Exp Iθ Research Articles

Selective edge enhancement using shifted anisotropic vortex filter

We propose a new method for selective edge enhancement using shifted anisotropic vortex phase mask. The shifted anisotropic phase mask is generated by introducing controllable anisotropy in conventional vortex mask (exp iθ ðÞ ) with the help of sine function and shifting the singularity away from the zero frequency component in the filter plane. The shifted anisotropic vortex mask is capable of enhanc- ing the edges of the given object selectively in any desired direction.

A Cauchy-Riemann equation for generalized analytic functions

We denote by T 2 the torus: z = exp iθ, ω = exp iφ, and we fix a positive irrational number α. A α denotes the space of continuous functions f on T 2 whose Fourier coefficient sequence is supported by the lattice half-plane n + mα > 0. R. Arens and I. Singer introduced and studied the space A α , and it turned out to be an interesting generalization of the disk algebra. Here we construct a differential operator X Σ on a certain 3-manifold Σ 0 such that X Σ characterizes A α in a manner analogous to the characterization of the disk algebra by the Cauchy-Riemann equation in the disk.

Phase Retrieval in Optical Spectroscopy: Resolving Optical Constants from Power Spectra

The problem of phase retrieval appears in optical spectroscopy when a power spectrum P(ω) = |f(ω)|2 is measured while the entire complex function f(ω) = | f(ω)|exp iθ(ω) is needed for obtaining the desired material properties. Recently we proposed a new approach to solve this problem in optical spectroscopy by using the maximum entropy model. Here we give a short review of its theory and show how to improve the phase retrieval procedure to work well in practice. The usage and applicability of the procedure, especially in reflectance spectroscopy of solids, are demonstrated with practical examples. Its use in other applications is also discussed.

Bose-Fermi equivalence of the two-dimensional torus for simply-laced groups

Bosonic and fermionic partition functions on the two-dimensional torus are explicitly calculated to establish a Bose-Fermi equivalence for each fundamental representation of every simple-laced group G. A one-to-one correspondence exists for bosons with momenta generated by the root lattice of G shifted by the element w k, where w k is a minimal weight of G, i.e. and element of the center of the covering group of G, and fermions with generalized boundary conditions ψ → (exp iθ k ) ψ (under rotation around the torus) where exp( iθ k ) is the same element of Z as is w k . The non-orthogonal weight lattices of G are converted into orthogonal lattices with constraints. It is shown that only for spin(2 N) can these constraints be written as projection operators, which correspond to sums over spin structure in fermion language. For SU( N), E 6 and E 7 the appropriate constraints are imposed by coupling the fermions to background U(1) world-sheet gauge fields which act as Lagrange multipliers, i.e. the equivalence is to constrained fermions. Explicit modular invariant partition functions are presented for closed strings compactified ti simply-laced groups associated to Kac-Moody algebras with central charge k = 1.