Biomedical Engineering Reference
In-Depth Information
Fig. 5.10. Feature height measurement techniques. Left: ISO 5436 profile measurement [357].
Thick lines show measured regions; the rest of the data is discarded to avoid influence from
edges. The measured parameter is h . Right: Illustration of the problem with simple line-profile
measurement. The small arrows indicate points in the line profile that the operator might choose in
order to measure the height. The selection of these points can affect the results: h 1 6¼ h 2 .
5.3.2 Roughness
Roughness is a very important surface property for technological applications, but is also
widely used as a quantitative measurement of surfaces changes in a wide range of samples.
For example, absorption of materials to a surface, or erosion of a surface will typically lead
to an increase in roughness. There are a number of different ways to measure roughness,
and it can be measured on lines or in particular regions within images, though whole
images are most usually measured.
The most commonly used roughness parameters are probably the arithmetic roughness,
( R a ) and the root-mean-squared roughness ( R q or R rms ). Both of these values have a
positive correlation, i.e. larger values mean greater topographical variation in the image.
Often, both values give rather similar results, but R q will always be somewhat larger than
R a , and is rather more sensitive to outlying points than R a . The formulas for these
parameters along with some other commonly calculated roughness parameters are
shown in Table 5.2. Roughness, measured by R a or R q , is one of the most commonly
used statistical parameters for describing AFM images. It gives useful information about
the sample surface, and can be correlated with results from other techniques [358-360].
Therefore the value of these roughness parameters can be considered characteristics of the
Table 5.2. Some commonly used roughness parameters [363].
Parameter name
Abbreviation
Formula
R a ¼ n n
Roughness average
R a
1 jy i j
s
1
n
n
1 y i
Root-mean-squared roughness
R q or R rms
R q ¼
þ
min y i
1# i # n
max y i
1# i # n
R t
R t ¼
Maximum height of the image (peak to peak height)
n
1 y i
Skewness
R sk
R sk ¼ 1
nR q
n
1 y i
Kurtosis
R ku
R ku ¼ 1
nR q
 
 
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