Hi Akutsu-san,
Related to your discussion of BS thing, I remembered the what was considered about polarization in the in-air GPT design.
When we designed it, we assumed that polarization of light coming to TMS was purely orthogonal to the interferometer plane, so called S-pol.
So the BS for IR is selected to be one for S-pol, 10Q20HBS.33S, Newport (https://www.newport.com/p/10Q20HBS.33S).
However, our assumption was wrong due to birefringence of the ITMs (Has it not been concluded yet? I'm not sure).
I cannot find any specification of the BS (10Q20HBS.33S) for P-pol...
The BS could be a problem as you mentioned (also for TMSX).