[Gwyddion-users] error bar in the roughness

[s***@bo.ismn.cnr.it]

Good morning,

my question is the following. I have to calculate the roughness with its
error bar from images with 3 nm height islands on silicon oxide.
Unfortunately, also some crystals are present. They are quite height and
not properly scanned by the afm. The roughness I have to calculte should
not be referred to those crystals so I decided to use masks to get rid of
them.

My problem is that with masks I cannot get a roughness value with its
error bar. If I use in Gwyddion the option "Calculate row/column
statistical function" there is not the possibility "Exclude masked
region".

I can get the roughness from the other option "Statistical quantities" but
again no error bar.

How can I get a roughness value with error bar even if I have to use masks
to get rid of crystals?

Thank for the help

Stefano


Stefano Chiodini, PhD Student
Institute for Nanostructured Materials Studies (ISMN)
National Research Council (CNR)
Via Piero Gobetti 101
I-40129 Bologna
I T A L Y
Phone:++39-051-639-9188
Cell: ++39-3393142341
***@bo.ismn.cnr.it
www.bo.ismn.cnr.it

[Andrés]

Post by s***@bo.ismn.cnr.it
Good morning,
my question is the following. I have to calculate the roughness with its
error bar from images with 3 nm height islands on silicon oxide.
Unfortunately, also some crystals are present. They are quite height and
not properly scanned by the afm. The roughness I have to calculte should
not be referred to those crystals so I decided to use masks to get rid of
them.
My problem is that with masks I cannot get a roughness value with its
error bar. If I use in Gwyddion the option "Calculate row/column
statistical function" there is not the possibility "Exclude masked
region".
I can get the roughness from the other option "Statistical quantities" but
again no error bar.
How can I get a roughness value with error bar even if I have to use masks
to get rid of crystals?
Thank for the help
Stefano

Would remove data from under masked region help? After that it should not matter if you have a mask.

[s***@bo.ismn.cnr.it]

Thanks for the help but I don't think that "Remove data under mask" option
would help.

When you use this option Gwyddion does a Laplacian correction which
strongly affects the topography of the image. You can clearly see it with
a 3D image of your scan before the Laplacian correction and after.
If I use "Remove data under mask" the roughness value will be referred
also to those Laplacian-corrected regions which, instead, I would like to
completely avoid.

What I would like to do is to force Gwyddion to calculate roughness with
error bar referring only to regions outside some masks I put to avoid
crystals.

Post by Andrés

Post by s***@bo.ismn.cnr.it
Good morning,
my question is the following. I have to calculate the roughness with its
error bar from images with 3 nm height islands on silicon oxide.
Unfortunately, also some crystals are present. They are quite height and
not properly scanned by the afm. The roughness I have to calculte should
not be referred to those crystals so I decided to use masks to get rid of
them.
My problem is that with masks I cannot get a roughness value with its
error bar. If I use in Gwyddion the option "Calculate row/column
statistical function" there is not the possibility "Exclude masked
region".
I can get the roughness from the other option "Statistical quantities" but
again no error bar.
How can I get a roughness value with error bar even if I have to use masks
to get rid of crystals?
Thank for the help
Stefano

Would remove data from under masked region help? After that it should not
matter if you have a mask.
--
Sent from my Android device with K-9 Mail. Please excuse my brevity.

Stefano Chiodini, PhD Student
Institute for Nanostructured Materials Studies (ISMN)
National Research Council (CNR)
Via Piero Gobetti 101
I-40129 Bologna
I T A L Y
Phone:++39-051-639-9188
Cell: ++39-3393142341
***@bo.ismn.cnr.it
www.bo.ismn.cnr.it

[David Nečas (Yeti)]

Post by s***@bo.ismn.cnr.it
my question is the following. I have to calculate the roughness with its
error bar from images with 3 nm height islands on silicon oxide.

This is impossible. More precisely, it is impossible without any a
priori information telling you what is the topography and what is the
error/uncertainty of topography.

If you calibrated the instrument
(http://gwyddion.net/documentation/user-guide-en/caldata.html) and
applied the calibration to the data then you would know a priori the
random and systematic errors for each data point. Gwyddion would
perform corrections and provide uncertainties of the statistical
characteristics automatically in the Statistical Quantities tool (and a
few other places).

Otherwise you may be able to roughly estimate uncertainties of some
statistical quantities only if you have a model to which the surface
must conform. This allows you to state that all deviations are
measurement errors. For instance, if you can say a part of the surface
is so flat that all observed variations from plane are measurement
errors, you can then estimate these errors.

Since roughness itself is a random deviation from some mean shape, the
situation is even more complex here. Generally, you need at least a
statistical model of the roughness. You can try to just estimate type A
uncertainties by repeated measurements, and this may be what you are
doing, however
- This is likely a small part of the total uncertainty; the main issue
is not the variation between individual measurements but systematic
errors due to noise, tip convolution effects, limited area effects, ...
- The Row/Column Statistics tool does not do this anyway.

So, what Row/Column Statistics does? It calculates the selected
quantity for all rows or columns and displays the average value and
inter-row or inter-column variation. This is not an error estimate!

There is probably only a single quantity whose average tells something
about the entire surface: the mean. The average of means is the mean
for the entire surface. All other quantities would have to be combined
in a more complex manner to obtain something describing the entire
surface or they are purely 1D quantities. So the average does not
correspond directly to a 2D quantity and the variation is not the error
of some 2D quantity.

I hope this, at least, clears up things.

Regards,

Yeti

[s***@bo.ismn.cnr.it]

Good morning,

I'm actually facing the following problem:

I have 2.4 nm islands on a flat substrate. I would like to count them as
precise as possible with Gwyddion.

The procedure I'm following is to mark by threshold the islands and then
in statistics check the number of grains.

Unfortunately this number is not so precise, by hand i get 134 islands
while with Gwyddion I get 294. The difference is too big. Moreover, if I
change just a bit the threshold that number changes a lot.

Instead, if I divide the projected area by pi times the square of the mean
grain size (as if the grains were circles) I get a more reasonable number.


Which method do you suggest?

Thank you a lot

Stefano

[David Nečas (Yeti)]

Post by s***@bo.ismn.cnr.it
I have 2.4 nm islands on a flat substrate. I would like to count them as
precise as possible with Gwyddion.
The procedure I'm following is to mark by threshold the islands and then
in statistics check the number of grains.
Unfortunately this number is not so precise, by hand i get 134 islands
while with Gwyddion I get 294. The difference is too big. Moreover, if I
change just a bit the threshold that number changes a lot.
Instead, if I divide the projected area by pi times the square of the mean
grain size (as if the grains were circles) I get a more reasonable number.
Which method do you suggest?

First, you can try other marking algorithms, such as Mark by Watershed
and Mark by Edge Detection. I'm also working on another method, but it
is not finished yet.

I don't know if you get too many grains due to oversegmentation or
marking of areas that should not be marked as grains (e.g. small
few-pixel ‘grains’ caused by noise). But the currently available
methods are more prone to the latter. If this is the case, you can use
grain filtering to get rid of the extra grains.

However, the area method may be still more robust. You can get good
threshold also from the height distribution or a Minkowski functional
and, if there is no serious under- or oversegmentation, divide the total
projected area by the median grain area. Median will likely to be
better than mean but you need to export the values for all grains using
Grains → Distribution, sort them and take the middle value.

Regards,

Yeti

[s***@bo.ismn.cnr.it]

ok, I will do. Thank you a lot for the suggestions.

Stefano

Post by David Nečas (Yeti)

Post by s***@bo.ismn.cnr.it
I have 2.4 nm islands on a flat substrate. I would like to count them as
precise as possible with Gwyddion.
The procedure I'm following is to mark by threshold the islands and then
in statistics check the number of grains.
Unfortunately this number is not so precise, by hand i get 134 islands
while with Gwyddion I get 294. The difference is too big. Moreover, if I
change just a bit the threshold that number changes a lot.
Instead, if I divide the projected area by pi times the square of the mean
grain size (as if the grains were circles) I get a more reasonable number.
Which method do you suggest?

First, you can try other marking algorithms, such as Mark by Watershed
and Mark by Edge Detection. I'm also working on another method, but it
is not finished yet.
I don't know if you get too many grains due to oversegmentation or
marking of areas that should not be marked as grains (e.g. small
few-pixel ‘grains’ caused by noise). But the currently available
methods are more prone to the latter. If this is the case, you can use
grain filtering to get rid of the extra grains.
However, the area method may be still more robust. You can get good
threshold also from the height distribution or a Minkowski functional
and, if there is no serious under- or oversegmentation, divide the total
projected area by the median grain area. Median will likely to be
better than mean but you need to export the values for all grains using
Grains → Distribution, sort them and take the middle value.
Regards,
Yeti
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Stefano Chiodini, PhD Student
Institute for Nanostructured Materials Studies (ISMN)
National Research Council (CNR)
Via Piero Gobetti 101
I-40129 Bologna
I T A L Y
Phone:++39-051-639-9188
Cell: ++39-3393142341
***@bo.ismn.cnr.it
www.bo.ismn.cnr.it