Finding Defocus with Ctfplotter for Four Example Tilt Series

(IMOD 4.12)

University of Colorado, Boulder

This document will guide you through running Ctfplotter to find defocus for a relatively recent high-resolution tilt series and for three different older tilt series, one where the signal of the CTF is fairly strong, one where it is sometimes strong and sometimes weaker, and one where it is weak.  It will explain some of the most important aspects of the process.  The first example represents a best-case scenario and the presentation includes new features in IMOD 4.12.  The second one is somewhat complementary, going into more detail on some topics.  The last  two illustrate strategies for dealing with weak signals.  For more details, consult the Guide to Ctfplotter, which fully explains each aspect of the interface and some of the underlying processing considerations and also has screen shots based on these data sets.  Labels in the Etomo or 3dmod interface are shown in Bold, and entries in fields are shown in italics.

1. Determining Defocus in a High-Resolution Tilt Series from a K2 Camera:

This tilt series is from the study of HIV virus-like particles in Schur et al., 2016, Science 353:506-598, based on the data set TS_43 from the EMPIAR-10164 deposition.  John Heumann produced the tilt series by aligning the super-resolution K2 frames with Alignframes, and the rest of the files in the sample data set are from his processing of the tilt series.  The pixel size is 0.135 nm; there are 41 images at 3 degree increments taken with a dose of 2 electrons/square Angstrom.

Getting started

• Manual download and unpacking:
• Download the sample data set from our web site.
• Move the data set file "TS43-CTF-Data.tar.bz2" to the directory where you want to work on it.  Its contents will unpack into a subdirectory named "TS43-ctf".
• cd to the directory with the file
• Enter the command:
      imoduntar TS43-CTF-Data.tar.bz2
  or, anywhere except on Windows without Cygwin, you can use
      tar -xjf TS43-CTF-Data.tar.bz2
• Or, download and unpack with imoduntar:
• cd to the directory where you want the subdirectory "TS43-ctf" created
• imoduntar -d TS43
• Enter the data set directory with:
      cd TS43-ctf
• Start Etomo with the command
      etomo TS43.edf
• Open the Final Aligned Stack page and switch to the Correct CTF tab.
Microscope parameters have been filled in already.
•  This tilt series was taken at a defocus of 2.5 microns, but to illustrate Ctfplotter's ability to find the initial defocus when the data set might be one of many with  different defocus values, Defocus range to scan has been set to 1.0,6.0 and Expected defocus has been left blank.
• Press Run Ctf Plotter.  Note that the CTF is analyzed in the raw stack, so the aligned stack does not need to exist before running Ctfplotter.

Initial points about Ctfplotter

• Three windows open: the plotter window, a dialog for setting parameters controlling which views are analyzed and various aspects of the power spectrum computation, and a dialog for setting parameters for fitting to the power spectra.
• The magenta curve in the plotter window shows the rotationally averaged power spectrum plotted versus spatial frequency.  The green curve is a fitted curve, which in general may not fit well until fitting parameters have been adjusted. 
• The frequency of the first zero determined from the fit is shown at the top of the plotter window after Z:, and the corresponding defocus is shown after D:.  The initial scanning found the correct defocus, 2.49 microns, and the curves line up through about the sixth zero.
• The units of spatial frequency along the X axis are reciprocal pixels and range from 0 to 0.5/pixel. Below the frequency labels are the corresponding values for periodicity (resolution) in Angstroms.
• Power is always very high at low frequencies, so the part of the curve that shows the CTF effect needs to be zoomed up.  The next example describes how to do that manually, but autotuning will take of this for us.
• The spectrum is initially averaged over multiple views in case the CTF signal is not that strong; the default initial angular range will result in 3 views for 3 degree tilt series and 3 or 4 for 2 degree series.  We will keep this summing for some preliminary steps.

A detour to enhance appreciation of autotuning

• Before autotuning, let us take a detour just to illustrate some of the advantages of autotuning.  First, increase the fitting range to include all of oscillations where the two curves match.  There are three ways to do this.  One is to change the value in the End fit at box in the Fitting Params dialog; a more convenient way is to double-click with the right mouse button at the desired frequency in the plot window.  Do the latter.
• There is now an alarming message in the Angle Range & Tile Selection dialog; for an End fit at value of 0.17, it says
  Crop to >= 0.197 nm to have >= 3.5 points/zero in the fitting range
• This is happening because there are only 100 points in the power spectrum graphs, so as the CTF zeros come closer and closer together at higher frequency, there are not enough points between each pair of zeros to represent the oscillations faithfully.  When there are only two points per zero, no oscillation can occur - this is what happens at frequencies of 0.18 - 0.20.  This phenomenon, where there are not enough sample points to represent the CTF curve, is called CTF aliasing.  The message refers to 3.5 points/zero because the oscillations can still be represented reasonably well with that many points.
• There are two ways to fix this problem: the number of points sampled for the graphs can be increased, or the same number of points can be sampled from a subset of the frequency range.  Cropping the frequency range is preferred because it spreads out the oscillations and makes them easier to see, so the message suggests doing that.
• To follow its directions, change the Analyze spectra cropped to pixel size text box from 0.135 to 0.2 and turn on the check box.  Notice that the end of the frequency range changes from 2.7 to 4.0 Angstroms because the frequencies past 4.0 have been thrown away.
• The curves immediately look better and the fit can obviously be made to go past 0.3.  Double click in the graph to do so.
• For an End fit at value of 0.315, the message is now
  Crop to >= 0.250 nm to have >= 3.5 points/zero in the fitting range
• The aliasing is still happening, just at a higher frequency.  Unfortunately, this could go on for another few iterations, and it will start recommending changing the power spectrum resolution (number of points in the graph) too.  Autotuning is much easier.
• Just turn off the checkbox for Analyze spectra cropped to pixel size and press the "Set" End button in the Fitting Params dialog to get back to the initial situation.

Finding astigmatism and autotuning

• It is worth checking for astigmatism before autotuning because if it is large, it could blur the spectra at high frequency and autotuning might not pick an optimal end to the fitting range.  Turn on the Find astigmatism checkbox in the Fitting Params dialog.
• You will see the spectra change as the program measures defocus from wedges in the 2-D power spectra at a range of angles, but the defocus hardly changes, and the value after Astig: above the graph is only 0.03.  Finding astigmatism is explained more in the next example where it is much more worthwhile.
• Finally, press the Autotune button in the plotter window.  Many changes occur:
• The spectrum cropping has been set to 0.239 nm.
• The Power spectrum resolution has been set to 136 to eliminate the CTF aliasing because cropping to any higher pixel size would throw away spectrum with CTF signal.
• The message is now in a comforting green because its suggestion is satisfied:
  Set PS resolution to 128 to have >= 3.5 points/zero in the fitting range
• The graph is scaled up to show the CTF signal well.
• The fit is set to go to 0.463, nearly to Nyquist in the cropped spectra.
• The option to Do autoweighting and truncation is selected; this makes the program compute the correlation coefficient between the spectrum and the fitted curve locally around each point, assign weights for each point, and redo the fit with those weights applied.  The resulting weights are plotted in the blue curve, with labels on the right to show the where the weights are 0, 0.05, or 1. You will see the importance of this weighting at higher tilt angles.
• "Which defocus to use" has been changed from Expected defocus to Current defocus estimate now that the program has optimized the fitting; this setting is always preferable when autofitting.

Testing tilt angle polarity and offset

• If a tilt angle offset was not applied during tomogram positioning, or if it is not clear whether the specimen will be flat in the X/Z view after positioning, it is a good idea to test for an offset at this point.  Press the + button next to "Tile & wedge parameters" to open the section with controls for this test.  The Test Left-Right Differences button can be used in two ways: to test if the tilt angle sign is wrong, and to find the tilt angle offset that would counteract the left-right difference for one set of views. The latter is of little use because there is an automated procedure for determining this offset from multiple sets of views.
• If you are processing data from an unfamilar source and there is any doubt about whether tilt angles need to be inverted, you should first test for that.  There is no need in this case, but let us do it to demonstrate that fact.  Enter 45 for the Middle tilt angle.  This is a good angle to test at, and summing over multiple views is recommended for these tests.
• Press Test Left-Right Differences.  It does separate fits to tiles on the left and right sides of the images with angles as currently defined, then fits with them inverted, and pops up a message with the results.  The difference between left and right defocus values is small with angles as currently defined, and large with angles inverted, so the angles are correct as they are.
• Before closing the message box, notice that the weights (the blue curve) fall to zero just past half-Nyquist in the fit with angles inverted.  The fit is truncated at this point because the local correlation coefficient fell below a threshold.
• Enter 0 for the Middle tilt angle and press Assess, to the right of the Tilt offset text box.  The program finds defocus on the left and right sides for 5 sets of views, computes an implied tilt angle offset from each pair of defocus values, averages the results, and sets an overall offset. This process is repeated for 2 more iterations or until the change in offset is small. Here the offset was found to be -3.9 degrees, with no change on a second iteration.
• An offset this large will result in a small but detectable reduction in high-frequency signal in the summed spectra at the highest tilts.  Determining this offset relies on very small defocus differences that need to be determined accurately, so the result will probably not be reliable if there are only a few zeros included in the fit.

Checking the fit to single views and autofitting

• With these preliminaries out of the way, reduce the Number of views to fit to 1.  The curve is still fine.
• Test the extreme tilt angles to see if they need to be excluded from autofitting.  Enter 60 for the Middle tilt angle and note that the weighting and truncation is doing its job well.  Enter -60 to see the same thing.  Then go back to a Middle tilt angle  of 0.
• To speed up the display of wedge fits for finding astigmatism, change the value in the Show wedge fits for  text box from 0.05 to 0.005, or just uncheck the option if you are tired of seeing them.
• To autofit, check Fit each view separately and then press Autofit All Views.  In this case the button alone (labeled Autofit All Steps) could be pressed but this is the case only if the Step view range by is 1.
• Autofitting runs from 0 to -60 then from 3 to 60 degrees so that it can start with a nearly correct defocus from the adjacent view when it steps to a higher tilt.
• The table is populated with defocus and astigmatism values for each tilt.  To visualize these easily, press Graph Values.  Graphs are displayed of defocus, astigmatism in microns, and the axis of astigmatism in degrees.  The axis values are remarkably consistent considering how small the astigmatism values are.
• There are no suspicious tilt angles in here.  Press Save to File and close the plotter window.
• Press Run Ctfplotter in Etomo again.  The defocus and astigmatism are loaded into the table from the file ("setname.defocus"). The program opens with essentially the same settings as when it was closed because settings for this data set were saved in a file, "ctfplotter.info".  You can remove this file and the .defocus file to start from scratch.  It is also possible, when starting for the first time, to load the settings from the last run of Ctfplotter on another data set by applying the "global settings" offered in the More... popup menu.

2. Determining Defocus in an Old Tilt Series from a K2 Camera:

This tilt series, from Cindi Schwartz, is of a flagellum of a Giardia cell, taken with a K2 camera on a Krios microscope at Janelia Farm.  The total dose was 26 electrons/square Angstrom.  Images were taken in super-resolution mode with an exposure time of 0.5 sec to avoid having to save and align subframes, and reduced by a factor of 4 with antialiasing.  With this protocol, they may have somewhat better high-frequency information than a typical tilt series taken in counting mode without binning, so the power spectra may be particularly good here.

Getting started

• Manual download and unpacking:
• Download the sample data set from our web site.
• Move the data set file "K2-CTF-Data.tar.bz2" to the directory where you want to work on it.  Its contents will unpack into a subdirectory named "K2-ctf".
• cd to the directory with the file
• Enter the command:
      imoduntar K2-CTF-Data.tar.bz2
  or, anywhere except on Windows without Cygwin, you can use
      tar -xjf K2-CTF-Data.tar.bz2
• Or, download and unpack with imoduntar:
• cd to the directory where you want the subdirectory "TS43-ctf" created
• imoduntar -d K2-CTF
• Enter the data set directory with:
      cd K2-ctf
• Start Etomo with the command
      etomo WTI042413_1series4.edf
• Open the Final Aligned Stack page and switch to the Correct CTF tab.
Notice that a spherical aberration of 0 is allowed, and is appropriate if data were collected on an aberration-corrected microscope, as these were.
• The Expected defocus has already been set to 6.0 in this data set.
• The Config file has already been selected to access a configuration file listing noise files in the "Janelia" subdirectory of the data set directory.
• Press Run Ctf Plotter. 

Initial adjustments and assessments

• The first operation is to zoom up the part of the curve that shows the CTF effect. Click the mouse just under the hump in the curve after 0.1/pixel and drag the zoom area out to the right edge, just under the curve, so that the Y axis range is about -0.1 to 0.5.
• Since the fitting looks good already, switch to use the Current defocus estimate in the Angle Range and Tile Selection dialog.
• The defocus shown after the D: at the top of the plotter window is ~4.6 microns instead of the nominal 6 microns. The fitting range in the Fitting Parameters dialog starts at a low frequency appropriate for the higher nominal defocus but too early for this lower actual defocus.  It is best if the fitting is done to a linearly falling part of the curve and excludes the portion before that curving away from a line.  Press Start to change Start fit at to 0.17., or double-click with the right mose button where the curve is about twice as high as the hump between first and second zeros, which will probably change the start to 0.18.
• It is not helpful to see the curves much beyond where the fitting starts, so the graph can be zoomed again. Click a bit above and to the left of where the fitting starts (which is at 0.17/pixel and 0.3 in Y) and drag out to just below the right end of the curves to give a Y axis range of about -0.05 to 0.35.
• This average over five views appears to have good signal out to the fourth zero, but the useful range for fitting may be less when fewer views are averaged. For now, change End fit at to 0.43, or double right-click past the middle of the hump bteween third and fourth zeros. When you change a text box box entry, press the Enter key or Apply (in either dialog) to fit with a changed value.
• Notice the entry for Error: on the output line in the plotter window, which shows the mean deviation between the power spectrum and the fitted curve over the fitting range, in the log units of the Y axis.
• If you turn on Vary exponent of CTF function, the defocus will not change and the error will drop only a little, from 0.0038 to 0.0036. To avoid overfitting by including too many parameters, it is best to leave this option off in this case, and turn it on only when there is a more substantial visual improvement in the fit between the two curves, or a bigger reduction in error, like 10%.

Checking quality of fit to a single image over the whole range

• To assess whether fitting to a single image is possible, go back to the Angle Range and Tile Selection dialog and change the Number of views to fit:. Notice the line below this spin box, summarizing the angular range and view numbers being fit. Click the down arrow of the spinner to reduce the number of views progressively down to 1. The curve does become noisier, but the fitting still appears good out to ~0.43/pixel.
• Turn on Do auto weighting and truncation to help keep the fit from being thrown off by noise past a certain point.  At this angle, the blue curve of weights stays close to 1 to the end of the fitting range.
• At this point, the fitting looks good enough that we could also try to find astigmatism before the following steps, but let us go through those steps without astigmatism so we can concentrate on the behavior of defocus.
• To see whether fitting is good throughout the tilt range, leave the number of views at 1, change the Step view range by: entry to 5, and press Step Up to go to the positive end of the tilt range, then Step Down to go back down to the negative end of the range. The power spectrum looks good enough and the fitting appears reliable at each tilt angle.
• If the first zero appears elevated when first stepping to an angle (such as 61 degrees), press Apply one or more times to see if the fitting to the baseline improves. In general, repeatedly computing the spectrum and fit in this way with each new defocus is a good way to assess the stability of fitting.
• This assessment sampled only a fifth of the angles; you can set to the Step view range by to 1 to step through every angle.
• Most of the single view spectra show signal out close to the fourth zero, so change the entry for End fit at in the Fitting Params dialog to 0.44. Note that with the autoweighting turned on, there is no real penalty for setting the fitting range too high for some views.

Autofitting to all views

• Turn on Fit each view separately and press Autofit All Views. The fitting goes in two directions from the current angle, unless that angle is at one end of the range. The table is filled in as the fitting proceeds.
• Press Graph values. A graph of defocus versus tilt angle pops up, showing variations of over 1 micron above 40 degrees. You can left-click at a point in this window and a popup will appear with its coordinates (you have to left-click again to dismiss the popup).
• Scroll the table in the Angle Range dialog to get to these angles with the big deviations.  Double-click a series of lines in the table to check the curve-fitting in this region, or set the Step view range to 1 and use Step Up and Step Down to look at successive views.  The curve-fitting is clearly correct; the defocus changes from image to image have been measured accurately.

Finding astigmatism

• Now that you have gone through the basics of determining defocus, the next step is to assess whether astigmatism can be determined as well. When there is astigmatism, the defocus varies with direction. In a 2-D power spectrum, the Thon rings (which correspond to the dips at CTF zeros in the rotationally averaged 1-D power spectra here) are approximately elliptical instead of circular. Astigmatism thus has two parameters, the difference between the maximum and minimum defocus and the angle of the axis of maximum defocus. Ctfplotter finds astigmatism by measuring the defocus in 1-D power spectra rotationally averaged over restricted angular ranges of the 2-D power spectrum, referred to as wedges.
• Return to low tilt by entering 0 in the Middle tilt angle text box. (The program will adjust the entry to the nearest actual angle.)
• Press the + button to the left of Find astigmatism in the Fitting Params dialog to open the controls for finding astigmatism.
• Notice that Min views for astigmatism has the default value of 5. This means that wedge spectra will be combined from 5 views when defocus is being found for single views. It is generally advisable to find astigmatism from more views than those used for finding defocus, because the wedge spectra have less data in them than full 1-D spectra, and combining more views will keep the signal-to-noise ratio up and make the CTF fitting comparably reliable. See the Guide to Ctfplotter for more details on this point.
• Turn on Find astigmatism and watch the wedge spectra as the angle of the wedge changes. It is important to see these wedge spectra initially to make sure that the fitting looks good and that the spectrum does not take on a strange shape in some part of the angular range. The whole process is iterated because the astigmatism is rather high for this data set.
• After the analysis, the program computes a spectrum for the single selected view that is fully adjusted for the astigmatism and measures defocus from that. Note that the CTF signal now appears clearly all the way out to 0.5/pixel.
• Check the fitting to the wedges at a few other angles by typing them into the Middle tilt angle text box, for example 30, 60, -30, and -60
• Return to zero tilt by entering 0 for the Middle tilt angle. It is generally advisable to start autofitting at zero tilt because fitting is likely to be more challenging at high tilt.
.
• Press Autofit All Views to fit to all views. The programs asks if you want to remove all existing entries from the table. Press Yes.
• You can turn off Show wedge fits in the Fitting Params dialog to save time if you are confident that the wedge fitting is reliable. It can be turned on and off during autofitting, so one approach is to turn it off for lower angles and turn it back on as it approaches high tilt.  Another option is to set the value very low, like 0.001, but this is more effective on Linux than Windows.
• Press Graph values; this time there are graphs for the astigmatism amount and axis angle as well as the defocus. It is not clear how much of the view-to-view variablity in the latter two parameters is real. There would be considerably more variability with Min views for astigmatism set to only 1.
• Press Save to File and exit Ctfplotter and Etomo.

3. Determining Defocus in a Tilt Series from a DE-12 Camera:

This tilt series, from Cindi Schwartz, is of a preparation of microtubules decorated with the motor protein Eg5, taken with a DE-12 camera during a demo on the F20 microscope in Boulder.  The tilt series had a 2 degree increment and the total dose was 79 electrons/square Angstrom.  Parts of the series have good signal for determining CTF, but not all of it.

• Manual download and unpacking:
• Download the sample data set from our web site.
• Move the data set file "DE-CTF-Data.tar.bz2" to the directory where you want to work on it.  Its contents will unpack into a subdirectory named "DE-ctf".
• cd to the directory with the file
• Enter the command:
      imoduntar DE-CTF-Data.tar.bz2
  or, anywhere except on Windows without Cygwin, you can use
      tar -xjf DE-CTF-Data.tar.bz2
• Or, download and unpack with imoduntar:
• cd to the directory where you want the subdirectory "DE-ctf" created
• imoduntar -d DE-CTF
• Enter the data set directory with:
      cd DE-ctf
• Start Etomo with the command
      etomo MTEg5series5D.edf
• Open the Final Aligned Stack page and switch to the Correct CTF tab.
• The Expected defocus has already been set to 6.0 in this data set.
• The Config file has already been selected to access a configuration file listing noise files in the "DE12-Div2" subdirectory of the data set directory.
• Press Run Ctf Plotter.
• Zoom the power spectrum by clicking on the magenta curve to the left of 0.1/pixel and dragging the selection region to a point before a frequency of 0.4/pixel and just below the baseline.
• The power spectrum shows a clear signal out to the third zero and the green fitted curve matches the location of the zeros fairly well, so the defocus estimate is good.  Select Current defocus estimate.
• In the Fitting Params dialog, set Start fit at to 0.11, since it is not helpful to fit any farther to the left of the first zero.   Set End fit at to 0.25 to fit out to the third zero, and press the Enter key or Apply.
• Turn on Vary exponent of CTF function; the fit does not look significantly better so there is no reason to leave this option on.  When the signal is weak, adding this fifth parameter to the fit can reduce the reliability and stability of the fits.  Turn it off.
• To see if single images can be fit, set the Number of views to fit to 1 .  This curve is noisier but the fitting still seems reasonable.
• To see if fitting is good at other tilt angles, sample some angles by setting Step view range by: to 3 and pressing Step Up and Step Down. Most of the negative angles give plausible fits, but many positive angles have much less signal and cannot be fit reliably, particularly around 20-30 degrees. Since inaccurate defocus values can do more harm than good, we need to fit to multiple views instead, with the reduced goal of estimating the trend in defocus through the series.
• Now switch Number of views to fit to 4 to fit to 8 degree ranges, and set Step view range by to 2. Step through some angles in the troublesome range. The signal is still quite weak in some spectra but the fit appears to work.
• Now assess whether and how to find astigmatism by pressing the + button next to Find astigmatism. Set Min views for astigmatism to 8 to start with, to maintain the same signal-to-noise ratio in the wedge spectra as in the full spectra. Set Middle tilt angle to 0 and turn on Find astigmatism. The wedge spectra all look good and the astigmatism is about 0.3 microns.
• Set Middle tilt angle to 21; notice that the spectrum changes shape dramatically and that the signal after the first zero essentially vanishes in some parts of the angular range. The astigmatism estimate is around 1.0, which is too big a change from zero degrees to be plausible. These data must be averaged over many more views to give reliable estimates of astigmatism.
• Set Min views for astigmatism to 20. The fits may appear better, but then set Middle tilt angle to 45. The spectrum still flattens out for some wedges, and you will probably see jumps up and down and failures of the baseline fitting.
• Given this result, we need to fall back to finding one astigmatism estimate for the whole tilt series. Set Min views for astigmatism to 100 (or any value as big as the number of views). The wedge spectra all look adequate.
• Set the Middle tilt angle of 0 and press Autofit All Steps.  Notice that it does not repeat the wedge fitting at each angle.
• Press Graph Values to see the graph of defocus versus tilt angle. There are still some sizable variations at positive tilt angles. Double-click the lines in the table at some of these angles to see how reliable these fits look.  The signal gets rather low at some tilts, but the noise is low enough to allow you to see that the defocus is being found adequately.

4. Determining Defocus in a Tilt Series from a CCD camera

This tilt series is of a preparation of bovine papilloma virus (BPV), taken by Mary Morphew on an F20 with a US4000 CCD camera at a nominal defocus of -3 microns.  It is the series used in the Ctfplotter Guide to illustrate program operations.  Here, it illustrates some of the challenges in doing CTF correction on relatively low-defocus tilt series take with a CCD, which provides poorer information at high frequencies than a direct detector.

• If you already unpacked the data set for the SIRT tutorial, skip to "Enter the data set directory".
• Manual download and unpacking:
Download the sample data set from our web site.
• Move the data set file "CTF-SIRT-Data.tar.bz2" to the directory where you want to work on it.  Its contents will unpack into a subdirectory named "ctf-sirt".
• cd to the directory with the downloaded file
• Enter the command:
      imoduntar CTF-SIRT-Data.tar.bz2
  or, anywhere except on Windows without Cygwin, you can use
      tar -xjf CTF-SIRT-Data.tar.bz2
• Or, download and unpack with imoduntar:
• cd to the directory where you want the subdirectory "ctf-sirt" created
• imoduntar -d CTF-SIRT
• Enter the data set directory with:
      cd ctf-sirt
• Start Etomo with the command
      etomo bpv_-3_3a.edf
• Open the Final Aligned Stack page and switch to the Correct CTF tab.
• As for the K2 data set, the Config file has already been selected to access a configuration file listing noise files in the "F20" subdirectory of the data set directory.
• Set the Expected defocus to 3.0.
• Press Run Ctf Plotter.
• If you press the help icon in the upper right of the Ctfplotter window, it will bring up the Ctfplotter Guide; the Examples section there shows screen shots from this data set.
• Notice that the angular range is 40 degrees, the old default angular range when starting Ctfplotter, and many views are summed.
• The power spectrum has two dips in the falling part of the curve, neither of which correspond to zeros.  The dip at the first zero is not evident until the curve is zoomed.  Zoom it up by selecting the top of the second hump in the magenta curve and dragging the selection region to a point before a frequency of 0.4/pixel and just below the baseline.
• Double-click the left mouse button at the first zero (frequency 0.25/pixel).  The defocus readout on the top line changes to show the defocus corresponding to this point, 3.6 microns. 
• The fitting range set from the nominal defocus is particularly inappropriate in this case.  Set X1 Starts to 0.185 to fit the falling phase of the power spectrum back to where its slope changes.  Set X2 Ends to 0.29 because the signal falls off there, well before the location of the second zero.  Press the Enter key or Apply to fit with the changes.
• You can now zoom up another step to make it easier to see the CTF signal.  Select a point just above where the two curves diverge on the left and drag the selection box out to the right edge under the baseline.
• Select Current defocus estimate in the Angle Range dialog now that the fitting is being done to an appropriate range.
• Press Step Up twice to reach the positive end of the tilt range, and then Step Down four times to get to the negative end of the range. The spectra look adequate, although at the positive end of the range, the dip is less well-defined.
• The dip at the positive end can be made deeper by skipping the last few tilts. One way to do this is to enter 1-3 in the Views to skip text box, which makes the tilt range being analyzed be the same as on the negative side. This is more convenient than adjusting the Middle tilt angle entry, and when you use the Step buttons or autofitting, the program will continue to leave these views out of the fit.
• You can now press Autofit All Steps to fit to 40-degree ranges at 20-degree intervals.
• Double-click each line in the table to check the result.  In general, if you think that the zero is not correctly found by a fit, you can double-click where you think the bottom of the dip is located, and press Store Defocus in Table to replace the value from the fit.
• It is possible to find astigmatism in this data set. Set Min views for astigmatism to 40 first, then turn on Find astigmatism and step through the tilt ranges. However, you may find that the fitting is unstable if you press Apply repeatedly at one high tilt end of the range. It is easy for the fitting to become unreliable with this data set; for example, a Baseline fitting order of 0 or 2 does not work throughout the tilt range.
• Press Save to File and exit Ctfplotter and Etomo.
• If you are going to do the practice SIRT reconstruction with this dataset, or if you want a corrected stack for any other reason, then select up to 12 CPUs in the parallel processing table, and press Correct CTF then Use CTF Correction when it is done.