ISO 29301:2023
(Main)Microbeam analysis — Analytical electron microscopy — Methods for calibrating image magnification by using reference materials with periodic structures
Microbeam analysis — Analytical electron microscopy — Methods for calibrating image magnification by using reference materials with periodic structures
This document specifies a calibration procedure applicable to images recorded over a wide magnification range in a transmission electron microscope (TEM). The reference materials used for calibration possess a periodic structure, such as a diffraction grating replica, a super-lattice structure of semiconductor or an analysing crystal for X-ray analysis, and a crystal lattice image of carbon, gold or silicon. This document is applicable to the magnification of the TEM image recorded on a photographic film, or an imaging plate, or detected by an image sensor built into a digital camera. This document also refers to the calibration of a scale bar. This document does not apply to the dedicated critical dimension measurement TEM (CD-TEM) and the scanning transmission electron microscope (STEM).
Analyse par microfaisceaux — Microscopie électronique analytique — Méthodes d'étalonnage du grandissement d'image au moyen de matériaux de référence de structures périodiques
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 29301
Third edition
2023-10
Microbeam analysis — Analytical
electron microscopy — Methods
for calibrating image magnification
by using reference materials with
periodic structures
Analyse par microfaisceaux — Microscopie électronique analytique
— Méthodes d'étalonnage du grandissement d'image au moyen de
matériaux de référence de structures périodiques
Reference number
© ISO 2023
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Image magnification . 5
4.1 Definition of the image magnification . 5
4.2 Expressing magnification . 6
5 Reference materials . 6
5.1 General . 6
5.2 Requirements for CRM/RM . 7
5.3 Storage and handling . 7
6 Calibration procedures .7
6.1 General . 7
6.2 Mounting CRM/RM . 8
6.3 Setting TEM operating conditions for calibration . 8
6.4 Capturing digitized image . 9
6.5 Digitizing the image recorded on photographic film . 10
6.5.1 General . 10
6.5.2 How to decide the pixel-resolution for digitization. 10
6.6 Measurement of the angle-corrected distance, D , from the digitized image .12
t
6.6.1 General .12
6.6.2 Measurement procedure . 13
6.7 Digitization of reference scale for pixel size calibration . 15
6.8 Calibration of image magnification . 16
6.8.1 General . 16
6.8.2 Calibration of scale unit (= pixel size), S . 16
6.8.3 Calculating image magnification . 18
6.9 Calibration of scale bar . 18
6.9.1 General . 18
6.9.2 Basic scale size corresponding to one pixel on the digitized image . 19
6.9.3 Calibration of scale bar . 19
6.10 Calibration procedure for length measurements using photographic film only .20
7 Accuracy of image magnification .20
8 Uncertainty of measurement result .21
9 Calibration report .23
9.1 General .23
9.2 Contents of calibration report . 23
Annex A (informative) Parameters that influence the resultant magnification of a TEM .25
Annex B (informative) Flowchart of image-magnification calibration procedure .26
Annex C (informative) How to decide the number of lines for averaging .27
Annex D (informative) Reference materials for magnification calibration .29
Annex E (informative) Example of test report for calibration of TEM magnification.33
Bibliography . 44
iii
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
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electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
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different types of ISO document should be noted. This document was drafted in accordance with the
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This document was prepared by Technical Committee ISO/TC 202, Microbeam analysis, Subcommittee
SC 3, Analytical electron microscopy.
This third edition cancels and replaces the second edition (ISO 29301:2017), of which it constitutes a
minor revision. The changes are as follows:
— the element name of Silver in Table D.1 has been corrected to Silicon;
— normative references in Clause 2 have been updated.
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.
iv
Introduction
The transmission electron microscope (TEM) is widely used to investigate the micro/nano-structure
of a range of important materials such as semiconductors, metals, nano-particles, polymers, ceramics,
glass, food and biological materials. The technique used involves the transmission of electrons through
an ultra-thin specimen, interacting with the specimen as they pass through. This interaction results
in a magnified image which is focused onto an imaging device, such as a photographic film, an imaging
plate, or an image sensor built into a digital camera. A TEM is capable of imaging at significantly
higher resolutions than ordinary (light) microscopes. It can be used to examine fine details as small
as a single atomic column in a given specimen. This document addresses the need for magnification
calibration of the images. It describes the requirements for calibration of the image magnification in
the transmission electron microscope using a certified reference material or a reference material with
periodic structures.
v
INTERNATIONAL STANDARD ISO 29301:2023(E)
Microbeam analysis — Analytical electron microscopy
— Methods for calibrating image magnification by using
reference materials with periodic structures
1 Scope
This document specifies a calibration procedure applicable to images recorded over a wide
magnification range in a transmission electron microscope (TEM). The reference materials used for
calibration possess a periodic structure, such as a diffraction grating replica, a super-lattice structure
of semiconductor or an analysing crystal for X-ray analysis, and a crystal lattice image of carbon, gold
or silicon.
This document is applicable to the magnification of the TEM image recorded on a photographic film, or
an imaging plate, or detected by an image sensor built into a digital camera. This document also refers
to the calibration of a scale bar.
This document does not apply to the dedicated critical dimension measurement TEM (CD-TEM) and the
scanning transmission electron microscope (STEM).
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 Guide 35, Reference materials — Guidance for characterization and assessment of homogeneity and
stability
ISO/IEC 17025:2017, General requirements for the competence of testing and calibration laboratories
ISO 17034, General requirements for the competence of reference material producers
3 Terms and definitions
For the purposes of this document, the following terms and definitions 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
accuracy
closeness of agreement between a test result and the accepted reference value
Note 1 to entry: A “test result” is the calibrated magnification obtained by the procedure outlined in this
document.
Note 2 to entry: The term “accepted reference value” is the magnification given by the TEM manufacturer.
1)
[SOURCE: ISO 5725-1:1994 , 3.6, modified — new Notes 1 and 2 to entry have been added.]
1) Now withdrawn. Replaced by ISO 5725-1:2023.
3.2
alignment
series of operations to align the incident direction of the electron beam to the optical axis (3.22) using
deflectors and/or mechanical knobs
3.3
certified reference material
CRM
reference material, accompanied by a certificate, one or more of whose property values are certified
by a procedure which establishes its traceability to an accurate realization of the unit in which the
property values are expressed, and for which each certified value is accompanied by an uncertainty at
a stated level of confidence
Note 1 to entry: For the purposes of this document, a CRM possesses periodic structure(s), with the desired range
of periodic interval and accuracy, to be used for the calibration of the image magnification (3.15).
3.4
contamination
formation of a deposited layer of any material due to the interaction of the electron beam with the
sample and/or its immediate environment
3.5
crystal orientation
direction of crystal which is represented by crystal index
Note 1 to entry: During TEM imaging, it is often useful to have a crystalline specimen aligned such that a specific
(low index) zone axis (3.36) is parallel, or nearly parallel, to the beam direction [optical axis (3.22)].
3.6
diffraction grating replica
shadow-casting carbon replica film constituting a grating which contains 500 to 2 000 parallel grooves
per millimetre, or cross-line grating with a similar line spacing
Note 1 to entry: A diffraction grating replica can be used as a reference material (3.25) for calibration of the image
magnification (3.15) in the low to medium-low magnification range.
3.7
digital camera
device that detects the image (3.13) using a chip-arrayed image sensor (3.18), such as a charge-coupled
device (CCD) or complementary metal-oxide semiconductor (CMOS), that converts a visual image to an
electric signal
3.8
dynamic range
range of detectable electron doses illuminated on the detector, in which the image signal can be
detected properly
3.9
excitation current
electric current applied to the coil of the magnetic lens
3.10
focus
focusing condition in which the specimen height coincides with the object plane of the objective lens
3.11
glass scale
ruler on which a fine scale is drawn and utilized as the reference scale to measure the distance in the
digitized image after digitizing it with an image scanner (3.17)
Note 1 to entry: The transparency and thermal stability of the glass scale are convenient to get the digitized
reference image with a transmitted image scanner and to make the contact image on the imaging plate (3.16).
3.12
horizontal field width
HFW
original length corresponding to full width in the horizontal direction on a magnified image
3.13
image
two-dimensional projection of the specimen structure generated by TEM (3.34)
Note 1 to entry: A photographic film (3.23), an imaging plate (3.16), and an image sensor (3.18) built into a digital
camera are examples of devices for detecting the image (3.13).
[SOURCE: ISO 16700:2016, 3.2, modified — the term “SEM” has been replaced by the term “TEM”.]
3.14
image file
computer file containing information relating to the digitized image
3.15
image magnification
ratio of the linear dimension of the specific structure/scaling on the image detector, such as a
photographic film (3.23), an imaging plate (3.16), and an image sensor (3.18) built into a digital camera,
to the corresponding linear dimension of the structure/scaling on the specimen (3.27)
3.16
imaging plate
IP
electron image detector consisting of a film with a thin active layer embedded with specifically designed
phosphors
3.17
image scanner
device that converts an analogue image into a digitized image with the desired pixel-resolution
Note 1 to entry: There are mainly two different types of scanners: flatbed type and drum type.
3.18
image sensor
device, such as a charge-coupled device (CCD) array or complementary metal-oxide semiconductor
(CMOS) sensor, that converts visual image information to an electric signal, built-in digital camera or
other imaging devices
3.19
image wobbler
deflection coil used to change the direction of incident electron beam onto the specimen (3.27)
Note 1 to entry: This coil is activated in a periodic manner with the aim of identifying easily the place of focus
(3.10).
3.20
lattice image
image (3.13) consisting of interference fringes formed by the interaction between the transmitted
electron beam and diffracted electron beam from a specific crystal plane
Note 1 to entry: Lattice fringes can be used to calibrate image magnification (3.15) at the high end of the
magnification range.
3.21
magnetic hysteresis
physical phenomenon related to the magnetizing loop in which the magnetic field strength depends on
the direction of the adjustment of the exciting current for the magnetic lens
3.22
optical axis
straight line passing through the symmetrical centre of the magnetic field of the electron lens
Note 1 to entry: The path of an electron beam along this axis goes through the lens without changing the direction.
3.23
photographic film
negative film
sheet or a roll of thin plastic coated by photographic emulsion for recording an image (3.13)
3.24
pixel-resolution
number of imaging pixels per unit distance of the detector
Note 1 to entry: The typical unit is sometimes expressed as dots per inch (dpi).
3.25
reference material
RM
material or substance, one or more of whose property values are sufficiently homogeneous and well-
established to be used for the calibration of an apparatus, the assessment of a measurement method, or
for assigning values to materials
Note 1 to entry: For the purpose of this document, an RM possesses periodic pattern(s) with the desired range of
periodic interval and accuracy, to be used for the calibration of the image magnification (3.15).
3.26
region of interest
ROI
region of the image (3.13) selected for a specific reason
3.27
specimen
small portion of a sample for observation
Note 1 to entry: For TEM (3.34), a specimen has to be thin enough to transmit the electron beam.
3.28
specimen cartridge
part of the specimen holder (3.31) which supports a specimen (3.27) and is attached to the tip of the
specimen holder for use
3.29
specimen drift
unintentional movement of the specimen (3.27) due to any source (thermal, mechanical, electric,
charging)
3.30
specimen height
specimen position along the optical axis (3.22) of the objective lens
Note 1 to entry: “Specimen height = 0” corresponds to the specimen position in correct focus under the standard
excitation condition (3.32) of the objective lens.
Note 2 to entry: See Reference [6].
3.31
specimen holder
device that supports a specimen (3.27) in the right position in the pole-piece gap of the objective lens
3.32
standard excitation condition
setting condition for excitation current to derive the highest performance of the objective lens
Note 1 to entry: Under this condition, specimen height (3.30) shall be set so that the image (3.13) is focused.
Note 2 to entry: This condition is provided by the TEM manufacturer for each instrument.
Note 3 to entry: Image magnification (3.15) is generally measured under this condition; however, as long as
reproducible conditions are established, the magnification can be calibrated at any of the instrument settings.
3.33
super-lattice
stable periodic structure which is fabricated by alternating layers of at least two different kinds of
materials
Note 1 to entry: The super-lattice can be used as a reference material (3.25) for calibration of image magnification
(3.15) from a medium-high to high magnification range.
3.34
transmission electron microscope
TEM
instrument that produces magnified images or diffraction patterns of the specimen (3.27) by an electron
beam which passes through the specimen and interacts with it
3.35
under focus
focusing condition in which the specimen height is further from the objective lens than its object plane
3.36
zone axis
crystallographic direction, designated [uvw], defined by the intersection of a number of crystal planes
(h , k , l … …h , k , l ) such that all of the planes satisfy the so-called Weiss zone law; hu + kv + lw = 0
1 1 1 i i i
4 Image magnification
4.1 Definition of the image magnification
The image magnification (or scaling factor) of the TEM is defined by the ratio of the linear dimension
of the specific structure on the detected image to the corresponding linear dimension of the specific
structure in the specimen. There are three main kinds of image detectors: photographic film, imaging
plate, and image sensor, such as CCD array or CMOS sensor built in the digital camera.
In general, the value of image magnification detected on an image sensor is different from the value
of image magnification detected on the photographic film or imaging plate under the same electron
optical conditions for TEM imaging, because the image-detecting positions are different from each
other (see Figure 1).
Key
1 electron gun 9 monitor
2 condenser lens 10 computer
3 specimen 11 digital camera (image sensor) 1
4 objective lens 12 screen/monitor
5 first magnified image 13 viewing screen
6 intermediate lens 14 photographic film/imaging plate
7 second magnified image 15 digital camera (image sensor) 2
8 projector lens
Figure 1 — Detector position in TEM system
4.2 Expressing magnification
The magnification of an image recorded on the photographic film or the imaging plate, or detected by the
image sensor, is given by a number representing the number of times, and the number is accompanied
by the symbol × (e.g. 10 000×, 10k×, 1 000 000×, 1M× or ×10 000, ×10k, ×1 000 000, ×1M, where 10 000,
10k, 1 000 000 and 1M are magnitude numbers). Alternatively, introducing a scale bar having a length
corresponding to unit length on the specimen can be used to represent the magnification. The digitized
image should also indicate a magnification by detailing the number of pixels per unit distance of the
raw data file.
NOTE The horizontal field width (HFW) is another way to define the scaling on a magnified image.
5 Reference materials
5.1 General
For calibrating the magnification of an image, wherever possible, choose a CRM that is produced in
accordance with ISO 17034 and certified in accordance with ISO Guide 35.
When a suitable CRM is not available, an RM produced in accordance with ISO 17034 may be used.
5.2 Requirements for CRM/RM
Ensure that the chosen CRM/RM
— is stable with respect to vacuum and repeated electron-beam exposure,
— is aligned to a low-index zone axis along the electron optical axis, if the specimen region is a single
crystal,
— provides a good contrast and clear interface for the periodic structure in the TEM image,
— can be cleaned to remove contamination without causing mechanical/electrical damage or
distortion,
— has a smooth surface on both sides and identical thickness for a super-lattice structure, at least
within the area used for the calibration process, and
— has an associated valid calibration certificate.
NOTE Single crystal specimens of pure elements used for calibration do not need a calibration reference
certificate.
5.3 Storage and handling
The CRM/RM shall be stored in a desiccating cabinet or in a vacuum container.
To ensure minimal handling of the actual CRM/RM, it may be permanently mounted on a specimen
holder or a specimen cartridge.
The CRM/RM should be carefully handled without causing damage during the handling.
Check the contamination and deterioration of the CRM/RM, as these may affect calibration. Do not use
the CRM/RM if it is damaged or grossly contaminated.
Check the calibration of the CRM/RM at intervals by comparing its calibration values with those of
other CRMs/RMs; record the results. The frequency of verification may depend on the nature and usage
of the CRM/RM.
The CRM/RM shall be used for calibration purposes only.
6 Calibration procedures
6.1 General
Parameters that influence the magnification of a TEM may cause systematic errors. These are listed in
Annex A for additional information.
A major factor that influences the reproducibility of the calibration is the magnetic hysteresis of the
electromagnetic lens. It is necessary to minimize its influence by adopting the procedure described
below in the same sequence each time, especially related to the direction of magnification setting
(higher to lower, or lower to higher). Also, the specimen height and focus setting will influence the
reproducibility of the calibration.
To obtain the value of the uncertainty within the laboratory, it is necessary to repeat the calibration
procedure periodically.
The selection of the CRM/RM depends on the magnification range being used and the accuracy required.
For the purpose of this document, ensure that the uncertainty and repeatability of the calibration is
less than ±5 % and 98 %, respectively.
The flowchart of the calibration procedure is shown in Annex B for additional information.
6.2 Mounting CRM/RM
At the time of mounting the specimen, ensure that the handling of the CRM/RM is carried out in
accordance with 5.3.
Mount the CRM/RM in accordance with the instructions provided by the TEM and the CRM/RM
manufacturers.
Check that the CRM/RM is securely fixed on the specimen holder or specimen cartridge so that it does
not move from its mounting. This enables any image degradation caused by vibration to be minimized.
Check that the height of the specimen in the specimen holder is at the position recommended by the
TEM manufacturer's instructions, in order to keep the eucentric condition.
It is desirable to use a double-tilt or tilt-rotate specimen holder for aligning the crystal orientation of
the specimen to the optical axis.
6.3 Setting TEM operating conditions for calibration
Set the operating condition of the TEM according to the following procedures to ensure, as far as
possible, use of the same conditions.
−4
a) Check that the degree of vacuum in the TEM column is lower than 10 Pa and stable.
b) The high voltage shall be applied and an appropriate time be allowed for it to stabilize.
NOTE Oil-filled 100 kV tanks take about 2,5 h; gas-filled tanks take about 45 min. Higher voltage
instruments are normally operated with the high voltage continually applied; therefore, a stabilization
period is not usually required.
c) Use an anti-contamination device, if needed.
d) Select a specimen region of interest (region) for the calibration which is clean and free from damage,
ensure the eucentric height of the region and adjust the height of the region, if necessary.
e) In order to minimize the effect of the magnetic hysteresis of the lenses, set the magnification of the
TEM to the target value for calibration according to the same sequence; for example, adjust a higher
magnification than the target magnification at first, then set the target magnification after that.
f) Set the excitation of the objective lens to the desired reproducible value; the standard condition is
recommended.
g) Adjust the specimen height to focus the magnified image projected on the fluorescent screen, the
TV monitor or the personal computer (PC) screen. If the TEM in question is not equipped with a
specimen-height control function, this procedure can be omitted.
h) Correct astigmatism at a slightly higher magnification than the target value and adjust the
accelerating voltage centre. For example, if the target calibration is ×100k, set the magnification in
the range ×150k to ×200k for alignment.
i) Switch the observation mode of the TEM to the selected-area electron-diffraction (SAED) mode
or the convergent-beam electron-diffraction (CBED) mode from the image mode. Also, make sure
that the objective aperture is removed. For the SAED mode, it is necessary to insert a selected-
area aperture over the area of interest of the specimen in order to project a selected-area electron-
diffraction pattern on the viewing device (fluorescent screen, TV monitor, PC screen).
j) Adjust the condenser lens system to provide nearly parallel illumination conditions.
k) Align a low-index zone axis of the crystal parallel to the optical axis (i.e. zone-axis illumination), if
the specimen is a single crystal (see Figure 2).
a) Off-axis condition b) Zone-axis condition
Figure 2 — Difference of diffraction pattern by crystal orientation
l) Insert the objective aperture, centring it about the electron optical axis.
m) Switch the observation mode of the TEM back to the image mode.
n) Return the magnification to the target value of calibration, and set the excitation current of the
objective lens to the standard exciting condition again.
o) Apply a relaxation function to relax the magnetic hysteresis of the objective lens, if the TEM has it.
p) Adjust the specimen height to focus the magnified image roughly. If the TEM in question is not
equipped with a specimen-height control function, this procedure can be omitted.
q) Adjust the fine focus by varying the exciting current of the objective lens. If necessary, it is possible
to use the image wobbler function for focusing the image. However, the function related to the
optimum under-focus condition linked with the image wobbler function shall be turned off, if the
TEM is equipped with this function.
r) Adjust the illumination condition of the condenser lens system (spot size and brightness) with
reference to the dynamic range of each detector to obtain image contrast in the whole dynamic
range.
The condenser lens system should be operated under conditions which approach parallel illumination.
Alternatively, they should be done under a condition where it is documented that the beam convergence
no longer affects the image focus. This can be done by recording multiple images under varying degrees
of beam convergence.
6.4 Capturing digitized image
It is necessary to digitize the image in order to minimize readout error on the measurement of
magnification. The bit depth of digitization of the image shall be larger than 8 bits. There are three
ways of digitizing the magnified image corresponding to each image detector (see Table 1).
Table 1 — Comparison table for image detector
Image detection Apparatus for digitization Pixel size
Photographic film Flatbed image scanner Determined by pixel-resolution applied to image
scanner
Imaging plate Dedicated image digitizer Determined by laser-beam diameter for readout
Image sensor (digital cam- — Same size as that of the image sensor
era)
a) Photographic film: the magnified image (for calibration) is directly exposed on it. The analogue
image recorded on the photographic negative film shall be converted to a digitized image by using
an image scanner, according to the procedure described in 6.5. It is preferable to use a flatbed
image scanner, because it is easy to set the glass scale in it for pixel size calibration.
b) Imaging plate (IP): the magnified image (for calibration) is directly exposed on it. The recorded
image shall be obtained with a dedicated image digitizer (IP reader) which in turn is connected to a
PC.
c) Image sensor: the image (for calibration), captured by the image sensor (built into a digital camera
and connected to a PC), is digitized and displayed on the monitor screen of the PC system. The
image shall be saved on the memory in the PC system as an image file with a reversible format.
Ensure that the procedure for normalization of gain is performed to get the uniform background of
the digital camera image.
Before and during the execution of the digitization procedure, ensure the following conditions.
— The correct sensitivity setting is used for the photographic film used to get the negative image with
proper density and contrast on the film.
— The exposure time is short so that the blurring of the image due to specimen drift is minimized in
the recorded image.
— The readout process of the magnified image detected by the digital camera does not use “binning”
treatment.
— Uncompressed file format, such as ESP, PICT, TIFF, or Windows bitmap, or a reversible (lossless)
compressed file format, such as GIF or PING, shall be used for saving the digitized image.
— Ethical digital imaging requires that the original uncompressed image file be stored on archival
media (e.g. CD-R) without any image manipulation or processing operation. All parameters of
the production and acquisition of this file, as well as any subsequent processing steps, shall be
documented and reported to ensure reproducibility. This is a quote from the MSA (Microscopy Society
of America) Policy on Digital Imaging. Generally, acceptable (non-reportable) imaging operations
include gamma correction, histogram stretching, and brightness and contrast adjustments. All
other operations (such as unsharp-masking, Gaussian blur, etc.) shall be directly identified by the
author as part of the experimental methodology. However, for diffraction data or any other image
data that is used for subsequent quantification, all imaging operations shall be reported.
6.5 Digitizing the image recorded on photographic film
6.5.1 General
The flatbed image scanner with a transparent manuscript unit can be used to convert the analogue
image recorded on the photographic negative film to a digitized image. The direction of the periodic
structure in the image on the negative film along the Y-axis of the PC display needs to be adjusted
within a few degrees. Also, in order to minimize the edge-distortion effects of the image scanner, set
the negative film near the centre of the scan area.
6.5.2 How to decide the pixel-resolution for digitization
Generally, when the length, L, is measured with the dispersion (measurement deviation), dL, the
minimum scale unit of the measurement shall be less than 1/10 of dL. This relation shall apply when
considering the pixel size setting at the digitization of the recorded image on the photographic negative
film by an image scanner.
Figure 3 shows the image of the specimen (CRM/RM) schematically in the plane of the image detector/
display (negative film, IP, PC display, etc.). Note that the periodicity of the specimen is approximately
aligned to the Y-axis. θ is the angle between the Y-axis and the axis (longitudinal direction) of the
specimen. As seen in Figure 3, the target length (i.e. the actual transverse length of the specimen), L ,
t
indicated by Key 1, in millimetres (mm), is calculated from the value of θ and the length, L , indicated
e
by Key 2, in millimetres (mm), is extracted in the parallel direction to the X-axis, using the formula,
L = L × cos θ.
t e
Also, L is the minimum extracted length from the whole series of recorded images and U, in
e(min)
per cent (%), is the dispersion obtained for the images of the CRM/RM. The pixel size or the scale unit,
S, can then be set so that the condition set in Formula (1) is satisfied. Note that all the recorded images
shall be digitized with the same value of S.
U 1
SL≤× × (1)
emin
()
100 10
where
S is the pixel size or the scale unit, in millimetres (mm);
L is the minimum extracted length from the whole series of recorded images, in
e(min)
millimetres (mm);
U is the dispersion obtained for the images of the CRM/RM in per cent (%).
The pixel-resolution, R (dpi), of the flatbed image scanner corresponding to the scale unit, S, in
s
millimetres (mm) is calculated using Formula (2):
25,425 400
R == (2)
s
SL ×U
em()in
where
R is the pixel-resolution (dpi) of the flatbed image scanner;
s
S is the pixel size or the scale unit, in millimetres (mm);
L is the minimum extracted length from the whole series of recorded images, in
e(min)
millimetres (mm);
U is the dispersion obtained for the images of the CRM/RM in per cent (%).
If S is smaller than 0,025 4 mm, set the pixel-resolution, R (dpi), to be greater than or equal to the
s
calculated value from Formula (2).
However, if S is larger than 0,025 4 mm, the calculated R will be smaller than 1 000 dpi. Such a low
s
value of the pixel-resolution is unsuitable for making the appropriate measurement. In such a case, set
the pixel-resolution to 1 000 dpi or more.
EXAMPLE 1 If the minimum length, L , and the dispersion, U, are 5 mm and 2 % respectively, the calculated
e(min)
value of S ≤ 0,01 mm. This corresponds to the pixel-resolution, R ≥ 2 540 dpi.
s
EXAMPLE 2 If the minimum length, L , and the uncertainty, U, are 20 mm and 2 % respectively, the
e(min)
calculated S and R values are 0,04 mm and 635 dpi, respectively. This value of pixel-resolution is too poor to
s
analyse the digitized image. In this case, set the pixel-resolution ≥ 1 000 dpi.
Key
– – – interface direction
auxiliary line for length, L
e
1 target length, L
t
2 measured length, L , parallel to the X-axis
e
Figure 3 — Schematic image of periodic pattern with a layered structure
6.6 Measurement of the angle-corrected distance, D , from the digitized image
t
6.6.1 General
To avoid artefacts in identifying the edges of the features to be measured, the analyst should define
the start and end points (edges) for measuring the angle-corrected distance, D (see Figure 5, Key 1) in
t
the digitized image corresponding to the target length, L (see Figure 3, Key 1). Automated computer
t
identification of edges should be used to assist in the detection of L . (see Figure 3, Key 1).
t
The measurement software should provide the following basic functions:
a) angle measurement;
b) length measurement of the pixel unit;
c) averaged line-profile function for arbitrary number of lines;
d) region function on the averaged line profile;
e) edge-detection function for the data in region, such as differential processing and maximum/
minimum peak detection.
Do not use a photocopy, or similar, of the digitized image to avoid introduction of an artificial error.
This is important to enable someone else to check this procedure with the same software.
6.6.2 Measurement procedure
Get the angle-corrected distance, D (see Figure 5, Key 1), in pixels, in the display plane of the image (PC
t
display) using the following procedures, and record the measured values in the data sheet.
a) Measure and record the tilt angle in degrees between the longitudinal direction of the periodic
structure in the digitized image (interface direction) and Y-axis of the PC display (see Figure 4).
Key
– – – interface direction
Figure 4 — Tilt angle, θ
b) Extract the basic pitch distance, D (see Figure 5, Key 2), in pixels, from an arbitrary line, LA,
e
parallel to the X-axis of the PC display (see Figure 5). Measure the basic pitch distance, D (see
e
Figure 5, Key 2) as the centre-to-centre; alternatively, the analyst can measure the distance either
“left edge of the first line”-to-“left edge of the last line” or “right edge of the first line”-to-“right
edge of the last line” for the target area of the periodic structures of the CRM/RM. Points, P (see
Figure 5, Key 3) and P (see Figure 5, Key 4), correspond to both ends of distance, D (see Figure 5,
2 e
Key 2).
— Use the pixel value as the measurement unit.
— To reduce the influence of image noise in the line profile along a line, LA, and to improve the
signal-to-noise ratio, apply an averaging processing along the periodic structure (not along the
Y-axis) for n lines (see Figure 6, Key 2).
— A procedure for choosing n (the number of lines for averaging) is described in Annex C for
additional information.
Key
– – – interface direction
auxiliary line for length, LA
1 angle-corrected distance, D
t
2 basic pitch distance, D
e
3 left end point, P , of basic pitch distance
4 right end point, P , of basic pitch distance
Figure 5 — Relationship between D , D and LA
t e
Key
1 averaging direction
2 n lines
Figure 6 — Scheme of averaging for n lines along the direction
...
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