Amplified dispersive Fourier transformation ADFT is a powerful technique that maps the spectrum of an optical pulse into a time-domain waveform using group-velocity dispersion GVD and simultaneously amplifies it in the optical domain. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector, greatly simplifying the system and, more importantly, enabl...

Many recent invertible neural architectures are based on coupling block designs where variables divided in two subsets which serve as inputs of an easily (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian very sparse and thus may lack expressiveness. This work presents simple remedy by noting that subdivision (affine) can be repeated recursively ...

We describe a Fourier Volume Rendering (FVR) algorithm for datasets that are irregularly sampled and require anisotropic (e.g., elliptical) kernels for reconstruction. We sample the continuous frequency spectrum of such datasets by computing the continuous Fourier transform of the spatial interpolation kernel which is a radially symmetric Gaussian basis function (RBF) that may be anisotropicall...

The fractional Fourier transform (FRT) is shown to be of potential use in analyzing the motion of a surface by use of holographic interferometry. The extra degree of freedom made available by the use of the FRT allows information regarding both translational and tilting motion to be obtained in an efficient manner.

In this paper, we are concerned with orbital integrals on a class C of real reductive Lie groups with non-compact Iwasawa K-component. The class C contains all connected semisimple Lie groups with infinite center. We establish that any given orbital integral over general orbits with compactly supported continuous functions for a group G in C is convergent. Moreover, it is essentially the limit ...

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...