Nonlinear distortion in atomic force microscopy (AFM) measurements

Abstract

In AFM measurements it is obvious that the shape of the tip scanning the surface function determines the measurement result: a certain tip radius will result in a remarkable distortion of edges. These effects are usually treated in a more or less heuristic way. Morphological operations to determine the tip shape were derived from image processing almost 15 years ago. They are also used to recalculate the original surface from the distorted measurement. They have also been explained as a convolution, which brings up the idea that a deconvolution could be applicable. The current paper deals with a mathematical model leading to a spectral description of the resulting signal. This is of interest in several aspects: (i) identification of the actual nonlinear nature of the distortion process, (ii) estimation of the influence of the tip geometry on reconstruction, (iii) consequences for the time/time-frequency-domain characteristics of the AFM and its closed-loop control. The presented approach is neither based on morphological image processing nor on convolution. It can be utilized to determine the obtainable quality of AFM measurements and the limits of surface reconstruction.

Viscosity measurements of thin polymer films from reflow of spatially modulated nanoimprinted patterns

“…All AFM measurements are done at room temperature; thus there is essentially no issue of temperature drift. It is however well known that tip geometry induces a distortion in the measured image [30,31]. This effect is a nonlinear convolution which can have a direct influence on the spectral density, and finally on the viscosity measurement.…”

Visualization of sound generation: special imaging techniques

“…[1][2][3] Because of the obvious analogy we used theoretical approaches from classic phonograph record playback theory [4][5][6][7] and derived spectral limits for the re-constructability of surface geometry from AFM measurements. Also practical investigations were partially conducted with test records.…”

Cantilever Tilt Causing Amplitude Related Convolution in Dynamic Mode Atomic Force Microscopy

“…Convolution, the well-known artifact in SPM images which leads to the difficulties in quantitative measurements, 5,6 is now one of the essential topics in SPM standardization. 3,4 The standard specimen, the theoretical convolution/deconvolution model and the standardized characterization process, are necessary for quantitatively analyzing and reducing this effect.…”