I thought that was done already!?

No, not at all as far as I know. The problem seems to be that the band intensities are unknown. Even the reflector intensities are only a very rough estimation based on kinematic theory which is definitely not the best choice for EBSD. Therefor the ranking is often wrong. As far as I know only EDAX enables to modify the ranking of reflectors in order to push one ot two reflectors into the list of considered hkl whereas some other will be removed since their predicted intensity is too strong in comparison to the band intensity observed.

Nevertheless, it would be nice to give it a try but obviously the relative intensities are so different that it would make an indexing even worse. But this is only my assumption. It seems so that the usage of band width is much more reliable than the intensity prediction. 

As already mentioned the intensities are affected by dynamical effects and stronly dependent on the experimental set up, particularly the preparation of the sample. Therefore they cannot be used for idenitfication purposes as, e.g., with XRPD.

Dear Giovanni, why do you think so? Dynamical simulations of patterns are since 2007 evailable. Unfortunately they are not yet used. 30years ago people also thought quantitative phase analysis with XRD cannot be done without any standard. 

Gert, I am not really an expert; I know that dynamical effects can be accounted for, but as I said before, the experimental intensities strongly depend on experimental parameters. Presumably, but I do not know, nobody has yet found the way to properly correct the experimental intensities.

I think Giovanni is correct..... often in EBSD you are looking at very small grains/crystallographic domains, and the intensities depend so strongly on the size and orientation of the portion of sample that is actually interacting with the electron beam that you can't rely on the intensities to be representative of a bulk sample (in the way you can when you have a randomly oriented powder of known thickness and orientation). This is why only the peak positions are used to index the unit cell, because the unit cell is still characteristic of a particular phase (as long as you aren't trying to detect minor changes in chemical composition).

For patterns acquired sufficiently far away from any boundary I think the relative intensities of the bands don't change that much with changing aquisition parameters. Even if you change the high voltage the simulated patterns look quite similar to the experimental one as shown above. In so far the simulation  is from my point of view not much worse than any other simulation for TEM. This means, we are already able to extract the band intensities. The reolution of EBSD is so high that for the majority of investigations boundaries do not play a significant role. But even if you go closer to boundaries I don't think that the current band detection without intensities has any advantage, in contrary. You observe two superimposed patterns where each of them still has the same relative intensity conditiones. Non-fitting bands (as part of the other pattern) can be excluded in this way. On the other hand, did you ask yourself how accurate or reliable a band detection along grain boundaries  really is? From my point of view the observed orientation noise along boundaries is mainly not the result of real orientation variations e.g. caused by dislocations (GND approach) but simply the consequence of a less accurate band detection caused by superimposing patterns, in fact blurred or less clear detectable bands. There an additional criterion like intensity could even help to extract a more reliable information.  

The intensity of the EBSD pattern only slighty depends on the orientations since only the part of the diffraction pattern collected in this direction is different. For some low-symmetric phases this might be measurable, but for the most interesting cubic phases where all band have the same positions, anyway which structure or lattice parameters they have, it is practically averaged since the screen covers always more that one fundamental sector. I am sure that this can be already confirmed since one can use the experimental orientation and replace the experimental pattern by the simulated and compare both of them.

From my point of view we have to admit that EBSD at the moment is comparable to powder XRD (60-70years ago?) when only the peak positions have been used to identify a phase. It works for many simple structures but nowadays a phase identification hopefully nowbody will do anymore on the basis of the peak positions only.  

I may be wrong, but I was under the assumption that the HKL software does use reflector intensities, even if only based on the kinematic theory (talkin about the old acquisition module). Analysing for instance a duplex steel, I will get misindexing if I choose a high numer of reflectors, say roughly about 40, i.e., something like 8-10 lattice plane families. Dropping reflectors to around 20 reflectors will improve indexing. Correct me if I'm mistaken, but I thought this was because now the low indexed, i.e., high intensity, reflectors are used for indexing only, and here we've got the difference in intensities of bands, which can easiily be mistaken for one another, such as the (110) in bcc, which has the highest inensity, and the {220} in fcc, which is only the third most intesive reflex in fcc. The {200} in bcc in turn has the second highest intensity in bcc, about 50% of the {110}, whereas the {200} in fcc has double the intensity of the {220}.

In any case, dynamic simulations are definitely a major step forward in terms of phase ID, even if the information is not going into the standard solver routine, at least for now.  

I can confirm Gert's experience with TSL/EDAX indexing routines: The band intensities are taken into account in their software during the Hough transform. We can imagine the Hough transform is done by "slicing" the pattern into discrete number of strips (defined by the binned pattern size, i.e. between 32 and 240) which are rotated around origin in discrete angular steps (defined by Theta step size, i.e. between 0,5° and 3°) and the gray scale values are integrated along each strip in each angular position and fed into the respecive bin in Rho - Theta Hough space. The more of a strip "cuts" of some band, the higher grayscale value results from the integration and therefore the higher the resulting peak in the Hough space; in other words the most intense peaks in the Hough space are those pertaining to the most intense bands in the pattern.

Since there arises the problem of dependence of resulting Hough peak intensity on the actual band length in the pattern image which is captured on a rectangular CCD chip, the actual transformed part of the pattern is limited by a circular crop mask centered in the x,y origin. The "length dependence problem" still persits even then, since the bands close to the mask edge also give less intensity due to shorter integration length, but this is treated aftewards in next steps of indexing algorithm by limiting the actual extent of the Hough space to be searched for peaks in Rho direction (e.g. to 90%, defined by the "Rho Fraction" parameter) thus omitting the near-edge short bands.

The resulting Hough peaks are then sorted according to their height (i.e. the band intensity) and only the first few (user defined number) most intense peaks are used for indexing and then for ranking the indexing solutions in multiphase cases.

From the above there arises a problem how to make the band intesity an objective measure even in case of the same sample but in different orientation: imagine the case of a bcc structure and a (110) band which, in one orientation, passes through the pattern close to the mask center (therefore gives the highest hough peak), and then in another orientation in which the same band passes close to the mask edge resulting in a lower Hough peak. The solution would be, as my first thought, to normalize the Hough intensity by the band length (and maybe also by the band width ?) or to define the band intensity on a defined chunk of a band (but which one, when you can easily position it incidentally into or close to a zone axis, thus introducing errors into the intensity measurement).

Hi Ondrej, the Hough transform uses a normalization so that equivalent bands appear very similar in their intensity. I only have to correct you a bit: The intensity of the peaks in the Hough transform is only used as threshold. Also the intensity prediction using the kinematic approach is using the intensity to kick out all planes which do not deliver a sufficient intensity. However, there is no BAND intensity considered, i.e. in case of 111, 222, 333 ,444 reflectors which are overlayed somehow only the most intense is used for the ranking. Often it works, but as already mentioned, sometimes it fails since the single reflectors are already wrong (e.g. Si 222 has zero intensity, but is the strongest visible edge, wereas 111 is assumed to be the strongest reflector, i.e. should have  100% relative intensity, but is practically invisible.) As far as I know, no system is using the intensity ranking for indexing. The reason is quite obvious: reflector and band intensities do not match for several reasons.  Nevertheless, dynamical intensity simulation is available for now already 7 years :-). I think it is time to use these opportunities to make especially phase identification more reliable.