Related papers: Arbitrary Transform Telescopes: The Generalization…
We propose and experimentally validate a joint estimation method for chromatic dispersion and time-frequency offset based on the fractional Fourier transform, which reduces computational complexity by more than 50% while keeping estimation…
Most statistical tools used to characterize the complex structures of the interstellar medium can be related to the power spectrum, and therefore to the Fourier amplitudes of the observed fields. To tap into the vast amount of information…
The Cosmic Microwave Background (CMB) data analysis and the map-making process rely heavily on the use of spherical harmonics. For suitable pixelizations of the sphere, the (forward and inverse) Fourier transform plays a crucial role in…
One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However,…
We introduce a convenient formalism to evaluate the frequency-shift affecting a light signal propagating on a general curved background. Our formulation, which is based on the laws of geometric optics in a general relativistic setting,…
A method to create instructive, nonuniform aperture functions using spatial frequency filtering is described. The diffraction from a single slit in the Fresnel limit and the interference from a double slit in the Fraunhofer limit are…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
The present `state of the art' and the path to future progress in high spatial resolution imaging interferometry is reviewed. The review begins with a treatment of the fundamentals of stellar optical interferometry, the origin, properties,…
Cosmological random fields are often analysed in spherical Fourier-Bessel basis. Compared to the Cartesian Fourier basis this has an advantage of properly taking into account some of the relevant physical processes (redshift-space…
In this paper are reviewed various designs of advanced, multi-aperture optical systems dedicated to high angular resolution imaging or to the detection of exo-planets by nulling interferometry. A simple Fourier optics formalism applicable…
Interferometry is a powerful technique for making sensitive, high-fidelity images of the sky, but is limited in its ability to measure extended or diffuse emission. Better images of extended astronomical objects can be obtained by…
Rotation is a common motional form in nature, existing from atoms and molecules, industrial turbines to astronomical objects. However, it still lacks an efficient and reliable method for real-time image processing of a fast-rotating object.…
The displacement of star images by atmospheric refraction observed by an Earth-bound telescope is dominated by a familiar term proportional to the product of the tangent of the zenith angle by the refractivity at the ground. The manuscript…
Observational astrophysics uses sophisticated technology to collect and measure electromagnetic and other radiation from beyond the Earth. Modern observatories produce large, complex datasets and extracting the maximum possible information…
Formation of a bright-field microscopic image of a transparent phase object is described in terms of elementary geometrical optics. Our approach is based on the premise that image replicates the intensity distribution (real or virtual) at…
In this paper, we mainly establish the uncertainty principle (UP) for a function and its quaternion Fractional Fourier transform (QFrFT), as well as the UP for two QFrFTs. Using the polar representation of quaternion-valued signals, we give…
Atmospheric remote spectrometry from space has become in the last 20 years a key component of the Earth monitoring system: their large coverage and deci-kelvin stability have demonstrated their usefulness for weather prediction, atmospheric…
The speckle imaging is a photographic technique that resolves objects viewed through severely distorted media. The results are insensitive to the errors caused by apparent size of the isoplanatic patch and the telescope aberrations. In this…
Birefringent crystals are extensively used to manipulate polarized light. The generalized transfer matrix developed allows efficient calculation of the full polarization state of light transmitted through and reflected by a stack of…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…