An algorithm for the numerical evaluation of the Hankel transform

For the design of DOE with rotational symmetric phase distribution, the Fourier Transform (FT) and Inverse Fourier Transform (IFT) take the form of the first order of Hankel transform. The speed of numerical calculation for Hankel transform becomes the bottleneck of phase retrieval algorithms. A new fast Hankel transform method is applied to DOE designing process, in which Hankel transform is achieved by one time's of projection integration and one time's of Fast Fourier Transform (FFT). Utilizing the merits of FFT, speed of Hankel transform is greatly improved. Therefore, rotational symmetric DOE can be designed with fast speed and good designed result can be obtained more easily. Some examples of DOE designing with the help of FHT are given.

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“…For the samples of ) (x p , it is somewhat less direct. Under discrete condition, equation (4) can be written as [3] …”

Section: Projection Methods For Fhtmentioning

confidence: 99%

Fast phase retrieval algrithm for rotational symmetric DOE designing

Wang

Zhang

et al. 2003

SPIE Proceedings

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“…(2) is the finite Hankel transform (FHT). Many numerical computation methods have been proposed for calculating the FHT and the corresponding FB coefficients in (Oppenheim et al, 1978;Cavanagh & Cook, 1979;Candel, 1981a;Candel, 1981b;Oppenheim et al, 1980). In this paper, the FHT and the corresponding FB coefficients are calculated by using numerical method proposed in (Guizar-Sicairos & Gutierrez-Vega, 2004) due to fast computation.…”

Section: Fourier-bessel (Fb) Expansionmentioning

confidence: 99%

An application to transient current signal based induction motor fault diagnosis of Fourier–Bessel expansion and simplified fuzzy ARTMAP

Tran

Althobiani

Ball

et al. 2013

Expert Systems with Applications

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The start-up transient signals have been widely used for fault diagnosis of induction motor because they can reveal early defects in the development process, which are not easily detected with the signals in the steady state operation. However, transient signals are non-linear and contain multi components which need a suitable technique to process and identify the fault pattern. In this paper, the fault diagnosis problem of induction motor is conducted by a data driven framework where the Fourier-Bessel (FB) expansion is used as a tool to decompose transient current signal into series of single components. For each component, the statistical features in the time and the frequency domains are extracted to represent the characteristics of motor condition. The high dimensionality of the feature set is solved by generalized discriminant analysis (GDA) implementation to decrease the computational complexity of classification. In the meantime, with the aid of GDA, the separation of the feature clusters is increased, which enables the more classification accuracy to be achieved. Finally, the reduced dimensional features are used for classifier to perform the fault diagnosis results. The classifier used in this framework is the simplified fuzzy ARTMAP (SFAM) which belongs to a special class of neural networks (NNs) and provides a lower training time in comparison to other traditional NNs. The proposed framework is validated with transient current signals from an induction motor under different conditions including bowed rotor, broken rotor bar, eccentricity, faulty bearing, mass unbalance and phase unbalance. Additionally, this paper provides the comparative performance of (i) SFAM and support vector machine (SVM), (ii) SVM in the framework and SVM combined with wavelet transform in previous studies, (iii) the use of FB decomposition and Hilbert transform decomposition. The results show that the proposed diagnosis framework is capable of significantly improving the classification accuracy.

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“…Note that this method relies on computing the inverse Hankel transform numerically. There are several approaches available to do so, which differ on how P 2 should be sampled (see, e.g., [25]). In this paper, the inverse Hankel transforms were evaluated as follows:…”

Section: B Practical Poem Implementationmentioning

confidence: 99%

Defocus Polar rOse Estimation Method (POEM): A Fast Defocus Estimation Method for STEM

Tejada

Dekker

2012

IEEE Trans. Instrum. Meas.

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Abstract-The defocus Polar rOse Estimation Method (POEM) has been introduced recently as an alternative method for defocus estimation in scanning transmission electron microscopy. Its principle of operation is expanded here to include more realistic image models. The details of the expansion are discussed in depth along with the results of new simulation-based performance tests that take into account the effect of measurement noise. The results clearly show that the defocus POEM has the potential to be fast and accurate.

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An algorithm for the numerical evaluation of the Hankel transform

Cited by 44 publications

References 3 publications

Fast phase retrieval algrithm for rotational symmetric DOE designing

Fast phase retrieval algrithm for rotational symmetric DOE designing

An application to transient current signal based induction motor fault diagnosis of Fourier–Bessel expansion and simplified fuzzy ARTMAP

Defocus Polar rOse Estimation Method (POEM): A Fast Defocus Estimation Method for STEM

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