Search results for "Fourier transform"
showing 10 items of 1138 documents
White-light optical implementation of the fractional fourier transform with adjustable order control.
2000
An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.
Holographically aided iterative phase retrieval
2012
Fourier transform holography (FTH) is a noise-resistant imaging technique which allows for nanometer spatial resolution x-ray imaging, where the inclusion of a small reference scattering object provides the otherwise missing phase information. With FTH, one normally requires a considerable distance between the sample and the reference to ensure spatial separation of the reconstruction and its autocorrelation. We demonstrate however that this requirement can be omitted at the small cost of iteratively separating the reconstruction and autocorrelation. In doing so, the photon efficiency of FTH can be increased due to a smaller illumination area, and we show how the presence of the reference p…
All-diffractive achromatic Fourier-transform setup
2009
An achromatic Fourier transformation under broadband converging spherical-wave illumination is optically achieved by use of only two on-axis blazed zone plates. The novel optical configuration provides the achromatic Fraunhofer diffraction pattern of an arbitrary input signal with adjustable magnification. Further analysis of the system permits us to obtain a simple analytical expression to evaluate both the longitudinal and the transversal residual chromatic aberration, resulting in a compact achromatic Fourier transformer with low chromatic errors, even for a wide spectral content of the point source.
Apodization of imaging systems by means of a random spatially nonstationary absorbing screen
1992
The amplitude impulse response (AIR) of coherent imaging systems with random binary apodizers is analyzed. Formulas for the mean value and the variance of the AIR are derived for two statistical one-dimensional models of apodizers: (1) nonuniform low-density shot noise and (2) a nonuniform unipolar synchronous random process. We show that for both models a high signal-to-noise ratio is achieved within the central peak and the low-order sidelobes of the AIR. Apodizers based on the second model permit higher values of the signal-to-noise ratio than those based on the first one.
Tapered Two-Wire Waveguide for Time-Domain Integration of Broadband Terahertz Pulses
2021
We show the time-domain integration of terahertz pulses achieved in a sub-wavelength, tapered two-wire waveguide. Both simulation and experimental results prove the time integration functionality of this waveguide topology.
Precise $\sf g_J$ - and $\sf g_I$ -factor measurements of Ba + isotopes
1998
Laser-microwave double and triple resonance experiments were performed on clouds of Ba+ ions confined in a Penning ion trap to induce and detect electronic and nuclear spin flip transitions. Collisions with buffer gas molecules in the trap was used to reduce the lifetime of a long lived metastable state of the ions, in which population trapping might occur, and to cool the ions to the ambient temperature. Loss of ions from the trap by collisions were prevented by coupling the magnetron and reduced cyclotron motions by an additional r.f. field at the sum frequency of the two motions. Electronic Zeeman transitions in 138Ba+ and 135Ba+ were observed at a full width of about 3 kHz at a transiti…
2019
We demonstrate experimentally ghost optical coherence tomography using a broadband incoherent supercontinuum light source with shot-to-shot random spectral fluctuations. The technique is based on ghost imaging in the spectral domain where the object is the spectral interference pattern generated from an optical coherence tomography interferometer in which a physical sample is placed. The axial profile of the sample is obtained from the Fourier transform of the correlation between the spectrally resolved intensity fluctuations of the supercontinuum and the integrated signal measured at the output of the interferometer. The results are in excellent agreement with measurements obtained from a …
Star-products, spectral analysis, and hyperfunctions
2000
We study the ⋆-exponential function U(t;X) of any element X in the affine symplectic Lie algebra of the Moyal ⋆-product on the symplectic manifold (ℝ × ℝ;ω). When X is a compact element, a natural specific candidate for U (t;X) to be the exponential function is suggested by the study we make in the non-compact case. U (t;X) has singularities in the t variable. The analytic continuation U(z;X),z = t + iy, defines two boundary values δ+ U (t;X) = limy↓0 U(z;X) and δ-(t;X) = limy↑0 U(z; X). δ+ U (t;X) is a distribution while δ- U (t;X) is a Beurling-type, Gevrey-class s — 2 ultradistribution. We compute the Fourier transforms in t of δ± U (t;X). Both Fourier spectra are discrete but different …
Heat Conduction Problem for Double-Layered Ball
2014
Heat conduction models for double layered spherical sample are developed. Parabolic (classic, based on Fourier’s Law) and hyperbolic (based on Modified Fourier’s Law) heat conduction equations are used to describe processes in the sample during Intensive Quenching. Solution and numerical results are obtained for 1D model using Conservative Averaging method and transforming the original problem for a sphere to a new problem for a slab, with non classic boundary condition. Models include boundary conditions of third kind and non-linear BC case. Numerical results are presented for several relaxation time and initial heat flux values.
Coulomb Fourier Transformation: Application to a Three-Body Hamiltonian with One Attractive Coulomb Interaction
2003
Consider a three-body system consisting of one neutral particle 1 and two charged particles characterized by the indices 2 and 3 with charges of opposite sign, i.e., e2e3 < 0. We use the following notation: (x ν , y ν ), v = 1, 2, 3, denotes the (mass-renormalized) coordinate vector within the pair ν, and between the center of mass of the pair ν and particle ν, respectively. The corresponding canonically coniugate momenta are (k ν , p ν ).