The unmodelled noise limiting Virgo in the bucket is still unexplained despite several physical mechanisms have been proposed and some ruled out [see wiki].

A possible candidate for mystery noise may be the coupling of the polarization fluctuations of the beam generated in the central interferometer with the (difference of) birefringence of the compensation plates.

The reason for this is that the compensation plates are mounted in a different way with respect to the mirrors and can have stress generated either by the supports on which they are placed or by the lateral screws by which they are tightened.

It is also doubtful whether the machining of the compensation plate, starting from the bulk, has left inner mechanical stress.

Indeed, as regards the compensation plates (to our knowledge), a constraint on birefringence apparently was not requested before the assembly  (see for example VIR-0075A-15, VIR-0153A-16, VIR-0380A-14).

The actual amount of residual stress should be simulated from the mounting conditions to evaluate the birefringence. In the bulk of the mirrors, the required value was of the order of dn < 10-7. This limit was reached (and also well surpassed) by the bulks. In the case of a mirror subjected to stress, the value can be higher, even ten times or more, so even if the compensation plates are thinner than the mirror bulk, their effect could be dominant. In this way the difference in polarization angle of the two plates could be up to Psi_0 = 10-2 rad. (Notice that this gives a contribution to contrast defect of 10-4 which is compatible with the requirement made on the mirror bulk)

Another point to evaluate is the birefringence fluctuations for a mirror subjected to stress. In literature, this is very difficult to find (at least for us) and what we found are polarization fluctuations of the order of 10-9 rad/\sqrt(Hz) with a slope of approximately 1\/sqrt(f), but on very different optical substrates. Recent measurements in Virgo give the upper limit dpsi < 10-9 rad/\sqrt(Hz) in the fluctuation of beam polarization in B5 [see wiki]

The way this noise enters the sensitivity is better evaluated not by considering the phase noise of the recombining beams but the power noise at the dark port. Such a calculation shows that this noise depends on the optical gain.

The noise can be calculated as \tilde(P)/Prc = (1/4)Psi_0 \tilde(Psi).  where Psi_0  is the angle at the beam splitter recombination, Prc the recycled power, and \tilde(Psi) is its fluctuation.

If we assume as value of Psi_0 and \tilde(Psi) the upper values given above, the resulting noise is compatible with the present sensitivity.

Better investigations are needed.