Needle-scattering analyzer moments
= Needle-scattering analyzer moments
For isotropically oriented independent needles illuminated with $z$ <polarization> and viewed along $y$, the amplitudes through $x$ and $z$ analysers are proportional to $u_xu_z$ and $u_z^2$. The moments $\langle u_x^2u_z^2\rangle=1/15$ and $\langle u_z^4\rangle=1/5$ give intensity ratio $1:3$.