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Applied Optics

Applied Optics


  • Vol. 11, Iss. 9 — Sep. 1, 1972
  • pp: 1919–1923

Computation of Bessel Functions in Light Scattering Studies

William D. Ross  »View Author Affiliations

Applied Optics, Vol. 11, Issue 9, pp. 1919-1923 (1972)

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Computations of light scattering require finding Bessel functions of a series of orders. These are found most easily by recurrence, but excessive rounding errors may accumulate. Satisfactory procedures for cylinder and sphere functions are described. If argument z is real, find Yn(z) by recurrence to high orders. From two high orders of Yn(z) estimate Jn(z). Use backward recurrence to maximum Jn(z). Correct by forward recurrence to maximum. If z is complex, estimate high orders of Jn(z) without Yn(z) and use backward recurrence.

© 1972 Optical Society of America

Original Manuscript: February 8, 1972
Published: September 1, 1972

William D. Ross, "Computation of Bessel Functions in Light Scattering Studies," Appl. Opt. 11, 1919-1923 (1972)

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  1. F. W. J. Olver, H. A. Antosiewicz, in Handbook of Mathematical Functions, M. Abramowitz, I. A. Stegun, Eds., Applied Mathematics Series 55 (U.S. Govt. Printing Office, Washington, D.C., 1964), Chaps. 9, 10.
  2. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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