One-Dimensional Fourier Transform

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D. V. Erofeev - One of the best experts on this subject based on the ideXlab platform.

  • Kinematics and Evolution of Local Features of the Large-Scale Magnetic Field – I. Kinematical Characteristics
    Solar Physics, 1998
    Co-Authors: D. V. Erofeev
    Abstract:

    Kinematics of local magnetic features (LMFs) have been investigated by analyzing a 22-year series of synoptic maps of the radial magnetic field of the Sun (the term ‘local’ refers hereinafter to magnetic features with an effective size of the order of an arc min). We applied the cross-correlation technique to analyse separately each of the harmonics obtained by using a One-Dimensional Fourier Transform of the magnetic field in longitude. Such an approach allowed us to trace the motion of the LMFs for a time interval as long as 12 Carrington rotations. The analysis also has shown that the effective size of the magnetic tracers grows significantly with increasing age, which indicates that the local-scale magnetic features undergo diffusion-like expansion and weakening, in agreement with Leighton's model of magnetic field evolution. The LMFs emerging at latitudes between 10° and 55° reveal a poleward directed motion with a maximum velocity of about 14 m s^-1 near the latitude of 37°. The profile of the meridional velocity agrees approximately with that derived by Komm, Howard, and Harvey (1993) for small-scale, short-lived magnetic features. We have found that the LMFs rotate differentially at latitudes of up to 55°, and do not exhibit the ‘quasi-rigid’ rotation that is assumed to be characteristic of long-lived magnetic features. This disagrees with the results obtained by Stenflo (1989) and by Latushko (1994), who applied direct cross-correlation analysis of the synoptic maps. Such a discrepancy may be treated as being a consequence of inhomogeneity of the large-scale solar magnetic field that consists of several components with different kinematic characteristics.

  • Kinematics and Evolution of Local Features of the Large-Scale Magnetic Field I. Kinematical Characteristics
    Solar Physics, 1998
    Co-Authors: D. V. Erofeev
    Abstract:

    Kinematics of local magnetic features (LMFs) have been investigated by analyzing a 22-year series of synoptic maps of the radial magnetic field of the Sun (the term ‘local’ refers hereinafter to magnetic features with an effective size of the order of an arc min). We applied the cross-correlation technique to analyse separately each of the harmonics obtained by using a One-Dimensional Fourier Transform of the magnetic field in longitude. Such an approach allowed us to trace the motion of the LMFs for a time interval as long as 12 Carrington rotations. The analysis also has shown that the effective size of the magnetic tracers grows significantly with increasing age, which indicates that the local-scale magnetic features undergo diffusion-like expansion and weakening, in agreement with Leighton's model of magnetic field evolution.

Pavel Cheben - One of the best experts on this subject based on the ideXlab platform.

  • Performance comparison of an anamorphic spatial heterodyne spectrometer with conventional spectrometer
    International Optical Design Conference 2006, 2007
    Co-Authors: Ian Powell, Pavel Cheben
    Abstract:

    This article describes the modeling of the generic spatial heterodyne spectrometer, which resembles a somewhat modified Michelson interferometer. The power spectrum of the input source is determined by performing a one dimensional Fourier Transform on the output intensity profile captured by a linear array detector. In order to illustrate the techniques employed in the modeling, an example of a heterodyne interferometer is developed and a comparison undertaken between its performance and that of a conventional spectrometer. Unlike the traditional FTIR system, the heterodyne spectrometer has the very desirable feature of having no moving components.

  • Modeling of the generic spatial heterodyne spectrometer and comparison with conventional spectrometer
    Applied Optics, 2006
    Co-Authors: Ian Powell, Pavel Cheben
    Abstract:

    We describe the modeling of the generic spatial heterodyne spectrometer. This instrument resembles a somewhat modified Michelson interferometer, in which the power spectrum of the input source is determined by performing a One-Dimensional Fourier Transform on the output intensity profile. Code has been developed to analyze the performance of this type of spectrometer by determining the dependence of both spectral resolution and throughput on parameters such as aperture and field of view. An example of a heterodyne spectrometer is developed to illustrate the techniques employed in the modeling and a comparison undertaken between its performance and that of a conventional spectrometer. Unlike the traditional Fourier Transform infrared system, the heterodyne spectrometer has the very desirable feature of having no moving components.

Jorge Ojeda-castaneda - One of the best experts on this subject based on the ideXlab platform.

  • On-axis diffractional behavior of two-dimensional pupils
    Applied optics, 1994
    Co-Authors: Manuel Martínez-corral, Pedro Andrés, Jorge Ojeda-castaneda
    Abstract:

    We show that, at any Fresnel number, a suitable One-Dimensional Fourier Transform relates the complex-amplitude distribution along the optical axis with the zero-order circular harmonic of the amplitude transmittance of a two-dimensional diffracting screen. First, our general result is applied to recognize that any rationally nonsymmetric screen generates an axial-irradiance distribution that exhibits focal shift. In this way we identify a wide set of two-dimensional screens that produce the same focal shift as that produced by the clear circular aperture. Second, we identify several apodizers for shaping the axial-amplitude distribution. We discuss some examples for achieving high-precision focusing, axial hyperresolution, or high focal depth.

  • Off-axis focal shift for rotationally nonsymmetric screens.
    Optics letters, 1993
    Co-Authors: Pedro Andrés, Manuel Martínez-corral, Jorge Ojeda-castaneda
    Abstract:

    We report on an analytical formulation for evaluating the amplitude distribution along any line directed toward the geometrical focus of a spherical wave front that passes through a rotationally nonsymmetric diffracting screen. Our formula consists of two factors. The first factor involves the One-Dimensional Fourier Transform of the projection of the screen function onto the off-axis line. The second factor depends on the inverse distance to the screen and permits us to recognize the existence of focal shift along off-axis lines.

G. W. Inverarity - One of the best experts on this subject based on the ideXlab platform.

  • Numerically inverting a class of singular Fourier Transforms: theory and application to mountain waves
    Proceedings of the Royal Society of London. Series A: Mathematical Physical and Engineering Sciences, 2003
    Co-Authors: G. W. Inverarity
    Abstract:

    Many partial differential equations of physics are solved using Fourier Transforms. Even when solutions to the Transformed equations can be found analytically it is rare for their inverse Transforms to be known in terms of simple functions. Instead, asymptotic and/or numerical approaches are commonly used to approximate the inverse Transforms. A numerical technique is here developed to invert a one–dimensional Fourier Transform with singularities on the real axis of the complex plane that are at worst simple poles, subject to the condition that the inverse Transform vanishes as its Transform variable becomes infinite in one direction. By way of demonstration, it is used to compute the respective solutions of Long and Wurtele for trapped and evanescent lee waves driven by flow over gently sloping hills.

Ian Powell - One of the best experts on this subject based on the ideXlab platform.

  • Performance comparison of an anamorphic spatial heterodyne spectrometer with conventional spectrometer
    International Optical Design Conference 2006, 2007
    Co-Authors: Ian Powell, Pavel Cheben
    Abstract:

    This article describes the modeling of the generic spatial heterodyne spectrometer, which resembles a somewhat modified Michelson interferometer. The power spectrum of the input source is determined by performing a one dimensional Fourier Transform on the output intensity profile captured by a linear array detector. In order to illustrate the techniques employed in the modeling, an example of a heterodyne interferometer is developed and a comparison undertaken between its performance and that of a conventional spectrometer. Unlike the traditional FTIR system, the heterodyne spectrometer has the very desirable feature of having no moving components.

  • Modeling of the generic spatial heterodyne spectrometer and comparison with conventional spectrometer
    Applied Optics, 2006
    Co-Authors: Ian Powell, Pavel Cheben
    Abstract:

    We describe the modeling of the generic spatial heterodyne spectrometer. This instrument resembles a somewhat modified Michelson interferometer, in which the power spectrum of the input source is determined by performing a One-Dimensional Fourier Transform on the output intensity profile. Code has been developed to analyze the performance of this type of spectrometer by determining the dependence of both spectral resolution and throughput on parameters such as aperture and field of view. An example of a heterodyne spectrometer is developed to illustrate the techniques employed in the modeling and a comparison undertaken between its performance and that of a conventional spectrometer. Unlike the traditional Fourier Transform infrared system, the heterodyne spectrometer has the very desirable feature of having no moving components.