Hi Gert,

My pattern centre definition is the "source volume position with respect to the screen coordinate system".

Why ? Because it allows to write the gnomonic projection and do all the geometry you want including spherical EBSD.

What are the other definitions you have in mind ?

Claire

Hi Claire, I don't want dosappoint you with my question. I have different definitions in mind regarding the determination. How do you determine the pattern center? And if you do so, why? I don't have to tell you that one is of course given by the installation using a Si crystal. But there are a few other ways to find the pattern center and all of them have certain advantages. You need a very accurate one for HiRes pattern analysis, I know :-). Did you analyse different techniques regarding their reliability?

Thanks for your answer,

Gert

Oh I see, it's not a matter of definition then, but how you determine the pattern centre.

If you have a robust insertion mechanism, a robust camera, etc, the method of choice is of course the "moving screen technique", an old technique that can be improved by using cross-correlation techniques. It is explained in one of my paper on this subject and is applied, I believe in the Aztec system.

If you don't, then you need to rely on the Si crystal, but then you are facing uncertainties in the camera orientation, Si alignement in the SEM and so on... this is not the most accurate.

There is of course the method proposed by the Brigham Young team, which relies on backprojecting the pattern on a sphere and move the sphere centre until your Kikuchi bands are parallel.

In the same spirit, you can play with a morphological analysis of 3D Hough peaks (presented in different conferences which you did attend..)

In any case, you must be aware of potential lens distorsions which will bias your results until you correct for this effect. Some cameras are definitely worse than others !

And finally, you should ask yourself what will be the consequence of an error in the pattern centre for your particular needs, and what is the acceptable uncertainty.

Cheers

Claire

Good summary of different techniques used. The Bringham Young idea is in fact the procedure Bruker is using since 2008 in their system. It works only if you know the phase. On the other hand, if you will get a pattern from somewhere - e.g. a paper - where you do not know anything, neither the phase nor any information about the geometric conditions of the acquiring system...which opportunities exist to find the pattern center?

Sorry, I forgot to mention the various shadow casting methods developed over the years. 

I don't remember and/or understand why you need to know the phase for the Brigham Young technique. 

As far as I know, I don't need this info for the 3D hough transform peak shape analysis...

You are right. If you only look for the best match of parallel bands you don't need to know the phase for the Brigham .

The shadow technique using spheres goes back to Kossel (if I remember correctly). Nevertheless a possibility although absolutely not practical.

I usually define the pattern center as center of the gnomonic projection, which appears obvious at the first glance. However, the consequences are the usual candidates:  shortest distance to the signal probe,  (as vertical projection onto the screen), or point of no distortion. This automatically means that not only the main axes of the inserted and disturing ball shadows are directing to the pattern center but also the directions of the shortest thickness of each band point to the pattern center. Since we have many bands in a pattern sholdn't this be an option to define the pattern center as well? I agree that this is another (similar) but direct discription as used for the Brigham Young idea (only  here gnomonically distorted and there minimizing distortions at all), only that I can estimate the pattern center immediately without any programming tool. Is this the only "technique" to approximate a pattern center from an unknown pattern, or are there other opportunities? 

Hi Gert,

yes of course, you're right : this is the exact same property that was applied for the shadow of spheres on Kossel patterns. So, in principle, if you were able to locate the direction of smallest band thickness for many bands and get their intersection, you will eventually find the pattern centre (but not the third coordinate, detector distance, or would you ?). However, the hyperbolae being as they are (i.e. very flat), I doubt that you would get a very good approximation without any programming tools.

Your technique is incidentally the same one I use when doing manual band detection for pattern centre refinement in Channel : I use short parallel segments running perpendicular to my initial guess for the PC.

Now, if you are given an unknown pattern from an unknown phase and you're asked to locate the pattern centre (off-line), then all these techniques (intersection of the smallest thickness directions, Brigham Young, peak shape analysis of 3DHough) which only rely on the geometrical properties of conics having the same appex, and don't call for crystallographic information, can be applied.

There might be other opportunities I can't think of... Let's see what other people have to say on this.

Good Morning Claire,

thanks for your comment. You are right if you want to know the pattern center with good   accuracy but simply to get a glue it is quite acceptable. In fact a refinement procedure should be able to find quite accurately the best point where for all bands the thickness of them are minimal. For DD (detector distance) you need to now the relation a:b:c which would be perfect in case of cubic materials, i.e. then you even can extract DD (indexing assumed...or alternatively the determination of the symmetry elements which are quite numerous in cubic materials (even if the used phase should be only pseudosymmetric :-) ).

Let see for other people comments...

I recommend Claire's answer

Best Regards