Scattering of unpolarized light

Figure 8.10 Phase function for scattering of unpolarized light by an infinite cylinder. The arrows indicate minima according to diffraction theory.

Figure 13.4 Scattering of unpolarized light by spheres. The top curves show the angular distribution of the scattered light and the bottom curves its degree of polarization. From Hansen and Travis (1974) copyright 1974 by D. Rcidel Publishing Company. Dordrecht. Holland.

Figure 13.7 Scattering of unpolarized light incident parallel (-) and oblique (—) to the...

Banderman, L. W., and J. C. Kemp, 1973. Circular polarization by single scattering of unpolarized light from loss-less non-spherical particles, Mon. Not. R. Astron. Soc., 162, 367-377. 

The scattering of unpolarized light can be handled by considering the incident beam to consist of two components of equal intensity, one polarized along the z-axis and the other along the y-axis in the preceding figures. We then get Equation 12-27 ... 

The scattering of unpolarized light by air molecules is generally described by Rayleigh theory. In this case, the scattering coefficient is expressed as a function of wavelength A by (see e.g., Penndorf, 1957)... 

The expression (V.39) for turbidity does not contain any information on polarization of light, and hence it can be applied to the scattering of unpolarized light as well. 

Having obtained an expression for the scattering of polarized light from a single oscillator we can now consider unpolarized light, then consider a dilute collection of such oscillators, as in a gas, and finally get to where we re going liquids and solutions. 

A beam of unpolarized light of intensity I is equivalent to two plane polarized beams, each of intensity I/2, polarized in mutually perpendicular directions, and incoherent in phase. Therefore, for a vertically polarized incident beam of unit intensity, the scattered intensity at 90° in the horizontal plane is twice as great as for an unpolarized incident beam of the same total intensity for in the latter case, only half the total intensity contributes to scattering in the horizontal plane at 90°. (For further discussion see Sinclair (1947).) For a system of small isotropic particles, there is of course no horizontal component in this direction as will be seen later, this is true also for scattering from iso-... 

Figure 9-7. A plot of the scattering of unpolarized incident light (I) small particles, (II) dilute solution of monodisperse spheres with diameter Xo/2.

Figure 4.4.18. General set-up of a scattering experiment kj, k, - wave vectors of the incident and the scattered plane waves, q - scattering (or wave) vector, D- detector, S - sample, 0 - scattering angle from the transmitted beam, I, - incident intensity of unpolarized light, r - the distance between sample and detector.

Since we are mostly interested in scattering unpolarised X-ray radiation we should average Eq. 5.7 over all directions of vector E perpendicular to the direction of the wavevector of the incident wave k(, i.e. around the z-axis. Then we find the differential cross-section of one-electron scattering in unpolarized light ... 

In general, the scattering intensity of unpolarized light by a single spherical particle... 

Note that this also involves the assumption of isotropic molecules, which have the same polarizability in all directions. Unpolarized light consists of equal amounts of vertical and horizontal polarization, so the fraction of light scattered in the unpolarized (subscript u) case is given by... 

Figure 10.6 Two-dimensional representation of i and i (broken lines) and their resultant ifotai (solid line) for scattering by a molecule situated at the origin and illuminated by unpolarized light along the x axis. The intensity in any direction is proportional to the length of the radius vector at that angle. (Reprinted from Ref, 2, p. 168.)...

If unpolarized light of irradiance /, is incident on one or more particles, the Stokes parameters of the scattered light are... 

Equation (5.6) applies to incident unpolarized light it is important to remember that the angular distribution of the scattered light depends on the polarization of the incident light ... 

Figure 5.2 Degree of polarization of light scattered by a sphere small compared with the wavelength for incident unpolarized light.

Extinction is easy to measure in principle but may be difficult in practice, especially for large particles where it becomes difficult to discriminate between incident and forward-scattered light. Spheres and ensembles of randomly oriented particles do not linearly polarize unpolarized light upon transmission. But single elongated particles or oriented ensembles of such particles can polarize unpolarized light by differential extinction. 

Other quantities commonly measured are the degree of linear polarization P of the scattered light for incident unpolarized light... 

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