Polarization of light for a fast moving observer

Question

For a fast moving observer the frequency of light becomes shifted due to the (relativistic) Doppler effect. But what about the polarization of the light? Could it be, that e.g. circular polarized light becomes elliptically polarized light for a fast moving observer due to Lorentz contraction?

Answer 1

It looks like the answer is negative: https://books.google.com/books?id=7Q13lMNYk6kC&pg=PA171&lpg=PA171&dq=light+polarization+under+Lorentz+transform&source=bl&ots=nCMsTa9-gN&sig=Z9owCnli8VV_3qTX6BjJt_2S7QQ&hl=en&sa=X&ei=5987VeTcAcShNpq1gdgJ&ved=0CDwQ6AEwBA#v=onepage&q=light%20polarization%20under%20Lorentz%20transform&f=false (Classical Electromagnetism in a Nutshell, By Anupam Kumar Garg, p. 171) - degree of circular polarization is invariant under Lorentz transformations.