Biomedical Engineering Reference
In-Depth Information
sample, not just of the technique. However, image processing history is important. The
degree of levelling applied to an image directly affects the roughness values obtained
[361], as does image size [359, 362], so all data should be obtained and processed
identically for comparison of roughness values to be valid. Some examples and more
details of roughness measurements using AFM images are given in Section 7.1.1.
While R a , R q and R t all describe the magnitude of the roughness-larger values mean
rougher surfaces-skewness and kurtosis describe the distribution of the sample height
data. Skewness is a measure of the asymmetry of the distribution of heights. Random
variations in topography will give rise to a skewness value of 0. Positive values of
skewness indicate the presence of height values considerably above the average, while
negative values indicate the presence of height values considerably below the average.
Thus a flat surface with protruding features would have a positive skewness, while pits or
depressions in the surface would lead to negative skewness. Kurtosis, describes the
'peakedness' of the distribution of height values. A distribution with high kurtosis
would have a small number of extreme heights (i.e. a few very high peaks or very low
valleys), as opposed to many moderate height features (which will give lower, or negative
kurtosis values). A Gaussian or normal distribution has a kurtosis value of 0. Skew and
kurtosis are used with AFM data much less commonly than the R a and R q parameters, but
are sometimes useful in characterization of surfaces [364-366].
5.3.3 Particle and grain analysis
Nanoparticle analysis is one of the most popular applications for AFM, due to the ability to
measure accurate particle dimensions with sub-nanometre accuracy. In order to generate
adequate statistics to characterize a sample of particles by any microscopy technique, it is
necessary to measure a large number of particles, typically in the hundreds, or even more.
For a small number of particles, the height and width of the particles can be quickly
measured with the line profile tool. However, for large samples, this rapidly becomes
tedious. For this reason, most AFM analysis packages include routines for automatic
particle counting and analysis. As explained in Section 5.1.1, images with particles on a
flat background need care to be levelled properly. This is particularly important if the
image is to be analysed by an automated routine. However, once good levelling is
achieved, identification, counting, and measuring can be performed with an automatic
particle analysis routine. For spherical particles on a flat, well-levelled background, a
simple thresholding routine can isolate the particles. In this process, the user selects a
value above which all features are counted as particles. The process of separating the
particles from the background is known as image segmentation. In addition to the
comparatively simple thresholding routine, there are a number of more sophisticated
segmentation routines which can be applied in non-ideal cases [367]. The reason a large
number of segmentation routines exist is that simple threshold segmentation is not a very
robust method for non-ideal cases. Another common application of such routines is
identification of grains in a sample surface. Because granular materials do not usually
have great height differences at the grain interphases, height thresholding does not usually
work very well for these samples. Other routines that are based on changes in slope work
rather well for grain analysis, as does the so-called 'watershed' segmentation method [368,
369]. This latter routine simulates water drops being placed in the image, and then
 
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