Biomedical Engineering Reference
In-Depth Information
Table 5.1. Effects of differing polynomial levelling orders.
Order
Effect
0
Only sets the height offset of each scan-line to the same value.
1
Fits a straight line equation to each scan-line, and does an offset.
2
Fits a quadratic equation to each scan-line, and does an offset.
3
Fits third order polynomial to each scan-line, and does an offset.
carried out on vertical lines. It is usually better to do this horizontally, because the
horizontal axis is usually the fast scan axis. Therefore, any change in imaging conditions
over the time of the scan will lead to horizontal discontinuities in the images, and will thus
be well accounted for by a horizontal line-by-line levelling. The lines might then be moved
up by a fixed amount such that the minimum of the image is at zero height, as it is a
common convention not to use negative heights in AFM. The order of the polynomial
equation can vary from 0 to 3 or more, as shown in Table 5.1.
For many images, a first order fit will suffice. If scanner bow is present in the image (often
the case for larger scans), a second order fit will usually be appropriate to remove the artefact.
Orders higher than third level are possible, but under these circumstances, the functions are
likely to be fitting to real features of the sample, rather than just to the background. It's worth
noting that line-by-line fitting procedures are particularly prone to causing levelling artefacts
(see Section 6.3.1), and so feature exclusion (see below) is often required. Despite this, line-
by-line, or polynomial fitting is often the most useful levelling procedure.
Two-dimensional plane fitting
This procedure tries to automatically fit a flat plane to the image, and subtracts the best-fit
plane; it works well where the background is really flat, and does not include any
curvature. The automatic routine will usually assume the entre image is to be fitted; this
means that it can be subject to errors as large height features will reduce the accuracy of
the fit to the background. Plane fitting does not introduce the kind of errors mentioned
above that can plague line-by-line fitting. It is therefore a rather conservative levelling
procedure, as although it's not very efficient with many images, it does not introduce any
errors. For this reason, some acquisition software saves files with a plane fit by default,
and some analysis software applies a plane fit whenever an AFM file is loaded. Usually,
the user can turn off these 'autofitting' functions if necessary.
Three-point fitting
This procedure is similar to two-dimensional plane fitting, but is a rather more 'manual'
approach. In this method, the AFM user identifies three points on the image. These points
define a plane which is then subtracted from the image. The advantage of this method
over the automatic plane removal routine is that if the user can distinguish the substrate
from the sample features, he can ensure the three points used are on the substrate only, and
this often leads to a better fit. However, because a flat plane is fitted, it is still only suitable
for images with no curvature or scanner bow. It is particularly appropriate for samples
with terraces. An example, showing the effect of different levelling algorithms on an
image with a large terrace, is shown in Figure 5.2.
