It has long been realized that imaging with hollow cone illumination (HCI) should, in theory, improve the directly interpretable resolution of TEM by as much as 100% (albeit at the expense of contrast). The principle of HCI was first proposed by Scherzer in 1949 and then reinvented by Hanssen and Trepte in 1971. As opposed to axial illumination, HCI effectively eliminates zeroes and reversals of the transfer function providing direct interpretability of the resulting images. In addition to the substantial resolution enhancement, HCI should reduce significantly the phase-contrast noise inherent in axial HRTEM images. However, there are experimental obstacles for high resolution HCI which make its practical application very difficult to implement. To our knowledge, all observations using HCI so far have not shown all of the expected improvement predicted theoretically. This is believed to be due to the fact that accurate coma-free alignment is required to substantially improve the resolution.