Convolution effects

Figure 3-18 (a) Fit of an H20t profile (from low to high H20t) from a diffusion-couple experiment. The misfit at x —120 imi is attributed to the convolution effect (limited spatial resolution of the measurements), (b) The dependence of DhjO, on H20t from the fit in (a). From Zhang and Behrens (2000). 

Ganguly J., Bhattacharya R.N., and Chakraborty S. (1988) Convolution effect in the determination of compositional profiles and diffusion coefficients by microprobe step scans. Am. Mineral. 73, 901-909. 

We have seen that electron microscopy and scanning probe microscopies are very complementary techniques to characterize the structure and the morphology of supported clusters. The internal structure can only be resolved by HRTEM while the surface atomic structure can be only revealed by STM or AFM. TEM gives accurate diameter measurements and height can only be measured in profile view that needs special sample preparation. STM or AFM give accurate height measurements but diameters can be obtained only after correction from the tip-sample convolution effect. 

A new class of artificial membranes, based on lipid bilayers supported on porous alumina, were recently studied by Hennesthal and Steinem using AFM [58], In this case, tip-sample convolution effects affecting the detection of pores (see Section 2.3) were clearly demonstrated by the authors on comparing the average pore size of the alumina support as obtained by SEM (60 nm) and by AFM (50 nm). 

More difficult is the differentiation of tip convolution effects if there is no hidden symmetry. In the images shown in Fig. 2.46, the tip was altered in the course of an experiment. In fact, the images show the same area of a vertically stretched... 

Fig. 3.38 Contact mode AFM height image of egg PC vesicles adsorbed on glass captured with an imaging force of 30 pN left) and 50 pN right). The halo in the fast scan direction right to left) indicates that the tip can no longer track the surface features accurately, when imaging force and noise of the deflection signal become comparable ( 30 pN in this case). When the imaging forces are increased to 50 pN, the surface is tracked better. The asymmetry of the features can be explained by tip convolution effects (asymmetry of the probe tip) [87]...

In semicrystalline polymers, fillers may act as reinforcement, as well as nucle-ation agents. For example in PP, nanoscale silica fillers may nucleate the crystallization resulting in spherulites that show enrichment in particles in the center of the spherulite (Fig. 3.64). For a quantitative analysis of, e.g., filler sizes and filler size distributions, high resolution imaging is necessary and tip convolution effects [137-140] must be corrected for. The particles shown below are likely aggregates of filler particles considering the mean filler size of 7 nm [136]. 

In contrast to the Fourier transformation, convolution effects a transformation of the function only, and not of the variable and the function together. Convolution denotes a folding operation (Faltung) of two signals ki(t) and jc(t) ... 

Figure 48. Comparison of experimental and simulated fluorescence polarization anisotropies for the S, + 789 cm 1 excitation of jet-cooled r-stilbene. The anisotropies include convolution effects associated with the finite excitation pulse width. The upper trace was calculated using the theoretical results of Ref. 49. The lower trace was obtained from experiment. The inset shows a simulated decay for this excitation band. 

It should be noted that the force measured in AFM is proportional to the inverse of the tip-sample distance to the power of n. This is less sensitive than the exponential variation of tunneling current as a function of tip-sample distance in STM. In addition, due to the restricted sharpness of the tip apex of an AFM probe (presently, the finest commercial probes have a radius 10 nm), the convolution effect of the tip shape may be... 

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