A discussion on the interest of the study of diffractional image formation theory in a course of Fourier Optics is carried out We develope a general description of the partially coherent illumination case. Images of extended objects like the line and periodical structures are given for different values of the coherence parameter. The apparent transfer function is introduced as a quality criteri...

The Soft X-ray Undulator beamline at the NSLS supports a soft x-ray imaging program including scanning transmission microscopy, scanning photoemission microscopy, Gabor and Fourier transform holography, and large angle diffraction. Zone plates from an LBL Center for X-ray Optics/IBM collaboration are used as optical elements. The current instrumentation of the beamline and the experimental stat...

The linear 2-dim irreducible representations of the dihedral groups (Dn) are interpreted as classical linear operators of geometrical optics. It is shown that the 2-dim irreducible representation of D4 is simply the refractive group described by Campbell [Optom. Vision Sci. 74, 381 (1997)]. The dihedral Fourier-inverse mechanism is introduced and shown to provide a systematic connection between...

We prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time-harmonic Maxwell equations in certain anisotropic settings. We give a uniqueness result in the inverse problem for Maxwell equations on an admissible Riemannian manifold, and a uniqueness result for Maxwell equations in Euclidean space with admissible matrix coefficients. The proo...

We prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time-harmonic Maxwell equations in certain anisotropic settings. We give a uniqueness result in the inverse problem for Maxwell equations on an admissible Riemannian manifold, and a uniqueness result for Maxwell equations in Euclidean space with admissible matrix coefficients. The proo...

Due to the variety of shapes and sizes that present both living organisms and static objects, the necessity to look for automated systems of identification, both in industry and scientific research has arisen. During the 1960s, the scientific community in the field of optics has used the Fourier transform and other types of mathematical transformations for pattern recognition, taking advantage ...

Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field prop...

Recently, optical interpretations of the fractional-Fourier-transform operator have been introduced. On the basis of this operator the fractional correlation operator is defined in two different ways that are both consistent with the definition of conventional correlation. Fractional correlation is not always a shift-invariant operation. This property leads to some new applications for fraction...

A general method is proposed for constructing templates of cells in differential interference contrast (DIC) microscopy. This takes account of the optics which generate DIC images, and is applicable to both transparent and semi-transparent cells of simple and complex shapes. Then, a template matching methodology is presented, which uses fast Fourier transforms to fit templates of a range of siz...

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the fast Fourier transform (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursiv...