SIST EN ISO 25178-2:2022
(Main)Geometrical product specifications (GPS) - Surface texture: Areal - Part 2: Terms, definitions and surface texture parameters (ISO 25178-2:2021)
Geometrical product specifications (GPS) - Surface texture: Areal - Part 2: Terms, definitions and surface texture parameters (ISO 25178-2:2021)
This document specifies parameters for the determination of surface texture by areal methods.
Geometrische Produktspezifikation (GPS) - Oberflächenbeschaffenheit: Flächenhaft - Teil 2: Begriffe, Definitionen und Oberflächen-Kenngrößen (ISO 25178-2:2021)
Dieses Dokument legt Kenngrößen für die Ermittlung der Oberflächenbeschaffenheit durch flächenhafte Messverfahren fest.
Spécification géométrique des produits (GPS) - État de surface: Surfacique - Partie 2: Termes, définitions et paramètres d'états de surface (ISO 25178-2:2021)
Le présent document spécifie les paramètres applicables à la détermination de l'état de surface au moyen de méthodes surfaciques.
Specifikacija geometrijskih veličin izdelka (GPS) - Tekstura površine: ploskovna - 2. del: Izrazi, definicije in parametri teksture površine (ISO 25178-2:2021)
Ta dokument določa parametre za ugotavljanje teksture površine s ploskovnimi metodami.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-marec-2022
Nadomešča:
SIST EN ISO 25178-2:2012
Specifikacija geometrijskih veličin izdelka (GPS) - Tekstura površine: ploskovna -
2. del: Izrazi, definicije in parametri teksture površine (ISO 25178-2:2021)
Geometrical product specifications (GPS) - Surface texture: Areal - Part 2: Terms,
definitions and surface texture parameters (ISO 25178-2:2021)
Geometrische Produktspezifikation (GPS) - Oberflächenbeschaffenheit: Flächenhaft -
Teil 2: Begriffe, Definitionen und Oberflächen-Kenngrößen (ISO 25178-2:2021)
Spécification géométrique des produits (GPS) - État de surface: Surfacique - Partie 2:
Termes, définitions et paramètres d'états de surface (ISO 25178-2:2021)
Ta slovenski standard je istoveten z: EN ISO 25178-2:2022
ICS:
17.040.20 Lastnosti površin Properties of surfaces
17.040.40 Specifikacija geometrijskih Geometrical Product
veličin izdelka (GPS) Specification (GPS)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EN ISO 25178-2
EUROPEAN STANDARD
NORME EUROPÉENNE
January 2022
EUROPÄISCHE NORM
ICS 17.040.20 Supersedes EN ISO 25178-2:2012
English Version
Geometrical product specifications (GPS) - Surface texture:
Areal - Part 2: Terms, definitions and surface texture
parameters (ISO 25178-2:2021)
Spécification géométrique des produits (GPS) - État de Geometrische Produktspezifikation (GPS) -
surface: Surfacique - Partie 2: Termes, définitions et Oberflächenbeschaffenheit: Flächenhaft - Teil 2:
paramètres d'états de surface (ISO 25178-2:2021) Begriffe, Definitionen und Oberflächen-Kenngrößen
(ISO 25178-2:2021)
This European Standard was approved by CEN on 27 November 2021.
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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2022 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 25178-2:2022 E
worldwide for CEN national Members.
Contents Page
European foreword . 3
European foreword
This document (EN ISO 25178-2:2022) has been prepared by Technical Committee ISO/TC 213
"Dimensional and geometrical product specifications and verification" in collaboration with 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 July 2022, and conflicting national standards shall be
withdrawn at the latest by July 2022.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 25178-2:2012.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
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, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 25178-2:2021 has been approved by CEN as EN ISO 25178-2:2022 without any
modification.
INTERNATIONAL ISO
STANDARD 25178-2
Second edition
2021-12
Geometrical product specifications
(GPS) — Surface texture: Areal —
Part 2:
Terms, definitions and surface texture
parameters
Spécification géométrique des produits (GPS) — État de surface:
Surfacique —
Partie 2: Termes, définitions et paramètres d'états de surface
Reference number
ISO 25178-2:2021(E)
ISO 25178-2:2021(E)
© ISO 2021
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
ISO 25178-2:2021(E)
Contents Page
Foreword .v
Introduction . vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 General terms . 1
3.2 Geometrical parameter terms . 5
3.3 Geometrical feature terms . . 11
4 Field parameters .15
4.1 General . 15
4.2 Height parameters. 15
4.2.1 General .15
4.2.2 Root mean square height . 15
4.2.3 Skewness . 15
4.2.4 Kurtosis .15
4.2.5 Maximum peak height . 16
4.2.6 Maximum pit depth . 16
4.2.7 Maximum height . 16
4.2.8 Arithmetic mean height . 16
4.3 Spatial parameters . 16
4.3.1 General . 16
4.3.2 Autocorrelation length. 16
4.3.3 Texture aspect ratio . 17
4.3.4 Texture direction . 18
4.3.5 Dominant spatial wavelength . 18
4.4 Hybrid parameters . . . 18
4.4.1 General . 18
4.4.2 Root mean square gradient . 18
4.4.3 Developed interfacial area ratio . 18
4.5 Material ratio functions and related parameters . 19
4.5.1 Areal material ratio . 19
4.5.2 Inverse areal material ratio . 19
4.5.3 Material ratio height difference . 20
4.5.4 Areal parameter for stratified surfaces . 21
4.5.5 Areal material probability parameters . 23
4.5.6 Void volume . 24
4.5.7 Material volume . 25
4.6 Gradient distribution . 26
4.7 Multiscale geometric (fractal) methods .28
4.7.1 Morphological volume-scale function .28
4.7.2 Relative area . .29
4.7.3 Relative length.29
4.7.4 Scale of observation .29
4.7.5 Volume-scale fractal complexity .29
4.7.6 Area-scale fractal complexity .29
4.7.7 Length-scale fractal complexity .30
4.7.8 Crossover scale .30
5 Feature parameters .30
5.1 General .30
5.2 Type of texture feature . 31
5.3 Segmentation . 32
5.4 Determining significant features . 32
iii
ISO 25178-2:2021(E)
5.5 Section of feature attributes .33
5.6 Attribute statistics .34
5.7 Feature characterization convention .34
5.8 Named feature parameters . 35
5.8.1 General . 35
5.8.2 Density of peaks . 35
5.8.3 Density of pits . 35
5.8.4 Arithmetic mean peak curvature . 35
5.8.5 Arithmetic mean pit curvature . 36
5.8.6 Five-point peak height . 36
5.8.7 Five-point pit depth . 36
5.8.8 Ten-point height . 36
5.9 Additional feature parameters . 37
5.9.1 General . 37
5.9.2 Shape parameters. 37
Annex A (informative) Multiscale geometric (fractal) methods.40
Annex B (informative) Determination of areal parameters for stratified functional surfaces .47
Annex C (informative) Basis for areal surface texture standards — Timetable of events .50
Annex D (informative) Implementation details .51
Annex E (informative) Changes made to the 2012 edition of this document .55
Annex F (informative) Summary of areal surface texture parameters .57
Annex G (informative) Specification analysis workflow .59
Annex H (informative) Overview of profile and areal standards in the GPS matrix model .60
Annex I (informative) Relation with the GPS matrix .61
Bibliography .62
iv
ISO 25178-2:2021(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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 213, Dimensional and geometrical product
specifications and verification, in collaboration with the European Committee for Standardization (CEN)
Technical Committee CEN/TC 290, Dimensional and geometrical product specification and verification, in
accordance with the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
This second edition cancels and replaces the first edition (ISO 25178-2:2012), which has been technically
revised. The main changes to the previous edition are described in Annex E.
A list of all parts in the ISO 25178 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
v
ISO 25178-2:2021(E)
Introduction
This document is a geometrical product specification (GPS) standard and is to be regarded as a general
GPS standard (see ISO 14638). It influences the chain link B of the chains of standards on areal surface
texture.
The ISO/GPS matrix model given in ISO 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 the specifications made in accordance with this
document, unless otherwise indicated.
For more detailed information of the relation of this document to other standards and the GPS matrix
model, see Annex I. An overview of standards on profiles and areal surface texture is given in Annex H.
This document develops the terminology, concepts and parameters for areal surface texture.
Throughout this document, parameters are written as abbreviations with lower-case suffixes (as in Sq
or Vmp) when used in a sentence and are written as symbols with subscripts (as in S or V ) when used
q mp
in formulae, to avoid misinterpretations of compound letters as an indication of multiplication between
quantities in formulae. The parameters in lower case are used in product documentation, drawings and
data sheets.
Parameters are calculated from coordinates defined in the specification coordinate system, or from
derived quantities (e.g. gradient, curvature).
Parameters are defined for the continuous case, but in verification they are calculated on discrete
surfaces such as the primary extracted surface.
A short history of the work done on areal surface texture can be found in Annex C.
vi
INTERNATIONAL STANDARD ISO 25178-2:2021(E)
Geometrical product specifications (GPS) — Surface
texture: Areal —
Part 2:
Terms, definitions and surface texture parameters
1 Scope
This document specifies parameters for the determination of surface texture by areal methods.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 16610-1:2015, Geometrical product specifications (GPS) — Filtration — Part 1: Overview and basic
concepts
ISO 17450-1:2011, Geometrical product specifications (GPS) — General concepts — Part 1: Model for
geometrical specification and verification
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16610-1:2015 and
ISO 17450-1:2011 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1 General terms
3.1.1
skin model
model of the physical interface of the workpiece with its environment
[SOURCE: ISO 17450-1:2011, 3.2.2]
3.1.2
surface texture
geometrical irregularities contained in a scale-limited surface (3.1.9)
Note 1 to entry: Surface texture does not include those geometrical irregularities contributing to the form or
shape of the surface.
ISO 25178-2:2021(E)
3.1.3
mechanical surface
boundary of the erosion, by a sphere of radius r, of the locus of the centre of an ideal tactile sphere, also
with radius r, rolled over the skin model (3.1.1) of a workpiece
[SOURCE: ISO 14406:2010, 3.1.1, modified — Notes to entry removed.]
3.1.3.1
electromagnetic surface
surface obtained by the electromagnetic interaction with the skin model (3.1.1) of a workpiece
[SOURCE: ISO 14406:2010, 3.1.2, modified — Notes to entry removed.]
3.1.3.2
auxiliary surface
surface, other than mechanical or electromagnetic, obtained by an interaction with the skin model
(3.1.1) of a workpiece
Note 1 to entry: A mathematical surface (softgauge) is an example of an auxiliary surface.
Note 2 to entry: Other physical measurement principles, such as tunnelling microscopy or atomic force
microscopy, can also serve as an auxiliary surface. See Figure 1 and Annex G.
3.1.4
specification coordinate system
system of coordinates in which surface texture parameters are specified
Note 1 to entry: If the nominal form of the surface is a plane (or portion of a plane), it is common (practice) to
use a rectangular coordinate system in which the axes form a right-handed Cartesian set, the x-axis and the
y-axis also lying on the nominal surface, and the z-axis being in an outward direction (from the material to the
surrounding medium). This convention is adopted throughout the rest of this document.
3.1.5
primary surface
surface portion obtained when a surface portion is represented as a specified primary mathematical
model with specified nesting index (3.1.6.4)
Note 1 to entry: In this document, an S-filter is used to derive the primary surface. See Figure 1.
[SOURCE: ISO 16610-1:2015, 3.3, modified — Note 1 to entry added.]
Figure 1 — Definition of primary surface
ISO 25178-2:2021(E)
3.1.5.1
primary extracted surface
finite set of data points sampled from the primary surface (3.1.5)
[SOURCE: ISO 14406:2010, 3.7, modified — Notes to entry removed.]
3.1.6
surface filter
filtration operator applied to a surface
3.1.6.1
S-filter
surface filter (3.1.6) which removes small-scale lateral components from the surface, resulting in the
primary surface (3.1.5)
3.1.6.2
L-filter
surface filter (3.1.6) which removes large-scale lateral components from the primary surface (3.1.5) or
S-F surface (3.1.7)
Note 1 to entry: When the L-filter is not tolerant to form, it needs to be applied on an S-F surface; when it is
tolerant to form, it can be applied either on the primary surface or on an S-F surface.
3.1.6.3
F-operation
operation which removes form from the primary surface (3.1.5)
Note 1 to entry: Some F-operations (such as association) have a very different action to that of filtration. Though
their action can limit the larger lateral scales of a surface, this action is very fuzzy. It is represented in Figure 2
using the same convention as for a filter.
Note 2 to entry: Some L-filters are not tolerant to form and require an F-operation first as a prefilter before being
applied.
Note 3 to entry: An F-operation can be a filtration operation such as a robust Gaussian filter.
3.1.6.4
nesting index
N , N , N
is ic if
number or set of numbers indicating the relative level of nesting for a particular primary mathematical
model
[SOURCE: ISO 16610-1:2015, 3.2.1, modified — definition revised and notes to entry removed.]
3.1.7
S-F surface
surface derived from the primary surface (3.1.5) by removing the form using an F-operation (3.1.6.3)
Note 1 to entry: Figure 2 illustrates the relationship between the S-F surface and the S-filter and F-operation.
Note 2 to entry: If filtered with N nesting index to remove the shortest wavelengths from the surface, the surface
is
is equivalent to a “primary surface”. In this case, N is the areal equivalent of the λs cut-off. See key reference 4 in
is
Figure 2 and Annex G.
Note 3 to entry: If filtered with N nesting index to separate longer from shorter wavelengths, the surface is
ic
equivalent to a “waviness surface”. In this case, N is the areal equivalent of the λc cut-off. See key reference 5 in
ic
Figure 2 and Annex G.
Note 4 to entry: The concepts of “roughness” or “waviness” are less important in areal surface texture than in
profile surface texture. Some surfaces can exhibit roughness in one direction and waviness in the perpendicular
direction. That is why the concepts of S-L surface and S-F surface are preferred in this document.
ISO 25178-2:2021(E)
3.1.8
S-L surface
surface derived from the S-F surface (3.1.7) by removing the large-scale components using an L-filter
(3.1.6.2)
Note 1 to entry: Figure 2 illustrates the relationship between the S-L surface and the S-filter and L-filter.
Note 2 to entry: If the S-filter nesting index N is chosen to remove the shortest wavelengths from the surface
is
and the L-filter nesting index N is chosen in order to separate longer from shorter wavelengths, the surface is
ic
equivalent to a “roughness surface”. See key reference 6 in Figure 2 and Annex G.
Note 3 to entry: A series of S-L surfaces can be generated with narrow bandwidth using an S-filter and an L-filter
of close nesting indices (or equal), in order to achieve a multiscale exploration of the surface. See Figure 3.
Key
1 S-filter
2 L-filter
3 F-operation
4 S-F surface
5 S-F surface
6 S-L surface
A small scale
B large scale
Figure 2 — Relationships between the S-filter, L-filter, F-operation and S-F and S-L surfaces
ISO 25178-2:2021(E)
Key
S S-filter
L L-filter
A small scale
B large scale
Figure 3 — Example of bandpass filters used to generate a bank of S-L surfaces
3.1.9
scale-limited surface
S-F surface (3.1.7) or S-L surface (3.1.8)
3.1.10
reference surface
surface associated to the scale-limited surface (3.1.9) according to a criterion
Note 1 to entry: This reference surface is used as the origin of heights for surface texture parameters.
EXAMPLE Plane, cylinder and sphere.
3.1.11
evaluation area
A
A
portion of the scale-limited surface (3.1.9) for specifying the area under evaluation
Note 1 to entry: See ISO 25178-3 for more information.
Note 2 to entry: Throughout this document, the symbol A is used for the numerical value of the evaluation area
and the symbol A for the domain (of integration or definition).
3.2 Geometrical parameter terms
3.2.1
field parameter
parameter defined from all the points on a scale-limited surface (3.1.9)
Note 1 to entry: Field parameters are defined in Clause 4.
3.2.2
feature parameter
parameter defined from a subset of predefined topographic features from the scale-limited surface
(3.1.9)
Note 1 to entry: Feature parameters are defined in Clause 5.
ISO 25178-2:2021(E)
3.2.3
V-parameter
material volume or void volume field parameter (3.2.1)
3.2.4
S-parameter
field parameter (3.2.1) or feature parameter (3.2.2) that is not a V-parameter (3.2.3)
3.2.5
height
ordinate value
z(x,y)
signed normal distance from the reference surface (3.1.10) to the scale-limited surface (3.1.9)
Note 1 to entry: Throughout this document, the term “height” is either used for a distance or for an absolute
coordinate. For example, Sz, maximum height, is a distance and Sp, maximum peak height, is an absolute height.
3.2.5.1
depth
opposite value of height (3.2.5)
3.2.6
local gradient vector
∂zx(), y ∂zx(), y
,
∂x ∂y
first derivative along x and y of the scale-limited surface (3.1.9) at position (x, y)
Note 1 to entry: See Annex D for implementation details.
3.2.7
local mean curvature
arithmetic mean of the principal curvatures at position (x, y)
Note 1 to entry: Principal curvatures are two numbers, k and k , representing the maximum and minimum
1 2
kk+
curvatures at a point. The local mean curvature is therefore .
Note 2 to entry: See Annex D for implementation details.
3.2.8
material ratio
M (c)
r
ratio of the area A of the surface portion intersected by a plane at level c, to the evaluation area (3.1.11),
c
A
Note 1 to entry: The curve representing material ratio as a function of the level is also called Abbott Firestone
curve.
Note 2 to entry: The level c is usually defined as a height taken with respect to a reference c . By default, the
reference is at the highest point of the surface. In the first edition of this document, the reference height was set
to the reference surface (3.1.10).
Note 3 to entry: The material ratio may be given as a percentage or a value between 0 and 1.
Note 4 to entry: See Figure 4 and Formula (1).
Note 5 to entry: See Annex D for the determination of the material ratio curve.
Ac()
c
Mc()= .100 % (1)
r
A
ISO 25178-2:2021(E)
Key
c intersecting level
c reference height
A areal portions intersected by plane at height c
c
Figure 4 — Area of the surface portion intersected by plane at level c
3.2.9
areal material ratio curve
material ratio function
function representing the areal material ratio (3.2.8) of the scale-limited surface (3.1.9) as a function of
a level c
Note 1 to entry: This function can be interpreted as the cumulative probability function of the ordinates z(x,y)
within the evaluation area. See Annex D.
Note 2 to entry: See Figure 5.
Key
A height
B areal material ratio
C intersection level c
D material ratio at level c
Figure 5 — Material ratio curve
ISO 25178-2:2021(E)
3.2.10
inverse material ratio
C(p)
intersecting level at which a given areal material ratio (3.2.8) p is satisfied
Note 1 to entry: See Formula (2).
−1
Cp()=Mp() (2)
r
3.2.11
height density curve
height density function
hc()
curve representing the density of points laying at level c on the scale-limited surface (3.1.9)
Note 1 to entry: When represented as a histogram with bins, the percentage per bin depends on their width.
Note 2 to entry: See Figure 6 and Formula (3).
dM c
()
r
hc =− (3)
()
dc
Key
A height
B density
Figure 6 — Height density curve
3.2.12
core surface
scale-limited surface (3.1.9) excluding core-protruding hills and dales
Note 1 to entry: The terms hills and dales in this definition refer to 3.3.1.2 and 3.3.2.2 but are defined by graphical
construction. See Figure 14 and Annex B.3.
3.2.13
areal material probability curve
representation of the areal material ratio curve (3.2.9) in which the areal material area ratio is expressed
as a Gaussian probability in standard deviation values, plotted linearly on the horizontal axis
Note 1 to entry: This scale is expressed linearly in standard deviations according to the Gaussian distribution. In
this scale, the areal material ratio curve of a Gaussian distribution becomes a straight line. For stratified surfaces
composed of two Gaussian distributions, the areal material probability curve will exhibit two linear regions (see
E and F in Figure 7).
ISO 25178-2:2021(E)
Key
A amplitude
B reference line
C material ratio expressed as a Gaussian probability in per cent
D material ratio expressed as a Gaussian probability in standard deviation
E plateau region
F dale region
G outlying hills (possibly including debris or dirt particles)
H outlying dales (possibly deep scratches)
I unstable region (curvature) introduced at the plateau-to-dale transition point based on the combination of two
distributions horizontal axis s is the standard deviation
Figure 7 — Areal material probability curve
3.2.14
autocorrelation function
f (t , t )
ACF x y
function which describes the correlation between a surface and the same surface translated by (t , t )
x y
Note 1 to entry: The autocorrelation used here is normalized between −1 and 1. The maximum value is always
met but the minimum may not always be at −1, it depends on the surface (it may be −0,76).
Note 2 to entry: See Formula (4).
zx(),,yz xt++yt dxdy
()
xy
∫∫
B
B
ft ,t = (4)
()
ACFx y
zx(), ydxdy
∫∫∫
A
A
where B is the intersecting area of the two surfaces at shifts t and t .
x y
3.2.15
Fourier transformation
F(p, q)
operator which transforms ordinate values (3.2.5) of the scale-limited surface (3.1.9) into Fourier space
Note 1 to entry: The Fourier transformation defined here is using a limited support A , therefore it approximates
the mathematical function called Fourier transformation which has an infinite support.
Note 2 to entry: See Formula (5).
ISO 25178-2:2021(E)
−+2ipπ xqy
()
Fp(),,qz= ()xy edxdy (5)
∫∫
A
where
p and q are spatial frequencies in x and y direction, respectively;
i is the imaginary unit.
3.2.15.1
angular spectrum
F (r, θ)
AS
Fourier transformation (3.2.15) expressed in polar coordinates, with respect to a reference direction
θ in the plane of the evaluation area (3.1.11)
ref
Note 1 to entry: The positive x-axis is defined as the zero angle.
Note 2 to entry: The angle is positive in an anticlockwise direction from the x-axis.
Note 3 to entry: See Formula (6).
Fr(),cθθ=−Fr() os()θθ,sr in()−θ (6)
AS refref
where
r is a spatial frequency;
θ is the specified direction;
F is the Fourier transformation.
3.2.15.2
angular amplitude density
angular amplitude distribution
f (θ)
AAD
integrated amplitude of the angular spectrum (3.2.15.1) for a given direction θ
Note 1 to entry: The term “density” refers to the value at a given angle and the term “distribution” refers to the
graph representing the values for all angles.
Note 2 to entry: See Formula (7).
R
fFθθ= rr, dr (7)
() ()
AAD AS
∫
R
where
r is a spatial frequency;
R to R (R < R ) is the range of integration of the frequencies in the radial direction;
1 2 1 2
θ is the specified direction;
F is the angular spectrum function.
AS
ISO 25178-2:2021(E)
3.2.15.3
angular power density
angular power distribution
f (θ)
APD
integrated squared amplitude of the angular spectrum (3.2.15.1) for a given direction θ
Note 1 to entry: The term “density” refers to the value at a given angle and the term “distribution” refers to the
graph representing the values for all angles.
Note 2 to entry: See Formula (8).
R
fF()θθ= ()rr, dr (8)
APDAS
∫
R
where
r is a spatial frequency;
R to R (R < R )is the range of integration of the frequencies in the radial direction;
1 2 1 2
θ is the specified direction;
F is the angular spectrum function.
AS
3.2.16
areal power spectral density
f
APSD
squared magnitude of the Fourier transformation (3.2.15) using an appropriate weighting function
Note 1 to entry: The areal power spectral density describes surface texture in a spatial frequency context
allowing the waviness or ripples in the surface to be described and controlled.
Note 2 to entry: See Formula (9).
Note 3 to entry: The areal power spectral density can also be calculated from a polar spectrum. It is usually the
case when exploring optics surfaces (see ISO 10110-8).
fp,,q = Fp q (9)
() ()
APSD
A
3.3 Geometrical feature terms
3.3.1
peak
point on the surface which is higher than all other points within a neighbourhood of that point
Note 1 to entry: There is a theoretical possibility of a plateau. In practice, this can be avoided by the use of an
infinitesimal tilt.
Note 2 to entry: See Figure 8.
3.3.1.1
hill
region around a peak (3.3.1) such that all maximal upward paths end at the
peak
Note 1 to entry: This definition is used for feature parameters.
Note 2 to entry: See Figure 8.
ISO 25178-2:2021(E)
3.3.1.2
hill
outwardly directed (from material to surrounding medium) contiguous portion of
the scale-limited surface (3.1.9) above the reference surface (3.1.10)
Note 1 to entry: This definition is used for field parameters.
Note 2 to entry: The reference surface is usually the mean plane of the scale-limited surface.
3.3.1.3
course line
curve separating adjacent hills (3.3.1.1)
Note 1 to entry: See Figure 8.
3.3.2
pit
point on the surface which is lower than all other points within a neighbourhood of that point
Note 1 to entry: There is a theoretical possibility of a plateau. In practice, this can be avoided by the use of an
infinitesimal tilt.
Note 2 to entry: See Figure 9.
3.3.2.1
dale
region around a pit (3.3.2) such that all maximal downward paths end at
the pit
Note 1 to entry: This definition is used for feature parameters.
Note 2 to entry: See Figure 9.
3.3.2.2
dale
inwardly directed (from surrounding medium to material) contiguous portion
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.
Loading comments...