Quantum Fourier transform (QFT) is a key function to realize quantum computers. A QFT followed by measurement was demonstrated on a simple circuit based on fiber-optics. The QFT was shown to be robust against imperfections in the rotation gate. Error probability was estimated to be 0.01 per qubit, which corresponded to error-free operation on 100 qubits. The error probability can be further red...

The structure and the properties of the eigenfunctions of the canonical integral transform are investigated. It is shown that a signal can be decomposed into a set of the orthogonal eigenfunctions of the generalized Fresnel transform. The property that the set contains a finite number of functions is obtained. The canonical integral transform, also known as the generalized Fresnel transform (GF...

We report a tomographic diffractive microscope, which permits imaging non-labelled transparent or semi-transparent samples. Based on a combination of microholography with a tomographic illumination, our set-up creates 3-D images of the index of refraction distribution within the sample. One acquires successively interferograms, rotating the illumination (the specimen being static) and using pha...

Optimal modal Fourier-transform wavefront control combines the speed of Fourier-transform reconstruction (FTR) with real-time optimization of modal gains to form a fast, adaptive wavefront control scheme. Our modal basis is the real Fourier basis, which allows direct control of specific regions of the point-spread function. We formulate FTR as modal control and show how to measure custom filter...

Due to wave nature of the light, harmonic analysis (Fourier transform) and superposition are used in design optical systems Fourier optics experiments. This study aims illustrate use fast transform computations order simulate spatial filter results. In experiments or devices, it is quite useful perform computer simulation obtain theoretical this study, based simulations for low-pass high-pass s...

The linear canonical transform (LCT), is the name of a parameterized continuum of transforms which include, as particular cases, the most widely used linear transforms and operators in engineering and physics such as the Fourier transform, fractional Fourier transform (FRFT), Fresnel transform (FRST), time scaling, chirping, and others. Therefore the LCT provides a unified framework for studyin...

By exploiting a causality property of the nonlinear Fourier transform, a novel decisionfeedback detection strategy for nonlinear frequency-division multiplexing (NFDM) systems is introduced. The performance of the proposed strategy is investigated both by simulations and by theoretical bounds and approximations, showing that it achieves a considerable performance improvement compared to previou...

Inverse elastic-wave scattering problems are shown to be ill-posed in general. Standard simplifying assumptions--the first Born approximation, the physical optics approximation, and the stopping power approximation of tomography--are shown to reduce to the same ill-posed mathematical problem, that of inverting a Fourier transform. Practical implications of this fact are illustrated with examples.

We experimentally demonstrate an 8 × 40 Gb/s all-optical coherent-OFDM system using an on-chip 1 × 8 Fourier-transform based on a modified arrayed-waveguide grating router, showing simultaneous receiving of 8 subcarriers with similar signal qualities. OCIS codes: (060.2330) Fiber optics communications; (060.1660) Coherent communications; (060.4230) Multiplexing; (080.1238) Array waveguide devic...