  We optimise the effective skin-depth and resolution of Ag-TiO2, Ag-SrTiO3,
and Ag-GaP multilayers for imaging with sub-wavelength resolution. In terms of
transmission and resolution the optimised multilayers outperform simple designs
based on combined use of effective medium theory, impedance matching and
Fabry-Perot resonances. For instance, an optimised Ag-GaP multilayer consisting
of only 17 layers, operating at the wavelength of 490 nm and having a total
thickness equal to one wavelength, combines 78% intensity transmission with a
resolution of 60 nm. It is also shown that use of the effective medium theory
leads to sub-optimal multilayer designs with respect to the trade-off between
the skin depth and resolution already when the period of the structure is on
the order of 40 nm or larger.
