4 deg is not an optimized number optimized for criteria, but to keep the cavity short width to 0.1m. But the justification of 4deg is found in Section 3 and 4 of T1000276 on Page 4.
Question for Koji: how is the aLIGO OMC angle of incidence of ~4 degrees chosen? Presumably we want it to be as small as possible to minimize astigmatism, and also, we want the geometric layout on the OMC breadboard to be easy to work with, but was there a quantitative metric? Koji points out that the backscatter is also expected to get worse with smaller angles of incidence.