Running the application¶

Import Notes about Image Intensity Recorded through
Tomography Node¶

Tomography node save the images in a different format from other Acquisition nodes. By
default, the flat-field correct CCD counts are multiplied by 10 and converted to signed
16-bit integer before the image is displayed and saved. This makes CCD counts of 3276.8 or
larger overflow to negatives. Other Leginon Acquisition images are saved as float without
manipulation.

To avoid this problem, find out what exposure time corresponds to the fractionated dose
from your tilt angle step and range and total dose and take an image at tomo preset with
such an exposure in Navigation node. You will need to reduce the total dose if a good
fraction of the counts are larger than 3200 even though it would not appear to be saturated
in the float scale without the 10x factor. Alternatively, change the scale factor in
Tomography node.

Multiscale Imaging¶

• Preset image shift alignment/beam shift alignment are the same as in MSI
  application

• New dark/bright references should be reacquired for "tomo" preset that acquires the
  final data. It is best to do this at the same dose per tomography image calculated from
  the total dose, the tilt parameters, and the dose measurement.

• For best focusing result, perform autofocus at the same magnification as the
  tomography data collection, align microscope well at the eucentric focus and the
  rotation center and save them before data collection.

Using Tomography Preview¶

• Preview targets (pink) can be selected when selecting targets in "Tomography
  Targeting"

• When the targets are processed, targets that are of the type "preview" are
  processed before focus and acquisition targets.

• Tomography Preview node acquires a image at the preview target using "preview"
  preset which should be set at minimal dose.

Dose Measurement¶

If "Measure Dose before collection" is checked in Tomography node, the stage will be
moved to the reference target and a dose image of the "tomo" preset will be acquired (center
512x512 of whateven binning of the preset) before each tilt series if the interval between
the series is longer than the limit time set in the settings of Dose Measurement node. The
measured value will then be used to recalculate the proper exposure time for tomography
imaging.

For this function to behave properly, the followings should be done during
operation:

• One, and only one, "reference" target should be selected in either "Square
  Targeting" or "Hole Targeting" or "Tomography Targeting" node. The reference target
  should be of either a broken square or a empty hole if no broken square can be
  found.

• "Measure Dose" before collection should be selected in Tomography node.

• "Exposure time max/min" in Tomography node should be in a range that can accommodate
  the electron beam fluctuation over time.

Align Zero Loss Peak¶

This function applies only to Gatan energy filter EFTEM. If "Align ZLP before
collection" is checked in Tomography node, the stage will be moved to the reference target
and starts the procedure to align zero loss peak before each tilt series if the interval
between the series is longer than the limit time set in the settings of Dose Measurement
node.

For this function to behave properly, the followings should be done during
operation:

• One, and only one, "reference" target should be selected in either "Square
  Targeting" or "Hole Targeting" or "Tomography Targeting" node. The reference target
  should be of either a broken square or a empty hole if no broken square can be found.
  This is the same reference target used for dose measurement.

• "Align ZLP" before collection should be selected in Tomography node.

Low Magnification Model Fitting¶

The fitting of optical axis offset does not always works if the offset is so large that
the feature moves out of view with even a small tilt. In such a case, it is worth first
collect a tomography series at a lower magnification to define roughly the model.

At beginning of each session, or forced by the user, the model is initialized. By
default, at the initialization, Tomography node uses past fitting results that show good
agreement with the experimental data at the magnification of the preset used. If a good
model is not found, that from lower magnifications will be used. It is possible to force the
node to use a model fitted at a particular magnification by selecting it in
Tomography/Settings/Model.

Therefore, we recommend that, in case of fitting failure on good contrast images, the
followings should be done:

1. Tomography/Settings/Image Acquisition> change the preset to "hl".
2. Tomography/Settings> adjust Tilt and Exposure parameters to match.
3. Acquire the tiltseries images.
4. If the tracking is good, change the preset back.
5. Tomography/Settings/Model> Initialize with the model of (the mag of "hl"
   preset).
6. Acquire the tomo-series.
7. If tracking is good, change back to Initialize with the model of "this preset and
   lower" mag.

What is a Good Tilt-Axis Model?¶

The goniometer-tilt-axis-based tracking model developed by Zheng et. al. corrects the
specimen height (z-axis) by a change of defocus using measured shift of feature shifts in
the images (x and y-axes). The tracking in the x and y directions does not involve the use
of such model, but is done by smooth curve fitting or preceding tilts. Therefore, to judge
the adequacy of the model, one should check the resulting defocii of the images in the
series remain unchanged.

On the other hand, the feature tracking in x and y is likely to fail only if the tilting
does not induce a smooth shift of the imaging feature a sudden drop of specimen position at
a particular tilt angle often throws off the smooth curve fitting. It is possible to reduce
such effect by increasing the number of data points included in the smoothing as set in the
model section of the tomography node settings window. Otherwise, the goniometer need to be
serviced.

Checking and Improving Tilt-Axis Model¶

Test runs should be done at the magnification, defocus, and tilts up to the highest
values planned for the real ones with a specimen with isotropic features in view and
adjusted to eucentric height. Tilt steps should be made to allow at least 15 images taken
per tilt direction.

First Test Run: Fixed Model¶

The first time the tomography application is used on a microscope, all model
parameters are default to zero. A test run should be done with the specimen at eucentric
height and all default settings including "keep the tilt axis parameters fixed" activated.
If the feature tracking is good, and the defocii of the images in the tilt series do not
significantly changed, the goniometer behavior and camera alignment are close to ideal,
and no improvement of the model is required.

If the xy tracking deteriorates quickly in the first few tilts, the magnification
should be dropped so that tracking is possible through out the tilt series. Once a rough
model is established, refinement can then be done at higher magnifications.

Runs to Improve the Model-Fitting¶

A complete tilt model fitting is difficult with small number of data points or at only
low tilts. Therefore, two tilt series need to be taken in order to get a good averaged
model that is later fixed.

1. tomography/settings/model>deactivate "keep the tilt axis parameters
   fixed".
2. tomography/settings/model>initialize the model with "this preset only" unless
   this is a refinement of <link linkend="Tomo_low_mag_fitting">a rough model obtained at
   a lower magnification</link>, in which case, initialize the model with "this preset
   and lower mags".
3. tomography/toolbar>click on "reset learning" to have
   a fresh start of tilt series data included in the fitting.
4. Presets Manager>send the "tomo" preset to scope.
5. tomography>Start the tilt series image collection by clicking on "Simulated
   Target" tool.
6. repeat 4 and 5 to dynamically fit the model the second time if the first one goes
   to completion.
   If the target shifts away during the run, reduce the magnification, repeat 1
   through 9 in this procedure and then return to the higher, intended mag and refined
   the model using the same procedure and proper setting for refinement as mentioned in
   2.
7. Check on web image viewer to see if the result of the second run in step 6
   produces images of constant defocus through out each half of the tilt seriese.
8. If the model is good, activate "keep the tilt axis parameters fixed" in the
   tomography settings.
9. Repeat step 2. Other than reset the learning, the tool produces an output of image
   shift you should copy down and apply to the "tomo" preset in the future runs.

Understand the results of the model fitting¶

If the above procedure does not yield a good model, it is necessary to study the graphs
output by the run to determine possible causes and derive the best fixed model that at least
work for most angles.

Figure 1 shows a typical result from the first dynamically fitted tilt series run. x and
y axes contains the tilt axis and are referenced to columns and rows on the images acquired.
z-axis is parallel to the electron beam. The "Prediction" data in the x and y-axis plot is
the extrapolated result of the smooth curve fitting from preceding (usually 4) tilts to the
current tilt angle. The "Position" is where features on the specimen end up to be relative
to the origin of the image shift at the scope as determined by correlation of images. Both
"Prediction" and "Position" are expressed in microns. The "Feature" is the shift of the
feature on the image. It corresponds to the difference between "Prediction" and "Position"
and is expressed in pixels of the image acquired. The z-axis "Prediction" is the correction
of defocus, i.e., specimen z-height change, the current model suggests and applied for each
tilt angle to keep the specimen focused. Originally, it is possible to measure defocus at
each tilt and obtain "Measured" values in this plot. However, the function is currently
disabled because the procedure does give accurate results.

According to the Zheng et. al. model, the tilt-axis can be characterized by three
parameters: phi, the angle between the tilt axis and the detector x axis (column), offset,
the distance between the center of the detector and the tilt axis on the xy plane, and z0,
the distance between the specimen from the xy plane that contains the tilt axis. If the tilt
axis is parallel to x-axis of the detector, and that the model does not change through the
tilt series, y-axis(row) "Prediction" and "Position" should remain constant. While the same
values for x-axis follows a cosine curve as it tilts if the only deviation from the ideal
model is an offset of the tilt axis from detector center in x-direction (non-zero offset).
On the other hand, if the only deviation the ideal model is an offset in z direction
(non-zero z0)

As a first tilt series used in the model fitting, the data is not fitted until it
accumulate enough data points and spread over more tilts. We arbitrarily select 30 degrees as
the starting angle where the fit is started. As can be seen in Figure 1, the model is
significantly different from the initial as z-axis "Prediction" jumps once the fitting is
started. In particular, the model z0 which corresponds to the offset of the specimen from
the tilt axis in z direction dominates deviation. Such problem is evident by the
near-straight line feature shift in x-axis over more than 1 um. There is also some offset in
x direction since the "Prediction" and "Position" flattens somewhat as it approaches zero
tilt. The tilt axis has minimal tilt from x-axis since in the y-direction, despite the bump
at about 40 degrees, the range of variation in the whole tilt series is about 0.06
um.

Figure 1

By activate "show model parameters" check box in the viewer, more plots are shown
(Figure 2). phi and "optical axis" offset remain fixed below 30 deg while z0 is recalculated
at each tilt. As you can see, the fitting of the former two parameters are not very stable
in this first trial. Therefore, we need to do the second run.

Figure 2

Figure 3 shows the z-axis plot of the second run since the x and y does not change
significantly. Figure 4 shows its corresponding model parameters. The zero and first tilt
uses the initial model and the rest are fitted dynamically. In this run, because more than
one tilt series is found in the memory since last "reset learning", the model fitting starts
after the first tilt image is acquired. model parameters are rather stable over the whole
tilt series and suggests that the tilt axis is tilted from x-axis by about -1.3 degree, and
offset from the center of the detector by -0.6 um, and the specimen is off from eucentric
height by about -0.7 um

Figure 3

Figure 4

Although it is not possible to maintain perfect defocus prediction in the full range of
the tilt by using a fixed model, we found that the overall performance is better if an
average tilt axis model that works well in the mid-range tilt is used as a fixed model. For
example, for the behavior in the above figure, we choose:

Use these custom values as initial model and turn on "Keep the tilt axis parameters
fixed". If the result is good, judging by consistent defocus and target tracking through out
the tilt series, this model will be saved in the database as best model automatically, and
you can revert back to initialize with the model of "only this preset".

Failure of xy feature tracking¶

Feature tracking in x and y axes is a 2nd order polynomial fit of preceeding data
points. The default uses 5 data points. When a sudden jump occurs in the tracking error, it
tend to follow the trend of the last point. If the jump is a temporary clich in the
goniometer, this tend to over correct the tracking error and eventually loose track as shown
in Figure 5. A possible fix is to increase the number of data points in the fitting. This
can be set in the tomography setting "Smooth n tilts for defocus prediction". 4 in defocus
prediction is equivalent to 5 points (n+1) for xy tracking.

Figure 5

Large tracking error between the first and second tilt
images¶

The first image in each tilt group of the tilt series at the "start" angle (normally 0
deg) and the second image at tilt of "step" angle from the "start" angle do not use the
fitted model. It is assumed that the eucentric height judged by stage alpha wobbling in the
"Tomo Focus" node gives a stage height that the tracking of feature by such a small tilt
would be good enough. In most cases this is a reasonable assumption. However, we have had
experience of goniometer alignment problem where the assumption fails. The symptom is
illustrated in Figure 6 below. Note that the Feature tracking error is displayed as
percentage of the image length.

Figure 6

This tilt series was taken with a starting angle of zero and at an image size of < 1
um. As can be seen here, apart from the 2 and minus 2 degree tilts, the tracking error was less
than 2 % of the image. Only the tracking of the feature between 0 and +/- 2 degrees are
large. At close to 20 % error, this made the overlap between plus and minus 2 degrees unacceptable and
often cause popular alignment programs to misalign the two half of the series.

The first solution is of course to report it to your microscope service engineer. When
we had this problem, many users noticed that it was difficult to adjust stage to eucentric
height manually with alpha wobbler. Features jumped while the goniometer changed rotation
direction. In addition, different magnitude of tilt range suggests different eucentric
heights. It is not easy to fix this, so it might take a while.

Before the hardware is fixed physically, it is still possible collect tomograms. The
model fitting of the overall curve in the above case gave z0 of +5 um through the whole tilt
series (Figure not shown). Therefore, by moving the stage up by such an amount after the
stage-tilt-based autofocusing can bring us to the correct height for tomography. This can
be acheived by saving the "tomo eucentric" focus current to the database, align rotation
center for this stage height and focus. Then change the correction type of the
"Beam_Tilt_Fine" focusing step to "Stage Z".

Failure of model-based correction¶

The model used in the defocus correction in Leginon tomography node is a very simplified
one. There are a few cases when the approach fails. Here are ones that we have
encountered:

Y-axis looping¶

The microscope goniometer does not move on only the tilt axis. With its complex
structure, a common problem is that when the stage is highly tilt, the position slips in
the y-direction. This is known as looping. Figure 7 shows an example of this problem.

Figure 7

While the x-axis position shifts monotonically as a stable model should be, the y-axis
in the positive tilt direction changes little from 0-30 degrees before it increases
rapidly after 30 degrees. Even though the tracking in xy plane is still good, the defocii
correction at these higher tilts may no longer be correct if the tilt axis parameters are
fitted dynamically. Figure 8 shows the model parameters of the same tilt series where the
fitted phi and offset starts to change above 30 degrees even though the tilt axis has not
moved according to the shrinking behavior of the images during the tilts. Note that in
this particular case the looping problem is still mild so that the over-correction is not
very strong. only a small slope change is resulted in z0 prediction. In worst cases, the
defocus over-correction is so large that the adjacent images can not correlate properly
and even the xy tracking would fail. The spikes around zero tilt is a display data sorting
error of the identical starting tilt of the two tilt groups.

Figure 8

Other than asking microscope service engineer to fix the looping, one can find the
best fixed model in the series to apply to future tilt data collection. To make the fixed
model permantly saved to the database, follow these steps:

• tomography/settings/model>activate "keep the tilt axis parameters
  fixed".

• tomography/settings/model>initialize the model with "custom values". Enter best
  estimate of the fixed model. For example, in the positive direction, enter phi as
  -2.17 degrees and axis offset as -1.52 um. since these are the stable values up to the
  point the y-looping starts.

• tomography>collect a full tilt series. If the run is successful with good
  tracking in all three axis, the model will be saved in the database for this
  magnification.

• tomography/settings/model>From now on, you can initialize the model with "only
  this preset" or "this preset and lower mags"

Grid slips between the first and second tilt directions¶

When the holder does not hold the grid tightly, the grid slips to a different position
when the first tilt direction ends and the goniometer quickly returns to zero tilt.
Leginon is designed to adjust the target before the second tilt group starts. The default
setting for this function is to use only the parent image (i.e. one ancestor) where the
target comes from as reference. If the slip is larger than the size of the parent image,
the adjustment may fail, and a random target would be acquired in the second tilt
group.

Starting from Leginon 1.6, the target adjustment can be done with all ancestor images
of the target by choosing "all" in the acquisition part of the tomography node setting to
adjust target with all ancestors. The node "Taget Adjustment" limits the lowest
magnification that this target adjustment would go up in ancestry. The default is at 300x
so that the presence of the objective aperture does not create difference in the reaquired
ancestor image from its original.

Strong and continuous specimen drift¶

The model used in Leginon considers any shift of feature in the image a result of tilt
axis not aligning to the center of the detector. With the phi and offset fixed, all errors
are accumulated in z0 and results in bad defocus correction. There is no solution to this
at the moment.