TTBOX
By Vinzenz Unger and Anchi Cheng
The changes in the amount of underfocus across images of highly tilted crystals induce a splitting of the high-resolution spots in the transform due to the effects of the so-called “tilt-transfer function” (TTF) (Shiske 1982, Hayward&Stroud, Henderson et al 1986,1990). An easy way to grasp the basic problem is to recall that a change in defocus across the image will manifest itself as a “breathing” of the Thon ring pattern. Calculating CTF-curves for increasing amounts of underfocus immediately shows that for any given amount of underfocus the spacing between neighboring modulations becomes smaller at higher transform radii (see Fig.6). Furthermore, the number of oscillations observed in the CTF goes up dramatically as the general level of underfocus increases. The apparent “breathing” of the Thon ring pattern is thus caused by accommodating a larger number of oscillations within the transform limits while moving the image in a direction perpendicular to the tiltaxis. The immediate effect on reflections at higher transform radius is that the CTF will no longer modify the phase of these reflections in a uniform manner for the parts of the image that do not have the same amount of underfocus (i.e. are perpendicular to the tilt axis). It is easiest to think of the consequences in terms of how this affects a single reflection at high radius in the transform. As the image is moved in a direction perpendicular to the tiltaxis the Thon rings “swipe over” the reflection, i.e. for different parts in real space the changes in the CTF would correspond to alternating contrast of the component. If these contrast reversals (i.e. whether being on an odd or even band of the CTF modulation) are plotted as function of the height increase across the image one finds that the contrast is changing in a sinusoidal manner. Affected reflections will appear split because the Fourier transform of an infinite sinusoidal oscillation is a pair of delta functions at a distance of ± [1/period] from the origin. However, because the number of contrast reversals is finite the split peaks will be broadend. Since the amount of split for the high-resolution reflections is directly dependent on the total number of reversals it follows that the effect depends on the actual position of the reflection in the transform, the amount of tilt and the size of the image. Usually a correction is necessary only at high specimen tilts (>40-45˚) and if the specimen is ordered to high resolutions. In these cases, the intensity of the diffraction spots will no longer be at the predicted peak position calculated from the general lattice vectors. Consequently, MMBOXA is not suitable to retrieve data from the transforms of images. To correct for the TTF and to retrieve data from these transforms, TTBOX combines features of MMBOXA and CTFAPPLY. Many of the input parameters are identical to those of the latter two programs and more detailed explanations can be found in the corresponding sections. However, a few parameters are unique to TTBOX and these will be explained in more detail here.
The final data that are written out by TTBOX are fully CTF-corrected and can be directly merged with other CTF-corrected data without any further treatment. In contrast to MMBOXA (which will generate output for all reflections to a certain resolution unless GENPTS=Y), TTBOX allows to select certain parts of the transform for output ($seg). A setting of $seg=±90 will result in all possible spots being analyzed. However, only the spots parallel or perpendicular to the tiltaxis will be treated and plotted for $seg=45 and $seg=-45 respectively. The statistical output that is provided in the logfile evaluates the final overall peak shape in a manner analogous to the scaled average intensity calculated by MMBOXA. It should be noted that the quality of the peak shape is largely dependent on the settings for underfocus and the tilt parameter. Hence, these parameter need to be very well defined! The option to automatically refine these parameter with TTREFINE should be used with caution, especially if more than the defocus values and astigmatism require adjustment. If TTREFINE is to be used, then keep in mind that the inital estimate for the underfocus needs to be within 1000Å of the true values as otherwise, the refinement will not converge and go into the opposite way until it reaches the next, smaller maximum.
Another important difference between TTBOX and MMBOXA is that TTBOX invariably shifts the phase origin to the middle of the image. Consequently, if TTBOX is used on transforms of images from crystals with less then ~40-45˚ of tilt (which we do not recommend - see below) and if in these cases the cross-correlation map suggests that a “best area” should be boxed then TTBOX (or TTMASK or TTREFINE) cannot be used unless the centre of gravity of the box around the best area coincides with the middle of the image. Importantly, in the images of highly tilted specimen (>45˚) the “best area” in the cross-correlation map will coincide with the part of the image that has the highest underfocus! In these cases, the whole concept of boxing a “best area” does no longer make sense and, if at all, the whole image has to be used (which allows the phase origin to be shifted to the middle as is required by TTBOX).
As outlined above, the tilt geometry needs to be known in order to fully correct for the TTF effects. The parameter $tltangl and $tiltaxis serve as input parameter to describe the specimen tilt. It is extremely important to not confuse these settings with $tangl and $taxa that describe the tilt geometry for phase origin calculations performed by ORIGTILTD. Settings for $tangl and $taxa define the absolute tilt and the angle between the tiltaxis and a*. In contrast, $tltangl will have the same numerical value as $tangl. However, the sign of $tltangl is completely unrelated to the true sign of tilt and depends only on the relation between the image origin and the direction of the underfocus gradient. By convention, the sign of $tltangl is positive if the starting point of the scan (!) at y=0 was on the side of the image that had less underfocus. This definition remains unchanged even if the true tilt of the crystal required $tangl to be negative in ORIGTILTD! If the tiltaxis is precisely parallel to the y-axis of the image, then the same convention should be applied for the x-coordinate, i.e. $tltangl is positive for less underfocus at start of scan for x=0. Like for $tltangl, the convention for describing the position of the tiltaxis, $tiltaxis, is also different from that in ORIGTILTD. For TTBOX, setting of $tiltaxis describes the angle between the tiltaxis and the x-axis of the transform. Values for $tiltaxis should be in the range of ±90˚ - however, values outside this range will be readjusted by the program. As pointed out for setting of the related parameter, $tiltaxis, in CCUNBENDE, the angle between the tilt- and x-axis of the transform will be very well determined at the high specimen tilts where TTBOX is applicable (usually >45˚).
The effects of the TTF are negligible at low specimen tilts especially if the resolution does not extend beyond 5Å. Hence we do not recommend using TTBOX in these cases, because the larger sophistication does not pay off if tilt and initial underfocus values are only known to within a few degrees and several hundred Å respectively. If anything we would advise against using TTBOX in these cases because it will distort the data and eliminates the only information that could be used as a guide for CTF-refinements, i.e. the explicit assignment of CTF-values for each reflection. Furthermore, if it turned out at a later stage that inaccurate underfocus settings had been used one would need to reprocess the image if the final transform was not stored or backed up since in contrast to CTFAPPLY, TTBOX requires a transform as input.