Related papers: Fourier Transform of Annular Beams
The composition of the Fourier transform in $\mathbb{R}^n$ with a suitable pseudodifferential operator is called a Fourier operator. It is compact in appropriate function spaces. The paper deals with its spectral theory. This is based on…
In this paper we generalize the continuous quaternion windowed Fourier transform called the multivariate two sided continuous quaternion windowed Fourier transform. Using the two sided quaternion Fourier transform we derive several…
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more…
Fast Fourier Transform (FFT) relies on the HRV frequency-domain analysis techniques. It requires re-sampling of the inherently unevenly sampled heartbeat time-series (RR tachogram) to produce an evenly sampled time series of the heartbeat.…
The Fourier transform method can be applied to obtain electromagnetic knots, which are solutions of Maxwell equations in vacuum with non-trivial topology of the field lines and especial properties. The program followed in this work allows…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral…
This comprehensive review paper delves into the intricacies of advanced Fourier type integral transforms and their mathematical properties, with a particular focus on fractional Fourier transform (FrFT), linear canonical transform (LCT),…
The Fourier transform proves indispensable in the processing of classical information as well as in the quantum domain, where it finds many applications ranging from state reconstruction to prime factoring. An implementation scheme of the…
We consider a large class of physical fields $u$ written as double inverse Fourier transforms of some functions $F$ of two complex variables. Such integrals occur very often in practice, especially in diffraction theory. Our aim is to…
This paper demonstrates a method of interpreting the mechanism of aberration of optical systems based on non-Fourier transform optical transfer function (OTF). According to the parameters of object plane cosine fringe, we obtain the…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
Treatments of Fraunhofer diffraction normally approximate the inclination factor in the diffraction integral by 1, but this is not necessary. In this paper, the Rayleigh-Sommerfeld diffraction integral is used and a complete description of…
Narrow-band filters are often used to constrain the chemical composition of astronomical objects through photometry. A challenge to derive accurate photometry is that narrow-band filters are based on interference of multiple reflections and…
Fourier optics enforces a tradeoff between length and narrowness in electromagnetic wavepackets, so that a narrow spatial focus diffracts at a large divergence angle, and only infinitely wide beams can remain non-diffracting. We show that…
We design freeform lenses refracting an arbitrarily given incident field into a given fixed direction. In the near field case, we study the existence of lenses refracting a given bright object into a predefined image. We also analyze the…
The homogenization of light is widely applied in various industrial sectors. The uniform high power processing of large areas requires a high degree of homogeneity. Sophisticated beam transformation techniques are used to optimize the…
Spiral phase contrast is an important and convenient imaging processing technology in edge detection, and a broader field-of-view (FOV) of imaging is a long-pursuing aim to see more regions of the illumination objects. Compared with…
Bandwidth smearing is a chromatic aberration due to the finite frequency bandwidth. In long-baseline optical interferometry terms, it is when the angular extension of the source is greater than the coherence length of the interferogram. As…
We demonstrate a Fourier Imaging system with centimeter field of view(FOV), and 0.0042{\deg}angular resolution at C band, for the entire 180{\deg} radiation angular range. To pursue omnidirectional Fourier imaging without aberration, a…