Design of a folded, multi-pass Fabry–Perot cavity for displacement metrology

We present a folded, multi-pass cavity design for displacement measuring Fabry-Perot interferometry. The cavity length is designed to be one-quarter of the physical length needed for a typical Fabry-Perot interferometer by using a quarter-wave plate and a retroreflector. This enhances the displacement sensitivity by a factor of four, allowing for higher resolution in viewing the effects caused by mechanical motions, refractive index changes and frequency fluctuations from the laser source. Furthermore, the geometrical error motions are minimized by using a retroreflector due to its tip-tilt insensitivity. In this note, a theoretical analysis of the folded, multi-pass Fabry-Perot cavity is described and analyzed with Jones matrices in ideal and non-ideal designs.