How we test an objective
Ideally, in testing whether or not an objective would be able to resolve atoms in a close-spacing lattice, we would like to have a substrate with nanometer-sized holes arranged in a square lattice. Then, we could back illuminate the pattern with a 405nm light source - varying the intensity, perhaps - and measure the resolution directly.
Unfortunately, we have not come by such a sample yet, and are making due with another resolution testing method.
The MRS-5 pattern
We have purchased an MRS-5 Geller SEM standard. In order to see the pattern, we have to illuminate the sample from the front so that light can be reflected back through the objective and into the camera. We can assume that most of the light reaching the camera is specularly reflected?
If we were just to illuminate the sample by placing a light source behind the objective, the objective would focus the illumination down to a small area on the focal plane. This poses problems, because most light sources are filaments - an extended sources, not a point source. As a result, we would focus an image of the source filaments onto to the focal plane of the objective - coincident with the sample plane, where the MRS-5 pattern is located. This results in the uneven illumination of the sample. Furthermore, we are illuminating the sample with many different frequency components - something which could artificially skew the resolution of the objective.
However, there is a way to mitigate this uneven intensity and spectral illumination - use a Kohler illumination setup. Kohler illumination provides a uniform illumination by placing an image of the light source at the back focal plane of the objective.
(source:Olympus "Microscopy U")
The Role of the Condenser Aperture
The first lens in the Kohler setup focuses in image of the source at the condenser aperture. The condenser aperture can then control both the amount of light that illuminates the source, as well as how extended that source is. That is, we can come close to point-source illumination of the sample by closing down the condenser aperture - provided we have enough power to burn. Point-source illumination means that we are illuminating the sample with only a single angle - 90 degrees to the sample plane if we have positioned the image correctly (i.e. at the back focal point).
Is illuimating with only one angle more relevant to us in determining an objective's fitness for observing atoms in a lattice? Not sure. As of right now, it is just another knob that allows us to find the optimum resolution in certain conditions.
Perhaps illuminating with as many angles as possible is best because it tests the objective's ability to capture all those rays of light? On the other hand, perhaps illuminating with many angles artificially increases the supposed resolution of the microscope?
I can think of reasons for both…none highly developed.
The Role of the Field Aperture
The second lens in the Kohler setup then collimates the image made by the first lens. A focal length in front of the third lens is placed another aperture - the field aperture. Its job is to select for the size of the sample to be illuminated. This is the knob that controls the "back NA" of illumination. Having control over the extent of the illuminated region allows one to minimize noise.
Our Illumination Setup