I was wondering whether a design using total internal reflection within 90-degree prisms at each end of the arms would be feasible for an instrument of this precision. I assume it is not, and I have a few guesses as to why not: 1) the Fabry-Perot resonator arrangement of mirrors in each arm creates a much higher intensity between the mirrors, and this is important for getting a measurable signal out; 2) the resonator rejects a lot of noise; 3) there's no good way to get power into, and a signal out of, an arrangement of prisms; 4) an arrangement of prisms puts too much glass in the path. I would be interested in hearing what the actual answer is.

Update: there's a lot more information here (though it is about the Advanced LIGO concept), but I don't think it addresses the failings of a prism arrangement directly:

https://iopscience.iop.org/article/10.1088/0264-9381/34/1/01...