ISO/DIS 24597

Microbeam analysis -- Scanning electron microscopy -- Methods for the evaluation of image sharpness

Analyse par microfaisceaux -- Microscopie électronique à balayage -- Méthodes d'évaluation de la netteté des images

Standards Content (sample)

DRAFT INTERNATIONAL STANDARD ISO/DIS 24597
ISO/TC 202/SC 4 Secretariat: JISC
Voting begins on: Voting terminates on:
2008-09-02 2009-02-02

INTERNATIONAL ORGANIZATION FOR STANDARDIZATION • МЕЖДУНАРОДНАЯ ОРГАНИЗАЦИЯ ПО СТАНДАРТИЗАЦИИ • ORGANISATION INTERNATIONALE DE NORMALISATION

Microbeam analysis — Scanning electron microscopy —
Methods for the evaluation of image sharpness

Analyse par microfaisceaux — Microscopie électronique à balayage — Méthodes d'évaluation de la netteté des

images
ICS 37.020

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International Organization for Standardization, 2008
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ISO/DIS 24597
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ii ISO 2008 – All rights reserved
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Contents
Foreword………………..………………………………………………………………………………………………………v
Introduction……………………………………………………………………………………………..………………………vi
1 Scope…………………………………………………………………………………………………………………………1
2 Normative references…………………………………………………………………..………………………...…………1
3 Terms, definitions and abbreviated terms………………………………………………………...………………………1

4 Steps for acquisition of SEM image…………………………….......................................................…………………2

4.1 General……………………………………………………………………………………….........………………………2
4.2 Specimen……………………………………………………………………………………......…………………………2
4.3 Specimen tilt………………………………………………………………………….......................……………………3
4.4 Selection of the field of view……………………………………………………………………… ……………………3

4.5 Selection of the pixel size…………………………………………………………………….........................…………3

4.6 Brightness and contrast of the image…………………………………………………………………….......…………4

4.7 Contrast-to-noise ratio of the image……………………………………………………………………….........………5

4.8 Focus and astigmatism of the image……………………………………….……………..............……………………7

4.9 Interference from external factors………………………………………………………............……….………………7

4.10 Erroneous contrast………………………………………………………………………………………............………7
4.11 SEM Image data file……………………………………………………………………………….......…………………7

5 Acquisition of an SEM image, and selection of an area within the image………………….........…….………………7

6 Evaluation methods………………………………………………………………………………................………………7
6.1 General…………………………………………………………………………………………………….…......…………7

6.2 Contrast-to-noise ratio (CNR) ……………………………………………………………….................….……………8

6.3 Fourier transform (FT) method………………………………………………………………………….......……………8
6.4 Contrast-to-gradient (CG) method…………………………………………………….........……………….…………11

6.5 Derivative (DR) method……………………………………………………………….........................…….…………13

7 Test report………………………………………………………………………………...……......................…...………15
7.1 General……………………………………………………………………………………………….......…….…………15
7.2 Contents of test report……………………………………………………………………………......……….…………15

Annex A (normative) Details of contrast-to-noise ratio (CNR) ……………………………………................…………17

iii
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Annex B (normative) Details of Fourier transform (FT) method……………………………..............………….………20

Annex C (normative) Details of contrast-to-gradient (CG) method……………………………….........……….………33

Annex D (normative) Details of derivative (DR) method…………………………………….........................….………43

Annex E (informative) Background of evaluation of image sharpness………………...………………..………………62

Annex F (informative) Characteristics and applicability of evaluation methods………..…………………….......……66

Annex G (informative) A method for preparing a standard specimen for evaluating image sharpness….....………70

Annex H (informative) Example of test report………………………………………………………….....……….………72

Bibliography (informative) ……………………………………………………………………….........................…………74

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Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO

member bodies). The work of preparing International Standards is normally carried out through ISO technical

committees. Each member body interested in a subject for which a technical committee has been established has

the right to be represented on that committee. International organizations, governmental and non-governmental, in

liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical

Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

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.

ISO 24597 was prepared by Technical Committee ISO/TC 202/SC 4, Microbeam analysis, Scanning electron

microscopy.
Annexes E, F, G, H and Bibliography are for information only.
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Introduction

The International Organization for Standardization (ISO) draws attention to the fact it is claimed that compliance

with this document may involve the use of patents concerning the evaluation method using contrast-to-gradient

(CG) method given in 6.4.

ISO takes no position concerning the evidence, validity and scope of this patent right.

The holder of this patent right has assured the ISO that he/she is willing to negotiate licences under reasonable and

non-discriminatory terms and conditions with applicants throughout the world. In this respect, the statement of the

holder of this patent right is registered with ISO. Information may be obtained from:

Patent holder: Hitachi, Ltd.

Address: Marunouchi Center Bldg., 6-1, Marunouchi 1-chome, Chiyoda-ku, Tokyo, 100-8220, Japan

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent

rights other than those identified above. ISO shall not be held responsible for identifying any or all such patent

rights.
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Microbeam analysis — Scanning electron microscopy —
Methods for the evaluation of image sharpness
1 Scope

This International Standard specifies the methods to evaluate the image sharpness of digitized images generated

by a scanning electron microscope (SEM) by applying Fourier transform (FT) method, contrast-to-gradient (CG)

method and derivative (DR) method.
2 Normative references

The following normative documents referenced in the text herein, constitute provisions of this International

Standard. For dated references, subsequent amendments to them, or revision of any of these publications do not

apply. However, parties to agreements based on this International Standard are encouraged to investigate the

possibility of applying the most recent edition of the normative document indicated below. For undated references,

the latest edition of the normative document referred to applies. Members of ISO and IEC maintain registers of

currently valid International Standards.
ISO 16700 :2004, Guideline for calibrating image magnification.

ISO 17025 :1999, General requirements for the competence of testing and calibration laboratories.

ISO / FDIS 22493 : SEM Terminology.
3 Terms, definitions and abbreviated terms

Definitions and abbreviations of the terms referred herein are listed in document 22493 (SEM Terminology,

ISO/DIS 22493) and ISO 16700:2004.

Additional definitions and abbreviations required for this standard are listed below.

3.1
pixel
smallest non-divisible image-forming unit on a digitized SEM image
3.2
pixel size
specimen length (nm) per pixel in an SEM image
NOTE Horizontal and vertical pixel sizes should be same.
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3.3
binary SEM image
a converted SEM image in which there are only two brightness levels
3.4
convoluted image

an image obtained by convolution of a binary SEM image with a two-dimensional Gaussian profile

3.5
sharpness factor

twofold standard deviation (2σ) of Gaussian profile used to make the convoluted image

3.6
image sharpness

2σ/√2, namely, the sharpness factor divided by the square root 2, where the sharpness factor of SEM image being

regarded as same as that of the convoluted image by Gaussian profile with standard deviation σ

3.7
contrast-to-noise ratio (CNR)

ratio of I – I to σ , where I and I are image intensities for the object and the background, and σ is the standard

A B n A B n
deviation of image noise
3.8
Fourier transform method (FT method)

method for evaluating the image sharpness by comparing Fourier transform profiles of an SEM image with those of

the convoluted images
3.9
contrast-to-gradient method (CG method)

method for evaluating the image sharpness using weighted harmonic mean gradients of the two-dimensional

brightness distribution map of an SEM image
3.10
derivative method (DR method)

method for evaluating the image sharpness by fitting error function profiles to gradient directional edge profiles of

particles in an SEM image
3.11
field of view
area of a specimen that corresponds to the whole SEM image
4 Steps for acquisition of SEM image
4.1 General

For SEM image acquisition, it is important to first adjust the microscope conditions (for example, see Annex B in

ISO 16700). Image sharpness is dependent upon (i) the specimen itself, (ii) structural smoothness of the

foreground and the background of the image, (iii) brightness and contrast and (iv) contrast-to-noise ratio (CNR).

Therefore, follow the procedures described in 4.2 to 4.10 corresponding to the above factors for evaluation of

image sharpness by all the three methods described herein. Particular attention must be paid to the adjustment of

electron probe current and focussing conditions in order to obtain optimum requirements for brightness and

contrast (4.6) and contrast-to-noise ratio (4.7).
4.2 Specimen

At the date of publication of this document there is no designated Certified Reference Material (CRM). Acceptable

results can be obtained using a specimen prepared by the method described in Annex G. Select a specimen with a

smooth and flat surface. For evaluations of the image sharpness, choose a part of the specimen which contains

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circular particles deposited on the substrate. Obtain desirable images at the chosen magnification, in accordance

with 4.4.

NOTE Sensitive material for electron dose is not suitable as a specimen for the evaluation of image sharpness.

4.3 Specimen tilt
Set the specimen tilt angle at 0 degree (non-tilting condition).

NOTE Error within +/- 3 degrees in tilt angle of the specimen will not affect the evaluation of image sharpness.

4.4 Selection of the field of view

Select the field of view containing a flat and smooth surface, because image sharpness varies with the uneven

features of the surface structure. Figure 1 (a) and (b) show the acceptable and unacceptable fields of view,

respectively. Choose particles extending to several ten pixels (see Figure 1(a)).

(a) Acceptable image (b) Unacceptable image

Figure 1 — SEM images with (a) acceptable and (b) unacceptable structured foreground images

4.5 Selection of the pixel size

Before evaluating the image sharpness, it is necessary to calibrate the image magnification and/or the scale

marker accordingly with ISO 16700.
4.5.1 Determination of the pixel size from a field of view
The pixel size L (nm) is determined from the formula:
FOV
L = ,

where L (nm) shows the horizontal size of the field of view on an SEM image, and N is the number of pixels

FOV p
covering to the horizontal field of view.
4.5.2 Determination of the pixel size from a scale marker
The pixel size L (nm) is calculated by using a scale marker as follows:
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scale
L = ,
scale

where L is the “indicator” value (e.g. nominal value in nm) of the scale marker and N is the number of pixels

scale scale
covering to the length of the scale marker.
4.5.3 Conversion of the pixel size

The image sharpness as derived by the methods described herein (R ) is in “pixel” unit. The image sharpness R

PX L
in “nm” unit is then converted by the expression:
R = L ⋅ R ,
L p PX
where L is the pixel size.

NOTE Set pixel size about 40% of the expected value of the image sharpness. For example, set the pixel size 0,8

nm when the image sharpness is expected to be 2 nm.
4.6 Brightness and contrast of the image

The signal intensity of the image should be widely distributed. Figure 2 (a), (b), (c) and (d) show examples of

images with acceptable and unacceptable brightness and contrast. Line profiles along the dotted lines at the same

vertical position for their images are shown as eye guideline.
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(a) Acceptable image (b) Unacceptable (over-saturated) image
(d) Unacceptable (both-saturated) image
(c) Unacceptable (under-saturated) image
Figure 2 — SEM images with acceptable and unacceptable brightness and contrast
4.7 Contrast-to-noise ratio of the image

Contrast-to-noise ratio (CNR) of the image must be 10 or larger. Here, the CNR is defined as a ratio of the image

contrast (C ) to the standard deviation (σ ) of the image noise (see Figure 3).
image n
CNR = C /σ.
image n
Procedures for the CNR evaluation are given in Annex A.
Figure 4 shows the simulated appearance of the images with CNR of 5, 10, and 50.
Figure 5 shows examples of SEM images with different CNR of about 4 and 30.

NOTE In order to obtain SEM images with good CNR, it is necessary to adjust the probe current and/or the image

acquisition time. One should be aware of the fact that variations in the above parameters will affect the evaluation

results of image sharpness.
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Region A Region A
22σσ
imageimage
RegRegiion B on B
22σσ SS
nn BB
Figure 3 — Intensity profile of an image

(a) CNR = 5 (b) CNR = 10 (c) CNR = 50

Figure 4 — Simulated images with different contrast-to-noise ratios (CNR)

(a) Low contrast-to-noise ratio (CNR ≈ 4) (b) High contrast-to-noise ratio (CNR ≈ 30)

Figure 5 — SEM images with different contrast-to-noise ratios (CNR)
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4.8 Focus and astigmatism of the image

Focus the electron beam as best as possible. Use an image that is free of astigmatism.

4.9 Interference from external factors

External factors such as mechanical vibrations, distortion by magnetic field and those listed in Annex B of ISO

16700 affect the image sharpness. Ensure, as far as possible, that images used are not affected by these factors.

4.10 Erroneous contrast

Make sure that images do not contain erroneous contrast (e.g. contrast due to charging-up of the specimen).

4.11 SEM Image data file

Image data, which is directly saved from an SEM, shall be in digital format with the greyscale at least 8 bits deep.

Data file of the image shall be in an uncompressed graphics file format, e.g. BMP or TIF.

NOTE Do not use the data obtained from a printed SEM image.
5 Acquisition of an SEM image, and selection of an area within the image
The procedures described in this section are common in this standard (see 6).

a) Use a specimen prepared according to the procedure described in 4.2. Acquire an image by paying attention to

conditions in 4.3 to 4.10.

b) Select a square area in the SEM image (hereafter referred to as the image) comprising at least 256 x 256 pixels.

The area shall not have superimposed extraneous data (e.g. magnification display, scale marker, characters,

arrows, etc.).
NOTE Choose an area containing images of preferably non-overlapping particles.

c) Store the selected SEM image in a data file in an un-compressed graphics file format specified in 4.11.

6 Evaluation methods
6.1 General

Evaluation methods described in 6.3 to 6.5 are based on the assumption that the electron beam has a Gaussian

profile. Hence the results obtained by the methods do not represent the actual beam size (see Annex E.4). Figure

6 shows a general flow chart of the evaluation of an SEM image including the common procedure for evaluation of

the CNR.
Basic procedures for obtaining the image sharpness are as follows:
a) Select an SEM image by following 5.

b) Determine the CNR for the selected SEM image (see 6.2) and ensure that it is larger than or equal to 10 before

proceeding further.

c) Calculate a sharpness factor 2σ of the selected SEM image, in the frequency space or the real space

(depending on methods applied). Here, the image sharpness of an SEM image is determined from an

equivalent image produced by convolution of a binary SEM image with a two-dimensional Gaussian profile with

the sharpness factor 2σ (i.e., a twofold standard deviation).
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NOTE The calculation procedures depend on the method.
d) The image sharpness is defined as k⋅2σ, where k = 1/ 2 .
Start
Start
Load an SEM image
Load an SEM image
Evaluate the CNR value
a) Calculation of the CNR value
Execute
the FT method, or
the CG method, or
b) CNR >= 10
the DR method
yes
End End Stop
Figure 6 — General flow chart of the
Figure 7 — Flow chart of the evaluation of CNR
evaluation of an SEM image
6.2 Contrast-to-noise ratio (CNR)

The basic concept of the contrast-to-noise ratio (CNR) was developed in the medical imaging field. Refer to 4.7.

The CNR for the selected SEM image of interest shall be evaluated. Only the images with CNR = 10 or larger can

be passed to the next step for the image sharpness. Figure 7 shows a brief flow chart of the CNR evaluation

following routines a) and b). Details of the routines are described in Annex A.

NOTE If the value of CNR < 10, discard the SEM image. Acquire a new SEM image with lower noise, and carry

out the evaluation again.
6.3 Fourier transform (FT) method

For evaluating image sharpness, the Fourier transform (FT) method is used with the spatial frequency components

given by the FT of an SEM image. The spatial frequency components of the SEM image are compared with those

of the convoluted images obtained by the convolution of the binarized SEM image via Gaussian profiles with

various sharpness factors 2σ (see Figures 8 and 9). Details of procedures for the FT method are given in Annex B.

NOTE 1 The signal intensity of an image I is expressed as I (i,j), and the coordinates i and j are chosen as 0, 1,

m m

…, L–1 for an image with x- and y-size L (= 256, 512, …). However, the coordinates i and j are treated as integers

ranging from –L/2 to L/2–1 for the FT pattern.
NOTE 2 The following explanation is applied to the image with L = 256 pixels.
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F (f )
OH j
F (f )+C
NH jH N
(b)
(a)
F (f )
NH jH
F (f ;2 =4)
CH j
F (f ;2σ )
CH j OH
P F (f ;2σ=6)
3H CH j
-25 -20 -15 -10 -5 0
(c) (d)
Horizontal coordinate : f [pixel]

Figure 8 — (a) a selected SEM image I (i,j) with Figure 9 — Averaged and smoothed FT curves

image size L = 256, (b) the binarized image taking common logarithm, F (f) for the

OH j

I (i,j), (c) and (d) the convoluted images selected SEM image I (i,j), F (f ;2σ) and

O CH j
I (i,j;2σ) with 2σ = 4 pixels, and I (i,j;2σ) with
F (f ;2σ ) for the convoluted images I (i,j;2σ)
C C CH j OH C
2σ = 6 pixels, respectively
and I (i,j;2σ )
C OH
a) Generation of convoluted images

1) Generate a filtered image I (i,j) processed by the 3x3 median filter, for a selected SEM image I (i,j).

OF O

2) Produce a histogram H(S) of I (i,j), and then obtain a smoothed histogram H (S) by using the moving

OF S
averages of 9 points. Then calculate h (S) = log {H (S) + 1}.
S 10 S

3) Determine S and S that correspond to the intensities of the substrate and the particles respectively, and

L H
determine a threshold level (S + S )/2 by using h (S).
L H S
4) Produce a binarized image I (i,j) by using (S + S )/2.
B L H

5) Add the white noise to the selected image I (i,j) by setting SNRp (signal-to-noise ratio for particles) = 30 for the

signal intensity S = 192.

6) Generate convoluted images I (i,j;2σ) by the convolution of the binarized image I (i,j) via two dimensional

C B

Gaussian profiles with various sharpness factors 2σ = 2σ(N) beginning with 2σ(1) = 1, where each σ

corresponds to the standard deviation of the Gaussian distribution and N (=1, 2, …) is the step number.

7) Adjust the intensity of the various convoluted images I (i,j;2σ) so that the maximum and the minimum

intensities are S and S , respectively.
H L
b) Generation of curves of FT patterns

1) Carry out the FT for the selected SEM image I (i,j) and the various convoluted images I (i,j;2σ). The G (f ,f )

O C O i j

and G (f ,f ;2σ) represent the FT patterns corresponding to I (i,j) and I (i,j;2σ), respectively.

C i j O C

2) Obtain the horizontally averaged-and-smoothed value of |Re[G (f ,f)]| and the vertically averaged-and-

O i j

smoothed value of |Re[G (f ,f)]|, and calculate the curves F (f) and F (f) by taking common logarithm of

O i j OHA j OVA i
them.
NOTE Re [...] denotes the real part, and |...| denotes the absolute value.

3) Obtain the averaged curves of F ( f ) and F ( f )by applying the moving averages of 5 points along the

OH j OV i

horizontal f and the vertical f directions for the curves F (f ) and F (f ), respectively.

j i OHA j OVA i
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4) Obtain the averaged curves F ( f ;2σ ) and F ( f ; 2σ ) for G (f ,f ;2σ), in a similar manner.

C i j
CHB j CVB i
c) Calculation of temporary image sharpness R
PXO

1) Determine the noise areas both for the curves F ( f ) and F ( f ) , and then obtain the noise functions

OH j OV i

F ( f ) and F ( f ) in the noise areas, respectively, by the linear approximation.

NH j NV i

2) Calculate the corrected curves F (f ;2σ) and F (f ;2σ) from the averaged curves F ( f ;2σ ) and

CH j CV i
CHB j
F ( f ;2σ ) by using the signal and noise intensities at the origin of (f ,f ).
i j
CVB i

3) Obtain the value f = f by using F (f ), F (f ) and a specified constant C , and then calculate the horizontal

j jC OH j NH j N
coordinate f from f by using the linear interpolation.
jH jC

4) Determine the coordinates of three points, P (on the curve F (f )), P (on the line F (f )) and P (on the

1H OH j 2H NH j 3H
curve F (f ;2σ )) by using several functions acquired.
CH j OH

NOTE These points are on a vertical line with horizontal coordinate f , in the graph as shown in Figure 9.

5) Determine the coordinates of three points, P (on the curve F (f )), P (on the line F (f )) and P (on the

1V OV i 2V NV i 3V
curve F (f ;2σ )), in a similar manner.
CV i OV

6) Obtain the sharpness factors 2σ and 2σ by applying the linear interpolation for 2σ(N), by increasing the step

OH OV
number N.
7) Calculate the sharpness factor 2σ by 2σ = (2σ + 2σ ) / 2.
O O OH OV
8) Calculate the temporary image sharpness R by R = .
PXO PXO 2σ / 2
d) Calculation of image sharpness R
1) Calculate the coefficient C from the sharpness factor 2σ for calibration.
F O
2) Obtain the calibrated sharpness factor 2σ by using the coefficient C .
C F
3) Evaluate the image sharpness R by R = .
PX PX 2σ / 2
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Start
Load an SEM
image
Generation of
convoluted image
Generation of curves for
FT pattern
Calculation of temporary
image sharpness R
PXO
Calculation of image
sharpness R
END
Figure 10 — Brief flow chart of processes in the FT method
6.4 Contrast-to-gradient (CG) method

The contrast-to-gradient (CG) method is based on both the extraction of intensity gradient at each pixel in the

image by fitting a quadratic surface to the 3x3 area, centred at each pixel point (see Figure 11 (b)). The CG image

sharpness R is inversely proportional to be a weighted harmonic mean of the gradients. Finally, the CG image

sharpness R is converted to the image sharpness Res using standard images with various sharpness factors 2σ.

quadratic surface
(b) Depth image corresponding to the
original image and a typical quadratic
surface fitting to the 3x3 area centred at
each pixel point
(a) Original SEM image

Figure 11 — Original SEM image and fitting a quadratic surface to the 3x3 area, centred at

each pixel point, of its depth image
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The image sharpness has little noise-dependency and is evaluated with CNR as a given parameter. Figure 12

shows a brief flow chart of the CG method composed of the following routines a) – d). Details of the routines are

given in Annex C.
a) Calculation of the CG image sharpness R for the original image.

A number of reduced images are generated using the value of reduction factor r = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15

and 20. Each reduced image is labelled as 1/r-th image. With the above convention, the 1/r-th image for r = 1 is

the original image. The image reduction works to reduce the image noise at the cost of image sampling

frequency. In the present process (b), the following four kinds of sharpness are calculated; i.e. local sharpness,

directional sharpness, directionally averaged sharpness, and CG image sharpness. The former three kinds of

sharpness are calculated for each reduced image. The last CG image sharpness, which characterizes the

image, is determined from curves of R and ∆R/R vs. r, where ∆R is the fluctuation of R.

1) Local sharpness
In each image, the local sharpness
...