ISO 25178-604:2013

INTERNATIONAL ISO
STANDARD 25178-604
First edition
2013-08-01
Geometrical product specifications
(GPS) — Surface texture: Areal —
Part 604:
Nominal characteristics of non-
contact (coherence scanning
interferometry) instruments
Spécification géométrique des produits (GPS) — État de surface:
Surfacique —
Partie 604: Caractéristiques nominales des instruments sans contact
(à interférométrie par balayage à cohérence)
Reference number
©
ISO 2013
© ISO 2013
All rights reserved. Unless otherwise specified, 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
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Terms and definitions . 1
2.1 Terms and definitions related to all areal surface texture measurement methods . 1
2.2 Terms and definitions related to x- and y-scanning systems . 6
2.3 Terms and definitions related to optical systems . 8
2.4 Terms and definitions related to optical properties of the workpiece .10
2.5 Terms and definitions specific to coherence scanning interferometric microscopy .10
3 Descriptions of the influence quantities .14
3.1 General .14
3.2 Influence quantities .14
Annex A (informative) Overview and components of a coherence scanning interferometry
(CSI) microscope .17
Annex B (informative) Coherence scanning interferometry (CSI) theory of operation .22
Annex C (informative) Spatial resolution .31
Annex D (informative) Example procedure for estimating surface topography repeatability .36
Annex E (informative) Relation to the GPS matrix model.37
Bibliography .39
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. 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. 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.
The committee responsible for this document is ISO/TC 213, Dimensional and geometrical product
specifications and verification. The document was prepared in collaboration with Technical Committee
CEN/TC 290, Dimensional and geometrical product specifications and verification.
ISO 25178 consists of the following parts, under the general title Geometrical product specifications
(GPS) — Surface texture: Areal:
— Part 1: Indication of surface texture
— Part 2: Terms, definitions and surface texture parameters
— Part 3: Specification operators
— Part 6: Classification of methods for measuring surface texture
— Part 70: Physical measurement standards
— Part 71: Software measurement standards
— Part 601: Nominal characteristics of contact (stylus) instruments
— Part 602: Nominal characteristics of non-contact (confocal chromatic probe) instruments
— Part 603: Nominal characteristics of non-contact (phase shifting interferometric microscopy) instruments
— Part 604: Nominal characteristics of non-contact (coherence scanning interferometry) instruments
— Part 605: Nominal characteristics of non-contact (point autofocus probe) instruments
— Part 606: Nominal characteristics of non-contact (focus variation) instruments
— Part 701: Calibration and measurement standards for contact (stylus) instruments
The following part is under preparation:
— Part 72: XML file format x3p
iv © ISO 2013 – All rights reserved

Introduction
This part of ISO 25178 is a geometrical product specification (GPS) standard and is to be regarded as
a general GPS standard (see ISO/TR 14638). It influences chain link 5 of the chains of standards on
roughness profile, waviness profile, primary profile and areal surface texture.
The ISO/GPS Masterplan given in ISO/TR 14638 gives an overview of the ISO/GPS system of which this
document is a part. The fundamental rules of ISO/GPS given in ISO 8015 apply to this document and
the default decision rules given in ISO 14253-1 apply to specifications made in accordance with this
document, unless otherwise indicated.
For more detailed information on the relation of this part of ISO 25178 to other standards and to the GPS
matrix model, see Annex E.
This part of ISO 25178 describes the metrological characteristics of coherence scanning interferometric
microscopes, designed for the measurement of surface topography maps. For more detailed information
on the coherence scanning technique, see Annex A and Annex B.
NOTE Portions of this document, particularly the informative texts, may describe patented systems and
methods. This information is provided only to assist users in understanding the operating principles of coherence
scanning interferometry. This document is not intended to establish priority for any intellectual property, nor
does it imply a license to any proprietary technologies that may be described herein.
INTERNATIONAL STANDARD ISO 25178-604:2013(E)
Geometrical product specifications (GPS) — Surface
texture: Areal —
Part 604:
Nominal characteristics of non-contact (coherence
scanning interferometry) instruments
1 Scope
This part of ISO 25178 specifies the metrological characteristics of coherence scanning interferometry
(CSI) systems for 3D mapping of surface height.
2 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
2.1 Terms and definitions related to all areal surface texture measurement methods
2.1.1
areal reference
component of the instrument that generates a reference surface with respect to which the surface
topography is measured
2.1.2
coordinate system of the instrument
right hand orthonormal system of axes (x, y, z) defined as:
— (x, y) is the plane established by the areal reference of the instrument (note that there are optical
instruments that do not possess a physical areal guide)
— z-axis is mounted parallel to the optical axis and is perpendicular to the (x, y) plane for an optical
instrument; the z-axis is in the plane of the stylus trajectory and is perpendicular to the (x, y) plane
for a stylus instrument (see Figure 1)
Key
1 coordinate system of the instrument
2 measurement loop
Figure 1 — Coordinate system and measurement loop of the instrument
Note 1 to entry: Normally, the x-axis is the tracing axis and the y-axis is the stepping axis. (This note is valid for
instruments that scan in the horizontal plane.)
Note 2 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].
2.1.3
measurement loop
closed chain which comprises all components connecting the workpiece and the probe, e.g. the means of
positioning, the work holding fixture, the measuring stand, the drive unit, the probing system
Note 1 to entry: The measurement loop will be subjected to external and internal disturbances that influence the
measurement uncertainty.
SEE: Figure 1.
2.1.4
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 considered for one type of optical instrument may be different from
the electro-magnetic surface for other types of optical instruments.
2 © ISO 2013 – All rights reserved

2.1.5
surface probe
device that converts the surface height into a signal during measurement
Note 1 to entry: In earlier standards, this was termed “transducer”.
2.1.6
measuring volume
range of the instrument stated in terms of the limits on all three coordinates measured 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, and the measuring range of the z-probing system.
[SOURCE: ISO 25178-601:2010, 3.4.1]
2.1.7
response curve
F , F , F
x y z
graphical representation of the function that describes the relation between the actual quantity and the
measured quantity
Note 1 to entry: An actual quantity in x (respectively y or z) corresponds to a measured quantity x
M
(respectively y or z ).
M M
Note 2 to entry: The response curve can be used for adjustments and error corrections.
[SOURCE: ISO 25178-601:2010, 3.4.2]
2.1.8
amplification coefficient
α , α , α
x y z
slope of the linear regression curve obtained from the response curve (2.1.7)
Note 1 to entry: There will be amplification coefficients applicable to the x, y and z quantities.
Note 2 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.
[1]
Note 3 to entry: See also “sensitivity of a measuring system” (ISO/IEC Guide 99:2007, 4.12)
[SOURCE: ISO 25178-601:2010, 3.4.3, modified —Note 3 to entry has been added.]
2.1.9
instrument noise
N
i
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, as e.g. amplifiers, or optical noise, as e.g. stray light.
Note 2 to entry: This noise typically has high frequencies and it limits the ability of the instrument to detect small
spatial wavelengths of the surface texture.
Note 3 to entry: The S-filter according ISO 25178-3 may reduce this noise.
Note 4 to entry: For some instruments, instrument noise cannot be estimated because the instrument only takes
data while moving.
2.1.10
measurement noise
N
M
noise added to the output signal occurring during the normal use of the instrument
Note 1 to entry: Notes 2 and 3 of 2.1.9 apply as well to this definition.
Note 2 to entry: Measurement noise includes instrument noise (2.1.9).
2.1.11
surface topography repeatability
repeatability of topography map in successive measurements of the same surface 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.
[1]
Note 2 to entry: See ISO/IEC Guide 99:2007, 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 determining the
measurement noise.
2.1.12
sampling interval in x
D
x
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. 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. Yet another
term, sampling zone, may be used to indicate the length or region over which a height sample is determined. This
quantity could either be larger or smaller than the sampling interval.
2.1.13
sampling interval in y
D
y
distance between two adjacent measured points along the y-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. 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. Yet another
term, sampling zone, may be used to indicate the length or region over which a height sample is determined. This
quantity could either be larger or smaller than the sampling interval.
2.1.14
digitization step in z
D
z
smallest height variation along the z-axis between two ordinates of the extracted surface
2.1.15
lateral resolution
R
l
smallest distance between two features which can be detected
[SOURCE: ISO 25178-601:2010, 3.4.10, modified —The word “separation” has been removed before
“distance”.]
2.1.16
width limit for full height transmission
W
l
width of the narrowest rectangular groove whose measured height remains unchanged by the measurement
Note 1 to entry: Instrument properties (such as the sampling interval in x and y, the digitization step in z, and the
short wavelength cutoff filter) should be chosen so that they do not influence the lateral resolution and the width
limit for full height transmission.
4 © ISO 2013 – All rights reserved

Note 2 to entry: When determining this parameter by measurement, the depth of the rectangular groove should
be close to that of the surface to be measured.
[SOURCE: ISO 25178-601:2010, 3.4.11, modified —The notes have been changed.]
2.1.17
lateral period limit
D
LIM
spatial period of a sinusoidal profile at which the height response of an instrument falls to 50 %
Note 1 to entry: The lateral period limit is one metric for describing spatial or lateral resolution of a surface
topography measuring instrument and its ability to distinguish and measure closely spaced surface features. Its
value 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 D for optical tools is the Rayleigh criterion (2.3.7). Another is
LIM
the degree of focus of the objective on the surface.
Note 4 to entry: One factor related to the value of D for contact tools is the stylus tip radius, r (see
LIM TIP
ISO 25178-601).
Note 5 to entry: Other terms related to lateral period limit are structural resolution and topographic spatial resolution.
2.1.18
maximum local slope
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.
2.1.19
instrument transfer function
ITF
f
ITF
function of spatial frequency describing how a surface topography measuring instrument responds to
an object surface topography having a specific spatial frequency
Note 1 to entry: Ideally, the ITF tells us what the measured amplitude of a sinusoidal grating of a specified spatial
frequency ν would be relative to the true amplitude of the grating.
Note 2 to entry: For several types of optical instruments, the ITF may be a nonlinear function of height except for
heights much smaller than the optical wavelength.
2.1.20
hysteresis
x , y , z
HYS HYS HYS
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 14978:2006, 3.24, modified —Note 2 to entry and the symbols have been added.]
2.1.21
metrological characteristic
metrological characteristic of a measuring instrument
characteristic of measuring equipment, which may influence the results of
measurement
Note 1 to entry: Calibration of metrological characteristics may be necessary.
Note 2 to entry: The metrological characteristics have an immediate contribution to measurement uncertainty.
Note 3 to entry: Metrological characteristics for areal surface texture measuring instruments are given in Table 1.
Table 1 — List of metrological characteristics for surface texture measurement methods
Metrological characteristic Symbol Definition Main poten-
tial error
along
Amplification coefficient α , α , α 2.1.8 x, y, z
x y z
Linearity deviation l , l , l Maximum local difference between x, y, z
x y z
the line from which the amplifica-
tion coefficient is derived and the
response curve.
Residual flatness z Flatness of the areal reference z
FLT
Measurement noise N 2.1.10 z
M
Lateral period limit D 2.1.17. z
LIM
Perpendicularity Δ Deviation from 90° of the angle x, y
PERxy
between the x- and y-axes
[SOURCE: ISO 14978:2006, 3.12, modified — The notes are different and the table has been added.]
2.2 Terms and definitions related to x- and y-scanning systems
2.2.1
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.
2.2.2
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 aspects 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. There are different ways in
which these may be configured and thus there will be a difference between different configurations as explained
in Table 2.
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 fields of view are linked together by stitching methods, see Reference [2] the system
is considered to be a scanning system.
6 © ISO 2013 – All rights reserved

Table 2 — Possible different configurations for reference guides (x and y)
Drive unit
a
Two reference guides (x and y) One areal reference guide
Px o Cy Px o Py Cx o Cy Pxy Cxy
A: without arcuate
Px o Cy-A Px o Py-A Cx o Cy-A Pxy-A Cxy-A
error correction
Probing
S: without arcu-
System
ate error or with
Px ο Cy-S Px o Py-S Cx o Cy-S Pxy-S Cxy-S
arcuate error cor-
rected
a For two given functions f and g, f ο g is the combination of these functions
Px = probing systems moving along the x-axis
Py = probing systems moving along the y-axis
Cx = component moving along the x-axis
Cy = component moving along the y-axis
2.2.3
drive unit x
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
2.2.4
drive unit y
component of the instrument that moves the probing system or the surface being measured along the
reference guide on the y-axis and returns the horizontal position of the measured point in terms of the
lateral y coordinate of the profile
2.2.5
lateral position sensor
component of the drive unit that provides the lateral position of the measured point
Note 1 to entry: The lateral position can be measured or inferred by using, for example, a linear encoder, a laser
interferometer, or a counting device coupled with a micrometre screw.
2.2.6
speed of measurement
v
x
speed of the probing system relative to the surface to be measured during the measurement along the x-axis
[SOURCE: ISO 25178-601:2010, 3.4.13]
2.2.7
static noise
N
S
combination of the instrument noise (2.1.9) and environmental noise on the output signal when the
instrument is not scanning laterally
Note 1 to entry: Environmental noise is caused by e.g. seismic, sonic and external electromagnetic disturbances.
Note 2 to entry: Notes 2 and 3 in 2.1.9 also apply to this definition.
Note 3 to entry: Static noise is included in measurement noise (2.1.10)
2.2.8
dynamic noise
N
D
noise occurring during the motion of the drive units on the output signal
Note 1 to entry: Notes 2 and 3 in 2.1.9 also apply to this definition.
Note 2 to entry: Dynamic noise includes the static noise.
Note 3 to entry: Dynamic noise is included in measurement noise (2.1.10).
2.3 Terms and definitions related to optical systems
2.3.1
light source
optical device emitting an appropriate range of wavelengths in a specified spectral region
2.3.2
measurement optical bandwidth
B
λ0
range of wavelengths of light used to measure a surface
Note 1 to entry: Instruments may be constructed with light sources with a limited optical bandwidth and/or with
additional filter elements to further limit the optical bandwidth.
2.3.3
measurement optical wavelength
λ
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.
2.3.4
angular aperture
angle of the cone of light entering an optical system from a point on the surface being measured
[SOURCE: ISO 25178-602:2010, 3.3.3]
2.3.5
half aperture angle
α
one half of the angular aperture
Note 1 to entry: This angle is sometimes called the “half cone angle” (see Figure 2).
8 © ISO 2013 – All rights reserved

Key
L lens or optical system
P focal point
α half aperture angle
Figure 2 — Half aperture angle
2.3.6
numerical aperture
A
N
sine of the half aperture angle multiplied by the refractive index n of the surrounding medium
A = n sinα
N
Note 1 to entry: In air for visible light, n ≅ 1.
Note 2 to entry: The numerical aperture is dependent on the wavelength of light. Typically, the numerical aperture
is specified for the wavelength that is in the middle of the measurement optical bandwidth.
2.3.7
Rayleigh criterion
quantity characterizing the spatial resolution of an optical system given by the separation of two point
sources at which the first diffraction minimum of the image of one point source coincides with the
maximum of the other
Note 1 to entry: For a theoretically perfect, incoherent optical system with a filled objective pupil, the Rayleigh
criterion of the optical system is equal to 0,61 λ /A .
0 N
Note 2 to entry: This parameter is useful for characterizing the instrument response to features with heights
much less than λ for optical 3D metrology instruments.
2.3.8
Sparrow criterion
quantity characterizing the spatial resolution of an optical system 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 λ /A , approximately 0,77 times the Rayleigh criterion (2.3.7).
0 N
Note 2 to entry: This parameter is useful for characterizing the instrument response to features with heights
much less than λ for optical 3D metrology instruments.
Note 3 to entry: Under the same measurement conditions as the notes above, the Sparrow criterion is nearly equal
to the spatial period of 0,50 λ /A , for which the theoretical instrument response falls to zero.
0 N
2.4 Terms and definitions related to optical properties of the workpiece
2.4.1
surface film
material deposited onto another surface whose optical properties are different from that surface
Note 1 to entry: This concept may also be called “surface layer”.
2.4.2
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 may be derived.
2.4.3
thick film
film whose thickness is such that the top and bottom surfaces can be readily separated by the optical
measuring system
2.4.4
optically smooth surface
surface from which the reflected light is primarily specular and scattered light is not significant
Note 1 to entry: An optically smooth surface behaves locally like a mirror.
Note 2 to entry: A surface that acts as optically smooth under certain conditions, such as wavelength range,
numerical aperture, pixel resolution, etc. can act as optically rough when one or more of these conditions change.
2.4.5
optically rough surface
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, pixel resolution, etc. can act as optically smooth when one or more of these conditions change.
2.4.6
optically non-uniform material
sample with different optical properties in different regions
Note 1 to entry: An optically non-uniform material may result in measured phase differences across the field of
view that can be erroneously interpreted as differences in surface height.
2.5 Terms and definitions specific to coherence scanning interferometric microscopy
2.5.1
coherence scanning interferometry
CSI
surface topography measurement method wherein the localization of interference fringes during a scan
of optical path length provides a means to determine a surface topography map
Note 1 to entry: CSI encompasses but is not limited to instruments that use spectrally broadband, visible sources
(white light) to achieve interference fringe localization.
Note 2 to entry: CSI uses either fringe localization alone or in combination with interference phase evaluation,
depending on the surface type, desired surface topography repeatability and software capabilities.
Note 3 to entry: Table 3 compiles alternative terms that conform at least in part to the above definition.
10 © ISO 2013 – All rights reserved

Table 3 — Summary of recognized terms for CSI
Acronym Term Bibliography reference
CSI Coherence scanning interferometry [3]
CPM Coherence probe microscope [4]
CSM Coherence scanning microscope [5]
CR Coherence radar [6]
CCI Coherence correlation interferometry [7]
MCM Mirau correlation microscope [8]
WLI White light interferometry [9]
WLSI White light scanning interferometry [10]
SWLI Scanning white light interferometry [11]
WLPSI White light phase shifting interferometry [12]
VSI Vertical scanning interferometry [10]
EVSI Enhanced VSI [10]
HDVSI High-definition Vertical Scanning Interferometry [13]
RSP Rough surface profiler [14]
RST Rough surface tester [15]
HIS Height scanning interferometer [16]
IRS Infrared scanning [17]
[SOURCE: ISO 25178-6:2010, 3.3.5]
2.5.2
optical path length
physical distance a light beam travels multiplied by the index of refraction of the traversed medium
Note 1 to entry: The optical path difference in a two-beam interferometer is the difference in optical path length
between the reference path and measurement path.
2.5.3
coherence scanning interferometry signal
CSI signal
intensity data recorded for an individual image point or camera pixel as a function of scan position
Note 1 to entry: See Figure 3 and A.1.
Key
1 modulation envelope (calculated)
2 CSI signal
3 intensity
4 scan position
Figure 3 — Typical CSI signal
2.5.4
interference fringes
rapidly modulating portion of the CSI signal, related to the interference effect and generated by the
variation of optical path length during the CSI scan
Note 1 to entry: The interference fringes are approximately sinusoidal as a function of scan position.
Note 2 to entry: The distance between interference-fringe peaks corresponds to scan position differences that
are approximately one-half the effective mean wavelength of the light source (see 2.3.1).
SEE: Figure 3.
2.5.5
interference phase
argument of the sine function used to approximate the form of interference fringes
Note 1 to entry: A complete fringe oscillation or period is equal to a 2π change in phase.
2.5.6
amplitude modulation
peak-to-valley or equivalent measure of the CSI signal
Note 1 to entry: Amplitude modulation depends mainly on radiance of the light source, camera sensitivity, and
reflectivities of object and reference mirror.
Note 2 to entry: Amplitude modulation is also often termed “signal strength”.
SEE: Figure 3.
12 © ISO 2013 – All rights reserved
2.5.7
modulation envelope
overall variation in amplitude modulation of a CSI signal as a function of scan position
Note 1 to entry: The modulation envelope (Figure 3) is not necessarily a rigorously-defined aspect of the signal.
The quantitative shape of the envelope is related closely to the means by which it is calculated.
Note 2 to entry: The modulation envelope is most closely associated with the idea of fringe localization, which is
a basic characteristic of CSI signals.
Note 3 to entry: The modulation envelope is a consequence of limited optical coherence, which follows from using
a spectrally-broadband light source (white light), a spatially extended light source, or both.
2.5.8
analysis mode
signal processing option
processing selection that determines whether the software makes use of the modulation envelope alone
to measure surface heights or both the envelope and the interference fringe phase
2.5.9
modulation threshold
minimum modulation
D
MOD
lowest amplitude modulation deemed usable by the software for further evaluation of surface height
Note 1 to entry: The minimum modulation level typically provides a selection for valid data points. Those points
with amplitude modulation falling below this level are considered invalid.
2.5.10
coherence scanning interferometry scan
CSI scan
mechanical or optical scan which varies the optical length of either the reference path or measurement
path to generate a signal that exhibits interference fringes
Note 1 to entry: In CSI microscopes, the most common (but not exclusive) scanning means is a physical translation
of an interference objective, which is pre-adjusted such that the peak CSI signal intensity coincides with the
position of best focus.
2.5.11
scan length
z
TOT
total range of physical path length traversed by the CSI scan
Note 1 to entry: The scan length is usually synonymous with the total displacement of a moving component of
the interferometer mechanically translated along its optical axis during data acquisition. The moving component
could be, for example, an interference objective or a mirror in the reference arm or the complete interferometer
moving with respect to the surface.
SEE: A.5.
2.5.12
scan increment
Δ
z
distance travelled by the CSI scan between individual images captured by the camera (camera frames)
or individual data acquisition points
Note 1 to entry: The scan increment is commonly equivalent to 4 frames per interference fringe, but can be any
number of frames.
2.5.13
scan speed
v
z
velocity of the CSI scan
Note 1 to entry: This can be expressed e.g. in micrometres per second.
2.5.14
effective mean wavelength
twice the period of the interference fringe closest to the modulation envelope peak
Note 1 to entry: The period of an interference fringe is the scan distance separating two neighbouring peaks in
the CSI signal.
Note 2 to entry: The effective mean wavelength is a function of the measurement optical wavelength (2.3.3), the

optical geometry and the data acquisition method, see Reference [18].
2.5.15
fringe-order error
error in the identification of the correct fringe when calculating relative heights using interference
phase for surface topography calculations
Note 1 to entry: Fringe-order errors in CSI can be the result of errors in the analysis of the modulation envelope.
Note 2 to entry: Fringe-order errors are integer multiples of one-half the equivalent wavelength in height.
Note 3 to entry: Fringe-order errors are sometimes termed 2π errors.
2.5.16
environmental vibration
N
VIB
mechanical motions that disturb the CSI scan in an unpredictable and unwanted way, leading to
measurement errors
Note 1 to entry: Environmental vibration may be caused by various sources (e.g. seismic, sonic and external
electro-magnetic disturbances), see B.6.
3 Descriptions of the influence quantities
3.1 General
CSI instruments provide a measurement of lateral (x, y) and height (z) values from which surface shape
and texture parameters are calculated.
3.2 Influence quantities
Influence quantities for CSI instruments are given in Table 4, which also indicates the metrological
characteristics (see 2.1.21, Table 1) that are affected by deviations of the influence quantities.
NOTE For a theoretically perfect, incoherent optical system with a filled objective pupil and when measuring
features with heights much smaller than λ , the lateral period limit D (2.1.17) of CSI systems is at least twice
0 LIM
the Rayleigh criterion (2.3.7).
14 © ISO 2013 – All rights reserved

Table 4 — Influence quantities for coherence scanning interferometry
Metrological
Compo-
Element Influence quantities characteristic
nent
affected …
λ Measurement optical wavelength (See 2.3.3.) α
0 z
B Measurement optical bandwidth (See 2.3.2.) α
λ0 z
Light source S, P, C, The state of polarization of the light impinging on α , α , α
x y z
E, U the measured surface. The polarization is typically
described as S, P, circular (C), elliptical (E), or unpolar-
ized (U).
A Microscope numerical aperture (2.3.6) α , α , α , D
N x y z LIM
M Magnification between object sizes on the surface and α , α
IMG x y
image sizes on the sensor
Δ Wavefront distortion, a function describing net devia- α
PATH z
tions in the measured optical path of the system,
derived from deviations in both the reference and
measurement arms
Interferometer imaging
Q General quality of the optical components used, α , α , α , z ,
OPT x y z FLT
system
including aberrations, transmission, alignment errors, l , l , l , D ,
x y z LIM
etc. Δ
PERxy
P Lateral distortion of the magnified image on the cam- α , α , z , l , l ,
DISxy x y FLT x y
era D Δ
LIM, PERxy
U (x, y) Illumination uniformity – Distribution of illumination α , α , α , z ,
I x y z FLT
across the field of view of the object (a highly uniform, l , l , l
x y z
constant distribution is desired)
Δ x-pixel spacing of the imaging camera D
x LIM
Camera
Δ y-pixel spacing of the imaging camera D
y LIM
V Scan speed (See 2.5.13, A.5 and B.4.) α , l
z z z
z Scan length (See 2.5.11, A.5 and B.4.) α , l
TOT z z
Δ Scan Increment (See 2.5.12, A.5 and B.4.) α
z z
Acquisition
Δ Scan linearity (See A.5 and B.4.) α , l
z-LIN z z
Software
T Integration time required to complete a single scan in
I
N
M
z
Controller D Height digitization step N
z M
A Measurement algorithm – Method for interpreting the α , l
ALG z z
CSI signal, including the option of using phase infor-
mation (See B.3.)
Profile Analy-
D Fringe intensity modulation threshold - the minimum α , l
MOD z z
sis Software
peak-valley intensity variation that the controller
recognizes to be an interference fringe
C z-Cal factor, height adjustment coefficient α , l
z z z
Lateral sampling interval, equal to the lateral pixel D
LIM
D or D spacing of the camera (Δ Δ ) divided by the magnifi-
x y x, y
cation
N Instrument noise (2.1.9) N
I M
Instrument Overall
N Environmental vibration (See B.6.) N
VIB M
x ,
HYS
y , Hysteresis (2.1.19) l , l , l
HYS x y z
z
HYS
Table 4 (continued)
Metrological
Compo-
Element Influence quantities characteristic
nent
affected …
θ * Tilt – Relative angle between the optical axis of the α , α , α
TLT x y z
system and the sample normal. Object surface slopes
that cause light to reflect at or near to the edge or out-
side of the numerical aperture of the objective A are
N
also likely to cause significant signal loss.
Φ * The relative phase shift upon reflection of dissimilar α
DIS z
materials.
T * Thickness of transparent or semi-transparent films. α
FLM z
These films typically have thickness comparable to
the illumination wavelength. Note that thinner con-
Sample
tamination or native oxide films do not necessarily
affect the CSI measurement process.
T * Thick transparent media - transparent media (such α
MED z
as cover glass or liquid) between the sample and the
instrument.
URF* Under resolved features - Object features having α
z
dimensions on the order of or smaller than the lateral
resolution. (See Annex C.)
*NOTE   These influence quantities arise from the interaction between the
instrument and the sample being measured.
16 © ISO 2013 – All rights reserved

Annex A
(informative)
Overview and components of a coherence scanning interferometry
(CSI) microscope
A.1 Overview
CSI instruments use the following measurement process.
— The instrument is focused on the surface as indicated by the appearance of interference fringes.
— For measurement of randomly rough surfaces, the sample tilt relative to the optical axis of the
system is adjusted to minimize the number of fringes across the field of view. For measurement of
step features on smooth surfaces, a sample tilt adjusted to provide one or more fringes across the
field of view and perpendicular to the step may be useful.
— The instrument executes a data acquisition during a CSI scan.
— Data analysis using either the modulation envelope, the interference fringes, or both, results in a
surface topography map.
Deviations of shape from a flat surface such as a residual tilt, curvature and cylinder are numerically
removed from the areal measurement producing a surface topography map. Further filtering may be
applied to the surface topography map as required.
Key
1 light source 7 scanner
2 aperture stop 8 pupil plane
3 field stop 9 reference mirror
4 illumination beamsplitter 10 interferometer beamsplitter
5 camera 11 object surface
6 tube or zoom lens 12 Mirau interference objective
NOTE Other configurations are listed in A.4.
Figure A.1 — Schematic diagram of a typical Mirau-configuration CSI microscope
A.2 Typical configuration
Figure A.1 illustrates the basic features of a CSI microscope. The object has height features h which vary
over the object surface. A mechanical scanner provides a smooth, continuous scan ζ of the interference
objective in the z direction. During the scan, a computer records intensity data, I(ζ), for each image
point or camera pixel xy, in successive camera frames.
A.3 Light source
A distinctive feature of CSI is that the light source is generally incoherent. Thus, typical light sources
either have a broadband spectrum (white light) or are extended (many independent point sources), or
both. A classic example is an incandescent lamp such as a tungsten halogen bulb. Solid state sources,
such as light emitting diodes (LEDs) are increasingly comm
...