For forward scattering (i.e. for scattering angles close to 0°), the dominant mechanism is generally that of diffraction, which can be modelled by the following equations:
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| Fig. 1 Diffraction theory calculations for r = 100,
10 and 1 µm
lambda = 0.65 µm, n = 1.33257 |
Fig. 1 compares the scattered intensity calculated using diffraction
theory for r = 100, 10 and 1 µm. The diffraction pattern consists
of maxima and minima which are defined by the 1st order Bessel function
- as indicated in Table 1 below:
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x = 2 Pi r / lambda |
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| Fig. 2 Calculations of scattering using Mie theory
and diffraction for r = 100 µm
lambda = 0.65 µm, n = 1.33257, perpendicular polarisation |
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| Fig. 3 Calculations of scattering using Mie theory
and diffraction for r = 10 µm
lambda = 0.65 µm, n = 1.33257, perpendicular polarisation |
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| Fig. 4 Calculations of scattering using Mie theory
and diffraction for r = 1 µm
lambda = 0.65 µm, n = 1.33257, perpendicular polarisation |
Figs. 2 - 4 compare the results of Mie theory calculations with the
diffraction pattern. Note that the diffraction model is NOT dependent
on the refractive index of the sphere, whereas Mie theory takes account
of other scattering mechanisms (such as direct transmission through the
sphere) which are dependent on refractive index. In practice, the
diffraction model is reasonably accurate for forward scattering for large
drops (e.g. x = 1000), at least for the first few maxima and minima.
However, it becomes much less accurate for smaller drops. It must
be emphasised that the diffraction model is appropriate only for calculations
of forward scattering.
Page updated on 14 May 2003
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