  Perfect imaging has been believed to rely on negative refraction, but here we
show that an ordinary positively-refracting optical medium may form perfect
images as well. In particular, we establish a mathematical proof that Maxwell's
fish eye in two-dimensional integrated optics makes a perfect instrument with a
resolution not limited by the wavelength of light. We also show how to modify
the fish eye such that perfect imaging devices can be made in practice. Our
method of perfect focusing may also find applications outside of optics, in
acoustics, fluid mechanics or quantum physics, wherever waves obey the
two-dimensional Helmholtz equation.
