I think it is called the mean angular deviation (MAD), which is defined by your preference before the mapping process. The limits of what? you mean of the experiment? and what parameters exactly you are asking about? The crystals or the indexing?

I think if you are below 4x4 binning you should have a good accuracy, because 6x6 binning is not good for phase analysis. 

A good website is http://www.ebsd.com/. 

I am talking about the lattice parameters and not about the angular resolution. In fact I am asking for the opportunity to extract the lattice parameters from Kikuchi patterns using e.g. band widths. The current limit is - as far as I know - around 5% but maybe some other people have a better knowledge or tested this by themselves. i know the paper of Dingley & Wright from 2009 in J. Appl. Cryst. and also about the more than 10 years old presentations from Geiss and Keller where they claimed they can do this with an accuracy of 3.4-3.6% for semiconductors (GaAs, GaP). But in contrast to Dingley & Wright they only used one band so that I am a bit irritated about this number. The patterns should be of course detected in a size of more than 512x512. The number of binning does not tell that much about the real size since it depends on the original resolution of the CCD chip used in the detector.

The quality of fitting the kikuchi patterns to the defined ones is called the Mean angular deviation (MAD). It means how much the indexed lattice parameters are similar to the ones you defined at the beginning of the experiment. 

If you are trying to extract the lattice parameters from a kikuchi pattern, then you have a very hard job. First, you need to know which band you are measuring. Then, you calculate the real width of the band and for that you need to know the sample centre, the specimen to film distance and the angle of projection etc. After that you use Bragg law to calculate the lattice parameters. 

That's what I know so far.

MAD only considers the trace position (predicted versus experimentally detected by Hough transform), not the band edges (as far as I know).

How it works I also know...

I am interested in the maximum accuracy and maximum precision of lattice parameter determination. Any idea about a paper which I did not already mention? 

as you mentioned EBSP is defined by the lattice parameters describes the maximum intensity gradient at the margins of the Kikuchi bands width in an EBSP. I am agree with 5% by taking account the resolution of detector.

The precision should be driven by the pixel density of your camera and you should be able to do some back of the envelope calculation if you know the the sample-to-phosphor screen distance. You can improve the measurement precision by moving the sample as close to the screen as possible and use as low of a kV as possible to increase the band width. In practice, with an unknown sample, the success of the measurement will probably depend on how well you can calibrate and realign the sample and detector for subsequent samples. I'm not aware of any recent work with modern EBSD systems and higher resolution cameras, but I'd love to read your paper when you publish.

Hi Benjamin, why do you think the short distance can be beneficial? This increases the relative error of the screen-sample distance. The reduction of kV is only theoretically a good idea since the bands disappear. If you go down to several hundrets of volts you finally only see the zone axes. This is a not well discussed effect but the problem is that the band profiles also scale with the Bragg angles (like in XRD). The band profiles become wider and the contrast smaller. But you are certainly right, that accuracy and precision are dependent on the correct pattern center and the detector-sample distance. More questionable is even the accuracy since who really knows the wavelength of the electrons? So your measurements cam be quite precise but less accurate.

The program EBSDL I am using is quite sensitive and surprises me, althogh good patterns are required. However, this is also the same in XRD or TEM techniques.  

My thought was that if you bring the camera closer, the bands get larger so you should have more precision in your measurement. Again, this assumes you are limited by pixel density on the camera, which I'm assuming is the case. But you are right, it would be more sensitive to how accurately you can position the camera. However, you could probably set up a calibration method that would allow you to measure a standard sample and then an unknown without moving the camera. By low kV, I meant down to 3-5 kV or so..any lower than 3kV and the phosphor is not sensitive (at least on our system). Band contrast at low kV will also depend much more on your surface finish, so it may not be useful for some samples.

How precisely do you think you need to know the beam energy? If you have an EDS detector you should be able to fit the background to determine the actual beam energy. You can certainly see the effects of charging, for example, by this method.

For accuracy and precision you need to have for all parameters a minimum of error (propagation of uncertainty). If you have band widths of 40 pixels in diameter and your profile is already described by 2 or 3 pixels (the Bragg angles is undetermined and neither a sharp edge, nor there where it is black or where it is still white ) you already have an error in the scale of at least 5 %. This is (from my point of view) also the reason, why this limit is nowadays well accepted. The closer you are going with the detector the worse this ratio becomes. You need to describe band widths in hundrets of a pixel in order to get a valuable accuracy and precision. But how reliable this can be if the band profiles are in the scale of pixels?

The same is valid for patterns center and detector distance. Especially the last one is concerned since at small distances the error becomes dramatically worse because of the low precision of positioning.

If you go to 3-5kV, not only  the information depth becomes smaller but also the diffraction conditions become worse (unlimited periodic arrangement of atoms and molecules is less correct), i.e. the bands (if visible) become wider but also more blurred. The  determination of the Bragg angle becomes then less accurate, and you also cannot identify that many bands anymore which is the actual reason that you can increase the precision of the technique by using many instead of only a  few bands. I only used this example of a few 100V in order to demonstrate into which direction the signal is moving. This blurring is indeed an effect which can be nearly ideally simulated, i.e. an unexpected impact of a bad surface preparation can be excluded. This is also the reason why high resolution images are not much better than 2x2 or 4x4 binned images. The degree in accuracy of band detection is practically not existent because of the pixel width of the profile and uncertainties in band width determination. Unfortunately the profile character is not equal for each band so that one cannot use a simple approximation algorithm for a general Bragg angle positioning. It assumes to be better than a manual, very subjective band edge determination, but it still needs a careful evaluation. The only very accurate information is the a:b:c ratio since zone axes can be really determined in higher accuracy since their distance depends on the screen resolution and can be several hundred or even thousand pixels. Unfortunately they only show you the lattice parameter ration but not the lattice parameters itself. Therfore it is the rule that the ratio is at least 10 times higher accurate than the lattice parameters itself.

The entire procedure is challenging but not hopeless. It perhaps only needs some good ideas :-). Thanks for your comment!