Summary:

I did some more calculations based on our discussions at the meeting yesterday. Posting preliminary results here for comments.

Details:

Attachment #1 - Schematic illustration for the scattering scenarios. For all three scenarios, we would like for the scattered field to be lower than unsqueezed vacuum (safety factor to be debated).

Attachment #2 - Requirements on a fraction  of the counter-propagating resonant mode of the OMC scattering back into the antisymmetric port, as a function of RIN and phase noise on this field (y-axis) and amount of field (depends on the amount of contrast defect light which can become resonant in the counter propagating mode). I don't encode any frequency dependence here.

Attachment #3 - Requirements on the direct scatter from the arm cavity resonant field (assumed to dominate any contribution from the PRC) onto the OMC DCPDs, for some assumed phase noise (y-axis) and fraction of the field that makes it onto the OMC DCPDs. This is a pretty stringent requirement. But the probability is low (it is the product of three presumably small numbers, (i) probablity of the beam scattering out of the TEM00 mode, (ii) BRDF of the scattering surface, (iii) probability of scattering back towards the DCPDs), so maybe feasible? I didn't model any RIN on this field, which would be an additional noise term to contend with. The range of the y-axis was chosen because I think these are reasonable amplitudes for chamber wall  / other scattering surface motion at acoustic frequencies.