TEM optical stability benchmark
The experimental section describes the experiment required to do a good stability test.
Concept and principal approach
Out of the many optical parameters of a transmission electron microscope, the coherent aberrations of the lower orders, such as defocus and twofold astigmatism, show the strongest variations during the timespan of electron microscopy experiments. Since these aberrations have a strong impact on the image contrast, and can be measured in quick sequence 1, they can serve as marker variables to benchmark optical stability.
From among the coherent lower-order aberrations the twofold astigmatism is of particular interest for our stability investigations, since it is least influenced by other sources of instability, such as by the mechanical drift of the sample holder. The twofold astigmatism can be monitored with a frequency around 1 Hz over a long timespan of approximately one hour and serves therefore as a variable to investigate short- and long-term instabilities. Expressing the optical stability in terms of the expected lifetime of a once adjusted optical state on the basis of the twofold astigmatism alone represents however only an upper limit of the true lifetime, which would include all optical parameters.
The experimental procedure to monitor the temporal evolution of the twofold astigmatism requires a continuous aquisition of high-resolution TEM images from a thin amorphous object as shown below. In order to extract the twofold astigmatism from each image of such a series, a strong defocus has to be applied 1. Due to the strong defocus, the diffractogram of an image, which is the absolute square of the image Fourier transform, shows a pattern of concentric Thon rings 2. While the average radii of the Thon rings depend on the chosen defocus, the twofold astigmatism is manifested in the ellipticity of the ring system. In order to allow for a robust and precise extraction of the twofold astigmatism, the diffractogram should display at least 3 or more Thon rings.
During the acquisition of the image series the microscope should be left untouched. The total acquisition time should be significantly longer than the expected or required time of stable microscope operation.
The extracted values of the twofold astigmatism should be saved in a kind of log file. Such a log file is for example generated automatically by the aberration measurement and correction software supplied with CEOS aberration correctors, or by the Jülich ATLAS software for aberration measurement. Support of other log file formats or measurement reports can be implemented on demand.
The evaluation of such a series of astigmatism measurements in terms of a lifetime of the optical state with PantaRhei is described in form of an example.
 J. Barthel and A. Thust, Ultramicroscopy 111 (2010) 27–46 , “Aberration measurement in HRTEM: Implementation and diagnostic use of numerical procedures for the highly precise recognition of diffractogram patterns”.
 F. Thon, Zeitschrift für Naturforschung 21a (1966) 476, “Zur Defokussierungsabhängigkeit des Phasenkontrastes bei der elektronenmikroskopischen Abbildung.”
 J. Barthel and A. Thust, Ultramicroscopy 134 (2013) 6–14 , “On the optical stability of high-resolution transmission electron microscopes”.