Twilight sky light collected at 90 degrees from the Sun has coherency matrix

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Polarisation and anisotropic media · Polarisation and anisotropic media

What an Instrument Can See, Ch Polarisation as a statistical object: coherency and Mueller matrices

Problem

Twilight sky light collected at 90 degrees from the Sun has coherency matrix, in an

(x,y)

basis,

\mathbf{J}_{\mathrm{coh}} = \begin{pmatrix} 2 & 0.6 \\ 0.6 & 1\end{pmatrix}\ \text{mW mm}^{-2}.

((a)) Find the eigenvalues of

\mathbf{J}_{\mathrm{coh}}

and use them to compute the degree of polarisation

P

. ((b)) Compute the Stokes parameters

S_0, S_1, S_2, S_3

from the Pauli expansion of

\mathbf{J}_{\mathrm{coh}}

and verify that

P = \sqrt{S_1^2+S_2^2+S_3^2}/S_0

gives the same value.