ISO - Cover page

Foreword

Introduction

1 Scope

2 Normative references

3 Terms and definitions

3.1 General terms

3.2 Geometrical parameter terms

3.3 Geometrical feature terms

4 Field parameters

4.1 General

4.2 Height parameters

4.2.1 General

4.2.2 Root mean square height

4.2.3 Skewness

4.2.4 Kurtosis

4.2.5 Maximum peak height

4.2.6 Maximum pit depth

4.2.7 Maximum height

4.2.8 Arithmetic mean height

4.3 Spatial parameters

4.3.1 General

4.3.2 Autocorrelation length

4.3.3 Texture aspect ratio

4.3.4 Texture direction

4.3.5 Dominant spatial wavelength

4.4 Hybrid parameters

4.4.1 General

4.4.2 Root mean square gradient

4.4.3 Developed interfacial area ratio

4.5 Material ratio functions and related parameters

4.5.1 Areal material ratio

4.5.2 Inverse areal material ratio

4.5.3 Material ratio height difference

4.5.4 Areal parameter for stratified surfaces

4.5.5 Areal material probability parameters

4.5.6 Void volume

4.5.7 Material volume

4.6 Gradient distribution

4.7 Multiscale geometric (fractal) methods

4.7.1 Morphological volume-scale function

4.7.2 Relative area

4.7.3 Relative length

4.7.4 Scale of observation

4.7.5 Volume-scale fractal complexity

4.7.6 Area-scale fractal complexity

4.7.7 Length-scale fractal complexity

4.7.8 Crossover scale

5 Feature parameters

5.1 General

5.2 Type of texture feature

5.3 Segmentation

5.4 Determining significant features

5.5 Section of feature attributes

5.6 Attribute statistics

5.7 Feature characterization convention

5.8 Named feature parameters

5.8.1 General

5.8.2 Density of peaks

5.8.3 Density of pits

5.8.4 Arithmetic mean peak curvature

5.8.5 Arithmetic mean pit curvature

5.8.6 Five-point peak height

5.8.7 Five-point pit depth

5.8.8 Ten-point height

5.9 Additional feature parameters

5.9.1 General

5.9.2 Shape parameters

Annex A (informative) Multiscale geometric (fractal) methods

Annex B (informative) Determination of areal parameters for stratified functional surfaces

Annex C (informative) Basis for areal surface texture standards — Timetable of events

Annex D (informative) Implementation details

Annex E (informative) Changes made to the 2012 edition of this document

Annex F (informative) Summary of areal surface texture parameters

Annex G (informative) Specification analysis workflow

Annex H (informative) Overview of profile and areal standards in the GPS matrix model

Annex I (informative) Relation with the GPS matrix

Bibliography

ISO 25178-2:2021

Gulf Standard GSO ISO 25178-2:2024

GSO ISO 25178-2:2024 Gulf Standard

GSO ISO 25178-2:2024

ISO 25178-2:2021

مواصفة قياسية خليجية

المواصفات الفنية للشكل الهندسي للمنتج (GPS) – بنية السطح - المساحية – الجزء الثاني : المصطلحات والتعاريف وسمات بنية السطح

Gulf Standard

Geometrical product specifications (GPS) — Surface texture: Areal — Part 2: Terms, definitions and surface texture parameters

ICS:

17.040.20

English Language – اللغةالإنجليزية Edition 2 – 25/04/2024 – 2 الطبعة

هذه الوثيقة محمية بالقانون COPYRIGHT PROTECTED DOCUMENT
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ISO 25178-2:2021

Gulf Standard GSO ISO 25178-2:2024

GSO ISO 25178-2:2024 Gulf Standard

تقديم خليجي

هيئة التقييس لدول مجلس التعاون لدول الخليج العربية هيئة إقليمية تضم في عضويتها أجهزة التقييس الوطنية في الدول الأعضاء ، ومن مهام الهيئة إعداد المواصفات القياسية واللوائح الفنية الخليجية بواسطة لجان فنية متخصصة.

قرر المجلس الفني لهيئة التقييس لدول مجلس التعاون لدول الخليج العربية في الاجتماع الـ (58) بتاريخ 1445/10/16 هـ ،الموافق 2024/04/25م اعتماد تحديث المواصفة القياسية الخليجية رقم GSO ISO 25178-2:2024 وعنوانها "المواصفات الفنية للشكل الهندسي للمنتج (GPS) – بنية السطح - المساحية – الجزء الثاني : المصطلحات والتعاريف وسمات بنية السطح" باللغة الانجليزية التي تم دراستها وتبنيها عن المنظمة الدولية للتقييس رقم ISO 25178-2:2021 بدون إدخال تعديلات فنية عليها ضمن برنامج عمل اللجنة الفنية الخليجية لمواصفات المقاييس (TC04) المدرجة في خطة سلطنة عمان . على أن تلغي وتحل محل المواصفة القياسية رقم GSO ISO 25178-2:2013 .

Gulf Foreword

GCC Standardization Organization (GSO) is a regional organization which consists of the national standardization bodies of GCC member states. One of GSO main functions is to issue gulf standards and technical regulations through specialized technical committees.

GSO Technical Council in its meeting number (58) held on 16/10/1445 H, which corresponds to 25/04/2024, has approved the update of Gulf Standard GSO ISO 25178-2:2024 titled "Geometrical product specifications (GPS) — Surface texture: Areal — Part 2: Terms, definitions and surface texture parameters" in English language which was studied and adopted from International Organization for Standardization Standard ISO 25178-2:2021 without any technical modifications through the technical program of GSO Technical Committee for Metrology (TC04) in OMAN schedule . This document will cancel and replace the Gulf Standard GSO ISO 25178-2:2013.

ISO 25178-2:2021(en)

Gulf Standard GSO ISO 25178-2:2024

GSO ISO 25178-2:2024 Gulf Standard

	International Standard ISO 25178-2
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(en)	Second edition 2021-12 © ISO 2021

ISO 25178-2:2021(en)

Gulf Standard GSO ISO 25178-2:2024

GSO ISO 25178-2:2024 Gulf Standard

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

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CH-1214 Vernier, Geneva

Tel. + 41 22 749 01 11

E-mail copyright@iso.org

Website www.iso.org

Published in Switzerland

ISO 25178-2:2021(en)

Gulf Standard GSO ISO 25178-2:2024

GSO ISO 25178-2:2024 Gulf Standard

Contents Page

Foreword

Introduction

1 Scope

2 Normative references

3 Terms and definitions

3.1 General terms

3.2 Geometrical parameter terms

3.3 Geometrical feature terms

4 Field parameters

4.1 General

4.2 Height parameters

4.2.1 General

4.2.2 Root mean square height

4.2.3 Skewness

4.2.4 Kurtosis

4.2.5 Maximum peak height

4.2.6 Maximum pit depth

4.2.7 Maximum height

4.2.8 Arithmetic mean height

4.3 Spatial parameters

4.3.1 General

4.3.2 Autocorrelation length

4.3.3 Texture aspect ratio

4.3.4 Texture direction

4.3.5 Dominant spatial wavelength

4.4 Hybrid parameters

4.4.1 General

4.4.2 Root mean square gradient

4.4.3 Developed interfacial area ratio

4.5 Material ratio functions and related parameters

4.5.1 Areal material ratio

4.5.2 Inverse areal material ratio

4.5.3 Material ratio height difference

4.5.4 Areal parameter for stratified surfaces

4.5.5 Areal material probability parameters

4.5.6 Void volume

4.5.7 Material volume

4.6 Gradient distribution

4.7 Multiscale geometric (fractal) methods

4.7.1 Morphological volume-scale function

4.7.2 Relative area

4.7.3 Relative length

4.7.4 Scale of observation

4.7.5 Volume-scale fractal complexity

4.7.6 Area-scale fractal complexity

4.7.7 Length-scale fractal complexity

4.7.8 Crossover scale

5 Feature parameters

5.1 General

5.2 Type of texture feature

5.3 Segmentation

5.4 Determining significant features

5.5 Section of feature attributes

5.6 Attribute statistics

5.7 Feature characterization convention

5.8 Named feature parameters

5.8.1 General

5.8.2 Density of peaks

5.8.3 Density of pits

5.8.4 Arithmetic mean peak curvature

5.8.5 Arithmetic mean pit curvature

5.8.6 Five-point peak height

5.8.7 Five-point pit depth

5.8.8 Ten-point height

5.9 Additional feature parameters

5.9.1 General

5.9.2 Shape parameters

Annex A (informative) Multiscale geometric (fractal) methods

Annex B (informative) Determination of areal parameters for stratified functional surfaces

Annex C (informative) Basis for areal surface texture standards — Timetable of events

Annex D (informative) Implementation details

Annex E (informative) Changes made to the 2012 edition of this document

Annex F (informative) Summary of areal surface texture parameters

Annex G (informative) Specification analysis workflow

Annex H (informative) Overview of profile and areal standards in the GPS matrix model

Annex I (informative) Relation with the GPS matrix

Bibliography

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.

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 Sq or Vmp) when used 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.

ISO 25178-2:2021(en)

Gulf Standard GSO ISO 25178-2:2024

GSO ISO 25178-2:2024 Gulf Standard

International Standard ISO 25178-2:2021(en)

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

<of a workpiece> model of the physical interface of the workpiece with its environment

[SOURCE: ISO 17450-1:2011, 3.2.2]

3.1.2

surface texture

<areal> 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.

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)

Figure 1 — Definition of primary surface

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.]

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

Nis, Nic, Nif

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 Nis nesting index to remove the shortest wavelengths from the surface, the surface is equivalent to a “primary surface”. In this case, Nis is the areal equivalent of the λs cut-off. See key reference 4 in Figure 2 and Annex G.

Note 3 to entry: If filtered with Nic nesting index to separate longer from shorter wavelengths, the surface is equivalent to a “waviness surface”. In this case, Nic is the areal equivalent of the λc cut-off. See key reference 5 in 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.

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 Nis is chosen to remove the shortest wavelengths from the surface and the L-filter nesting index Nic is chosen in order to separate longer from shorter wavelengths, the surface is 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.

Figure 2 — Relationships between the S-filter, L-filter, F-operation and S-F and S-L surfaces

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 3 — Example of bandpass filters used to generate a bank of S-L surfaces

Key

S	S-filter
L	L-filter
A	small scale
B	large scale

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 texture> 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

\tilde{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

\tilde{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.

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

(\frac{\partial z (x, y)}{\partial x}, \frac{\partial z (x, y)}{\partial 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, k1 and k2, representing the maximum and minimum curvatures at a point. The local mean curvature is therefore

\frac{k_{1} + k_{2}}{2}

Note 2 to entry: See Annex D for implementation details.

3.2.8

material ratio

Mr (c)

ratio of the area

A_{c}

of the surface portion intersected by a plane at level c, to the evaluation area (3.1.11), 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 c0. 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.

M_{r} (c) = \frac{A_{c} (c)}{A} .100 %

(1)

Figure 4 — Area of the surface portion intersected by plane at level c

Key

c	intersecting level
c0	reference height
Ac	areal portions intersected by plane at height 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.

Figure 5 — Material ratio curve

Key

A	height
B	areal material ratio
C	intersection level c
D	material ratio at level c

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).

C (p) = M_{r}^{- 1} (p)

(2)

3.2.11

height density curve

height density function

h (c)

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).

h (c) = - \frac{d M_{r} (c)}{d c}

(3)

Figure 6 — Height density curve

Key

A	height
B	density

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).

Figure 7 — Areal material probability curve

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

3.2.14

autocorrelation function

fACF(tx, ty)

function which describes the correlation between a surface and the same surface translated by (tx, ty)

where

\tilde{B}

is the intersecting area of the two surfaces at shifts tx and ty.

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).

f_{ACF} (t_{x}, t_{y}) = \frac{\frac{1}{B} \iint_{\tilde{B}} z (x, y) z (x + t_{x}, y + t_{y}) d x d y}{\frac{1}{A} \iint_{\tilde{A}} z^{2} (x, y) d x d y}

(4)

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

where

	p and q	are spatial frequencies in x and y direction, respectively;
	i	is the imaginary unit.

Note 1 to entry: The Fourier transformation defined here is using a limited support

\tilde{A}

, therefore it approximates the mathematical function called Fourier transformation which has an infinite support.

Note 2 to entry: See Formula (5).

F (p, q) = \iint_{\tilde{A}} z (x, y) e^{- 2 i π (p x + q y)} d x d y

(5)

3.2.15.1

angular spectrum

FAS(r, θ)

Fourier transformation (3.2.15) expressed in polar coordinates, with respect to a reference direction θref in the plane of the evaluation area (3.1.11)

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).

F_{AS} (r, θ) = F (r \cos (θ - θ_{ref}), r \sin (θ - θ_{ref}))

(6)

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

fAAD(θ)

integrated amplitude of the angular spectrum (3.2.15.1) for a given direction θ

where

	r	is a spatial frequency;
	R1 to R2 (R1 < R2)	is the range of integration of the frequencies in the radial direction;
	θ	is the specified direction;
	FAS	is the angular spectrum function.

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).

f_{AAD} (θ) = \int_{R_{1}}^{R_{2}} | F_{AS} (r, θ) | r d r

(7)

3.2.15.3

angular power density

angular power distribution

fAPD(θ)

integrated squared amplitude of the angular spectrum (3.2.15.1) for a given direction θ

where

	r	is a spatial frequency;
	R1 to R2 (R1 < R2)	is the range of integration of the frequencies in the radial direction;
	θ	is the specified direction;
	FAS	is the angular spectrum function.

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).

f_{APD} (θ) = \int_{R_{1}}^{R_{2}} F_{AS}^{2} (r, θ) r d r

(8)

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).

f_{APSD} (p, q) = \frac{1}{A} {| F (p, q) |}^{2}

(9)

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

<watershed segmentation> 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.

3.3.1.2

hill

<reference plane> 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

<watershed segmentation> 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

<reference plane> inwardly directed (from surrounding medium to material) contiguous portion of the scale-limited surface (3.1.9) below 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.

3.3.2.3

ridge line

curve separating adjacent dales (3.3.2.1)

Note 1 to entry: See Figure 9.

3.3.3

saddle

point or set of points on the scale-limited surface (3.1.9) where ridge lines (3.3.2.3) and course lines (3.3.1.3) cross

3.3.3.1

saddle point

saddle (3.3.3) consisting of one point

Figure 8 — Representation of a hill in the context of watershed segmentation with the peak and the course line

Key

A	peak
B	hill
C	course line

Figure 9 — Representation of a dale in the context of watershed segmentation with the pit and the ridge line

Key

A	pit
B	dale
C	ridge line

3.3.4

motif

hill (3.3.1.1) or dale (3.3.2.1) defined with watershed segmentation

Note 1 to entry: The term motif is used to designate an areal feature obtained by segmentation.

Note 2 to entry: The term motif as defined on a profile in ISO 12085 is a cross-section of a dale.

3.3.5

topographic feature

areal feature, line feature or point feature on a scale-limited surface (3.1.9)

3.3.5.1

areal feature

hill (3.3.1.1) or dale (3.3.2.1)

3.3.5.2

line feature

course line (3.3.1.3) or ridge line (3.3.2.3)

3.3.5.3

point feature

peak (3.3.1), pit (3.3.2) or saddle point (3.3.3.1)

3.3.6

contour line

line on the surface consisting of adjacent points of equal height

3.3.7

segmentation

method which partitions a scale-limited surface (3.1.9) into distinct features

3.3.7.1

segmentation function

function which splits a set of “events” into two distinct sets called the significant events and the insignificant events and which satisfies the three segmentation properties

Note 1 to entry: Examples of events include ordinate values and point features.

Note 2 to entry: A full mathematical description of the segmentation function and the three segmentation properties can be found in Reference [26] and ISO 16610-85.

3.3.8

change tree

graph where each contour line (3.3.6) is plotted as a point against height in such a way that adjacent contour lines are adjacent points on the graph

Note 1 to entry: Peaks and pits are represented on a change tree by the end of lines. Saddle points are represented on a change tree by joining lines. See ISO 16610-85 and Annex A for more details concerning change trees.

3.3.8.1

pruning

method to simplify a change tree (3.3.8) in which lines from peaks (3.3.1) [or pits (3.3.2)] to their nearest connected saddle points (3.3.3.1) are removed

3.3.8.2

hill local height

difference between the height of a peak (3.3.1) and the height of the nearest connected saddle point (3.3.3.1) on the change tree (3.3.8)

3.3.8.3

dale local depth

difference between the height of the nearest connected saddle point (3.3.3.1) on the change tree (3.3.8) and the height of a pit (3.3.2)

3.3.8.4

Wolf pruning

pruning where lines in the change tree (3.3.8) are removed, starting from the peak (3.3.1) [pit (3.3.2)] with the smallest hill local height (3.3.8.2) [dale local depth (3.3.8.3)] up to the peak (pit) with a specified hill local height (3.3.8.2) [dale local depth (3.3.8.3)]

Note 1 to entry: The peak local heights and pit local depths change during Wolf pruning as removing lines from a change tree also removes the associated saddle point.

3.3.9

height discrimination

minimum hill local height (3.3.8.2) or dale local depth (3.3.8.3) of the scale-limited surface (3.1.9) which should be considered during Wolf pruning (3.3.8.4)

Note 1 to entry: The height discrimination is specified by default as a percentage of Sz (4.2.7).

ISO 25178-2:2021(en)

Gulf Standard GSO ISO 25178-2:2024

GSO ISO 25178-2:2024 Gulf Standard

Bibliography

[1]		ISO 4287, Geometrical Product Specifications (GPS) — Surface texture: Profile method — Terms, definitions and surface texture parameters
[2]		ISO 8015, Geometrical product specifications (GPS) — Fundamentals — Concepts, principles and rules
[3]		ISO 12085, Geometrical Product Specifications (GPS) — Surface texture: Profile method — Motif parameters
[4]		ISO 12179, Geometrical product specifications (GPS) — Surface texture: Profile method — Calibration of contact (stylus) instruments
[5]		ISO 13565-2, Geometrical Product Specifications (GPS) — Surface texture: Profile method; Surfaces having stratified functional properties — Part 2: Height characterization using the linear material ratio curve
[6]		ISO 13565-3:1998, Geometrical Product Specifications (GPS) — Surface texture: Profile method; Surfaces having stratified functional properties — Part 3: Height characterization using the material probability curve
[7]		ISO 14253-1, Geometrical product specifications (GPS) — Inspection by measurement of workpieces and measuring equipment — Part 1: Decision rules for verifying conformity or nonconformity with specifications
[8]		ISO 14406:2010, Geometrical product specifications (GPS) — Extraction
[9]		ISO 14638, Geometrical product specifications (GPS) — Matrix model
[10]		ISO 16610-20, Geometrical product specifications (GPS) — Filtration — Part 20: Linear profile filters: Basic concepts
[11]		ISO 16610-61, Geometrical product specification (GPS) — Filtration — Part 61: Linear areal filters — Gaussian filters
[12]		ISO 16610-85, Geometrical product specifications (GPS) — Filtration — Part 85: Morphological areal filters: Segmentation
[13]		ISO 21920-1, Geometrical product specifications (GPS) — Surface texture: Profile — Part 1: Indication of surface texture
[14]		ISO 21920-2, Geometrical product specifications (GPS) — Surface texture: Profile — Part 2: Term, definitions and surface texture parameters
[15]		ISO 21920-3, Geometrical product specifications (GPS) — Surface texture: Profile — Part 3: Specification operators
[16]		ISO 25178-3, Geometrical product specifications (GPS) — Surface texture: Areal — Part 3: Specification operators

Fundamental references

[17]		Stout K.J. et al. The development of methods for the characterisation of roughness in three dimensions. European Report EUR 15178 EN
[18]		Blunt L., & Jiang X. (2003) Advanced techniques for assessment surface topography – Development of a basis for the 3D Surface Texture Standards “SURFSTAND”, Kogan Page Science

References related to field parameters

[19]		Leach R. (2013) Characterisation of areal surface texture, Springer, Berlin
[20]		Blateyron F. (2013) 'The areal field parameters', In Leach, R., Characterisation of areal surface texture, Springer, Berlin

References related to feature parameters

[21]		Blateyron F. (2013) 'The areal feature parameters', In Leach R., Characterisation of areal surface texture, Springer, Berlin
[22]		Maxwell J.C. (1870) On hills and dales. The London, Edinburgh, and Dublin Phil. Mag. and J. Sci., Series 4, 40, pp. 421-425
[23]		Takahashi S. et al. (1995) Algorithms for extracting correct critical points and constructing topological graphs from discrete geographical elevation data. Computer Graphics Forum, 14 (3), pp. C181-C192
[24]		Kweon I.S., & Kanade T. (1994) Extracting topographic terrain features from elevation maps, CVGIP: image understanding, 59 (2), pp. 171-182
[25]		Scott P.J. (1992) The Mathematics of motif combination and their use for functional simulation. Int. J. Mech. Tools Manufact., 32 (1-2), pp. 69-73
[26]		Scott P.J. (2004) Pattern Analysis and Metrology: The extraction of stable features from observable measurements. Proc. R. Soc. Lond. A, 460, pp. 2845-2864
[27]		Serra J., & Vincent L. (1992) An Overview of Morphological Filtering. Circuits, Systems, and Signal Processing, 11 (1), pp. 47-108
[28]		Wolf G.W. (1991) A Fortran subroutine for cartographic generalization. Computers and Geoscience, 17 (10), pp. 1359-1381
[29]		Bleau A., & Leon L.J. (2000) Watershed-based segmentation and region merging. Computer Vision and Image understanding, 77, pp. 317-370
[30]		Barré F., & Lopez J. (2000) Watershed lines and catchment basins: a new 3D-motif method. Int. J. Mech. Tools Manufact., 40, pp. 1171-1184
[31]		Batalha G F, & Stipkovic Filho M (2001) Quantitative characterization of the surface topography of cold rolled sheets – new approaches and possibilities, J Materials Processing Tech, 113, 732-738

References related to fractal methods

[32]		DeChiffre L., Lonardo P., & et al (2000) Quantitative Characterisation of Surface Texture. Annals of the CIRP, 49 (2), pp. 635-652
[33]		Johnsen W.A., & Brown C.A. (1994) Comparison of Several Methods for Calculating Fractal-Based Topographic Characterization Parameters. Fractals, 2/3, pp. 437-440
[34]		Dubuc B., & Zucker S.W. et al. (1989) Evaluating the Fractal Dimension of Surfaces. Proc. R. Soc. Lond. A, 425, pp. 113-127
[35]		Brown C.A., & Charles P.D. et al. (1993) Fractal Analysis of Topographic Data by the Patchwork Method. Wear, 161, pp. 61-67
[36]		Brown C.A., & Siegmann S. (2001) Fundamental scales of adhesion and area-scale fractal analysis. Int. J. Mech. Tools Manufact., 41, pp. 1927-1933
[37]		McRae G.A. et al. (2002) Atomic Force Microscopy of Fractal Anodic Oxides on Zr-2.5Nb. J. of Applied Surface Science, 191 (1-4), pp. 94-105
[38]		Johnsen W.A. (1997) Advances in the design of pavement surfaces. PhD dissertation, Worcester Polytechnic Institute, Worcester, Massachusetts, USA
[39]		Briones V. et al. (2006) Scale-sensitive fractal analysis of the surface roughness of bloomed Chocolate. J. American Oil Chemists Society, 83 (3), pp. 193-199
[40]		Scott R.S., & Ungar P.S. et al. (2005) Dental microwear texture analysis within-species diet variability in fossil hominins. Nature, 436 (4), pp. 693-695
[41]		Jordan S.E., & Brown C.A. (2006) Comparing texture characterization parameters on their ability to differentiate ground polyethylene ski bases. Wear, 261 (3-4), pp. 398-409
[42]		Karabelchtchikova O., & Brown C.A. et al. (2007) Effect of surface roughness on kinetics of mass transfer during gas carburizing. International Heat Treatment and Surface Engineering, 1/4
[43]		Narayan P., & Hancock B. (2006) Using fractal analysis to differentiate the surface topography of various pharmaceutical excipient compacts. Materials Science and Engineering, A: Structural Materials: Properties, Microstructure and Processing, 430(1-2), pp. 79-89
[44]		Mandelbrot B.B. (1977) Fractals: Form, Chance and Dimension. W. H. Freeman and Co., New York
[45]		ASME B46.1-2003, Surface Texture, Surface Roughness, Waviness and Lay

Other references

[46]		Burrows J.M., & Griffiths B.J. (1998) A vector modelling technique for the representation of 3-dimensional surface topography. Int. J. Mech. Tools Manufact., 38, pp. 537-542
[47]		Blateyron F Maintenance of ISO 25178, ISO TC213/WG16 N584
[48]		Franco L A, & Sinatora A (2014) 3D Surface parameters (ISO 25178‑2): actual meaning of Spk and its relationship to Vmp, Prec Eng
[49]		Blateyron F (2018) 'Stratified Surface'. In: Chatti S, Laperrière, L., Reinhart, G., Tolio T., (ed). CIRP Encyclopedia of Production Engineering. Berlin, Heidelberg: Springer Berlin Heidelberg; p. 1-7. ISBN: 978-3-642-35950-7
[50]		ISO 10110-8, Optics and photonics — Preparation of drawings for optical elements and systems — Part 8: Surface texture
[51]		ISO 25178-1, Geometrical product specifications (GPS) — Surface texture: Areal — Part 1: Indication of surface texture

Gulf Standard GSO ISO 25178-2:2024

GSO ISO 25178-2:2024 Gulf Standard


ICS 17.040.20 Price based on 64 pages © ISO 2021All rights reserved	iso.org