Ronchigram

A schematic view of a ronchigram looks like this: [img[1][EmbeddedImages]] What are these lines and what are we seeing exactly? those lines are sagittal (spoke lines) and tangential (rings) lines due to spherical aberration of lens (usually objective lens in TEM/STEM). It will be a long story trying to explain these. Let's do it step by step.

  1. The reason we see Ronchigram is due to spherical aberration. Without spherical aberration, the image above will be either feature-less (at exactly beam focal plane) or a shadow image of the sample.
  2. The Ronchigram is normally spherical symmetrical (not with Cs-corrected scope, see below) due to the cylindrical symmetry of lens. In fact, the roundness of Ronchigram is the best judge for adjusting condenser lens astigmation. An astigmation-free lens should form a round Rochingram.
  3. The contrast within Ronchigram is due to sample plus spherical aberration. Without sample, you will not see anything. (you cannot see the convergent beam itself). In this sense, it is a shadow. But a shadow with severe distoration.
  4. The cause of aberration is due to high convergent angle, or the beam off axis. Beam passing through the margin of objective lens will be focused more than those closer to the optical axis. In front of paraxial beam focal point (the Gaussian focus), the beam passing through outer zone intersets those passing through inner zone at a ring around the optical axis. When the sample plane intersect that zone of focused beam, the shadow of the sample forms the ring and radial patterns in Ronchigram.
  5. If you change the focal strength of lens (or just move the viewing plane), you will see the rings expand and contract. That is like you are moving the sample to intersect different zone of focused beams. 
  6. To be able to see Ronchigram, there must be one or more lenses after the focal point to project the focal plane onto our viewing screen. What we see with Ronchigram is the projection of back-focal plane, not the image plane (even though we see the shadow of the sample). We are looking at the focus situation after the beam pass through a very spherical aberrated objective lens.
  7. The detailed pattern, spokes and rings, has to be discussed with this lens (which is normally the lower half of the objective lens) after the beam focus. The focus point is at the front focal plane of the lens. If the beams converged onto this plane, they will emerge from the lens as column of parallel beam. The magnification is, of cause, infinite, because the source (the focal point) is zero size. The center flat region is formed this way. Now the "spokes": they are from the beams focused on a tangential lines. With rotation symmetry, the tangential line is actually a ring. The beam focused onto this ring emerge from the lens have finite magnification in azimuth, but infinite magnification in radial direction. Thus any "shadow" is stretched radially. The next is "rings": they are due the sagittal focal lines. A beam from off-axis location will focuses into a line in radial direction. Sagittal lines are further out after the tangential lines. By the same mechanism, those sagittal lines (radial oriented) emerge as a ring pattern with infinite azimuth magnification. Why do we see both spokes and rings at the same time? It is due to the curvature of tangential and sagittal points. (now I see this discuss is too long. This needs to be rewrite into an article with more sketches. Stay tuned.)
  8. Ronchigram is best viewed through a thin amorphous area. If the sample is thick, we will see overlapping of different Ronchigrams from different depths of the sample, thus the overal Ronchigram is blurred. For crystalline sample, because of high magnification within Rochigram (almost infinite magnification) lattice image due to phase contrast is superimposed. This make Ronchigram less clear. Thin amorphous material is like an object with evenly distributed point object. The various stretching of them on the Ronchigram is ideal to image the feature of spherical aberration.  
  9. What happens for the ronchigram of Cs corrected STEM/TEM?
 10. First of all, the circular symmetry is destroyed. The best aligned ronchigram is hexagonal or octagonal, depends on the corrector lens design. 
 11. Secondly, the central disk is larger (that is the whole purpose of Cs correction - to extend the Cs-free region to a larger convergent angle. 
 12. One more note: the central featureless disk (we may call it Cs-free disk) is referred to the region of infinite magnefication. this is because the sample to front-focal plane distance is zero. The magnefication can be expressed to the division of that distance, thus the magnification is infinite. Moving away from that plane forward a little, the central region will show a shadow of the sample with some very high magnification (somewhat less than infinity). 

A 'real' example looks like this:

[img[2][EmbeddedImages]]