Resolution enhancement by extrapolation of coherent diffraction images: a quantitative study on the limits and a numerical study of nonbinary and phase objects.

In coherent diffractive imaging, the resolution of the reconstructed object is limited by the numerical aperture of the experimental setup. We present here a theoretical and numerical study for achieving super-resolution by postextrapolation of coherent diffraction images, such as diffraction patterns or holograms. We demonstrate that a diffraction pattern can unambiguously be extrapolated from only a fraction of the entire pattern and that the ratio of the extrapolated signal to the originally available signal is linearly proportional to the oversampling ratio. Although there could be in principle other methods to achieve extrapolation, we devote our discussion to employing iterative phase retrieval methods and demonstrate their limits. We present two numerical studies; namely, the extrapolation of diffraction patterns of nonbinary and that of phase objects together with a discussion of the optimal extrapolation procedure.

Fabrication and characterization of low aberration micrometer-sized electron lenses.

Intrinsic spherical aberrations of electron lenses have been the major resolution limiting factor in electron microscopes for several decades. While effective correctors have recently been implemented, an alternative to correct these aberrations is to circumvent them by scaling down lens dimensions by several orders of magnitude. We have fabricated electrostatic lenses exhibiting one micrometer diameter apertures and evaluated their beam forming properties against predictions from numerical ray tracing simulations. It turns out that it is routinely possible to shape a paraxial low-energy electron beam by such micron-sized lenses. Beam profiles have been measured both at a distant detector as well as in a plane close to the lens. It is shown that the lens can form a parallel beam extending no more than 800 nm from the optical axes at a distance of 200 microm beyond the lens exit. We believe that these findings constitute a prerequisite to derive novel tools for high resolution microscopy using low-energy electrons.

Electrical conduction through DNA molecules.

The question of whether DNA is able to transport electrons has attracted much interest, particularly as this ability may play a role as a repair mechanism after radiation damage to the DNA helix. Experiments addressing DNA conductivity have involved a large number of DNA strands doped with intercalated donor and acceptor molecules, and the conductivity has been assessed from electron transfer rates as a function of the distance between the donor and acceptor sites. But the experimental results remain contradictory, as do theoretical predictions. Here we report direct measurements of electrical current as a function of the potential applied across a few DNA molecules associated into single ropes at least 600 nm long, which indicate efficient conduction through the ropes. We find that the resistivity values derived from these measurements are comparable to those of conducting polymers, and indicate that DNA transports electrical current as efficiently as a good semiconductor. This property, and the fact that DNA molecules of specific composition ranging in length from just a few nucleotides to chains several tens of micrometres long can be routinely prepared, makes DNA ideally suited for the construction of mesoscopic electronic devices.