INTERNATIONAL ISO

STANDARD 25178-600

First edition
2019-02

Geometrical product specifications

(GPS) — Surface texture: Areal —
Part 600:
Metrological characteristics for areal
topography measuring methods
Spécification géométrique des produits (GPS) — État de surface:
Surfacique —
Partie 600: Caractéristiques métrologiques pour les méthodes de
mesure par topographie surfacique

Reference number
ISO 25178-600:2019(E)

© ISO 2019
ISO 25178-600:2019(E)


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Contents Page

Foreword......................................................................................................................................................................................................................................... iv
Introduction...................................................................................................................................................................................................................................v
1 Scope.................................................................................................................................................................................................................................. 1
2 Normative references....................................................................................................................................................................................... 1
3 Terms and definitions...................................................................................................................................................................................... 1
3.1 All areal topography measuring methods........................................................................................................................ 1
3.2 x- and y-scanning systems ......................................................................................................................................................... 10
3.3 Optical systems..................................................................................................................................................................................... 11
3.4 Optical properties of the workpiece................................................................................................................................... 14
4 Standard metrological characteristics for surface texture measurement.............................................15
Annex A (informative) Maximum measurable local slope vs. AN..........................................................................................16
Annex B (informative) Relation to the GPS matrix model............................................................................................................19
Bibliography.............................................................................................................................................................................................................................. 20

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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.
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.

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Introduction
This document is a geometrical product specification standard and is to be regarded as a general GPS
standard (see ISO 14638). It influences the chain link F of the chains of standards on areal surface
texture and profile 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 B.
This document describes the metrological characteristics of areal topography methods designed for
the measurement of surface topography maps. Several standards (ISO 25178-601, ISO 25178-602,
ISO 25178-603, ISO 25178-604, ISO 25178-605 and ISO 25178-606) have already been developed
to define terms and metrological characteristics for individual methods. Although we have striven
for consistency throughout the series, some slight differences can appear between them. Therefore
Technical Committee ISO/TC 213 decided in 2012 to concentrate all common aspects into one standard
– this document – and to describe in ISO 25178-601 to ISO 25178-606 only the terms relevant to each
individual method. For the existing standards of ISO 25178-601 to ISO 25178-606 it will be necessary
to adapt this decision within the next revision. Until then it will be possible to have different definitions
for a single term. Further, if any differences between the current ISO 25178-601 to ISO 25178-606 are
discovered that give rise to conflict, then parties involved in the conflict should agree how to handle the
differences.
NOTE Portions of this document describe patented systems and methods. This information is provided
only to assist users in understanding basic principles of areal surface topography measuring instruments. This
document is not intended to establish priority for any intellectual property, nor does it imply a license to any
proprietary technologies described herein.

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INTERNATIONAL STANDARD ISO 25178-600:2019(E)

Geometrical product specifications (GPS) — Surface

texture: Areal —
Part 600:
Metrological characteristics for areal topography
measuring methods

1 Scope
This document specifies the metrological characteristics of areal instruments for measuring surface
topography. Because surface profiles can be extracted from surface topography images, most of the
terms defined in this document can also be applied to profiling measurements.

2 Normative references
There are no normative references in this document.

3 Terms and definitions

For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:​//www​.iso​.org/obp
— IEC Electropedia: available at http:​//www​.electropedia​.org/

3.1 All areal topography measuring methods

3.1.1
areal reference
component of the instrument that generates a reference surface with respect to which the surface
topography is measured
3.1.2
coordinate system of the instrument
right handed orthogonal system of axes (x,y,z) consisting of:
— the z-axis oriented nominally parallel to the z-scan axis (for optical systems with z-scan), the
optical axis (for non-scanning optical systems) or the stylus trajectory (for stylus or scanning probe
instruments);
— an (x,y) plane perpendicular to the z-axis.
Note 1 to entry: See Figure 1.

Note 2 to entry: Normally, the x-axis is the tracing axis and the y-axis is the stepping axis. (Valid for instruments
that scan in the horizontal plane.)

Note 3 to entry: See also specification coordinate system [ISO 25178-2:2012, 3.1.2] and measurement coordinate
system [ISO 25178-6:2010, 3.1.1].

Note 4 to entry: Certain types of optical instruments do not possess a physical areal guide.

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Note 5 to entry: The z-axis is sometimes referred to as the vertical axis, and the x- and y-axes are sometimes
referred to as the horizontal axes.

3.1.3
z-scan axis
<measuring instrument> instrument axis used to scan in the z-direction to measure the surface
topography
Note 1 to entry: The z-scan axis is nominally but not necessarily parallel to the z-axis of the coordinate system of
the instrument.

3.1.4
measurement area
area that is measured by a surface topography instrument
Note 1 to entry: For point optical sensors and stylus methods, the measurement area is typically the scan area of
the lateral translation stage(s). For topography microscopes the measurement area can be a single field of view
as determined by the objective or a larger area realized by stitching or only part of a field of view as specified by
the operator.

Note 2 to entry: For related concepts, evaluation area and definition area, see ISO 25178-2:2012, 3.1.9 and 3.1.10.

Key
1 coordinate system of the instrument
2 measurement loop
3 z-scan axis

Figure 1 — Coordinate system and measurement loop of the instrument

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3.1.5
measurement loop
closed chain which comprises all components connecting the workpiece and the probe, for example the
means of positioning, the work holding fixture, the measuring stand, the drive unit and the probing system
Note 1 to entry: See Figure 1.

Note 2 to entry: The measurement loop will be subjected to external and internal disturbances that influence the
measurement uncertainty.

3.1.6
real surface
<of a workpiece> set of features which physically exist and separate the entire workpiece from the
surrounding medium
Note 1 to entry: The real surface is a mathematical representation of the surface that is independent of the
measurement process.

Note 2 to entry: See also mechanical surface [ISO 25178-2:2012, 3.1.1.1 or ISO 14406:2010, 3.1.1] and
electromagnetic surface [ISO 25178-2:2012, 3.1.1.2 or ISO 14406:2010, 3.1.2].

Note 3 to entry: The electro-magnetic surface determined with different optical methods can be different.
Examples of optical methods are found in ISO 25178-602 to ISO 25178-607.

[SOURCE: ISO 17450-1:2011, 3.1, modified — Notes to entry added.]

3.1.7
surface probe
device that converts the surface height into a signal during measurement
Note 1 to entry: In earlier standards this was termed transducer.

3.1.8
measuring volume
range of the instrument stated in terms of the limits on all three coordinates measurable by the
instrument
Note 1 to entry: For areal surface texture measuring instruments, the measuring volume is defined by:

— the measuring range of the x- and y- drive units;

— the measuring range of the z-probing system.

3.1.9
response function
Fx, Fy, Fz
function that describes the relation between the actual quantity and the measured quantity
Note 1 to entry: The response curve is the graphical representation of the response function. See Figure 2.

Note 2 to entry: An actual quantity in x (respectively y or z) corresponds to a measured quantity xM (respectively

yM or zM).

Note 3 to entry: The response function can be used for adjustments and error corrections.

3.1.10
amplification coefficient
α x, α y, αz
slope of the linear regression line obtained from the response function
Note 1 to entry: See Figure 2.

Note 2 to entry: There will be amplification coefficients applicable to the x, y and z quantities.

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Note 3 to entry: The ideal response is a straight line with a slope equal to 1, which means that the values of the
measurand are equal to the values of the input quantities.

Note 4 to entry: See also sensitivity of a measuring system (VIM, 4.12[10]).

Note 5 to entry: This quantity is also termed scaling factor.

3.1.11
linearity deviation
lx, ly, lz
maximum local difference between the line from which the amplification coefficient is derived and the
response function
Note 1 to entry: For example, see element 4 in Figure 2.

Key
a actual input quantities
b measured quantities
0 coordinate origin
1 ideal response curve
2 actual response curve of the instrument
3 line from which the amplification coefficient α (slope) is calculated
4 local linearity deviation (l)

Figure 2 — Example of linearity deviation of a response curve

3.1.12
flatness deviation
zFLT
deviation of the measured topography of an ideally flat object from a plane
Note 1 to entry: Flatness deviation can be caused by residual flatness of an imperfect areal reference or by
imperfection in the optical setup of an instrument.

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3.1.13
x-y mapping deviation
Δ x (x,y), Δy (x,y)
gridded image of x- and y-deviations of actual coordinate positions on a surface from their nominal
positions
Note 1 to entry: The mapping deviations can be used to calculate the x- and y- linearity deviations, and x-y axis
perpendicularity.

3.1.14
instrument noise
NI
internal noise added to the output signal caused by the instrument if ideally placed in a noise-free
environment
Note 1 to entry: Internal noise can be due to electronic noise, such as that arising in amplifiers, or optical noise,
such as that arising from stray light.

Note 2 to entry: The S-filter according to ISO 25178-3 can reduce the high spatial frequency components of
this noise.

Note 3 to entry: For some instruments, instrument noise cannot be completely separated from other types of
measurement noise because the instrument only takes data while moving. If so, any measured noise includes a
dynamic component. See also static noise (3.2.6) and dynamic noise (3.2.7).

Note 4 to entry: Because noise is a bandwidth-related quantity, its magnitude depends on the time over which it
is measured or averaged.

3.1.15
measurement noise
NM
noise added to the output signal occurring during the normal use of the instrument
Note 1 to entry: 3.1.14 Notes to entry 2 and 4 also apply to this definition.

Note 2 to entry: Measurement noise includes the instrument noise as well as components arising from the
environment (thermal, vibration, air turbulence) and other sources.

Note 3 to entry: Figure 3 provides an illustration of typical sources of noise and shows the contrast between
laboratory conditions producing instrument noise and measurement noise.

3.1.16
surface topography repeatability
closeness of agreement between successive measurements of the same surface topography under the
same conditions of measurement
Note 1 to entry: Surface topography repeatability provides a measure of the likely agreement between repeated
measurements normally expressed as a standard deviation.

Note 2 to entry: See VIM[10], 2.15 and 2.21, for a general discussion of repeatability and related concepts.

Note 3 to entry: Evaluation of surface topography repeatability is a common method for estimating measurement
noise and other time-varying errors, such as drift.

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3.1.17
x-sampling interval
Dx
distance between two adjacent measured points along the x-axis
Note 1 to entry: In many microscopy systems the sampling interval is determined by the distance between
sensor elements in a camera, called pixels[11], and by the magnification of the optical setup. For such systems, the
terms ‘pixel pitch’ and ‘pixel spacing’ are often used interchangeably with the term ‘sampling interval’. Another
term, ‘pixel width’, indicates a length associated with one side (x or y) of the sensitive area of a single pixel and is
always smaller than the pixel spacing.

Note 2 to entry: Another term, ‘sampling zone’, is sometimes used to indicate the length or region over which a
height sample is determined. This quantity can be different from the sampling interval.

Note 3 to entry: x is replaced by y in the term and the symbol when referring to the y-axis.

a) Conditions under which the instrument noise might be assessed for some types of
instruments

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b) Conditions under which the measurement noise might be assessed for some types of
instruments
Key
A instrument D signal
B sample E environmental vibration
B′ sample plus interaction F external light sources
C data processing G thermal changes

Figure 3 — Typical sources of instrument noise and measurement noise

3.1.18
digitisation step in z
Dz
smallest height variation along the z-axis between two ordinates of the extracted surface
Note 1 to entry: The term extracted surface is defined in ISO 12180-1:2011, 3.2.1.

3.1.19
instrument transfer function
ITF
fITF
curve describing an instrument’s height response as a function of the spatial frequency of the surface
topography
Note 1 to entry: Ideally, the ITF tells us what the measured height of a sinusoidal grating of a specified spatial
frequency ν would be relative to the true height of the grating.

Note 2 to entry: For several types of optical instruments, the ITF can be a nonlinear function of height except for
heights much smaller than the optical wavelength.

Note 3 to entry: A number of methods can be used to characterize properties of the instrument transfer function
with a single parameter. See 3.1.20 for an introduction.

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Note 4 to entry: See also References [12] and [13].

3.1.20
topographic spatial resolution
WR
<surface topography> metrological characteristic describing the ability of a surface topography
measuring instrument to distinguish closely spaced surface features
Note 1 to entry: The topographic spatial resolution designates an important property of a surface topography
measuring instrument, but several parameters and functions can be used to actually quantify the topographic
spatial resolution, depending on the application and the method of measurement. These include:

— lateral period limit DLIM (see 3.1.21 and ISO 25178-3);

— stylus tip radius r TIP (see ISO 25178-601);

— lateral resolution Rl (see 3.1.22);

— width limit for full height transmission W l (see 3.1.23);

— small scale fidelity limit T FIL (see 3.1.27);

— Rayleigh criterion (see 3.3.8);

— Sparrow criterion (see 3.3.9);

— Abbe resolution limit (see 3.3.10).

Note 2 to entry: Other quantities can also be defined for characterizing topographic spatial resolution.

Note 3 to entry: Another related term is structural resolution.

3.1.21
lateral period limit
DLIM
spatial period of a sinusoidal profile at which the height response of the instrument transfer function
falls to 50 %
Note 1 to entry: The lateral period limit is one measure for describing spatial or lateral resolution of a surface
topography measuring instrument and its ability to distinguish and measure closely spaced surface features.
The value of the lateral period limit depends on the heights of surface features and on the method used to probe
the surface. Maximum values for this parameter are listed in ISO 25178-3:2012, Table 3, in comparison with
recommended values for short wavelength (s-) filters and sampling intervals.

Note 2 to entry: Spatial period is the same concept as spatial wavelength and is the inverse of spatial frequency.

Note 3 to entry: One factor related to the value of DLIM for optical tools is the Rayleigh criterion (3.3.8). Another
is the degree of focus of the objective on the surface.

Note 4 to entry: One factor related to the value of DLIM for contact tools is the stylus tip radius, r TIP (see
ISO 25178-601). For a discussion of spatial resolution issues involving stylus instruments, see Reference [14].

3.1.22
lateral resolution
Rl
smallest distance between two features which can be recognized
3.1.23
width limit for full height transmission
Wl
width of the narrowest rectangular groove whose step height is measured within a given tolerance
Note 1 to entry: When evaluating Rl and W l by measurement, instrument properties, such as

— the sampling interval in x and y,

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— the digitisation step in z, and

— the S-filter (see ISO 25178-2:2012, 3.1.4.1),

are normally chosen so that they do not influence the result.

Note 2 to entry: Implementation of this concept depends on both the width and step height of the grooved surface
used. When evaluating W l by measurement, the depth of the rectangular groove is normally chosen to be close to
that of the surface to be measured.

Note 3 to entry: This concept is mainly useful for contacting (stylus) instruments. See Figure 4 for examples.

Note 4 to entry: For a discussion of spatial resolution issues related to measurement of sinusoidal surfaces by
stylus instruments, see Reference [14].

a) Rectangular grid with groove width t and depth d

b) Profile measured with a stylus instrument when t is greater than W l; the depth of the grid is
measured correctly

c) Profile measured when t is less than W l; the depth of the grid is attenuated and points in the
bottoms of the valleys are not accessible by the stylus
Key
t groove width
d groove depth
d′ measured groove depth
Wl width limit for full height transmission

Figure 4 — Examples of results for measurement of narrow grooves

3.1.24
maximum measurable local slope
ΦMS
greatest local slope of a surface feature that can be assessed by the probing system
Note 1 to entry: The term local slope is defined in ISO 4287:1997, 3.2.9.

Note 2 to entry: This property depends on both the surface texture to be measured and the measuring instrument.
For more information see Annex A.

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3.1.25
hysteresis
xHYS, yHYS, zHYS
property of measuring equipment, or characteristic whereby the indication of the equipment or value
of the characteristic depends on the orientation of the preceding stimuli
Note 1 to entry: Hysteresis can also depend, for example, on the distance travelled after the orientation of stimuli
has changed.

Note 2 to entry: For lateral scanning systems, the hysteresis is mainly a repositioning error.

[SOURCE: ISO 14978:2018, 3.5.11, modified — Notes to entry added.]

3.1.26
topography fidelity
T FI
<line profiling> <areal topography> closeness of agreement between a measured surface profile or
measured topography and one whose uncertainties are insignificant by comparison
Note 1 to entry: When the concept of topography fidelity is applied to profiles, the term profile fidelity is
sometimes used.

3.1.27
small scale fidelity limit
T FIL
smallest lateral surface feature for which the reported topography parameters deviate from accepted
values by less than specified amounts
Note 1 to entry: Deviations can be positive or negative.

Note 2 to entry: A practical value for the maximum deviation could be 10 %, for example.

Note 3 to entry: This property depends on the type of surface feature under investigation.

3.1.28
metrological characteristic
<measuring equipment> characteristic of measuring equipment, which can influence the results of
measurement
Note 1 to entry: Calibration of metrological characteristics is often necessary[15][16][17].

Note 2 to entry: The metrological characteristics have an immediate contribution to measurement uncertainty.

[SOURCE: ISO 14978:2018, 3.5.2, modified — Notes to entry replaced.]

3.2 x- and y-scanning systems

3.2.1
areal reference guide
component(s) of the instrument that generate(s) the reference surface, in which the probing system
moves relative to the surface being measured according to a theoretically exact trajectory
Note 1 to entry: In the case of x- and y-scanning areal surface texture measuring instruments, the areal reference
guide establishes a reference surface [ISO 25178-2:2012, 3.1.8]. It can be achieved through the use of two linear
and perpendicular reference guides [ISO 3274:1996, 3.3.2] or one reference surface guide.

3.2.2
lateral scanning system
system that performs the scanning of the surface to be measured in the (x,y) plane
Note 1 to entry: There are essentially four components to a surface texture scanning instrument system: the
x-axis drive, the y-axis drive, the z-measurement probe and the surface to be measured.

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Note 2 to entry: When a measurement consists of a single field of view of a microscope, x- and y-scanning is
not used. However, when several stationary fields of view, overlapping along the lateral directions, are linked
together by stitching methods[18], the system is customarily considered to be a scanning system.

3.2.3
x-drive unit
component of the instrument that moves the probing system or the surface being measured along the
reference guide on the x-axis and returns the horizontal position of the measured point in terms of the
lateral x-coordinate of the profile
Note 1 to entry: x is replaced by y in the term when referring to the y-axis.

3.2.4
lateral position sensor
component of the drive unit that provides the lateral position of the measured point
Note 1 to entry: The lateral position is customarily measured or inferred by using, for example, a linear encoder,
a laser interferometer or a counting device coupled with a micrometer screw.

3.2.5
speed of measurement
Vx
speed of the probing system relative to the surface to be measured during the measurement along
the x-axis
3.2.6
static noise
NS
combination of the instrument noise (3.1.14) and environmental noise on the output signal when the
instrument is not scanning laterally
Note 1 to entry: Environmental noise is caused by, for example, seismic, sonic or external electromagnetic
disturbances.

Note 2 to entry: Notes to entry 2 and 4 in 3.1.14 also apply to this definition.

Note 3 to entry: Static noise is included in measurement noise (3.1.15).

3.2.7
dynamic noise
ND
noise occurring during the motion of the drive units on the output signal
Note 1 to entry: Notes to entry 2 and 4 in 3.1.14 also apply to this definition.

Note 2 to entry: Dynamic noise includes static noise (3.2.6).

Note 3 to entry: Dynamic noise is included in measurement noise (3.1.15).

3.3 Optical systems

3.3.1
light source
optical device emitting light with an appropriate range of wavelengths in a specified spectral region
3.3.2
measurement optical bandwidth
Bλ0
range of wavelengths of light used to measure a surface
Note 1 to entry: Instruments are normally constructed with light sources with a limited optical bandwidth and/
or with additional filter elements to further limit the optical bandwidth.

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Note 2 to entry: Bandwidth is quantifiable in different ways, such as the full width at half maximum (FWHM) or
the full width between 1/e points, where e (2,713…) is the base of the natural logarithms.

3.3.3
measurement optical wavelength
λ0
effective value of the wavelength of the light used to measure a surface
Note 1 to entry: The measurement optical wavelength is affected by conditions such as the light source spectrum,
spectral transmission of the optical components and spectral response of the image sensor array.

3.3.4
angular aperture
maximum angle of the cone of light entering an optical system emerging from a point on the surface
being measured
3.3.5
half aperture angle
α
one half of the angular aperture
Note 1 to entry: This angle is sometimes called half cone angle, see Figure 5.

Key
L lens or optical system
P focal point
α half aperture angle

Figure 5 — Half aperture angle

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3.3.6
numerical aperture
AN
sine of the half aperture angle multiplied by the refractive index n of the surrounding medium
AN = n(λ) sinα

Note 1 to entry: In air for visible light, n ≅ 1 but has a slight dependence on optical wavelength and on ambient
temperature and pressure[19][20].

Note 2 to entry: Typically the numerical aperture is specified for the wavelength that is in the middle of the
measurement optical bandwidth.

3.3.7
optical lateral resolution
quantity that characterizes the influence of the optical system on the topographic spatial resolution
Note 1 to entry: The optical lateral resolution depends, among other factors, on the configuration of the lenses,
mirrors, light source bandwidth and degree of coherence of the optical system.

Note 2 to entry: Factors other than the optical lateral resolution, including data sampling, processing or
interpretation methods, also influence the topographic spatial resolution.

3.3.8
Rayleigh criterion
quantity characterizing the optical lateral resolution given by the separation of two point sources
at which the first diffraction minimum of the intensity image of one point source coincides with the
maximum of the other
Note 1 to entry: The Rayleigh criterion is normally applied to incoherent imaging systems. For a theoretically
perfect, incoherent optical system with a filled objective pupil, the Rayleigh criterion of the optical system is
equal to 0,61 λ0/AN.

Note 2 to entry: This parameter is useful for characterizing the instrument response to features with heights
much less than λ0 for optical topography measuring instruments.

Note 3 to entry: See also References [12], [21] and [22].

3.3.9
Sparrow criterion
quantity characterizing the optical lateral resolution given by the separation of two point sources at
which the second derivative of the intensity distribution vanishes between the two imaged points
Note 1 to entry: For a theoretically perfect, incoherent optical system with filled objective pupil, the Sparrow
criterion of the optical system is equal to 0,47 λ0/AN, approximately 0,77 times the Rayleigh criterion (3.3.8).

Note 2 to entry: Under the same measurement conditions as Note 1 to entry, the Sparrow criterion is nearly equal
to the spatial period of 0,5 λ0/AN, for which the theoretical instrument response falls to zero.

Note 3 to entry: For a theoretically perfect, coherent (e.g. laser-based) optical system, the Sparrow criterion of
the optical system is equal to 0,73 λ0/AN.

Note 4 to entry: This parameter is useful for characterizing the instrument response to features with heights
much less than λ0 for optical topography measuring instruments.

Note 5 to entry: Several spatial resolution concepts defined here and earlier are discussed in References [23]
and [24].

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3.3.10
Abbe resolution limit
quantity characterizing the optical lateral resolution given by the smallest diffraction grating pitch that
can be detected by the optical system
Note 1 to entry: For a theoretically perfect, incoherent optical system with a filled objective pupil, the Abbe
resolution limit of the optical system is equal to 0,5 λ0/AN.

Note 2 to entry: For a theoretically perfect, coherent (e.g. laser-based) optical system, the Abbe resolution limit of
the optical system is equal to λ0/AN.

3.4 Optical properties of the workpiece

3.4.1
surface film
material deposited onto another surface whose optical properties are different from that surface
Note 1 to entry: Depending on their materials and thickness, surface films can be opaque, partially transparent
or highly transparent, or can exhibit more complex spectral properties. Transparency depends also on the optical
wavelengths used in the system.

Note 2 to entry: The surface film can also be called the surface layer.

3.4.2
thin film
film whose thickness is such that the top and bottom surfaces cannot be readily separated by the optical
measuring system
Note 1 to entry: For some measurement systems with special properties and algorithms, the thicknesses of thin
films can be derived.

3.4.3
thick film
film whose thickness is such that the top and bottom surfaces can be readily separated by the optical
measuring system
3.4.4
optically smooth surface
<GPS> surface from which the reflected light is primarily specular and scattered light is not significant
Note 1 to entry: An optically smooth surface behaves like a mirror.

Note 2 to entry: A surface that acts as optically smooth under certain conditions, such as wavelength range,
numerical aperture or pixel resolution, can act as optically rough when one or more of these conditions change.

Note 3 to entry: An alternative definition in ISO 10110-8:2010, 3.3, emphasizes the point that an optically smooth
surface has height variation of the surface texture that is considerably smaller than the wavelength of light.

3.4.5
optically rough surface
<GPS> surface that does not behave as an optically smooth surface, i.e. where scattered light is
significant
Note 1 to entry: A surface that acts as optically rough under certain conditions, such as wavelength range,
numerical aperture or pixel resolution, can act as optically smooth when one or more of these conditions change.

3.4.6
optically non-uniform material
sample with different optical properties in different regions
Note 1 to entry: An optically non-uniform material can result in measured phase differences across the field of
view that can be erroneously interpreted as differences in surface height.

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4 Standard metrological characteristics for surface texture measurement

The metrological characteristics for areal surface texture measuring instruments are listed in Table 1.
When topographic spatial resolution is specified, the specific parameter (see 3.1.20) shall be stated
explicitly.

Table 1 — Metrological characteristics for surface texture measurement methods

Main
Metrological characteristic Symbol Definition potential
error along
Amplification coefficient α x, α y, α z 3.1.10 (see Figure 2) x, y, z
Linearity deviation lx, ly, lz 3.1.11 (see Figure 2) x, y, z
Flatness deviation zFLT 3.1.12 z
Measurement noise NM 3.1.15 z
Topographic spatial resolution WR 3.1.20 z
x-y mapping deviations (Note 1) Δ x(x,y), Δy(x,y) 3.1.13 x, y
Topography fidelity T FI 3.1.26 x, y, z
NOTE 1   Depending on the measurement application, other axis motion errors (see ISO 230-1, ISO 10360-7 and ISO 10360-8)
can also be significant, but are not listed here for surface texture measurement.
NOTE 2   The maximum measurable slope is an important limitation to be specified for a surface topography measurement
instrument. However, a user does not need to measure this parameter unless it is part of a measurement model.

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Annex A
(informative)

Maximum measurable local slope vs. AN

For some types of optical instruments, the numerical aperture of the objective largely determines the
maximum local slope measurable on a surface. Figure A.1 shows three cases for an optical system in
which illumination fills the objective pupil. In Figure A.1 a), most of the reflected light returns through
the objective and is detected. In Figure A.1 b), light reflected from the tilted surface does not return
through the objective and no signal is produced. In Figure A.1 c), larger slopes are measurable for rough
surfaces that scatter light broadly; some of the scattered light might enter the imaging objective and
provide sufficient signal. In this case, the maximum measurable slope can be greater than the limit
imposed by the numerical aperture.

a) Surface providing signal

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b) Surface with significant tilt with respect to the optical axis such that no light signal returns
through the objective to the detector

c) Surface with sufficient roughness to scatter some light into the objective
Key
1 objective
2 incident light, centred around the optical axis
3 optically smooth surface
4 optically rough surface
5 surface normals
6 reflected light
7 scattered light

Figure A.1 — Considerations that determine maximum measurable slope

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ISO 25178-600:2019(E)


It is possible to use dry objectives with up to 0,95 AN providing a maximum measurable local surface
slope up to 72 degrees. Larger slopes can be measured with higher AN objectives, such as water
immersion or oil immersion, although they might not be practical for three-dimensional measurements
of technical surfaces.

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Annex B
(informative)

Relation to the GPS matrix model

B.1 General
The ISO GPS matrix model given in ISO 14638 gives an overview of the ISO GPS system of which this
document is a part, see Reference [25].
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.

B.2 Information about this document and its use

This document defines the methods, specific terminology and metrological characteristics for
instruments used to measure areal surface texture.

B.3 Position in the GPS matrix model

This document is a general ISO GPS standard, which influences chain link F of the chains of standards on
profile and areal surface texture in the GPS matrix model (see Table B.1). The rules and principles given
in this document apply to all segments of the ISO GPS matrix which are indicated with a filled dot (•).

Table B.1 — Position in the ISO GPS Standards matrix model

Chain links
A B C D E F G
Symbols Conformance
Feature Feature Measurement
and and non- Measurement Calibration
requirements properties equipment
indications conformance
Size
Distance
Form
Orientation
Location
Run-out
Profile
surface ⦁
texture
Areal surface
•
texture
Surface imper-
fections

B.4 Related international standards

The related International Standards are those of the chains of standards indicated in Table B.1.

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Bibliography

[1] ISO 3274:1996, Geometrical Product Specifications (GPS) — Surface texture: Profile method —
Nominal characteristics of contact (stylus) instruments
[2] ISO 4287:1997, Geometrical Product Specifications (GPS) — Surface texture: Profile method —
Terms, definitions and surface texture parameters
[3] ISO 14406:2010, Geometrical product specifications (GPS) — Extraction
[4] ISO 17450-1:2011, Geometrical product specifications (GPS) — General concepts — Part 1: Model
for geometrical specification and verification
[5] ISO 14978:2018, Geometrical product specifications (GPS) — General concepts and requirements
for GPS measuring equipment
[6] ISO 25178-2:2012, Geometrical product specifications (GPS) — Surface texture: Areal — Part 2:
Terms, definitions and surface texture parameters
[7] ISO 25178-3:2012, Geometrical product specifications (GPS) — Surface texture: Areal — Part 3:
Specification operators
[8] ISO 25178-6:2010, Geometrical product specifications (GPS) — Surface texture: Areal — Part 6:
Classification of methods for measuring surface texture
[9] ISO 25178-601:2010, Geometrical product specifications (GPS) — Surface texture: Areal —
Part 601: Nominal characteristics of contact (stylus) instruments
[10] JCGM 200:2012, International vocabulary of metrology — Basic and general concepts and
associated terms (VIM), 3rd edition
[11] Umbaugh S.E. Computer Imaging: Digital Image Analysis and Processing. CRC Press, Boca
Raton, FL, 2005
[12] de Groot P. Phase Shifting Interferometry. In: Leach R. Optical Measurement of Surface
Topography. Springer-Verlag, Berlin, 2011
[13] de Groot P., & Colonna de Lega X. “Interpreting interferometric height measurements using
the instrument transfer function,” in Proc. FRINGE: 5th International Workshop on Automatic
Processing of Fringe Patterns (Springer, Berlin, 2005) pp 30 - 37
[14] Bennett J.M., & Mattsson L. Introduction to Surface Roughness and Scattering (Optical Society
of America, Washington, DC, 1989) Sec. 3.A.2
[15] Giusca C.L., Leach R.K., Helery F., Gutauskas T., Nimishakavi L. Calibration of the scales
of areal surface topography measuring instruments: Part 1 — Measurement noise and residual
flatness. Meas. Sci. Technol. 2012, 23 p. 035008
[16] Giusca C.L., Leach R.K., Helery F. Calibration of the scales of areal surface topography
measuring instruments: Part 2 – Amplification coefficient, linearity and squareness. Meas. Sci.
Technol. 2012, 23 p. 065005
[17] Giusca C.L., & Leach R.K. Calibration of the scales of areal surface topography measuring
instruments: Part 3 – Resolution. Meas. Sci. Technol. 2013, 24 p. 105010
[18] Wyant J.C., & Schmit J. Large Field of View, High Spatial Resolution, Surface Measurements.
Int. J. Mach. Tools Manuf. 1998, 38 (5-6) pp. 691–698
[19] Smith W.J. Modern Optical Engineering. Chapter 1. McGraw-Hill, New York, Third Edition, 2000

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[20] Born M., & Wolf E. Principles of Optics, fifth edition (Pergamon, Oxford, 1975) Sec. 2.3.4
[21] Smith W.J. Modern Optical Engineering. Chapter 6. McGraw-Hill, New York, Third Edition, 2000
[22] Born M., & Wolf E. Principles of Optics, fifth edition (Pergamon, Oxford, 1975) Sec. 7.6.3
[23] Colonna de Lega X., & de Groot P. “Lateral resolution and instrument transfer function as
criteria for selecting surface metrology instruments,” OSA Proc. Optical Fabrication and Testing
OTu1D 2012 (Optical Society of America, Washington, DC)
[24] de Groot P., Colonna de Lega X., Sykora D.M., Deck L. The Meaning and Measure of Lateral
Resolution for Surface Profiling Interferometers. Opt. Photonics News. 2012, 23 (4) pp. 10–13
[25] ISO 14638, Geometrical product specifications (GPS) — Matrix model

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