Find the stokes parameters

Question

1) Find the Stokes parameters (I, Q, U, V) the following elliptically polarized waves:

a) E = (hˆ+ vˆ)e^-j(koz+π/6)

b) E = (hˆ+ jvˆ)e^-jkoz

2) The radiative transport equation is written as follows:

a) Give the physical meaning of each term on the right hand side of the equation.

dB_f(r_,sˆ)/ds = - ρσ_tB_f(r_,sˆ) + ρσ_t/4π ∫_4π P(sˆ, sˆ')B_f(r_,sˆ)dΩ + ρσ_aB_bb(r_,sˆ)

b) Express B_bb(r_,sˆ) in terms of Plank's Radiation Law. Show how this expression simplifies when the frequency is low enough.

c) Express the transport equation in part a) in terms of the apparent temperature, TAP (again assume the frequency is low).

3) A radiometer views a half space of water particles having extinction coefficient, k_a, and a temperture profile

T(z) = T_se^αz + T_g (1 -e^αz), z < 0

Here, T_s, T_g and α are constants

The radiometer observes the half space at an angle of θ_o with repect to the normal as is show in figure. Find the apparent temperature at the radiometer. The albedo of the scatters is small, so neglect scattering effects. There are non particles in the region z>0 and as a result, T_AP(z,θ_o), is constant for z>0