Take any three points
F, T and E in the earth's atmosphere, and a point
O'on its surface. Define a system of rectangular coordinates
X1, Y1 and
Z1 with its center at F, with X1 axis drawn towards the Sun. Resolve the direct insolation reaching
F into two plane polarized rays; the one travels to X1 and oscillates in
Z1 direction, which is denoted by (1), the other travels to X1 and oscillates in
Y1, which is denoted by (2). The primary scattered ray generated at
F when (1) encounters one air particle at F, travels in
FT direction and oscillates in a direction normal to it.
FT direction is denoted by
X2 and the direction of oscillation by
Z2 and determined by
X1, Y1, Z1 and the positions of F and
T. This scattered ray is denoted by
E1.
The primary scattered ray generated at
F when (2) encounters one air particle at F, travels in FT direction and oscillates in a direction normal to FT. This direction is denoted by Z2' and determined by
X1, Y1, Z1, F, and T. This scattered ray is denoted by
E1'.
E1 travels in FT direction and is scattered at T when it encounters one air particle there. This secondary scattered ray is denoted by E2 and its direction of oscillation by
Z3. In the same way, the secondary scattered ray which is caused by the scattering of E1' at
T, is denoted by E2' and its direction of oscillation by
Z3'. Furthermore,
E2 and
E2' are scattered at E and the resulting tertiary scattered rays E3, reach O'.
If ω1 ω1', ω2, ω2', ω3 and ω3' are respectively the angle between FT and
Z1, FT and
Y1, TE and
Z2,
TE and
Z2',
EO' and
Z3, EO' and
Z3', then the phase function in the tertiary scattering is expressed by Π3n=1sin2ωn+3Πn=1sin2ωn'.
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