B I O G R A P H YToshihiro Kogure is anassociate professor atthe Department of Earthand Planetary Science atthe Graduate School ofScience in the Universityof Tokyo. His researchinterest is the investigation of fine struct-ures in natural inorganic materials, espe-cially clay minerals, biominerals, nanoparti-cles, etc., mainly by using high-resolutionelectron microscopy.

A B S T R A C TIn the investigation of crystalline materialsby high-resolution electron microscopy(HRTEM), the overlap of amorphous sub-stances with crystalline materials is oftenunavoidable. In HRTEM images, these amor-phous substances appear as noisy contrastthat smears the contrast from the crystallinematerials and hinders their analysis. Toremove the noisy contrast by image process-ing, we have developed new noise filters,particularly by improving the algorithm toestimate the noise or background compo-nent. These optimum noise filters have beensuccessfully used to remove the noisy con-trast in HRTEM images from layered miner-als with stacking disorders, cross-section oftubular structures, and nanoparticles dis-persed in a glassy matrix.

K E Y W O R D Shigh-resolution transmission electronmicroscopy, noise filter, Wiener filter, imageprocessing, stacking disorder, nanotube,nanoparticle

A C K N O W L E D G E M E N T SThe authors are grateful to Prof. A. Matsudaand Dr Y. Banno for donating specimens.They also thank T. Takeshige for the prepa-ration of TEM specimens.

A U T H O R D E TA I L SProfessor Toshihiro Kogure, Department of Earth and Planetary Science,Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan.Email: kogure@eps.s.u-tokyo.ac.jp.

Microscopy and Analysis 22(6):S11-S14 (EU),2008

NO I S E FI L T E R S F O R HRTEM

I N T R O D U C T I O NHigh-resolution transmission electron micro-scopy (HRTEM) is a powerful and often irre-placeable technique, especially to investigatelocal atomic structures in condensed materi-als. Its performance has been further advancedduring the 21st century by the development ofa spherical-aberration corrector. However, theresolution of HRTEM images is often degradedby the overlap of noisy contrast from amor-phous substances with the surface of periodicstructures, which hinders their analysis. Theamorphous substances may be: 1. Damage lay-ers formed by ion-milling or a focused ion-beam (FIB) during thin film preparation, orformed by beam radiation during HRTEMobservation and recording; 2. Carbon coatingformed on insulating specimens for electronconductivity, or contamination by hydrocar-bon during TEM observation; and 3. Originalmaterials in the specimens, for instance, anamorphous matrix or the substrate used tosupport nanoparticles.

Conventionally, removal of such noisy con-trast in HRTEM images was tried by masking allareas except reciprocal spots or periodic latt-ices in the Fourier transform (FT) of an image,and then taking an inverse FT. However, ambi-guity in selecting the masking areas consider-ably influences the processed image, whichoften results in the formation of artifactsand/or loss of the original information.

To overcome this problem, Marks [1] andKilaas [2] proposed the use of a Wiener filteror its derivatives to remove the noisy contrastin HRTEM images. For instance, the algorithmproposed by Kilaas [2] is used to estimate thenoise component, which appears as a broadbackground in the FT, by obtaining anazimuthal average of the intensity in the FT.His method is valid for general HRTEM imagesfrom periodic structures, however, it is not at

all effective in several cases. This article brieflydescribes new optimum noise filters with amore advanced algorithm for backgroundestimation, and reports some applications ofthe filters in mineralogy and related sciences.

M E T H O D S

Principle of the Noise FilteringThe FT (F0 ) of an observed image may beexpressed as the sum of a signal Fc originatingfrom the periodic part (the crystals) and abroad background Fb from the non-periodicpart (the amorphous materials), and thusF0 = Fc + Fb. The signal Fc is confined to dif-fraction-like spots and is usually strong, whilethe background Fb distributes more evenly.Thus, if the image contains a single domain ofa crystal, it is easy to select Fc by using a maskthat is made up of a set of periodic holes. How-ever, this simple periodic masking does notwork for a non-ideal crystal.

The Wiener filter uses an adaptive mask Mwwhich is obtained by seeking a solution thatminimizes the summed square differencebetween the signal Fc and its estimate Fw :

Σ |Fw − Fc|2 = Σ |Mw F0 − Fc|2 ⇒ minimum

where we approximate the estimate with aproduct of a mask Mw and the FT of anobserved image: Mw F0.

When we assume that the signal and noiseare uncorrelated, the appropriate solution forMw is given by:

Mw = |Fc |2 / |F0 |2 ≈ ( |F0 |2 _ |Fb |2 ) / |F0 |2

where we use |F0|2 ≈ |Fc |2 + |Fb |2.Thus, we have an applicable form of theWiener filter given by:

Fw = Mw F0 ≈|F0 |2 _ |Fb |2

F0 = [1_ |Fb |2 ] . F0|F0 |2 |F0 |2

Application of Optimum HRTEM NoiseFilters in Mineralogy and Related Sciences Toshihiro Kogure,1 Paul H. C. Eilers 2 and Kazuo Ishizuka 3. 1. Department of Earth and Planetary Sciences, The University ofTokyo, Japan. 2. Department of Medical Statistics, Utrecht University, The Netherlands. 3. HREM Research Inc., Japan.

Figure 1: (a) High-resolution transmission electron microscope image of kaolinite with a heavy stacking disorder and its Fourier transform. (b) The image processed using a radial background Wiener filter (RWF) and its Fourier transform.

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where |Fb|2 is an estimate of a non-periodicbackground. Here, Mw and thus Fw is set tozero, if |F0 |− |Fb | ≤ 0 , in other words when theestimated background is higher than theobserved value.

Estimation of BackgroundIn order to use the Wiener filter given abovewe have to estimate the background contri-bution |Fb | in Fourier space. Here, we assumethat the contribution from amorphous (non-periodic) materials varies slowly [1,2]. Then,the background may be estimated asexplained below.

Radial BackgroundThe background is normally estimated as anazimuthal average of the Fourier transform ofthe whole image. Here, an average is takenafter excluding strong intensities correspond-ing to diffraction originating from a periodicstructure [1,2]. A Wiener filter using this radialbackground is denoted by RWF hereafter.

Two-Dimensional BackgroundHowever, the radial background will not workwhen structure information appears at thesame distance from the origin in Fourier space.Thus, we developed a novel approach basedon P-spline fitting [3] to estimate a smoothedtwo-dimensional background in Fourier space.A Wiener filter using a two-dimensional back-ground is denoted by 2DWF hereafter.

Local Two-Dimensional BackgroundWhen a periodic structure is small in size andits orientation changes locally, the backgroundestimated from the Fourier transform of thewhole image may not be adequate. Thus, atwo-dimensional background in Fourier spaceis locally estimated for each small image areagiven by dividing a whole image. A Wiener fil-ter using a local two-dimensional backgroundis denoted by 2DLWF hereafter.

Transmission Electron MicroscopySpecimens for TEM experiments were pre-pared by mechanical grinding down to a spec-imen thickness of ~50 µm. They were furtherthinned to electron transparency by ion-milling with argon ions with an energy ofabout 5 keV and an ion-incidence angle of 20o,without liquid nitrogen cooling. The speci-mens were carbon-coated to ensure electricalconductivity.

HRTEM experiments were conducted using aJEOL JEM-2010 UHR (Cs = 0.5 mm) operated at200 kV. Images were recorded on films or aGatan Model 794 bottom-mounted multi-scancamera. The direct magnification on the filmswas 400,0003. Images on the films were digi-tized using a CCD camera.

R E S U LT S A N D D I S C U S S I O N

Disordered Stacking Sequence in KaoliniteKaolinite (Al2Si2O5(OH)4) is one of the mostabundant and industrially important clay min-erals. Kaolinite has a layer structure and eachlayer consists of a SiO4 tetrahedral sheet andan AlO2(OH)4 octahedral sheet. Although thestructure of the layer itself is steady, the inter-layer relation can be varied, which results instacking disorders or the loss of three-dimen-sional periodic structure. HRTEM imaging isthe only technique to analyze the stacking dis-order, by observing the stacking sequences ofthe layers directly. However, kaolinite is sobeam-sensitive that the contrast from thelayer structure is generally overlapped by noisycontrast originating from amorphous sub-stance formed by radiation damage [4].Accordingly, image processing by noise filtersis often necessary to investigate the structureand stacking sequences in kaolinite.

Figure 1a shows an HRTEM image of kaolin-ite and its FT. Discrete spots are aligned per-pendicularly at the centre in the FT, which cor-respond to the layer periodicity of ca. 0.72 nm.

On the other hand, the side row is almoststreaked, suggesting heavy stacking disorderin the structure. The contrast of the layer struc-ture, however, is smeared by the noisy contrastin the original image (Figure 1a). The noisycontrast corresponds to the broad backgroundaround the centre in the FT. Conventionalnoise suppression using a periodic lattice maskcannot be applied to the streaked FT pattern.Figure 1b shows a filtered image using RWF.The contrast in individual layers is greatlyenhanced compared with the original image.

Cross-sections of Tubular ChrysotileAfter the discovery of the carbon nanotube byIijima [5], tubular fine materials are receivingbroad attention. Chrysotile (Mg3Si2O5(OH)4),known as a kind of asbestos, is a natural multi-wall nanotube [6]. The structure of chrysotile isclose to kaolinite, but the layers are rolled upto accommodate the misfit of lateral dimen-sions between the tetrahedral and octahedralsheets in a layer. Chrysotile is also electron-beam sensitive.

Figure 2 shows an original image of thecross-section of a chrysotile tube. In Figure 2a,the region near the bottom of the figure wasdamaged by the electron beam and becameamorphous. It was also suspected that in theregion where the chrysotile structure wasimaged, amorphous substance formed by theradiation damage was overlaid beside amor-phous materials formed during the samplepreparation. Owing to the noisy contrast fromthese amorphous materials, the contrast fromthe chrysotile structure is not clear enough toanalyze its structure. Figure 2b is an enlarg-ment of the red squared region in Figure 2aand Figure 2c its FT. In the FT, two rings corre-spond to ca. 0.72 and 0.36 nm periodicities per-pendicular to the layers, and two arcs correspond to 0.46 nm periodicity along thelayers.

The results of image processing using the

Figure 2: (a) HRTEM image of a cross-section of a chrysotile multi-wall tube. (b) A portion of the image as indicated by the rectangle in (a). (c) The FT of the image in (b)..

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NO I S E FI L T E R S F O R HRTEM

three noise filters are presented in Figure 3.The left and right columns are the filteredimage with its FT, and mathematical subtrac-tion of the filtered image from the originalimage (Figure 2b), respectively. The top row(Figure 3a) shows the result using RWF.Although RWF works fine for the case of kaoli-nite, the quality of the tubular contrast in thefiltered image is not improved at all, com-pared with the original image (Figure 2b). Thereason is that subtraction of the azimuthalaverage of the intensity in the FT decreases notonly the background but also the periodiccomponents because the FT intensity of theperiodic components is distributed circumfer-entially. As a result, the contrast of the periodicstructure is weakened, similar to the contrastfrom the amorphous materials. This isexpressed in the subtracted image in the rightcolumn, where the chrysotile structure isclearly observed.

In comparison, the result using 2DWF (Figure3b) is far better, proving the effectiveness ofthe smoothed two-dimensional backgroundestimation for such a specific FT pattern. TheFT of the filtered image indicates the effectivesuppression of only background. However, thesubtracted image in the right column shows aweak periodic contrast. This is attributed to acontinuous change in the orientation of theperiodic structure over the image, owing tothe tubular structure. Because the backgroundintensity in the FT is just the average of thewhole area, its estimation can be weaker orstronger than local intensities for periodicstructure. Moreover, there is an amorphousregion at the bottom of the original image(Figure 2b). Due to this region, the estimatedbackground intensity becomes too strong forthe upper region.

Next, the result using 2DLWF is shown in thebottom column (Figure 3c). In this case, thesuppression of the noise is very effective andthe periodic contrast is very clear in the filteredimage. There is almost no periodic contrast inthe mathematical subtraction, indicating thatthe periodic contrast is properly extractedfrom the original image. In conclusion, 2DWFcan solve the problem by circumferential dis- Figure 4:

(a) HRTEM image of a SiO2-TiO2 nanocomposite film on silicon substrate. (b) A portion of the image as indicated by the rectangle in (a). (c) The Fouriertransform of the image in (b).

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Figure 3: Left: Processing of the images shown in Figure 2b, using three versions of the noise filters. Centre: The FTs of the processed images. Right: Mathematical subtraction of the processed image from the original images in Figure 2b. (a) RWF. (b) 2DWF. (c) 2DLWF. For 2DLWF, the originalimage with 512 x 512 pixels was divided into partial images with 64 x 64 pixels.

tribution of the FT intensity from the periodicstructures, and 2DLWF can solve the problemarising from a continuous change in the orien-tation of the periodic structure over theimage.

TiO2 Nanoparticles in SiO2 Glass MatrixTitanium dioxide (TiO2) is an extensively inves-tigated material because of its photocatalyticproperty [7]. For instance, a dispersion of TiO2

nanoparticles in a SiO2 glassy matrix, derivedfrom a homogeneous SiO2-TiO2 amorphousgel, has been developed as a high-photocat-alytic composite material [8]. In the SiO2

matrix, the TiO2 component crystallizes intoanatase, a polymorph of TiO2. Anatase ismetastable compared to rutile, another TiO2

polymorph. However, the nucleation ofanatase in the SiO2 matrix is favoured owing toits lower surface energy [9]. In TEM, discrimi-nation between anatase and rutile for individ-ual nanoparticles is possible by observing thelattice fringe in the particles. For this purpose,clear HRTEM images showing a finer latticefringe are preferable. However, contrast fromamorphous SiO2 smears the lattice fringe andsuppression of aperiodic contrast by imageprocessing is necessary.

An HRTEM image of the specimen is shownin Figure 4a. The specimen is a SiO2-TiO2 com-posite film (the molar ratio is 5:1) formed on asilicon substrate [8]. Figures 4b and 4c are thesquared portion of 4a and its FT, respectively.In Figure 4b, a lattice fringe of ca. 0.35 nm thatcorresponds to (101) of anatase (d101) is visiblebut it is difficult to find a finer lattice fringe,for instance 0.238 nm (d004) or 0.189 nm (d020),in the image.

The processed images using the three noisefilters are shown in Figure 5. RWF (Figure 5a)slightly enhances the lattice fringe but a pro-nounced effect is not observed. As seen in Fig-ures 4b and 4c, the original image contains anumber of crystallites and the spots corre-sponding to the lattice fringe form discreteDebye-Scherrer rings in the FT. Hence, subtrac-tion of the azimuthal average of the intensityin the FT considerably decreases the intensitiesof the spots as well as the background. As aresult, the contrast of the lattice fringe is notenhanced enough compared with the amor-phous contrast. On the other hand, they aremore enhanced by 2DWF (Figure 5b) and fur-ther more by 2DLWF (Figure 5c). Especially, thelattice fringe of ca. 0.24 nm is clearly visible inthe processed image by 2DLWF. Furthermore,a faint lattice fringe of circa 0.19 nm can beobserved in the circled area around the centreof 2DLWF.

C O N C L U S I O N S The new filters with advanced background-estimation techniques suppress noisy contrastfrom amorphous materials effectively inHRTEM images of nanometre-sized periodicstructures. As a result, the periodic contrast inquestion is enhanced without any problematicartifact. Although in this study the effective-ness of the new filters has been demonstratedfor HRTEM images from a layered structurewith heavy stacking disorder, cross-sections of

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Figure 5: Left: Processing of the images shown in Figure 4b, using three versions of the noise filters. Right: Magnified portion (rectangle) of the processed imageson the left. (a) RWF. (b) 2DWF. (c) 2DLWF. For 2DLWF, the original image with 512 x 512 pixels was divided into partial images with 64 x 64 pixels.

nanotubes and aggregates of nanoparticles,more applications will easily be found. Theoptimum noise filters used in the present study(HREM Filters Pro) are available from HREMResearch Inc. [10] as a plug-in module forGatan DigitalMicrograph. RWF and some use-ful utilities are available as freeware (HREMFilters Lite) [10].

R E F E R E N C E S1. Marks, L. D. Wiener-filter enhancement of noisy HRTEM

images. Ultramicroscopy 62:43-52, 1996. 2. Kilaas, R. Optimal and near-optimal filters in high-resolut-

ion electron microscopy. J. Microscopy 190:45-51, 1998.3. Eilers, P. H. C. et al. Fast and compact smoothing on large

multidimensional grids. Computational Statistics and DataAnalysis 50:61-76, 2006.

4. Kogure, T. and Inoue, A. Determination of defect structures

in kaolin minerals by high-resolution transmission electronmicroscopy (HRTEM). Am. Mineral. 90:85-89, 2005.

5. Iijima, S. Helical microtubules of graphic carbon. Nature354:56-58, 1991.

6. Yada, K. Study of chrysotile asbestos by a high resolutionelectron microscope. Acta Cryst. 23:704-707, 1967.

7. Negishi, N. et al. Preparation of transparent TiO2 thin-filmphotocatalyst and its photocatalytic activity. Chem. Lett.9:841-842, 1995.

8. Matsuda, A. et al. Transparent anatase nanocomposite filmsby the sol-gel process at low temperatures. J. Am. Ceram.Soc. 83:229-231, 2000.

9. Zhang, H. Z. and Banfield, J. F. Thermodynamic analysis ofphase stability of nanocrystalline titania. J. Mater. Chem.8:2073-2076, 1998.

10. HREM Research Inc: www.hremresearch.com.

©2008 John Wiley & Sons, Ltd