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Previous pages have examined the choice of parameters for Gaussian beam calculations using Mie theory and the Debye series. However, in practice, other difficulties often arise with calculations for large spheres (e.g. r >= 1000 μm) or for very narrow Gaussian beams.

One problem is that the numerical values of intermediate results can exceed the program's permitted range: for example, as MiePlot uses double precision for most of its variables, the absolute value of any variable must be less than about 10

Various steps can be taken to avoid overflow problems: for example, consider evaluation of a simple equation such as

Other types of overflow are much more difficult to avoid in, for example, evaluation of the following equation:

Reproduced by kind permission of J. A. Lock ©

Note that this equation involves:

- Exponents of
*j*, (*j*-*p*) and*p* - Factorials of (
*j*-*p*) and*p*

Note that

N.B. The Mie calculations used a fixed value of

Fig. 1 compares Mie calculations with

N.B. In one case, the value of J

Special measures in MiePlot have been taken to handle variables that exceed the double precision limit of 10

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