ISO 13322-1:2004

INTERNATIONAL ISO
STANDARD 13322-1
First edition
2004-12-01
Particle size analysis — Image analysis
methods —
Part 1:
Static image analysis methods
Analyse granulométrique — Méthodes par analyse d'images —
Partie 1: Méthodes par analyse d'images statiques

Reference number
©
ISO 2004
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ii © ISO 2004 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Terms, abbreviated terms, definitions, and symbols. 1
3.1 Terms, abbreviated terms and definitions. 1
3.2 Symbols . 3
4 Sample preparation demands for method description . 4
4.1 General recommendations. 4
4.2 Suggested preparation methods. 5
5 Image capture. 6
5.1 General. 6
5.2 Procedures . 7
5.3 Operating conditions for an image capture instrument. 7
6 Microscopy and image analysis . 8
6.1 General. 8
6.2 Size classes and magnification . 9
6.3 Counting procedure. 9
7 Calculation of the particle size results . 13
8 Test report. 13
Annex A (normative) Study on the sample size required for the estimation of mean particle
diameter . 15
Annex B (normative) Operating magnification. 34
Annex C (normative) Resolution and sizing limits for typical objective lenses . 35
Annex D (informative) Flow chart showing a typical image analysis method . 36
Annex E (informative) Statistical tests of mean and variance — Analysis of variance and multiple
comparisons. 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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 13322-1 was prepared by Technical Committee ISO/TC 24, Sieves, sieving and other sizing methods,
Subcommittee SC 4, Sizing by methods other than sieving.
ISO 13322 consists of the following parts, under the general title Particle size analysis — Image analysis
methods:
 Part 1: Static image analysis methods
 Part 2: Dynamic image analysis methods
iv © ISO 2004 – All rights reserved

Introduction
The purpose of this part of ISO 13322 is to give guidance for a measurement description and its validation
when determining particle size by image analysis.
Image analysis is a technique used in very different applications on image material with variations in material
properties. Hence, it is not relevant to describe an exact standard method for determination of particle size by
image analysis. The aim of this part of ISO 13322 is limited to give a standardized description of the technique
used and a standardized validation.
This part of ISO 13322 includes methods of calibration verification using a certified standard graticule as a
reference or by using certified standard particles. It is sensible to make some measurements on particles, or
other reference objects, of known size so that the likely systematic uncertainties introduced by the equipment
can be calculated.
This part of ISO 13322 gives a recommendation for a precise description of the distribution including the
number of analyzed particles and an analysis window to make sure that the obtained information is valid.
Measurement of particle-size distributions by microscopy methods is apparently simple, but because only a
small amount of sample is examined, considerable care has to be exercised in order to ensure that the
analysis is representative of the bulk sample. This can be demonstrated by splitting the original sample and
making measurements on three or more parts. Statistical analysis of the data, for example using the Student's
t-test, will reveal whether the samples are truly representative of the whole.
Errors introduced at all stages of the analysis from sub-division of the sample to generation of the final result
add to the total uncertainty of measurement and it is important to obtain estimates for the uncertainty arising
from each stage. Indications where this is required are given at the appropriate point in the method.
Because of the diverse range of equipment and sample preparation expertise available, it is not intended to
give a prescriptive procedure where use of individual methods does not jeopardize the validity of the data.
However, essential operations are identified to ensure that measurements made conform to this part of
ISO 13322 and are traceable.
INTERNATIONAL STANDARD ISO 13322-1:2004(E)

Particle size analysis — Image analysis methods —
Part 1:
Static image analysis methods
1 Scope
This part of ISO 13322 is applicable to the analysis of images for the purpose of determining particle size
distributions. The particles are appropriately dispersed and fixed on an optical or electron microscope sample
stage such as glass slides, stubs, filters, etc. Image analysis can recover particle images directly from
microscopes or from photomicrographs.
Even though automation of the analysis is possible, this technique is basically limited to narrow size
distributions of less than an order of magnitude. A standard deviation of 1,6 of a log-normal distribution
corresponds to a distribution of less than 10:1 in size. Such a narrow distribution requires that over 6 000
particles be measured in order to obtain a repeatable volume-mean diameter. If reliable values are required
for percentiles, e.g. D or other percentiles, at least 61 000 particles must be measured. This is described in

Annex A.
2 Normative references
The following referenced documents are indispensable for the application 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 9276-1, Representation of results of particle size analysis — Part 1: Graphical representation
ISO 9276-2, Representation of results of particle size analysis — Part 2: Calculations of average particle
sizes/diameters and moments from particle size distributions
3 Terms, abbreviated terms, definitions and symbols
3.1 Terms, abbreviated terms and definitions
For the purposes of this document, the following definitions apply.
3.1.1
view field
field which is viewed by a viewing device, e.g. optical microscope or electron scanning microscope
3.1.2
measurement frame
field in a view field in which particles are counted for image analysis
NOTE The set of measurement frames composes the total measurement field.
3.1.3
binary image
digitized image consisting of an array of pixels, each of which has a value of 0 or 1, whose values are
normally represented by dark and bright regions on the display screen or by the use of two distinct colours
3.1.4
edge finding
one of many edge detection methods used to detect transition between objects and background
3.1.5
Euler number
number of objects minus the number of holes inside the objects, which describes the connectedness of a
region, not its shape
NOTE A connected region is one in which all pairs of points can be connected by a curve lying entirely in the region.
If a complex two-dimensional object is considered to be a set of connected regions, where each one can have holes, the
Euler number for such an object is defined as the number of connected regions minus the number of holes. The number of
holes is one less than the connected regions in the set compliment of the object. It is important to report the Euler number
together with the connectivity applied, i.e., 4-connectivity or 8-connectivity.
3.1.6
Feret diameter
distance between two parallel tangents on opposite sides of the image of a particle
3.1.7
equivalent circular diameter
ecd
diameter of a circle having the same area as the projected image of the particle
NOTE It is also known as the Haywood Diameter.
3.1.8
grey image
image in which multiple grey level values are permitted for each pixel
3.1.9
image analysis
processing and data reduction operation which yields a numerical or logical result from an image
3.1.10
numerical aperture
NA
product of the refractive index of the object space and the sine of the semi-aperture of the cone of rays
entering the entrance pupil of the objective lens from the object point
3.1.11
pixel
picture element
individual sample in a digital image that has been formed by uniform sampling in both the horizontal and
vertical directions
3.1.12
segmentation
〈noun〉 part into which something can be divided; subdivision or section
3.1.13
segmentation
〈verb〉 act of dividing something into segments
2 © ISO 2004 – All rights reserved

3.1.14
threshold
grey level value which is set to discriminate objects of interest from background
3.2 Symbols
δ error
θ half-angle subtended by the particle at the objective lens
λ wavelength, expressed in micrometres
µ refractive index of the surrounding medium
ϕ shape factor
A projected area of particle i
i
d minimum feature length
H horizontal calibration factor
cal
K constant numerically determined by the confidence limit
N number of particles to be measured
n numbers of particles of size X
i i
P probability
P
probability that particle i exists in the measurement frame (also called Miles-Lantuejoul factor)
i
V vertical calibration factor
cal
V relative volume of particle i
i
X diameter of spherical particle i
A
X area equivalent diameter of particle i
Ai
X horizontal Feret diameter of object
F1
X vertical Feret diameter of object
F2
X dimension of particle i
i
X longest dimension of particle i, also called maximum Feret diameter
imax
X shortest dimension of particle i, also called minimum Feret diameter
imin
X lower limit of a class interval
LIL
X mean of X
mean i
X upper limit of a class interval
UIL
X horizontal dimension of object
X horizontal dimension, expressed in micrometres
1,m
X horizontal dimension, expressed in pixels
1,p
X vertical dimension of object
X vertical dimension, expressed in micrometres
2,m
X vertical dimension, expressed in pixels
2,p
Z horizontal side length of the rectangular measurement frame
Z vertical side length of the rectangular measurement frame
4 Sample preparation demands for method description
4.1 General recommendations
4.1.1 General
The following recommendations provide a sampling of standard microscopy practices.
NOTE See References [4], [5] and [10] for additional suggestions.
4.1.2 Sample subdivision
As only a small amount is needed to prepare a sample, the whole sample shall be subdivided in a manner that
ensures that the portion taken is representative of the whole.
The method used to subdivide the sample is likely to be dictated by the sample preparation method and will
be decided by the laboratory performing the analysis.
Provided that the sample is well dispersed by the method and that there is no segregation of particles by size,
the choice of method is left to the expertise of the laboratory, since any specialized equipment required by a
particular method might not be available to all.
4.1.3 Touching particles
The number of particles touching each other should be minimized.
It is a prime requirement of the method that measurements shall be made on isolated particles. There should
be as few particles as possible touching each other. Touching particles measured as one particle without a
proper separation will introduce error.
4.1.4 Particle distribution
There should be an adequate distribution of particles on the sample support. The whole area of the
preparation should be examined to ascertain whether there is noticeable segregation of particles (by size).
Statistical comparison of the results on a frame-by-frame basis will test for uniform distribution of particles.
This procedure is detailed in Clause 7.
4.1.5 Sample preparation
Electron microscope samples should be coated with a thin layer of metal (e.g. Au, Au/Pd, Pt/Pd) to reduce
charging effects.
4 © ISO 2004 – All rights reserved

Samples should be examined as soon as possible after preparation, and should contain an expiration date.
The sample preparation method used should be fully described in the final particle size analysis report by
giving quantitative details of the nominal masses, volumes and compositions of particles and products used at
each stage of the preparation procedure.
4.1.6 Number of particles to be counted
The number of particles measured should be determined based on the particle-size distribution and the
desired confidence limits. Assuming the particles are log-normally distributed, the required number (N) of
particles with a given error ()δ and a given confidence limit is estimated in accordance with Equation (1):
log N = −2 log δ + K (1)
where K is numerically determined by the confidence limit, particle distribution and other parameters; see
References [1] and [2].
NOTE See Annex A for detailed information.
4.2 Suggested preparation methods
Several methods can be investigated for preparing samples for measurement. The following methods may be
used. They are based on the assumption that a representative sample be used to give an adequate dispersion
of the particles and a sharply contrasted image.
4.2.1 Camphor-naphthalene (C-N) method
This method uses a eutectic mixture of 60 % mass fraction camphor and 40 % mass fraction naphthalene that
melts at 32 °C and sublimates rapidly in a vacuum. To prepare the sample, a 1 g sample of the particles to be
counted is kneaded by hand inside a plastic bag with the requisite amount of the C-N eutectic mixture. When
the particles sample is fully disaggregated and well dispersed in the C-N by the heat of the hand, the plastic
bag is cooled to solidify the resulting mixture. Small lumps of this solid mixture are then transferred to a
microscope slide resting on a warm plate. The sample, when melted, is flattened under a cover-slip that is
afterwards removed to allow the C-N eutectic to sublimate under vacuum.
This technique was found to give good dispersion of irregular quartz particles and has the advantages that the
particles are viewed in air, which results in a good contrast in the refractive index, and that the slides do not
age. However, tests with glass beads have been unsuccessful, as the particles segregate on the slide, do not
stick well and tend to roll off, making the method unusable; see Reference [3].
4.2.2 Paste-dilution method
A sample of about 1 g of particles is mixed with a viscous liquid (gelatine, sucrose or glycerol in water,
collodion in amyl acetate) on a watch glass with a spatula to give a thick paste, thus ensuring mechanical
disaggregation and dispersion. A sample of the paste is then taken with the point of a spatula and diluted in
the same viscous liquid to a concentration such that, after homogenization, one drop of the resulting
suspension, flattened under a cover-slip, will give the required number of particles on a microscope slide, that
is, about 20 particles per view frame. Depending on the choice of liquid, the slides can have only a temporary
life or might be able to be stored indefinitely. Using glycerol, this method has been successful for glass beads.
It gives a good uniform dispersion and a reasonably contrasted image. The use of a cover-slip aids resolution
with high-magnification objectives. However, the slides tend to dry out within an hour or so and repeat counts
with the same slide are not possible; see Reference [4].
4.2.3 Filtration methods
4.2.3.1 Powder or dry suspensions
A 1 g sample of particles is suspended in a suitable liquid and dispersed. A given volume of this suspension is
then filtered to dryness on a suitable membrane. The concentration of the suspension and the membrane area
of filtration are such that the particles are deposited in the required concentration for counting (about
20 particles per measurement frame). After air-drying, the membrane is cut into small sections which are
attached by their edges to a microscope slide using an acetone-resistant glue (e.g. cyanoacrylate or “super-
glue”). The gluing is to prevent the membrane from shrinking. The slide is then put in a closed container on a
support over a free surface of liquid acetone, whose vapour renders the membrane transparent for viewing
and particle-counting. The method has the advantage that the particles are viewed in air giving a good
contrast in refractive index. Tests indicate that to avoid the membrane re-opacifying, it is preferable to perform
the exposure to acetone very slowly over several hours; see Reference [5].
4.2.3.2 Liquid suspensions
A known volume of suspension, typically 100 ml, is vacuum-filtered, as described below, through a membrane
of compatible material and known pore size, typically 0,8 µm cellulose nitrate for mineral oils. Particles larger
than the pore size should appear well scattered across the membrane with little or no overlap. If the number of
particles is too great and overlapping is excessive, the test should be repeated with a smaller known volume
of suspension. Conversely, if the number of particles is too few, a greater volume of known amount should be
1)
used. The vacuum arrangement, for example a Millipore filtration system, consists of a membrane holder
attached to an open flask, with a vacuum pump attached below the filter holder. A separate spray container
with an integral filter attachment, typically 0,45 µm, is used with a compatible solvent to wash down the sides
of the open flask to ensure that all particles are collected on the membrane for analysis, and to remove the
liquid from the suspension, leaving a reasonably dry membrane for examination. The membrane should be
examined as soon as possible; if there is a delay, it can be inserted between two pre-cleaned microscope
slides. Appropriate glue for making the membrane transparent may be used; see Reference [6].
4.2.4 Dry deposition method
Particles may be prepared for counting by dry deposition onto a slide covered with double-sided transparent
adhesive tape. Care shall be taken that all the particles in a given sample effectively stick on the slide, so as
to ensure that there is no selective capture of particles by size. A microscope slide is positioned in the bottom
of a vacuum chamber having a volume of about 1 l. A conical metal plug is fitted in the top of the chamber and
the particles to be analyzed are placed in a groove all around the plug. When the vacuum is released by lifting
the plug, the particles are sucked as a cloud into the chamber and fall on the slide. Adhesion on the slide may
be enhanced by using double-sided tape or a film of grease. This method also has the advantage that
particles are viewed in air, resulting in a good contrast in refractive index.
5 Image capture
5.1 General
Particle-size data can be influenced by specific parameters affecting the image formation process. It is
possible to distort the reported size, particularly of the smallest particles, by using inappropriate image-capture
conditions, e.g. magnification, illumination, etc. Distortion in the image might arise from a number of causes,
but its presence and effect on the image can be measured by selecting a recognizable object at a number of
points and orientations in a frame of view. It is important to note that the measurements made provide only
two-dimensional, X and Y, information. The imaging instrument should be set up and operated in accordance
with its manufacturer's recommendations considering the conditions given below.

1)
Millipore is an example of a suitable product available commercially. This information is given for the convenience of

users of this part of ISO 13322 and does not constitute an endorsement by ISO of this product.

6 © ISO 2004 – All rights reserved

5.2 Procedures
At each operating condition used for the analysis, carry out the following steps.
a) Select a recognizable object in the image.
b) Place the feature in the centre and at the corners of the field of view in turn and measure its horizontal
length X .
( )
c) Rotate the sample stage 90 degrees and repeat the measurements ( X ) .
d) Record the values of X and X with the final result.
1 2
e) Calibrate the imaging instrument prior to the examination of samples using a certified graticule or
equivalent.
f) If possible, mount the traceable calibration graticule together with the specimen in the imaging instrument.
g) Select the magnification in accordance with Annex B or Annex C and set the corresponding illumination
and imaging conditions.
h) Place the calibration grating in the field of view, select a suitable area and focus it.
i) Obtain the image to be analyzed and then capture it either digitally or by use of a suitable photographic
image.
j) Record a significant number of measurement frames for each sample by scanning the sample in a raster
pattern as indicated in Figure 1. Once this operation is started, no changes to the operating conditions
should be made.
Figure 1 — Sample raster pattern
k) At the end of measurement, place the calibration graticule in the field of view and check the calibration
once more. The comparison of two calibration images taken at the beginning and the end of the
examination will provide a measure of the variability in instrument magnification.
l) Report the calibration constants obtained before and after the analysis together with the precise details of
the microscope settings (working distance, spot size, electron microscope magnification, etc.).
5.3 Operating conditions for an image capture instrument
5.3.1 General
There are various imaging systems used for particle sizing. The setup for particle sizing using an electron or
optical microscope is briefly described in 5.3.2 and 5.3.3.
5.3.2 Operating conditions for an electron microscope
The following special conditions are required for measuring particle size using an electron microscope:
a) image contrast mode: used to adjust the desired peak signal level;
b) accelerating voltage: set according to the material to be measured;
c) specimen position: The sample working distance specified by the electron microscope
manufacturer for high resolution imaging should be selected. The
sample should be mounted flat on the specimen holder with the stage
tilt set to zero;
d) dynamic focus and tilt correction: both of these controls should be switched off.
e) Select the operating magnification after reference to Annex B. The total magnification is the product of
electron microscope magnification and any image analyzer transfer magnification.
5.3.3 Operating conditions for an optical microscope
For bright-field images in the light microscope which are commonly used for particle sizing, the minimum
feature length, d, expressed in micrometres, distinguishable in monochromatic light is given by Equation (2):
0,6λ
d = (2)
µ sinθ
where
λ is the wavelength, expressed in micrometres;
θ is the half angle, expressed in degrees, subtended by the particle at the objective lens;
µ is the refractive index of the surrounding medium.
The theoretical lower limit is approximately 0,2 µm, but the diffraction halo around the particle gives a gross
overestimate of size. Special attention should be given to range of particle size to be measured, then to the
measurement in order to obtain the required accuracy. Annex C gives the resolutions and smallest resolvable
feature lengths for some typical objectives. As a rule of thumb, the smallest dimension of the smallest particle
to be measured should be at least 10 times larger than this resolution limit.
6 Microscopy and image analysis
6.1 General
Modern image analyzers usually have algorithms available for enhancing the quality of the image prior to
analysis and for separating touching particles. Enhancement algorithms may be used, provided that the
measurements can be unambiguously associated with the particles in the original image. Irregularly shaped
particles or particles with sharp corners should not be separated since this would distort the shape of the
particles. All touching particles of this kind should be rejected from the measurement and a note should be
made of the proportion of particles rejected from each measurement frame; see 6.3.4. Touching spherical
particles may be separated, as this will give minor distortion of the area of particles. A flow-chart showing
typical procedures used in carrying out measurements by image analysis is given in Annex D.
8 © ISO 2004 – All rights reserved

6.2 Size classes and magnification
The theoretical limit for resolution of objects by size using image analysis is one pixel and counts should be
stored particle-by-particle with a maximum resolution of one pixel. Note that any compression of images might
reduce the resolution. However, it is necessary to define the size classes for the final reporting of results; the
desire for maximum resolution should be tempered by the necessity for precision, which is a function of the
total number of particles counted, the dynamic range and the number of pixels included in the smallest objects
to be considered. It is, therefore, recommended that pixels be converted to real-world dimensions prior to any
reporting of size for quantitative analysis.
The magnification used should be such that the smallest particles counted have a projected area sufficient to
meet the accuracy required. All particles measured should be sized and stored with a resolution of one pixel.
The final results are to be reported by grouping the particles into size classes. For samples with a narrow size
distribution, the grouping may be based on a linear progression and for samples with a wide distribution, the
grouping may be based on a logarithmic progression. The intervals for these progressions should be based on
the dynamic range and total number of particles counted. The particles assigned to a given class are those
that have a diameter that is equal to or greater than the lower limit of the class interval, X , and less than the
LIL
upper limit, X , as specified in Equation (3):
UIL
XXu LIL UIL
Counts are to be checked on a frame-by-frame basis for significance using Student’s t-test on the mean
diameter and the F test on the variances. Counts not meeting the requirements should be rejected.
6.3 Counting procedure
6.3.1 General
The particle-size distributions should be determined by counting all particles in each measurement frame and
then summing over all frames.
6.3.2 Particle edges
A suitable grey-level threshold setting should define the particle edges. Techniques for doing this depend on
the sophistication of the image analysis equipment.
A half-amplitude method can be done manually, if necessary. A small region of the background located a few
pixels away from the boundary of a typical particle is selected. The threshold level at which approximately half
the pixels in the selected region are detected is recorded. This procedure is repeated for an area located a
few pixels inside the particle boundary. The threshold level should be set at a value midway between these
values; see Reference [7].
A second option is to “auto-threshold” the image, and then perform a manual check before proceeding with
the measurement
Whenever the threshold level is changed, the threshold image should be superimposed on the original image
and a visual check made to determine whether all of the particles have been “thresholded” correctly. If not, the
reason should be investigated and corrected before proceeding with the measurement.
6.3.3 Particles cut by the edge of the measurement frame
6.3.3.1 If all the objects that appear in the image frame are accepted for measurement, the accuracy of
the final distribution will be impaired because some of the objects will be cut by the edge of the image frame.
To overcome this, a measurement frame is defined within the image frame. The measurement frame can be
used in the following two ways.
a) All the objects are allocated one pixel (e.g. the centroid) as the feature count point. Objects are accepted
only when their feature count point lies within the measurement frame; see Figure 2 a). The measurement
frame can be of any shape provided that there is enough space between the edges of the two frames so
that no accepted particle is cut by the edge of the image frame.
b) A rectangular frame is used with the bottom and right edges defined as reject sides. Objects lying partially
or wholly within the measurement frame and not touching the reject sides are accepted; see Figure 2 b).
There has to be sufficient space between the top and left edges of the two frames so that no accepted
object is cut by the edge of the image frame. This covers all eventualities except for particles intersecting
the two opposite sides of the frame; these would either be too large to be measured at the magnification
or would be so acicular as to be unsuitable for classification by area anyway. Image analysis systems that
reject all particles intersecting a frame edge use an effective frame size that is different for each size
class and also different for each particle shape.

a)
b)
NOTE Shaded particles are included in count; unshaded particles are excluded from count.
Figure 2 — Treatment of particles cut by the edge of the measurement frame — Counting isolated
measurement frame (a); counting strip (b)
6.3.3.2 All particles entirely inside the measurement frame are accepted for counting. All particles outside,
or cut by the edge, are neglected. This creates the situation where the probability for a particle to be included
in the measurement frame varies inversely with the size of the particle. This, therefore, introduces a bias that
is greater the larger the size of the particle considered. The probability, P , of particle i having a horizontal
i
Feret, X , and a vertical Feret, X , in a rectangular measurement frame of size Z by Z is given by
F1 F2 1 2
Equation (4):
()ZX−−(Z X)
1F2 2 F2
P = (4)
i
ZZ
For spherical particles of diameter X this reduces to Equation (5):
A
()ZX−−(Z X)
1A 2 A
P = (5)
i
ZZ
10 © ISO 2004 – All rights reserved

The population of particles in the measurement frame should, therefore, be divided by the probability, P .
i
EXAMPLE A square frame of size 100 units × 100 units is used for counting a population of particles of sizes ranging
from 2 units to 10 units. The count of the particles wholly in the measuring frame and the correction factors are shown in
Table 1:
Table 1 — Example of a corrected count
Diameter Raw count Probability Corrected count
X n P n /P
i i i i i
arbitrary units
2 81 0,96 84
4 64 0,92 70
6 49 0,88 56
8 36 0,85 42
10 25 0,81 31
6.3.4 Touching particles
The slide-preparation method should be chosen to give a minimum number of touching particles.
Nevertheless, it is inevitable that there will be touching particles in each measurement frame and some
method of dealing with them is necessary.
However, the first requirement is to have an automatic method of identifying touching particles. This can be
done (a) by following the number of particles “created” by numerical separation procedures, (b) by some
criterion, such as the shape factor or the Euler number (the number of holes in an object) or even (c) by
manual intervention. The statistical procedure for evaluating slides might also give some indications.
Numerical separation procedures are not recommended for separating particle aggregates into individual
particles as they can change the size of the particles in the image and, in any case, make it difficult to ensure
traceability. Such procedures for identifying aggregates can be investigated by comparing the results with the
size counting performed on the original untreated image, but this would seem to be very laborious.
Identification of touching particles on the basis of shape or Euler number is not foolproof, in particular for
compact overlapping agglomerates, and will not distinguish real out-of-shape or oversized particles. ln cases
where touching particles cannot be avoided, careful use of various techniques, e.g. fractal analysis to identify
aggregates or model-based separation techniques, may be used to separate the particles.
6.3.5 Measurements
The measurement of the perimeter of particles depends strongly on the image-analysis system used.
Accordingly, the primary measurement is the projected area of each particle, expressed in pixels, then the
longest dimension of each particle, X , expressed in pixels.
imax
These two determine the shortest dimension of each particle, X , thus allowing the definition of a shape
imin
factor with the greatest discrimination. It is, therefore, recommended that the primary values be
a) area of each object, A ;
i
b) longest dimension of each particle, maximum Feret diameter, X ;
imax
c) shortest dimension of each particle, minimum Feret diameter, X .
imin
These are used to calculate the area-equivalent diameter, X , in accordance with Equation (6), and the
Ai
shape factor,ϕ , in accordance with Equation (7).
4A
i
X = (6)
Ai
π
X
imax
ϕ = (7)
X
imin
Appropriate correction shall obviously be made if the equipment used is not based on square pixels. To aid
comparison with the corresponding volumetric or mass certification method, the relative volume, V , of each
i
particle i can be calculated from the projected area-equivalent diameter, X , of the particle weighted by the
Ai
Miles-Lantoujoul factor, P , (see Table 1) for the contribution of the particle i to the whole population, in
i
accordance with Equation (8):
()X
Ai
V = (8)
i
P
i
6.3.6 Calibration and traceability
6.3.6.1 General
The equipment is first calibrated to convert pixels into SI length units, e.g., nanometres, micrometres,
millimetres, etc., for the final results. The calibration procedure shall include verification of the uniformity of the
field of view. An essential requirement of the calibration procedure is that all measurements shall be traceable
back to the standard metre. This can be done by calibrating the image analysis equipment with a certified
standard stage micrometer.
EXAMPLE The National Physical Laboratory certified chrome-on-glass reference stage graticule, National Institute
of Standards Technology SRM 475 and SRM 484 or with certified spherical particles.
6.3.6.2 Recommendations and requirements
6.3.6.2.1 Touching particles
Each object in an image frame should be counted and reported in the results, together with its area, maximum
and minimum Feret diameter, Euler number or a manual recognition mark indicating that the object is a group
of touching particles. These data will allow the testing of criteria for detecting and rejecting touching particles.
6.3.6.2.2 Distortion
Distortion is identified as follows.
a) Select a square on a multiple-square grid feature from a reference stage graticule, e.g. the same size as
the average particle. Place it at the centre and measure its width, X , and its height, X .
1 2
b) Place it at each of the four corners and measure its width, X , and its height, X , at each of the four
1 2
additional positions.
c) Report the five values of X and X with the final results.
1 2
6.3.6.2.3 Calibration
Each setting of the microscope is calibrated as follows.
a) Determine the correspondence between image size in pixels and the size in micrometres using the
multiple-square grid feature on the reference stage graticule.
12 © ISO 2004 – All rights reserved

b) Report the results as H , calculated in accordance with Equation (9), and V , calculated in
cal cal
accordance with Equation (10):
X
1, m
H = (9)
cal
X
1, p
where
X is the horizontal dimension, expressed in micrometres;
1,m
X is the horizontal dimension, expressed in pixels.
1,p
X
2, m
V = (10)
cal
X
2, p
where
X is the vertical dimension, expressed in micrometres;
2,m
X is the vertical dimension, expressed in pixels.
2,p
When using a matrix camera, either X or X and either H or V may be reported.
1 2 cal cal
7 Calculation of the particle size results
The mean particle size, X , and the variance, s , for a given number of particles, n, each with an
mean i
associated diameter, X , are calculated in accordance with Equations (11) and (12), respectively:
i
Xn
ii
∑
X = (11)
mean
n
i
∑
nX()−X
ii mean
∑
s = (12)
n −1
i
∑
In order to ensure the homogeneity of the measurements, the mean diameter and the variance obtained in
each measurement frame should to be tested by the analysis-of-variance and multiple-comparison tests
(Annex E).
8 Test report
The test report shall contain as a minimum the following information:
a) identification of the test specimen;
b) reference to this part of ISO 13322 (ISO 13322-1:2004);
c) complete description of the method used for sub-sample preparation, with full quantitative details of the
nominal weights, volumes and compositions of particles and products used at each stage of the sub-
sample preparation procedure;
d) mean particle size, X ;
mean
e) variance, s ;
f) full particle-by-particle results, with all dimensions in pixels, including the following:
 reference number of the particle;
 reference number of the sample;
 reference number of the sub-sample;
 reference number of the view field;
 objective used;
 frame size;
 area of particle;
 maximum and/or minimum Feret diameter;
 Euler number;
 X calibration factor;
 X calibration factor;
 relative volume of particle;
 any other useful information.
Usable results should be reported in tables and graphs in accordance with ISO 9276-1 and ISO 9276-
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