Quasi-discrete Hankel transform

Yu, Li; Huang, Meng; Chen, Mouzhi; Wenzhong, Chen; Huang, Wenda; Zhu, Zhizhong

doi:10.1364/ol.23.000409

Cited by 115 publications

(62 citation statements)

References 4 publications

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“…The zeroth-order Hankel transform in the continuous case keeps the fundamental property of the Fourier transform we need: convolutions are converted to products in the transformed space. 21 Now we turn to the discrete zeroth-order Hankel transform, [22][23][24] which is the form of this transform that we will use in fact. It is analogous to the discrete Fourier transform, which is actually used in many physical problems instead of the Fourier transform definition.…”

Section: Iic the Zeroth-order Hankel Transform "Fourierbessel Transmentioning

confidence: 99%

“…This means that the Bessel functions set forms a near-orthogonal base, instead of an orthogonal base, 23,24 when a finite series of functions is taken. But, as the base is very close to be orthogonal strictu sensu, in practice the convolution property can be used.…”

Section: Iic the Zeroth-order Hankel Transform "Fourierbessel Transmentioning

confidence: 99%

“…But, as the base is very close to be orthogonal strictu sensu, in practice the convolution property can be used. We have performed our own implementation of an algorithm for calculating the zeroth-order Hankel transform, based on the work by Lemoine 22,23 and Yu et al 24 ͑see the Appendix͒. The number of zeros to calculate depends on the number of data in the original signal.…”

Section: Iic the Zeroth-order Hankel Transform "Fourierbessel Transmentioning

confidence: 99%

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A system for intensity modulated dose plan verification based on an experimental pencil beam kernel obtained by deconvolution

Azcona¹,

Burguete²

2007

Medical Physics

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The number of intensity modulated radiation therapy ͑IMRT͒ procedures is continuously growing worldwide and it is necessary to develop tools for patient specific quality assurance ͑QA͒ that avoid using machine time that could be employed in treating additional patients. One way of achieving this goal is to perform a multileaf collimator quality assurance periodically in the linear accelerator and check the treatment planning system ͑TPS͒ calculation by employing an independent calculation system. Within the work frame of the pencil beam kernel approach, a new system was developed for obtaining an experimental kernel. This new technique is based on a deconvolution procedure using the Hankel transform. The resulting kernel is obtained in a way completely independent of those employed in commercial treatment planning systems, usually calculated by Monte Carlo simulations. Also provided are comparisons between calculated and measured doses with radiographic film, linear array of diodes, and ionization chamber. Measurements taken in polystyrene and water for clinical IMRT plans demonstrate that this method can calculate IMRT dose distributions, as well as treatment times, with great accuracy. Apart from other applications, it can be used as a double-check algorithm for IMRT QA.

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Section: Iic the Zeroth-order Hankel Transform "Fourierbessel Transmentioning

confidence: 99%

Section: Iic the Zeroth-order Hankel Transform "Fourierbessel Transmentioning

confidence: 99%

Section: Iic the Zeroth-order Hankel Transform "Fourierbessel Transmentioning

confidence: 99%

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A system for intensity modulated dose plan verification based on an experimental pencil beam kernel obtained by deconvolution

Azcona¹,

Burguete²

2007

Medical Physics

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“…Following earlier works, we applied a quasi-discrete Hankel transform (QDHT) routine (Yu et al, 1998;Guizar-Sicairos & GutierrezVega, 2004) to model diffractive X-ray optics because it gives a very high accuracy agreement with the exact analytical transforms and it requires neither the interpolation of the data points nor the use of extensive zero padding. Unlike other Hankel transform algorithms such as the one used by VilaComamala et al (2011), the QDHT is energy preserving by construction and the original function is retrieved after two successive applications of the Hankel transform with a precision comparable with the fast Fourier transform routines.…”

Section: Methodsmentioning

confidence: 99%

Angular spectrum simulation of X-ray focusing by Fresnel zone plates

Vila‐Comamala

Wojcik

Díaz

et al. 2013

J Synchrotron Radiat

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A computing simulation routine to model any type of circularly symmetric diffractive X-ray element has been implemented. The wavefield transmitted beyond the diffractive structures is numerically computed by the angular spectrum propagation method to an arbitrary propagation distance. Cylindrical symmetry is exploited to reduce the computation and memory requirements while preserving the accuracy of the numerical calculation through a quasidiscrete Hankel transform algorithm, an approach described by Guizar-Sicairos & Gutierrez-Vega [J. Opt. Soc. Am. A, (2004), 21, 53-58]. In particular, the code has been used to investigate the requirements for the stacking of two highresolution Fresnel zone plates with an outermost zone width of 20 nm.

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“…And the most robust algorithm is for J 0 (ks)-transform which has been devised by Lado, 39 and more than two decades later was rediscovered by Yu et al 40 The transforms of higher (even) order are reduced to zero order transform by special "raising" and "lowering" operations. 6,37 According to Lado's recipe, 39 we assume that the function f(s) is defined for s ≥ 0, that f(s) vanishes for s ≥ S, and that its Fourier (Hankel) transformf (k) vanishes for k ≥ K, i.e., the function is band-limited both in space and in frequency.…”

Section: Appendix A: Numerical Hankel Transformsmentioning

confidence: 99%

Reference hypernetted chain theory for ferrofluid bilayer: Distribution functions compared with Monte Carlo

Polyakov

Vorontsov-Vèlyaminov

2014

The Journal of Chemical Physics

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Properties of ferrofluid bilayer (modeled as a system of two planar layers separated by a distance h and each layer carrying a soft sphere dipolar liquid) are calculated in the framework of inhomogeneous Ornstein-Zernike equations with reference hypernetted chain closure (RHNC). The bridge functions are taken from a soft sphere (1/r 12 ) reference system in the pressure-consistent closure approximation. In order to make the RHNC problem tractable, the angular dependence of the correlation functions is expanded into special orthogonal polynomials according to Lado. The resulting equations are solved using the Newton-GRMES algorithm as implemented in the publicdomain solver NITSOL. Orientational densities and pair distribution functions of dipoles are compared with Monte Carlo simulation results. A numerical algorithm for the Fourier-Hankel transform of any positive integer order on a uniform grid is presented. © 2014 AIP Publishing LLC.

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Quasi-discrete Hankel transform

Cited by 115 publications

References 4 publications

A system for intensity modulated dose plan verification based on an experimental pencil beam kernel obtained by deconvolution

A system for intensity modulated dose plan verification based on an experimental pencil beam kernel obtained by deconvolution

Angular spectrum simulation of X-ray focusing by Fresnel zone plates

Reference hypernetted chain theory for ferrofluid bilayer: Distribution functions compared with Monte Carlo

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