Our desired accumulated Gouy phase shift for a full round trip of the LFC is 120 degrees. I used this target to find the length of the LFC using the code in the Laser Filter Cavity Repo. To run the code run the test in T_Gouy_phase.py. Also included in this code is the finesse3 calculation for the LFC. 

The first plot "zero2seven_gouy_phase.pdf" shows the accumulated Gouy phase for different cavities of different lengths. They all have the same ROC on the M3 optic of 3 m. all other mirrors are flat. 

The second plot shows the Gouy phase accumulated for the desired cavity as well as its beam profile.