[Gwyddion-users] Grain Analysis Measurements

[Milano, Stefania]

Hi there!
I have a couple of questions about grain analysis (I’m a new Gwyddion user so I apologize for these really basic questions):

1. Regarding the orientation of the major ellipse, when exported the output data are expressed in φ angles. Is it possible to covert these values in degrees and how?

2. I need to get information about grains shape factors. Which one do you reckon is the best with the data available in the grain distributions?
I am trying to calculate the circularity through this ratio:

C= 4πA/P^2 (A= area, P=perimeter) .

In this case I am using the projected area (A_0) and the projected boundary length (Lb_0) but I am not sure if this approach is right or there is a better way to do it.

Thanks

[David Nečas (Yeti)]

Post by Milano, Stefania
1. Regarding the orientation of the major ellipse, when exported the
output data are expressed in φ angles. Is it possible to covert these
values in degrees and how?

All angular values are in radians, so multiply them with 180/π.

Post by Milano, Stefania
2. I need to get information about grains shape factors. Which one do
you reckon is the best with the data available in the grain
distributions? I am trying to calculate the circularity through this
C= 4πA/P^2 (A= area, P=perimeter) .
In this case I am using the projected area (A_0) and the projected
boundary length (Lb_0) but I am not sure if this approach is right or
there is a better way to do it.

Well, there are many different quantities and many different opinions.
And also many different norms and standards.

You can use for instance
- maximum inscribed and minimum circumscribed radius
- minimum and maximum bounding direction
- area and boundary length
- area and mean radius
- half-axes of the equivalent ellipse
- ...

Some of them are more sensitive to contours, e.g. the projected boundary
length can change a lot depending on how jagged the boundary is even
though the overall shape is almost the same.

Some are more sensitive to the overall isotropy, e.g. the area inside
the Koch curve is nicely circular if you look at the equivalent ellipse
even though the boundary is a fractal.

Some of them are more sensitive to how flawless the shape is, e.g. the
inscribed/exscribed circle radii can change a lot when there are just a
few pixel sticking out or on the other hand there is a crevice in the
grain.

So, imagine different types of deviations from a perfect circle, say
‘this is an important deviation for my application; this I can still
consider mostly circular’, and decide based on that.

Regards,

Yeti