Conceptual studies and numerical simulations are performed for imaging devices that transform a near-field pattern into magnified far-zone images and are based on high-order spatial transformation in cylindrical domains. A lens translating a near-field pattern from an almost circular input boundary onto a magnified far-field image at a flat output boundary is considered. The lens is made of a m...

The Seidel aberrations of a rotationally-symmetric diffractive lens with an arbitrary phase profile are presented. It is shown that by a proper choice of phase function and aperture stop position, third-order coma and astigmatism can be eliminated for any chosen conjugate ratio. Since a diffractive lens has an inherent zero value for the Petzval sum, the image plane is flat in both tangential a...

In 1966, Roger Penrose 1 suggested that an appropriate quasi-local measure of the energy density content of a region of space would be the focusing power of the region on a passing null geodesic congruence. This geometric lens effect would be sensitive to both non-gravitational and gravitational energy because it depends on both the Ricci and the Weyl curvature in the region; the former governs...

Cosmological simulation of gravitational weak lensing in open models with (Ω0, λ0) = (0.2, 0) and (0.4, 0) is treated using the direct integration method, which is independent of the multi-lens-plane method. Statistical averages of optical quantities (the convergence, shear, and amplification) are derived for ray bundles passing through the clumpy universe, in which the initial state has the CD...