines Oberflächenprofils getrennt werden.
Spécification géométrique des produits (GPS) - Filtrage - Partie 21: Filtres de profil linéaires: Filtres gaussiens (ISO 16610-21:2011)
L'ISO 16610-21:2011 sp�cifie les caract�ristiques m�trologiques des filtres gaussiens utilis�s pour le filtrage des profils. Elle sp�cifie notamment la fa�on de s�parer les composantes de longueurs d'onde longue et courte d'un profil de surface.
Geometrične specifikacije izdelkov - Filtriranje - 21. del: Filtri linearnih profilov: Gaussovi filtri (ISO 16610-21:2011)
Ta del standarda ISO 16610 določa metrološke značilnosti Gaussovih filtrov za filtriranje profilov. Zlasti določa, kako ločiti dolgovalovne in kratkovalovne dele površine.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 16610-21:2012
01-oktober-2012
1DGRPHãþD
SIST EN ISO 11562:2000
SIST EN ISO 11562:2000/AC:2008
*HRPHWULþQHVSHFLILNDFLMHL]GHONRY)LOWULUDQMHGHO )LOWULOLQHDUQLKSURILORY
*DXVVRYLILOWUL ,62
Geometrical product specifications (GPS) - Filtration - Part 21: Linear profile filters:
Gaussian filters (ISO 16610-21:2011)
Geometrische Produktspezifikation (GPS) - Filterung - Teil 21: Lineare Profilfilter: Gauß-
Filter (ISO 16610-21:2011)
Spécification géométrique des produits (GPS) - Filtrage - Partie 21: Filtres de profil
linéaires: Filtres gaussiens (ISO 16610-21:2011)
Ta slovenski standard je istoveten z: EN ISO 16610-21:2012
ICS:
17.040.20 Lastnosti površin Properties of surfaces
SIST EN ISO 16610-21:2012 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN ISO 16610-21:2012
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SIST EN ISO 16610-21:2012
EUROPEAN STANDARD
EN ISO 16610-21
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2012
ICS 17.040.20 Supersedes EN ISO 11562:1997
English Version
Geometrical product specifications (GPS) - Filtration - Part 21:
Linear profile filters: Gaussian filters (ISO 16610-21:2011)
Spécification géométrique des produits (GPS) - Filtrage - Geometrische Produktspezifikation (GPS) - Filterung - Teil
Partie 21: Filtres de profil linéaires: Filtres gaussiens (ISO 21: Lineare Profilfilter: Gauß-Filter (ISO 16610-21:2011)
16610-21:2011)
This European Standard was approved by CEN on 13 July 2012.
CEN members are bound to comply with the 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 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 as 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, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2012 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 16610-21:2012: E
worldwide for CEN national Members.
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SIST EN ISO 16610-21:2012
EN ISO 16610-21:2012 (E)
Contents Page
Foreword .3
2
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SIST EN ISO 16610-21:2012
EN ISO 16610-21:2012 (E)
Foreword
The text of ISO 16610-21:2011 has been prepared by Technical Committee ISO/TC 213 “Dimensional and
geometrical product specifications 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 Standard 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 of 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
countries 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, 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.
3
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SIST EN ISO 16610-21:2012
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SIST EN ISO 16610-21:2012
INTERNATIONAL ISO
STANDARD 16610-21
First edition
2011-06-01
Geometrical product specifications
(GPS) — Filtration —
Part 21:
Linear profile filters: Gaussian filters
Spécification géométrique des produits (GPS) — Filtrage —
Partie 21: Filtres de profil linéaires: Filtres gaussiens
Reference number
ISO 16610-21:2011(E)
©
ISO 2011
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SIST EN ISO 16610-21:2012
ISO 16610-21:2011(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2011
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 permission in writing from either ISO at the address below or
ISO's 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 copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2011 – All rights reserved
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SIST EN ISO 16610-21:2012
ISO 16610-21:2011(E)
Contents Page
Foreword .iv
Introduction.vi
1 Scope.1
2 Normative references.1
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 Transmission characteristic of the long wave component for an open profile.3
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 Introduction.7
5.2 Gaussian weighting function for a closed profile.7
5.3 Transmission characteristic of a closed profile filter.9
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 profiles (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
Bibliography.23
© ISO 2011 – All rights reserved iii
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SIST EN ISO 16610-21:2012
ISO 16610-21:2011(E)
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 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 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 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 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 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 general 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 [Technical 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 Specification]
⎯ 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 filters: 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
iv © ISO 2011 – All rights reserved
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SIST EN ISO 16610-21:2012
ISO 16610-21:2011(E)
⎯ 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: Robust 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 areal filters: Motif filters
⎯ Part 89: Morphological areal filters: Scale space techniques
© ISO 2011 – All rights reserved v
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SIST EN ISO 16610-21:2012
ISO 16610-21:2011(E)
Introduction
This part of ISO 16610 is a geometrical product specification (GPS) standard and is to be regarded as a
global GPS standard (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 decision 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 Gaussian 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.
vi © ISO 2011 – All rights reserved
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SIST EN ISO 16610-21:2012
INTERNATIONAL STANDARD ISO 16610-21:2011(E)
Geometrical 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 short 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 amendments) 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 — 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, ISO/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]
© ISO 2011 – All rights reserved 1
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SIST EN ISO 16610-21:2012
ISO 16610-21:2011(E)
3.1.2
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 16610-20:2006]
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 λ , where c is cut-off. The equation is given by:
c
2
⎡⎤
⎛⎞
1 x
⎢⎥
sx()=×exp−π (1)
⎜⎟
αλ××⎢⎥αλ
cc
⎝⎠
⎣⎦
where
x is the distance from the centre (maximum) of the weighting function;
λ is the cut-off wavelength;
c
α is a constant, to provide 50 % transmission characteristic at the cut-off λ .
c
For implementation, the weighting function equation is as follows:
2
⎧
⎡⎤
⎛⎞
1 x
⎪
⎢⎥
×−expπ for−Lx×λλuuL×
⎜⎟
cc c c
⎪
αλ⎢⎥αλ
××
cc
⎝⎠
sx() = (2)
⎨
⎣⎦
⎪
⎪
0 Otherwise
⎩
where
L is a truncation constant of the weighting function (see Annex A for recommended values);
c
α is given by:
ln2
α=≈ 0,469 7 (3)
π
The graph of the weighting function is shown in Figure 1.
2 © ISO 2011 – All rights reserved
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SIST EN ISO 16610-21:2012
ISO 16610-21:2011(E)
Y
2,5
2
1,5
1
0,5
0
-1 -0,5 0 0,5 1 X
Key
X x λ
c
Y λ × s()x
c
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 the weighting function by means of the
Fourier transformation. The transmission characteristic of the long wave component (mean line) is given by:
2
⎡⎤
a αλ×
⎛⎞
1 c
⎢⎥
=−expπ (4)
⎜⎟
a ⎢⎥λ
0 ⎝⎠
⎣⎦
where
a is the amplitude of a sinusoidal wave profile before filtering;
0
a is the amplitude of this sinusoidal profile in the mean line;
1
λ is the wavelength of this sinusoidal profile.
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SIST EN ISO 16610-21:2012
ISO 16610-21:2011(E)
Y
100
90
80
70
60
50
40
30
20
10
0
-2 -1 0 1
...
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