Biomedical Engineering Reference
In-Depth Information
5.1.1 Levelling
Levelling is described first here both because it is usually the first processing operation
carried out on the data, and also because it is the most important, since it is the most widely
used processing step applied to AFMdata. Inmany cases, levelling is the only processing step
carried out on the data, and it is required in nearly all cases. The reason levelling is required is
that AFM images usually measure sample height. If the background in the image (such as the
substrate on which the sample was deposited) has considerable tilt in it, the change in height
of the background will mask the changes in height associated with the sample. AFM is often
used to measure samples with very small heights, so even a small tilt in the sample
background can have serious effects. Imagine a 20
m image which contains
some 50 nanometre nanoparticles, which are the features the user wishes to examine. If the
substrate is tilted by only 1
m
20
, the height change from one side to the other of the substrate will
be about 350 nm. This is more than enough tomask nearly all the nanoparticles. This concept,
along with some examples of flattening operations, is shown in Figure 5.1.
In addition to tilting in the image caused by the AFM and sample not being perfectly
orthogonal, a common problem in AFM images is scanner bow. An example of this
artefact is also shown in Section 6.2.3. It occurs mainly in instruments that use tube
scanners, and is caused by a swinging motion of the free end of the scanner. This leads to a
curve in the image plane as shown in Figure 5.1. There are a number of different methods
that can be used for image levelling, and these are discussed below.
8
Polynomial fitting
A very common method for levelling AFM images is by polynomial fitting, or 'line-by-
line' levelling. In this routine, each line in the image is fit to a polynomial equation. Then,
the polynomial shape is subtracted from the scan line, which leads to the line being not
only flattened, but also shifted such that it centres on zero height. Typically each
horizontal line of the image is processed in this way, although the process can also be
Fig. 5.1. Illustration (top: line profiles; below: images) of the effect of first and second order
polynomial line levelling. Left: unlevelled (raw) AFM image of nanoparticles showing tilt and
scanner bow. Middle: effect of first order horizontal levelling - the nanoparticles are much clearer,
but the curvature of the background due to scanner bow is still evident. Right: the effect of second
order levelling with exclusions, the background is now flat.
 
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