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...

Rotational transformation based on coordinate rotation in Fourier space is a useful technique for simulating wave field propagation between nonparallel planes. This technique is characterized by fast computation because the transformation only requires executing a fast Fourier transform twice and a single interpolation. It is proved that the formula of the rotational transformation mathematical...

In this paper we study the application of the Sobolev gradients technique to the problem of minimizing several Schrödinger functionals related to timely and difficult nonlinear problems in Quantum Mechanics and Nonlinear Optics. We show that these gradients act as preconditioners over traditional choices of descent directions in minimization methods and show a computationally inexpensive way to...

In this paper, we describe easy and cheap optics experiences for teaching undergraduate students the fundamental properties of Fourier transforms on an experimental basis. By exploiting eye as transforming device, a common magnifying lens, quasi-coherent light from small white LED, quantitative results can be easily obtained about theorems used in analysis. The concept coherence is also introdu...

We have developed digital 3D Fourier transform methods for comparing the 3D spatial frequency content and hence the axial and transverse resolution of confocal versus conventional microscope images. In particular, we have utilized these techniques to evaluate the performance of our recently-developed confocal transmission microscope for bright field and Nomarski DIC imaging. We have also found ...

In this work, we address phase-signature based digital image watermarking. The signature is extracted from the Fourier phase information of the digital media. It is then embedded in the Fourier magnitude spectrum. The detection and/or authentication is based on the well established area of phase-only filter based correlation techniques in the optics community. We propose to analyze the distorti...

Spatial heterodyne spectroscopy (SHS) is a Fourier-transform spectroscopic technique that simultaneously records all path differences using a detector array. Compared to conventional Fourier-transform spectroscopy that measures interferogram samples sequentially in the time domain, SHS is insensitive to a changing scene; however, the effects caused by differences in the detector elements and/or...

Fourier optics is a powerful tool for the coherent manipulation of optical fields, for the spatial frequency analysis of images, and for the construction of real time correlators. One property that makes optics an exciting tool for frequency analysis is that, in free-space propogation of light, one can see the effects of lenses and filters on a light beam as the beam propogates through the syst...