  A slab of negatively refracting material, thickness d, can focus an image at
a distance 2d from the object. The negative slab cancels an equal thickness of
positive space. This result is a special case of a much wider class of
focussing: any medium can be optically cancelled by an equal thickness of
material constructed to be an inverted mirror image of the medium, with,
$\epsilon$ and $\mu$ reversed in sign. We introduce the powerful technique of
coordinate transformation, mapping a known system into an equivalent system, to
extend the result to a much wider class of structures including cylinders,
spheres, and intersecting planes and hence show how to produce magnified
images. All the images are perfect in the sense that both the near and far
fields are brought to a focus and hence reveal sub wavelength details.
