10. TOMOGRAPHY

Tomography is a method for reconstructing the interior of an object from its projections. Especially the term electron tomography is used for any technique that employs the transmission electron microscope to collect projections of an object and uses those projections to reconstruct the object in its entirety ( overview in [1] ).
The automated electron tomography (AET) is a technique for automatic acquisition of a tilt series with tilt induced displacement cottection. As the displacement has components in X, Y and Z direction, the image has to be shifted back and the focus has to be readjusted. The lateral displacement is measured by cross-correlating an image with an previosly recorded reference image and corrected using the image shift facility of the microscope. For compensation of very large displacements corrections are performed in lower magnifications. For the focus adjustment the autofocus procedure developed by Koster et al.[4] is used.
For low dose imaging 5 different specimem positions ( areas ) are used:

*) relative to the detail of interest.

Generally the positions will be aligned as shown below. To fulfil low dose conditions the condensor should be adjusted to illuminate only the circular area around the corresponding position.

Positions overview

The following list gives an overview of the ( idealized ) data acquisition procedure.

1. Start ( Initializations, etc. )
2. Goto start angle, take reference images of SEARCH and TRACKING positions
3. Increment angle
4. Goto SEARCH position and correct the displacement roughly
5. Goto FOCUS position and correct the defocus
6. Goto TRACKING position and correct the fine displacement
7. Goto EXPOSURE position and take the desired image
8. If not ( last tilt angle reached ) then goto step 3
9. Stop

For more details see the following references:

[1] Electron Tomography, Edited by Joachim Frank (Plenum Press, New York, 1992 )

[2] K. Dierksen, D. Typke, R. Hegerl, A.J. Koster, W. Baumeister: Towards Automatic Electron Tomography, Ultramicroscopy 40 (1992 ) 71-87

[3] W. Hoppe, R. Hegerl in: Computer Processing of Electron Microscope Images, Topics in Current Physics, Vol.13, Ed.P.W. Hawkes (Springer, Berlin,1980) p.127

[4] A.J. Koster, D. Typke and M.J.C. de Jong: Fast and accurate autotuning of a TEM for high resolution and low dose electron microscopy,Proceedings of the XIIth International Congress for Electron Microscopy 1990

The 'Positions' dialog is opened with .

The 'Positions' dialog

The 'Position' dialog consists of the following sections

General

Calibrate the goniometer and the electron optics.

Position control

The commands in this section are used to control the positions SCANNING, EXPOSURE, FOCUS, TRACKING and SEARCH. The actual position is shown next to the text Current position.

Goto

Change between the 5 positions

Copy

Copy the data from the current position to another position.

Position alignment

Load or save the actual alignment data of all positions.

Work

Update the current position data, show ( and edit ) position data, center detail in a position, select the acquisition areas and lock/unlock positions.

Check

Check the current position by taking exposures and computing power spectra.

Applications

Start the tilt series acquisition or the spotscan image acquisition.

With a click on in the positions dialog the calibraion dialog will be opened.

The Calibration dialog

The calibration is necessary for most of the other operations performed on the positions. It is at least necessary to execute the calibration for all the magnification / high tension combinations you will use. To calibrate, insert a specimem with a good contrast to receive better cross-correlations. Select the desired magnification on the TEM, then click and to check whether you have "something" good correlating visible.

Click the CALIBRATE XXX buttons from top to bottom and follow the instructions. Some calibrations need some time, while others are fast, some need user interaction, some not. If a calibration has been performed successfully, the field right to the corresponding button is filled with the date and time of the calibration as well as with calibration dependent data.

Note: A 512*512 image format is sufficient for the calibrations. It has also the advantage of a higher calibration speed ( compared to 1024*1024 or 2048*2048 image format ) due to drastically shorter computation times e.g. for cross-correlation ( 1 cross-correlation requires besides other operations: 2 forward FFTs and 1 inverse FFT ).

Calibration	Comment
	The goniometer x and y shift are calibrated. This calibration can take a few minutes. The result angle should be near 90 degree ( or 270 degree ) and the ratio should be near 1.0
	The tilt axis angle relative to the CCD image x axis is calibrated. This is very fast. Note: You will receive the best results ( both for the tilt series acquisition algorithm and the reconstruction ) if the camera is mounted in such a way that the tilt axes angle is (near) 0 degree for the magnification used for the EXPOSURE position, i.e. you will possibly have to turn your camera.
	The ratio between the changes in ticks of e.g. beam shift, illumination, etc. and their internal TEM data representation is calibrated. On most TEMs this is 1:1, but some use a 1:2 or other ratios. This calibration is very fast.
	The image shift is calibrated. This can take up to 1 minute.
	The beam shift is calibrated relative to the image shift. User interaction is required. Follow exactly the orders in the dialog boxes when they appear. It is not necessary to minimize the radius of the beam to a spot.

The 5 different positions ensure that there is not too much dose on the specimen's area of interest. There is a position for the area of interest ( EXPOSURE position ), for focussing ( FOCUS area ), coarse displacement correction ( SEARCH position ) and fine displacement correction ( TRACKING position )
The chapters 10.4.x describe how to work with those 5 positions.

10.4.1 Goto position

To go to to a position means: Reload the last used settings of that position and treat this position as current position. To go to a position, select the desired position in the dropdown dialog element, then click the Goto position button.

The goto position dropdown

10.4.2 Copy position

To copy the current settings into the settings of a specific position, select the desired position in the corresponding dropdown element, then click the Copy Position button. To copy the current settings into the settings of all positions, select ALL in the dropdown element.

The copy position dropdown

10.4.3 Show position

The 'Show positions' dialog

The 'Show positions' dialog both enables to monitor the position settings and change the settings by hand. The left half of the dialog is for information only and to compare corresponding settings of the different positions. To change entries of a specific position, click on the corresponding tab to select the position, change the value(s) in the edit fields, drop down elements or radio buttons and click Apply or OK.

The following data can be changed:

Format

Select one of the available formats by selecting it from the dropdown list. Tip: Use the maximal format for the EXPOSURE position to receive the best results and use smaller formats to increase the speed for focussing and displacement correction.

Gain

Select gain by selecting the corresponding value. For cameras with 2 gains 0 means low gain and 1 means high gain.

Exp.time

Enter the desired exposure time in units of milli-seconds.

Mag. index

The direct input of the magnification is not possible. It is required to enter the magnification index in the corresponding edit field. As soon as Apply is clicked, both the changed magnification index and the corresponding magnification is displayed in the info part of the 'Show positions' dialog.

Spotsize

Enter the spotsize value into the corresponding edit field. This is an EM dependent value.

Intensity

Enter the intensity value into the corresponding edit field. This is an EM dependent value.

Beam shift X/Y

Enter the values for the X and Y beam shifts into the corresponding edit fields. Those are EM dependent values.

Image shift X/Y

Enter the values for the X and Y image shifts into the corresponding edit fields. Those are EM dependent values.

Defocus

Enter the value for the defocus into the corresponding edit field. This is an EM dependent value.

Offset defocus

Enter the value for the offset defocus into the corresponding edit field. This is an EM dependent value. This value is only required for the FOCUS position.

The 'Show positions' dialog is opened with a click on in the 'Positions' dialog.

10.4.4 Update position

A click on reads the current EM settings and stores it into the setting data of the current selected position.
Note: The camera settings of the positions are not changed.

10.4.5 Center detail

Before starting the centering of the detail of interest, check whether you want to lock the positions or not. Locking of positions means that if one position is moved, all the other positions are moved accordingly as if they are connected. To lock the positions check the option 'Lock positions' in the 'Positions' dialog. If this option is not selected, 'Center detail' will only influence the currently selected position.

'Lock positions' option

The 'Center detail' dialog

After clicking OK the position settings for the image shift are adapted in such a way that the detail of interest will be visible in the center of the image. To verify that an additional exposure is taken and displayed.

10.4.6 Areas

Even it is possible to select the positions for EXPOSURE, FOCUS and TRACKING individually, a powerful tool is available. This tool is only available in SCANNING position. The 3 positions are displayed as squares where the edge sizes are defined by the ratios of the magnifications of the 3 positions to the magnification of the SCANNING position. Also the tilt axis is drawn.
Note: Every time the Areas tool is started, the 3 positions will be set to the default positions, i.e. all the previous settings are lost. This is to avoid positions out of the SCANNING position and with that out of the display screen.
Clicking on will take an exposure and suggest settings for EXPOSURE, FOCUS and TRACKING positions. Then the 'Areas' dialog will open.

The 'Areas' dialog

The 'Areas' dialog provides 3 sections for user interaction:

Area

Here you can select which of the 3 position you would like to move.

Control area

Here you can move around the position selected in the area section either by using the up/down/left/right buttons or with the cursor keys of the keyboard.

Speed

Here you can select the moving speed of the positions. If e.g. speed = 100 pixel is selected and you use the cursor left key once, the selected position will move on the display screen 100 pixels to the left. It is possible, though not recommended, to move a position out of the display screen.

Screenshot during position definition with the 'Areas' tool

Note: Due to dose problems for some specimems the positions should not overlap.

10.4.7 Load/Save

Clicking on or opens the file selector dialog where you have to specify the filename. The position settings will be loaded from this file or written to this file, respectively.
Note: If the settings are loaded from file, the current settings are "overwritten", i.e. the microscope settings of the current position are sent to the microscope. E.g. EXPOSURE is current position and the settings are loaded, then after loading is finished the settings of the EXPOSURE position in the file will be the current settings now. That also means that the beam shift and the image shift are probably changed.

10.4.8 Exposure/Power

Both buttons and are used to check the quality of the position settings. Exposure takes an exposure with the current position settings and Power computes the power spectrum of the last exposure.

This is a short "recipe" how to define the positions for a standard tomography session:

• Start "Positions". You are now in position SCANNING. Choose a full area/2x binning camera format
• Choose magnification and condenser settings as desired for recording the tilt series. Center your tomography object roughly to the microscope screen. Press UPDATE POSITION.
• Perform an exact centering to CCD with CENTER DETAIL.
• Copy current position (SCANNING) to EXPOSURE, FOCUS and TRACKING.
• Reduce the magnification by a factor 2 - 4, adjust condenser settings. Press UPDATE POSITION.
• Center again your tomography object to CCD with CENTER DETAIL. Press UPDATE POSITION.
• Copy current position (SCANNING) to SEARCH.
• Note: If you want to choose another tomography object, you should do the following steps
• Center the new object with the goniometer.
• Check the box "Lock positions". Do a fine centering with CENTER DETAIL.
• Uncheck "Lock positions".
• Define the positions TRACKING, FOCUS and - if required - EXPOSURE with the AREAS function. Stay close to the tilt axis if possible.
• Click SHOW POSITIONS. For each position, define the settings for camera format, exposure time and focus.
• Before sarting the tilt series now, you should check each position with GO TO POSITION

A click on starts the 'Tilt series' dialog:

The 'Tilt series' dialog ( with linear scheme )

The 'Tilt series' dialog consists of 4 sections:

File parameter

Click on and the Browse folder dialog will open. Select a folder ( = directory ) where you want to store the images acquired during the AET.
Enter the basename of the files in the edit field labeled 'Name:' and enter the file number to start with.
The complete filename will consist of the directory name, the basename, the number and the suffix .dat.
Example: Directory: D:\data, Name: tilt_cryo1, First file number: 35
The image files will have the names: D:\data\tilt_cryo1_035.dat, D:\data\tilt_cryo1_036.dat, D:\data\tilt_cryo1_037.dat, ...

Note: The 'First file number' field is of interest if you split your tilt series into several tilt series, e.g. series 1 from -60 degree to 0 degree, series 2 from 0 degree to 60 degree, series 3 from 60 degree to 72 degree, ...

Series parameter

Here the start angle and the end angle of the tilt series in degree are defined in the edit fields labeled 'Start angle' and 'End angle' respectively.
You can select what positions should be used during the tilt series acquisition. Less positions make the total acquisition faster, but maybe displacements occur that cannot be corrected...
This 'Series parameter' section is dependent on the option 'Angles by Saxton scheme'. If this option us unchecked the linear scheme is used, otherwise the Saxton scheme is used.
Linear scheme: Enter for all used position the angle increment for this position. E.g. Exposure every degree, tracking every 2 degrees, etc. Note: If the start angle ( e.g. 20 degree ) is greater than the end angle ( e.g. -20 degree ) the angle increments have to be negative, e.g. exposure every -1 degree, tracking every -5 degree, etc.
Saxton scheme: (See also Saxton scheme) Enter for all used position the frequency for this position, e.g. exposure every (=1) step/angle, focus every 3^rd step/angle, ...
Note: The start angle has always to be a positive number, independent of the tilt direction.

Options

• Fully automatic tracking: The tracking is performed automatically. If this option is not selected the tilt series acquisition runs in the so-called semi-automatic mode. Here appears - instead of the tracking - a the 'Semi-automatic' dialog box ( See Semi automatic )
• Display focussing steps: If this option is selected the acquired images necessary for focussing are displayed.
• Display tracking steps: If this option is selected the acquired images necessary for tracking are displayed.
• Exposure time cosine adapted: If this option is not checked the exposure time for an exposure in EXPOSURE position is used as it is specified in the 'Show positions' dialog. If this option is used this exposure time is divided by the cosine of the tilt angle.
• Angles by Saxton scheme: If this option is selected the Saxton scheme is selected. You also have to specify the 0 degree increment that defines all other angles in this scheme.

  The 'Tilt series' dialog ( with Saxton scheme )

• Store tracking images: Store also the reference images used for the fine displacement correction in TRACKING. The filename is the same as the image file name for the EXPOSURE position, except that an '_track' is added to the basename of the file.

Succession of parameters

The succession of the positions within one cycle at a certain tilt angle can be changed. Default is SEARCH, FOCUS, TRACKING, EXPOSURE. This succession is also displayed if the default button is clicked. To change the succession, click on a position name and after that on the button Up or downto move this selected position up or down. A double-click on a position moves this position to the top. The top to bottom succession corresponds to the succession of execution. If a position is not selected in the 'Series parameter' section, this position appears indeed in the succession list, but has no effect, since no actions for this positions will be generated.

A click on generates the position flow for the tilt series acquisition out of the specified parameters and options. The result is displayed in the 'Tilt series exposure map' dialog.

The 'Tilt series exposure map' dialog

The 'Tilt series exposure map' dialog displays in its left half the indexed positions as they will be executed during the acquisiton. Here you can see how the tilt series acquisition will work. In the dialog displayed above, the algorithm will

1. Change the tilt angle to 0 degree
2. Goto SEARCH position and perform the coarse displacement correction
3. Goto FOCUS position and correct the defocus
4. Goto TRACKING position and perform the fine displacement correction
5. Goto EXPOSURE position and take the desired exposure and save it to file
6. Change the tilt angle to 2 degree
7. Goto FOCUS position and correct the defocus
8. Goto TRACKING position and perform the fine displacement correction
9. Goto EXPOSURE position and take the desired exposure and save it to file
10. Change the tilt angle to 4 degree
11. Goto SEARCH position and perform the coarse displacement correction
12. Goto FOCUS position and correct the defocus
13. Goto TRACKING position and perform the fine displacement correction
14. Goto EXPOSURE position and take the desired exposure and save it to file
15. and so on ...

Here you have the (last) change to modify the succession of positions. You can delete one or more positions, swap positions and add entries:

Delete entries

Type in the index of the first position to delete and the index of the last position to delete ( may be the same index ) and click on .

Swap entries

Type in the index of the first position to swap and the index of the second position to swap and click on .

Add entry before/after

Type in the index of the position to add a different position before or after it. Then select the type of the new position ( e.g. TRACKING ) and define the angle of that position. A click on adds the new position.

A click on starts the new series.

The saxton scheme ensures that you have equidistant sampling points in the three-dimensional fourier space. In the real space you can see the criterion displayed in the figure below:

The Saxton scheme

Starting with an angle of alpha ( here in this example: alpha = 10 degree ) against the x-axis defines the size h of the red vertical line as h := r * sin(alpha), where r is the radius.
The next angle is defined by the following constraints: The red vertical line with fix size h sits on the line OA and ends at the circle line and defines B. The angle between x-axis and OB is the new angle.
In that manner all the (infinite number of) angles are constructed. (Infinite, because it will never reach 90 degrees ).

With this algorithm and an start angle of 10 degree the first 19 angles ( besides 0.00000 degree ) are:

1. 10.00000 degree
2. 19.84655 degree
3. 29.24704 degree
4. 37.96158 degree
5. 45.83057 degree
6. 52.78009 degree
7. 58.80931 degree
8. 63.96891 degree
9. 68.33949 degree
10. 72.01436 degree
11. 75.08797 degree
12. 77.64913 degree
13. 79.77775 degree
14. 81.54370 degree
15. 83.00696 degree
16. 84.21836 degree
17. 85.22068 degree
18. 86.04967 degree
19. 86.73512 degree

If e.g. the tilt series start angle is -70 degree and the end angle is +20 degree and the 0 degree increment is 10 degree, the following angles are used:

1. -68.33949 degree
2. -63.96891 degree
3. -58.80931 degree
4. -52.78009 degree
5. -45.83057 degree
6. -37.96158 degree
7. -29.24704 degree
8. -19.84655 degree
9. -10.00000 degree
10. 0.00000 degree
11. +10.00000 degree
12. +19.84655 degree

Either by pressing the SPACE key during the tomography or by not selecting the Fully automatic tracking option in the 'Tilt series' dialog, the tilt series acquisition will switch into the semi automatic mode. Semi automatic mode means that no automatic fine or coarse displacement correction is performed in the TRACKING or SEARCH position, respectively. Every time TRACKING or SEARCH has its turn, the 'Semi automatic dialog will open.

The 'Semi automatic' dialog

The 'Semi automatic' dialog provides all the possibilities to perform coarse and fine displacement corrections.

General

A click on takes an exposure of the current position.

Tools

A click on starts the Center detail tool.
Note:During a tomography session all positions are generally locked. There is no possibility to switch locking off.

Image shift / Undo image shift

Here it is possible to enter either direct shift values or click on to compute the image shift by taking an exposure and correlate it with the last reference image of that position. The result of the correlation will be pasted into the edit fields. A click on will execute the image shift. As soon as the image shift is performed, the shift distances will appear in the fields in the 'Undo image shift' section. A click on the Undo button cancels the last image shift action. There is only a one-step-undo available.

Gonio shift ( in microns )

To shift the goniometer in XY direction, enter the distance in µm and click on in the same section.

After the displacement corrections you can decide how to proceed

	Stay in semi automatic mode, i.e. the next time the turn is on TRACKING or SEARCH, this dialog will open again.
	Continue in full automatic mode, i.e. this dialog will no more open unless the SPACE key is pressed.

A click on in the positions dialog opens the spotscan dialog.

The 'Spotscan' dialog

Enter the directory and filename to save the spotscan images in the section 'File parameter'.
Also enter in the section 'Spotscan parameter' the values for the number of images in X and Y direction as well as the desired corresponding overlap of the images.

Note: Check that the goniometer tilt angle is set to zero, otherwise the spotscan procedure will fail.

Note: The calibrations for the current magnification/high tension must be available.

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