The key component in the AFM is the tip, since this is what makes contact with the surface and "reads" the sample
topography. This isn't such a big problem if you're looking at a very large surface, since the tip is relatively small. On the
other extreme, if your looking at atoms people seem to think tip size doen't matter either since it's like two egg cartons
passing over each other (one carton's the atoms of the tip, the other of the sample: passing over they produce atomic "bumps").
The problem with tip size most often happens when looking at features from 50 to 500 nm in size, which is about the
size of biological things. Clearly, if you have a blunt tip it won't be able to feel the finer features of the surface as well as a very
sharp tip will. Imagine trying to read braille with your elbow as opposed to you finger!
The AFM collects data on where it thinks the tip is, based on the position of the cantilever. This is something like trying to judge road conditions based on the position of the axle. Imagine someone's got a car with a special hub cap having a light at its center. It's dark out and your a bystander on the other side of the street. You've also got a photographic memory. You see the path the light takes and ask yourself "Hey, did that car just go over the curb or does the street have a speed bump?" Well, of course, it all depends on the size of the wheel and the shape of the bump. You can imagine that on passing over a sharp curb a large wheel will give a broad, gradual rise while a small wheel will give a sharper rise. Note that regardless of what wheel is used the height of the "bump" is always the same. This effect is an example of the geometric convolution of the tire geometry and the curb/street.
AFM data of small objects often have this convolution seen in the images collected. The width of the objects is distorted due to the combination of the tip and sample geometries, while the height is correct. This convolution of tip and sample differs from what most people think of when they hear the term convolution. Traditionally, convolution is the linear combination of two functions. As an example, if one function represents the true surface features and the second is the machine function (reflecting how sharp an image can be obtained) the convolution is what one would see with that machine. The result is a slightly blurred image (like the early Hubble stuff). Note that the fuzziness is applied everywhere, giving a smoothed edge on either side of a sharp ridge. The geometric convolution experience with the AFM differs in that rounded edges only show up to the one side of where there are steep rises in the sample.
As with the tire/curb example above,
the sharper the tip the less of this distortion occurs. Quite alot of research is being spent on trying to make AFM tips
which are very sharp and very narrow. Unfortunately, this geometric convolution always occurs, so as people try to look at smaller
objects the more this effect is being seen.
In a related topic, you can imagine that if the tip has some sort of defect, that defect might show up on the AFM images that one obtains. Just as a tire which has a nail in it goes "Clump, Clump, Clump" on a smooth road, a distorted tip will reflect in the images. An example of this is the AFM image of polystyrene spheres which shows up as several chili peppers. In this case is was easy to determine that the tip was responsible for the features seen since the sample should be rather featureless. Images of more complex samples would be further distorted and could lead to some misinterpretation.
Once you realize that the AFM images obtained are a combination of the tip and sample geometry, you can often visually remove
the effect of the tip from cross sections. You should be able to "see" an imaginary tip whose point is moving along
the AFM profile and be able to estimate what volumes the tip had occupied. Thus, you can redraw the profile to account
for the tip and get a better representation of the sample surface. If you can't see this result, try cutting out a mask
in the shape of the tip profile and run this along the AFM cross section. Placing the apex of the tip on the line, sketch
around the mask to show where the tip was. You'll find that some surfaces can be drastically changed!
What the MIDAS and other AFM deconvolution program works in just this way: a representation of the tip is placed at every AFM data point and the surrounding data is adjusted to account for that tip. If the AFM data at a specific point is higher than the tip's, then that data is lowered or made equal to that of the tip.
It might be worthwhile to digress slightly and discuss how a more traditional deconvolution such a Fourier transforms
would work on an AFM image. For the elctron microscope example given above, if we start with the blurred image (the
last one) and use the Fourier transform of a sphere (which looks like a Mexican hat) we can get back exactly the true
surface feature (the first image). In this way we've unblurred or restored the image of the surface.
Unlike this, the
geometric deconvolution does not fully restore the image, but rather gives improvements which depend on how
severe the distortion was and on the shape of the tip.
With the use of geometric deconvolution, the widening effect seen in many of the AFM images can be reduced to give a more accurate image. Alternatively, if you have an image of a known sample geometry such as a sphere, cube, etc... then you can deconvolute that image using the sample geometry to give you an image of the tip (instead of using the tip to get an image of the sample). This is important if you want to check to see if the tip broke or need to know its size for future deconvolution of images to get the sample geometries.
Some examples of the results from the deconvolution of AFM images are given elsewhere at this Web site.
Last revised on 01-12-2000 by Peter Markiewicz