Related papers: Arbitrary Transform Telescopes: The Generalization…
The Fourier transform operation is an important conceptual as well as computational tool in the arsenal of every practitioner of physical and mathematical sciences. We discuss some of its applications in optical science and engineering,…
This paper provides a general introduction to the problem of image reconstruction from interferometric data. A simple model of the interferometric observables is given and the issues arising from sparse Fourier data are discussed. The…
Optical interferometry provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Through direct observation of rotationally distorted photospheres at sub-milliarcsecond scales, we are now able to…
Radio interferometry is a powerful technique that allows astronomers to create high-resolution images of astronomical objects. The distribution of radio telescopes in an interferometer is a critical factor that determines the resolution and…
Fourier imaging is an indirect imaging method which records the diffraction pattern of the object scene coherently in the focal plane of the imaging system and reconstructs the image using computational resources. The spatial resolution,…
For the first time, complete source distributions for the emission and absorption of acoustic and electromagnetic wavelets are defined and computed, both in spacetime and Fourier space. The biggest surprise is the great simplicity of the…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
The Fast Fourier Transform (FFT) is a numerical operation that transforms a function into a form comprised of its constituent frequencies and is an integral part of scientific computation and data analysis. The objective of our work is to…
Dispersive Fourier transformation is a powerful technique in which spectral information is mapped into the time domain using chromatic dispersion. It replaces a spectrometer with an electronic digitizer, and enables real-time spectroscopy.…
Spatial phase-referencing in dual-field optical interferometry is reconsidered. Our analysis is based on the 2-sample variance of the differential phase between target and reference star. We show that averaging over time of the atmospheric…
Double-Fourier interferometry is the most viable path to sub-arcsecond spatial resolution for future astronomical instruments that will observe the universe at far-infrared wavelengths. The double transform spatio-spectral interferometry…
The algorithm behind the Fast Fourier Transform has a simple yet beautiful geometric interpretation that is often lost in translation in a classroom. This article provides a visual perspective which aims to capture the essence of it.
The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
Radio interferometry is an observational technique used to study astrophysical phenomena. Data gathered by an interferometer requires substantial processing before astronomers can extract the scientific information from it. Data processing…
The ultimate astronomical observatory would be a formation flying interferometer in space, immune to atmospheric turbulence and absorption, free from atmospheric and telescope thermal emission, and reconfigurable to adjust baselines…
Many adaptive optics systems operate by measuring the distortion of the wavefront in one wavelength range and performing the scientific observations in a second, different wavelength range. One common technique is to measure wavefront…
For many decades the determination of accurate fundamental parameters for stars (masses, radii, temperatures, luminosities, etc.) has mostly been the domain of eclipsing binary systems. That has begun to change as long-baseline…
We perform a high resolution Fourier Transform Spectroscopy of optical sources in the few-photon regime based on the phenomenon of two-photon interference in a beam splitter. From the heterodyne interferogram between test and reference…
In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of…