Related Experiment Video
Updated: Nov 14, 2025

Quantitative Optical Microscopy: Measurement of Cellular Biophysical Features with a Standard Optical Microscope
Published on: April 7, 2014
Improved algorithm for the quasi-discrete Hankel transform
Abstract:
An improved algorithm for numerical evaluation of the Hankel transform is developed. The algorithm originally proposed by Yu et al. [Opt. Lett.23, 409 (1998)OPLEDP0146-959210.1364/OL.23.000409] uses the quadrature in which the nodes are zeros of the Bessel function. In this work, it is shown that the accuracy of the algorithm can be significantly improved, with virtually no increase in computation time, via two steps. One is to halve the weight of the last node, and the other is to extrapolate a function tail using the modified Bessel function of the second kind, which gives the analytical estimation of the integral remainder.
Related Concept Videos
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
Inverse z-Transform by Partial Fraction Expansion
To begin the process, the poles of the function are identified and the function is...
Discrete-time Fourier transform
One of the notable...
Difference Equation Solution using z-Transform
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
Reconstruction of Signal using Interpolation
Downsampling
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...

