An improved algorithm for the numerical computation of the Hankel transform of nth order is presented and is tested with some well-known functions.

© 2004 Optical Society of America

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  1. J. Markham, J.-A. Conchello, “Numerical evaluation of Hankel transforms for oscillating functions,” J. Opt. Soc. Am. A 20, 621–630 (2003).
  2. J. A. Ferrari, “Fast Hankel transform of order zero,” J. Opt. Soc. Am. A 12, 1812–1813 (1995).
  3. J. A. Ferrari, D. Perciante, A. Dubra, “Fast Hankel transform of nth order,” J. Opt. Soc. Am. A 16, 2581–2582 (1999).

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Figures (2)

Fig. 1
Fig. 1

2D rectangular grid with equally spaced points.

Fig. 2
Fig. 2

2D grid obtained by interception of the lines xl=lh with the circles rm=mh.

Equations (4)

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Φn(x)=2(-i)n0f((x2+y2)1/2)cos[n θ(x, y)]dy,
Φn(xl)=Φn(lh)=(-i)nhm=0N{f(h(l2+m2)1/2)cos[n θ(l, m)]+f(h(l2+(m+1)2)1/2)cos[n θ(l, m+1)]}.
Φn(xl)=Φn(lh)=(-i)nm=lN{f(mh)cos[n θ(l, m)]+f((m+1)h)cos[n θ(l, m+1)]}×(yl,m+1-yl,m),