M. Pancorbo

Fractal characterization by frequency analysis. I: Surfaces

A study of the quality and accuracy of the methods based on frequency analysis for the fractal characterization of surfaces as measured by scanning tunnelling microscopy (or profilometry) is made. The study is based on computer simulation of images of fractal surfaces. A discussion of the mathematical algorithms used for computer generation of fractal surfaces then follows. The main conclusion is that studies of fractal characterization by frequency analysis reported in previous papers in the STM field, as well as conclusions about the performance of the various methods, are doubtful. New methods for frequency analysis that in some cases produce more reliable results are proposed.

Fractal characterization by frequency analysis. II: A new method

A new frequency analysis method, fractal analysis by circular average (FACA), and an image replication procedure are proposed that together produce accurate measurements of the fractal dimension of surfaces and profiles, eliminating Fourier transform artefacts which arise from the lack of periodic continuity in real surfaces and profiles.

PROFILES FRACTAL CHARACTERIZATION BY FREQUENCY ANALYSIS

A discussion of the different methods for fractal profiles generation and of the methods for fractal characterization of profiles by frequency analysis is made in the whole range (1 < D < 2). We obtain the conclusion that all methods for measurement of fractal dimension that has been proposed are doubtful.

A Wiener filter with circular-aperture-like point spread function to restore scanning tunneling microscopy (STM) images

Abstract With a suitable noise analysis and a relative Wiener filter, utilizing a Point Spread Function in analogy with optical cases, a good restoration of noisy fast-STM images can be achieved. Correlation between consecutive scans and integration along the scan direction could be the greatest disturbing facts.

New filtering techniques to restore scanning tunneling microscopy images

Abstract An asymmetric transfer function — based on the symmetric one used in optical cases to correct blurring and defocusing effects in systems with circular aperture — is presented here to restore STM (scanning tunneling microscopy) images. A Wien filter is implemented that utilize this transfer function. In the STM case, the defocusing has two different origins depending on the scan direction that produce a set of two fitting parameters.

Fractal characterization by frequency analysis: III. Effect of noise

The effect of noise in the fractal characterization by frequency analysis of surface images obtained by scanning tunnelling microscopy (STM), atomic force microscopy (AFM) or profilometry has been studied. The origin of noise and its relationship to the signal is discussed. A procedure to simulate noisy images is presented. From the study it is concluded that the method usually used to characterize noise in STM is not valid and it is shown that fractal characterization of surfaces when noise is present by traditional frequency analysis methods is not possible. A new method to perform both the noise characterization and the fractal characterization of surfaces when noise is present is proposed.

Digital filters to restore information from fast scanning tunnelling microscopy images

A transfer function—similar to that used in optical cases to correct blurring effects due to the circular aperture of the system—is presented here to restore scanning tunnelling microscopy (STM) images. Due to the conical geometry of the tip‐sample system, we have established an analogy between the process of image formation in STM and in optical systems. The transfer function utilized, similar to that calculated by Stokseth, allows us to differentiate between the blurring effects introduced along the x and y axes. These effects are different due, mainly, to the different velocities achieved along the x and y directions. Furthermore we have measured the β parameter that characterizes the classical 1/fβ noise present in STM data, demonstrating its independence from experimental conditions. A Wiener filter is utilized to restore the images using the previous assumptions given for the transfer function and noise effects.

EVALUATION OF FRACTAL DIMENSION MEASUREMENTS BY FREQUENCY ANALYSIS METHODS

A study of the quality and accuracy of the methods, based on frequency analysis, for fractal characterization of surfaces is carried out. The study is based on computer simulation of fractal surfaces images and then a discussion of the mathematical algorithms used for computer generation of fractal surfaces is also made. The main conclusion is that the studies of fractal characterization by frequency analysis reported in previous papers as well as the conclusions about the performance of the different methods are doubtful and questionable. We propose new methods for frequency analysis that in some cases yield the more accurate results.

Study of the surface roughness of Co-based amorphous alloys by STM

Abstract Since the STM gives the vertical dimension of surfaces, it allows us a quantitative evaluation of the surface roughness by analyzing the STM images. This kind of evaluation is of importance in Co-based alloys because the surface roughness is related to magnetic properties in low and medium magnetostriction. This paper presents a study of the surface roughness of Co-based alloys obtaining the fractal dimensionality, the amplitude of the superficial features as well as the mean size of those features and its relation to magnetic properties.

Noise characterization in Scanning Tunneling Microscopy (STM)

Abstract In this paper we discuss the characterization of noise in STM. The characteristic noise in STM images is the 1/ f β -like one, thus noise is characterized by giving the β value. We show that the method (proposed by Stoll and Marti) utilized by STM users for measurement of β is erroneous. We propose here a new method for noise characterization by frequency analysis based on image replication that yields accurate values of the β exponent.