We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate...

The metaplectic transform (MT), a generalization of the Fourier sometimes called linear canonical transform, is tool used ubiquitously in modern optics, for example, when calculating transformations light beams paraxial optical systems. MT also an essential ingredient geometrical-optics modeling caustics that was recently proposed by authors. In particular, this application relies on near-ident...

The Special Affine Fourier Transform or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Unlike the Fourier transform, the SAFT does not work well with the standard convolution operation. Recently, Q. Xiang and K. Y. Qin introduced a new convolution operation that is more suitable for the SAFT and by whi...

We show that transformation optics can be applied to extend the functionalities of conventional optical devices. In particular, geometrically compressing the input facet of any conventional optical elements can extend the input spatial frequency bandwidth. As an example, we design a Fourier lens that can transform the image to its reciprocal space and operate for incident light of subwavelength...

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...

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...