A bit of a follow up, sorry if this is not of interest to you. The reason the height distribution histogram method is not a "robust" way of finding the step heights is because tilting the image will not only blur the histogram, but it will also change the spacing between peaks in the histogram. This is because as you tilt the "staircase" the heights of the centres of the steps get closer together in "z." This of course leads to inaccurate step height measurements if you are using the histogram peak separations.
When the image is correctly tilted, the histogram should be maximally "sharp." I wrote a matlab script to generate histograms of some data at various tilts. In the linked images, the histogram data lies along the rows, with the y-coordinate being the tilt used to generate that histogram (the colour indicates the height of the histogram). Here is a simulated staircase pattern and the resultant tilt-histogram plot: http://www.phas.ubc.ca/~swebster/afm/simulated.png http://www.phas.ubc.ca/~swebster/afm/ideal.png As you can see, the histogram is maximally sharp at 0 tilt and the histogram plot looks like you would expect. Here is some real AFM data (R-plane sapphire atomic steps) and the resultant histogram: http://www.phas.ubc.ca/~swebster/afm/realimg.png http://www.phas.ubc.ca/~swebster/afm/real.png The image was quite close to being level at the start, but the maximally sharp position seems like it is around "2" on the tilt axis. Unfortunately it is not very easy to determine which histogram is really the best, and the peak spacing varies quite a bit, perhaps illustrating some of the problems with this method. While playing around with this stuff, I often wished Gwyddion had the ability to tilt the image by some fixed amount (that I could input, in both x and y). I found myself using the 3-point level and dragging the points around to induce my desired tilt. Maybe there is some way to tilt the image by a numerical amount that I don't realize? Scott Webster On Fri, Nov 28, 2008 at 2:39 AM, David Necas (Yeti) <[EMAIL PROTECTED]> wrote: > On Wed, Nov 26, 2008 at 11:39:50PM -0800, Scott Webster wrote: >> But I too often use Gwyddion to determine step heights in my images. >> I have been using the three-point level tool on one terrace in order >> to try to make that (and the other) steps flat. Then I use the 1-D >> statistical height distribution tool. Ideally the distribution >> consists of a series of peaks that correspond to the different heights >> of the steps (these can be measured with the "distance" tool after you >> accept the height distribution). >> >> I believe that this method should in theory be more accurate than >> analyzing sections, or at least it should do some more averaging for >> you, so you don't have to look at so many section lines. There are >> some papers written on this. >> >> Unfortunately, I find that my results are quite dependent on exactly >> how the three-point level is done. Just a slight change of one of the >> points or the averaging size changes the result, and it is quite >> difficult to notice that it is not ideal. > > I know this method and I recently discouraged one my colleague from > using it because, as you observed, it looks very clever in theory but I > do not think it is sufficiently robust in practice. > > While averaging the profiles in a direction more-or-less along the > edge works with non-ideal data well, the distributions are too sensitive > to distorsions. True, the step smears out a bit by the averaging (more > if the direction is not exactly along the edge), but this is something > Critical Dimension can cope with. > > Yeti > > > ------------------------------------------------------------------------- > This SF.Net email is sponsored by the Moblin Your Move Developer's challenge > Build the coolest Linux based applications with Moblin SDK & win great prizes > Grand prize is a trip for two to an Open Source event anywhere in the world > http://moblin-contest.org/redirect.php?banner_id=100&url=/ > _______________________________________________ > Gwyddion-users mailing list > [email protected] > https://lists.sourceforge.net/lists/listinfo/gwyddion-users > ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ Gwyddion-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/gwyddion-users
