Tilt Geometry Definition
An email from Richard Henderson, sent on June 12, 2000 to Henning Stahlberg.
TO: Henning Stahlberg
FROM: Richard Henderson
SUBJ: TTBOX
12-June-2000
Dear Henning,
Concerning TTBOX, in order to avoid problems later with remembering how any film has been scanned, I always scan films in the same way - with the number at the top and the edge of the film parallel to the edge of the scanner. TTBOX is written in such a way that the tilt-axis can be described in whatever orientation it happens to occur. I don't recommend turning the film because that is one extra thing you have to remember - always scan things in the same way, and thus with the same microscope the tilt-axis will always be more or less in the same direction.
y=0 means the x-axis which is horizontal. It is indeed the bottom line of the image. The first point on that line is (0,0), the second point (1,0) and so on [e.g. (x,0)]. Therefore all points on the line have y=0. If the tiltaxis is horizontal, parallel to x and the defocus gets stronger as you go to higher values of y (i.e. further up the image), then TLTANGL is positive. This is a robust definition and TLTAXIS can take any number between -89.999 and +89.999. If it happens to be exactly 90.000 (note that this has never occurred in practice), then you have to know how the program reacts and that is where the extra x=0 description arises. In practice, if your film orientation is such that the tiltaxis is mostly vertical but varies a bit with some of them on different sides of the vertical, then those with TLTAXIS of 85 degrees, for example, would have TLTANG positive, whereas those with TLTAXIS of 95 (i.e. -85) degrees would have TLTANGL negative. So, the TLTANGL sign would change at 90. This does not happen with the tiltaxis roughly horizontal, when there is no change in the definition as the TLTAXIS passes from -10 to +10. I hope this is now clearer.
TTBOX and TTMASK do not have REVHK, so I assume you are referring to TTREFINE. In TTREFINE, REVHK is only used in the comparison with reference data from an MTZ 3D data file - obviously you have to get the indexing right before the phases will agree and the FIDDLE subroutine should make all the necessary changes so you should not need to worry about TLTAXA provided you get the values for TLTANGL and TLTAXIS correct. In particular, REVHK has no effect on the tilt-transfer-function which is defined alsolutely from TLTAXIS and TLTANGL. TTREFINE should tell you what the correct values for TAXA and TANGL are and this is always done before REVHK is applied. Subsequently, when you are merging data using ORIGTILT, you simply use the values of TAXA and TANGL that TTREFINE tells you to use. Then if you wish to reverse the indexing using REVHK, this is done using the same FIDDLE subroutine. Thus, the H and K exchange in all cases is done after all the tilt geometry, so you should not change anything else. The idea is to get the correct values for TLTAXIS and TLTANGL which has nothing to do with indexing, and concerns only the micrograph. Then REVHK can be used to correct an incorrect crystal indexing without having to change or worry about anything else.
In summary, TLTAXIS and TLTANGL refer to the micrograph which in principle might not have any crystal on it (the values would still be correctly defined by the defocus on the carbon film), whereas TAXA, TANGL and REVHK refer to the crystal. Since TTREFINE knows where the a-axis and b-axis of the crystal are (since they are input parameters), it can calculate TAXA and TANGL which are used by ORIGTILT which knows nothing about the micrograph. Only REVHK, or ROT180 in some spacegroups, need to be checked by the experimenter.
Best wishes, Richard Henderson
TLTAXIS: Xax→Tiltax (on image) [grd]
TLTANG: Tiltangle (of sample support film) [grd] (TLTANG = TLTANGL, same thing, two names)
TLTAXA: Tiltax→A* (on image) [grd]
TAXA: Tiltax→A* (in 3D sample reconstruction) [grd]
TANGL=(AISABOVE*SIGNTLTAXA*HAND) * TLTANGL (of tilted plane in 3D reconstruction)