  Plane mirror can make one object into two for observers on the object's side.
Yet, there seems no way to achieve the same effect for observers from all
directions. In this letter, we will design a new class of gradient index lenses
from multivalued optical conformal mapping. We shall call them the conformal
lenses. Such lenses can transform one source into two (or even many)
omnidirectionally. Like the overlapped illusion optics does, they can even
transform multiple sources into one. Rather than using negative index
materials, implementation here only needs isotropic positive index materials
like other gradient index lenses. One obvious drawback however, is that they
have singular permittivity values which restrict them to functioning at one
single frequency. This however, needs not be the case when applying
transmutation methods, which enable the lenses to work in a broadband frequency
range.
