Rayleigh ratio

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The Rayleigh ratio is a quantity used to characterize the scattered intensity as a function of scattering angle q, and is defined as

R( \theta ) = \frac{I_\theta r^2}{I f V}

where I is the intensity of the incident radiation, Iθ is the total intensity of scattered radiation observed at an angle q and a distance r from the point of scattering and V is the scattering volume. The factor f is introduced to compensate for polarization phenomena, and is dependent of the type of radiation used as follows:

1. For light scattering, f depends on the polarization of the incident beam, and is f = 1 for vertically polarized light, f = cos2(q) for horizontally polarized light and f = 0.5(1 + cos2(q)) for unpolarized light.

2. For small-angle neutron scattering, f = 1.

3. For small-angle X-ray scattering, f > > 1, if q < ca. 5°.

Notes:

1. The dimension of R(q) is an inverse length.

2. In small-angle neutron scattering the term cross-section is frequently used in place of R(q).

3. IUPAC also recommends the symbol Rq.

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