New filtering techniques to restore scanning tunneling microscopy images

New filtering techniques to restore scanning tunneling microscopy images

Surface 418 New filtering techniques microscopy images M. Pancorbo ‘, M. Aguilar to restore ‘, E. Anguiano scanning ’ and A. Diaspro 1 October...

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Surface

418

New filtering techniques microscopy images M. Pancorbo

‘, M. Aguilar

to restore

‘, E. Anguiano

scanning

’ and A. Diaspro

1 October

1990: accepted

for publication

6 February

‘,’

Scanning tunneling microscopy (STM) is a well established experimental technique to observe and to study surfaces down to the atomic scale level that has the capacity to operate in different media as vacuum, air and liquid [l] and makes it a promising tool for high resolution microscopy. The principle of the STM is the tunnel current that is established by applying a voltage between a tip and the sample when the separation between them is a few A. A feedback circuitry keeps this current constant and a scanning system moves the tip over the surface. By measuring either the tunnel current or the feedback signal as a function of the tip position the sample topography is obtained. The measured magnitude can be digitized and stored on a computer as a matrix which when displayed on a monitor represents an image of the surface. The images are affected by noise stemming from different sources with the most important

’ Permanent address; lstituto di Biofisica, nova. Via Giotto 2. 16153-Geneva, Italy. 0039-6028/91/$03.50

C’ 1991

Universita’

di Ge-

Elsevier Science Publishers

28049 Madrid.

Spain

1991

An asymmetric transfer function - based on the symmetric one used in optical systems with circular aperture - is presented here to restore STM (scanning implemented that utilize this transfer function. In the STM case, the defocusing direction that produce a set of two fitting parameters.

1. Introduction

(1991) 41X-423 North-Holland

tunneling

‘I Insrituto Ciencla de Materiales, Sede B (CSIC), Umuersidad Aut6noma de Madrid (C-III), h IBM Scientific Center. Uniuersidad Auionoma Madrid (C-XVI), 28049 Madrrd. Spam Received

Science 251/252

cases to correct blurring and defocusing effects tn tunneling microscopy) images. A Wien filter is has two different origins depending on the scan

type of the pink, l/f”, noise. On the other hand, the data, picked point by point, are in a certain sense blurred in the image formation system point spread function (PSF) due to the finite lateral resolution of the STM probe. Finally, the electronic system can modify the PSF, i.e.. the actual PSF can be completely different from that expected from the physical process that occurs. The usual procedures to eliminate the noise in the STM images are imported from other types of microscopy where the noise and defocusing in the image formation process is symmetric. On the other hand, STM is a technique with a strong asymmetry between the two scanning directions and therefore one must differentiate between blurring affecting the two scan directions. This asymmetry is particularly important in the case of fast scanning because along the scanning direction there is usually a strong electronic integration that asymmetrizes the PSF. Thus, we have proposed in a previous paper [2] a particular digital filter that allows to properly restore STM images. The aim of this paper is to discuss in depth the significance of the different parameters involved in the filter that we proposed in the previous paper and to present different examples of its utilization.

B.V. (North-Holland)

A4. Pancorbo et al. / New filtering techniques to restore STM images

419

2. Experimental techniques

3. Digital image processing

The STM mechanical part is from WA Technology, the feedback circuit was developed in collaboration with the electronic department of our Institute and the STM automation, data and image processing was made in collaboration with the IBM Scientific Centre in Madrid. The main characteristics of our STM is the high speed - of image acquisition (100000 pixels/s) and high resolution (16 bits). Our STM system is built around an IBM PS/280 which communicates through an IEEE488 interface with all the STM electronics, performs data acquisition, and real-time image display, as well as some image processing operations and checking. The digital image display used was an IBM 8514 with the 8514A Adapter that yields 1024 X 768 8-bits pixels resolution.

When the digitalization is performed one must be careful with the spatial and temporal frequencies that are involved. In particular three theorems must be satisfied: (a) the Whittaker-KotelnikovShannon theorem [3], which establishes that the size of the measured zone represented within the digital image should be such that the increments along and perpendicular to the scan direction should be smaller than the lateral resolution of the system; (b) the Shannon-Whittaker theorem [4] which establishes that the maximum sampling rate has to be smaller than two times the cut-off frequency of the measurement system, otherwise there will be an oversampling (this theorem sets an upper limits to the scanning speed); (c) the Shannon theorem [4] that imposes a minimum to the sampling frequency - and then to the scanning

Fig. 1. Image simulation and restoration: (a) simulated STM image with integration along x direction; (b) same as (a) but with noise Stokseth transfer function with added (noise/signal = 10); (c) filtered with the function that we propose, i.e., an asymmetric defocusing factors 8, = 0.1 and 8, = 6; (d) original disposition of the atoms in the model.

420

Fig. 2. Image of 1 Aycrystalline

M. Pancnrbo er al. / New: filterrng technique.r 10 restore STM mages

gold: 60 A

X

60 A. (a) Original

speed ~ and establishes that the maximum sampling rate m ust be higher than two times the frequ’ ency of interest. otherwise an &zing will occur Th e PSF and the noise in STM are related to

image: (b) filtered with the function 6, = 12.

that we propose

with 8, = 0.1 and

the equipment, which means that they do not depend on the surface profile, i.e.. on the IIleasured signal. This very reasonable assumption was first used by Stoll and Baratoff [5]. This me tans that the noise is additive and uncorrelated to the

M. Pancorbo et al. / New filtering techniques to restore STM images

Fig. 3. Image

of polyc~stalline gold: 700 A x 700 A. (a) Original image; (b) filtered with the function that we propose, asymmetric Stokseth transfer function with defocusing factors 8, = 0.1 and 6,. = 3.

signal. This implies that - in the Fourier frequency domain - G(q) = P(q)H(q) + N(q), where G(q) is the recorded image profile, P(q) the true surface

421

i.e., an

profile, f?(q) the PSF Fourier transform, also called transfer function, and N(q) the signal-independent noise.

M. Pancorho et ul. / New filtering

422

To evaluate P(q) it is necessary to find out an appropriate filter that - by applying it to the digitized image G(q) - yields the true image without noise P(q). The best option is to use a Wien filter, W(q), that produces an optimal leastsquares-error estimate P,(q). i.e.: P,(q) = kQ)G(q). The derivation of W(q), which depends on H(q) and on the spectral density of the noise G(q), can be found in ref. [3]. Thus, in order to restore the image a model for H(q) and +(q) is necessary. The most characteristic noise in STM images in the l/fa-like noise [6] with /3 a parameter whose value is a matter of discussion. We have estimated it by a procedure described in detail elsewhere [7] and we obtained p = 1.0 k 0.1. The p value is rather independent of all the experimental parameters and differs from that calculated by St011 and Marti [6]. Therefore we assume for the noise-tosignal density power ratio a l/f@ spectrum [5] (that we call G@(q))for low frequencies with fl= 1. and a uniform noise (white noise) for high frequencies. The models for the spatial distribution of the tunnel current implies that the transfer function H(q) should be Gaussian for sufficiently weakly corrugated surfaces [8]. Thus, for image restoration in STM, a Gaussian expression - involving a parameter q, related to the system resolution - is used. However, qc depends on experimental parameters that are only approximately known as the tip-sample distance, tip shape and effective potential barrier height. The Gaussian transfer function has probed to be very useful in STM image restoration by using estimated values for qc. However it takes into account only the physical process that occurs - i.e., the tunnel current between tip and sample - and not the electronic equipment. In fact, the way of measurement produces a modification of the transfer function, in particular when the STM is working in a fast mode with strong integration the Shannon-Whittaker theorem is usually not fulfilled. Then, the transfer function becomes asymmetric and the Gaussian expression cannot account for the proCZSS.

If we take into account

the conical

geometry

of

technrques to restore STM images

the tip-sample system we can make analogies between the process of image formation in STM and in optical systems with circular aperture and that are defocused. Thus we can implement a Wiener filter for STM images utilizing a transfer function as used to correct defocus effects in optical systems with a circular aperture. To describe the tip-sample interaction we can make a model utilizing a smearing function as the one derived by Stokseth [9] for a circular aperture with defocus. The Stokseth equation is valid for optical systems with circular aperture and small angles of aperture. In STM we have conical symmetry. i.e.. circular aperture and the angle involved in the tunnel process is very small, i.e., smclll aperture. Thus, the Stokseth equation could be valid for STM only changing the physical meaning of the involved parameters. In the STM case, there is an asymmetry between the two scanning directions that is equivalent to an asymmetric defocusing. In a defocused image the borders are not defined, they are blurred. This means that the high frequency components in the Fourier space have decreased relatively to the low frequencies. In STM. when the signaf integration is large, this same effect occurs and then we have the equivalent of a defocusing. In STM the electronic signal integration along the scan directiou is related to the scan speed and the finite-time sampling window or temporal aperture of the measurement system. The thermal drift and instabilities on the slowest movement of the tip produce a correlation between adjacent pixels in the image but the importance of the correlation is quite different when the pixels belong to the same scan as when they belong to consecutive scans. Therefore we introduce two parameters, 6, and 6,) relative to these two effects, who will be treated as fitting parameters and have a completely different physical meaning. We will denominate them as defocusing factors.

With these considerations we build up a transfer function based on the Stokseth one: W(q) = (1 - 0.69s + 0.0076s’+

X.j,,,[3,!1

- ~)I.

0.043.~‘)

(1)

M. Pancorbo et al. / New filtering techniques to restore STM images

where r is a new variable which value is related to the 8, and 8,. values by the following expression:

4c

The only objective measure to judge the quality of the image restoration is the quality of the details at atomic level that are clarified by the restoration itself. In fact, STM is the only technique that gives information of surfaces with atomic resolution and therefore it is not possible to compare the STM pictures of the surface with any picture or information obtained by other techniques. Thus, we have made a theoretical calculation of the image that will be observed by an STM with strong integration along x direction. The model that we used for the theoretical calculations is based on a model of hard-spheres for the atoms. After the STM “image” is obtained (see fig. la) then an experimentally measured l/f@ noise is added with noise to signal ratio of 10. Thus, it is obtained a noisy and defocused or blurred image (see fig. lb) that is filtered by using the transfer function proposed in this paper. The result is a very good recovering of the original image, fig. lc, that can be compared with the original one: fig. Id. Fig. 2 shows the effect of filtering utilizing the asymmetric transfer function on an experimentally obtained image with atomic resolution of about the same size (60 A x 60 A) as the simulated one. In the original image (fig. 2a) it is very difficult to distinguish the atoms because of the strong integration along the scan direction and the large noise. After filtering (fig. 2b) the individual atoms are clearly observed as well as details at atomic level (dislocations and other linear defects). In the case of STM images that cover several

423

hundreds A the blurring, noise and integration are not very important because they do not hide details and structures. In fig. 3 a case is shown in this range where the typical noise related phenomena are apparent: the appearence of lines in the scan direction. After filtering (fig. 3b) the problems have been resolved and details were clarified. In conclusion, the asy~et~c transfer function for the Wiener filter is the best one suited for STM picture restoration.

We wish to thank IBM ACIS and IBM Madrid Scientific Center for partial financial support, and J.P. Secilla - of IBM SC - for his helpful 2D-DFT algorithms and other supporting software. Moreover, the data acquisition system was developed as part of a collaboration with the IBM Scientific Centre in Madrid. We also thank the Comett project that has made possible the collaboration between the three groups.

References PI P.K. Hansma and J. Tersoff, J. Appl. Phys. 61 (1987) Rl. PI M. Pancorbo, E. Anguiano, A. Diaspro and M. Aguilar,

Pattern Recogn. Lett. 11 (1990) 553. and A.C. Kak, Digital Picture Processing, Vol. 1 (Academic Press, Orlando, Florida, USA) p. 72. [41 C.E. Shannon, Proc. IRE 37 (1949) 10. [51E. Stoll and A. Baratoff, Ultramicroscopy 25 (1988) 149. 161E. Stall and 0. Marti, Surf. Sci. 181 (1987) 222. [71 M. Aguilar, M. Pancorbo, E. Anguiano and A. Diaspro, J. Microsc. (1990), submitted. 181 E. Stoll, A. Baratoff. A. Selloni and P. Carnevali, J. Phys. C 17 (1984) 3073. [91 P.A. Stokseth, J. Opt. Sot. Am. 59 (1969) 1314. 131A. Rosenfeld