Here is a note about choosing finesse of the new cavity. I'll try to incorporate all the change in the system due to the change of the finesse.

1) Coating thickness(thermal noise level):

     For high reflectivity, the finesse is ~ pi*sqrt(1-T)/T, where T is the transmission (300ppm). A further simplification give         Finesse ~ pi/T. So, with thicker coating, lower transmission, higher Finesse. ( add plot of finesse vs coating thickness). With thicker coating, we also have higher Brownian noise in the coating.

2) Gain in frequency discriminator for PDH lock (shot noise and electronic noise)

    With higher finesse the gain in the PDH signal is increased. We can better suppress laser noise, and noise in RFPD electronics and shot noise. With the servo we have, we can suppress laser noise down to thermal noise already. However, we can improve shot noise and electronic noise if we have higher finesse.