Cs Correction

Microscopy was revolutionised in the 1930s by using electrons to illuminate specimens, creating images at much higher magnifications than optical microscopes allowed.

But electron lenses are inherently poor compared to optical lenses and soon the design of electron microscopes had improved to the state where the performance was mainly limited by spherical aberration C_s, a feature of all round lenses that causes image distortion and limits the resolution.

Schematic ray diagram of spherical aberration

Lens aberrations

In a perfect lens all rays that emerge from a point object P are brought to focus at a conjugate point P´ in the image plane (black line). The image is therefore a true representation of the object being imaged.

In reality, high-angle rays (blue, red and green lines in the figure) are brought to a premature focus by lens aberrations so that the point object P appears blurred in the image plane. This phenomenon is called spherical aberration.

The Ronchigram

or shadow image, is the common method of observing and diagnosing aberrations in a STEM instrument. The ray diagram of a Ronchigram from an amorphous sample in moderate under focus is shown on the right. The centre of this image faithfully transfers the spatial information of the sample and is known as the ‘sweet spot’ of the Ronchigram. (See also: the effect of Cs correction on the size and shape of the ‘sweet spot’). Due to spherical aberration, the rays that are further away from the optical axis will be focused more strongly giving rise to the distorted features of the Ronchigram known as the rings of infinite magnification.

An optical equivalent would consist in trying to magnify a random pattern through the bottom of a glass bottle, or a wine glass full of water. The image in the centre of the glass is rather faithfully magnified, while closer to the edges the image is radially distorted.

The era of aberration correction : it all began in 1936…

In 1936, Scherzer proved that any electron optical system will always suffer from spherical aberration (Cs) and chromatic aberration (Cc) if simultaneously:

the optical system is rotationally symmetric
the system produces a real image of the object
the fields of the system do not vary with time
there is no charge on the axis

Breaking the rotational symmetry

Breaking the first of Scherzer’s assumptions is the basis of currently commercially available aberration correction technologies. This is achieved using multipole lenses.

A schematic representation of multipole lenses and their primary effect of the electron beam are shown are shown on the right. A dipole shifts the beam, a quadrupole focuses the beam into a line, a sextupole imparts a triangular distortion to the beam and an octupole imparts a square distortion to the beam.

Implementation of aberration correction

Although proposals to correct spherical aberration were made as early as 1947, the realisation of spherical aberration correction kept physicists busy for another 50 years. Among the first people to show that spherical aberration could be overcome were Ondrej Krivanek and Nicklas Dellby in Cambridge working with Mick Brown in the Microstructural Physics group in 1997

The idea behind the current spherical aberration corrected electron microscopes is to introduce a corrector that produces negative spherical aberration. This then combines with the positive aberration of the objective lens to give a total of zero spherical aberration. There are two approaches both using multipole lenses: the so-called quadrupole-octupole (QO) corrector and the hexapole corrector.

First working quadrupole/octupole probe Cs corrector: Krivanek O.L., Dellby N., Spence A.J., Camps R.A., and Brown L.M. (1997) “Aberration correction in the STEM”, in: Inst. Phys. Conf. Ser. 153 (Proceedings 1997 EMAG meeting) Ed. Rodenburg JM, 35

The Quadrupole-Octupole corrector

The SuperSTEM microscopes are all fitted with Nion QO correctors. The basic schematic representation and ray path diagram of a quadrupole-octupole (QO) corrector is shown on the left

Such a corrector uses three octupoles (O2, O4 and O6) and four quadrupoles (Q1, Q3, Q5 and Q7). The radial elongation of the beam through the corrector is indicated along to two orthogonal axes y and y (the traces overlap when the beam is round).

The image aberration measured in terms of shifts in beam offsets, tilts and changing of defocus is recorded and translated into computer-controlled adjustment of all the quadrupole and octupole currents - in effect introducing the negative of the microscope’s aberration.

In an aberration corrected microscope all rays are more or less brought to a common focus. This results in a sharper image. With aberration correction all electrons are focused within the region of interest, which in our case is the size of a single atom, so that it is possible to determine not justhow individual atoms are brought together to form a bulk solid, but the chemical identity of those atoms as well.

The SuperSTEM microscopes achieve a resolution of 1Å or better (that's a millionth of the size of a single human hair!)

Other resources

A more detailed discussion of aberration correction and its history can be found here:

Aberration correction past and present (Phil. Trans. R. Soc. A 28 September 2009 vol. 367)

Imaging at the picoscale (materialstoday, Volume 7, Issue 12, December 2004, Pages 42-48)

SuperSTEM the highest resolution microscope in the world (azom.com, 2003)