  The sensitivity of high-precision interferometric measurements can be limited
by Brownian noise within dielectric mirror coatings. This occurs, for instance,
in the optical resonators of gravitational wave detectors where the noise can
be reduced by increasing the laser beam size. However, the stability of the
resonator and its optical performance often impose a limit on the maximally
feasible beam size. In this article we describe the optical design of a 10\,m
Fabry-P\'erot Michelson interferometer with tunable stability. Our design will
allow us to carry out initial commissioning with arm cavities of high
stability, while afterwards the arm cavity length can be increased stepwise
towards the final, marginally stable configuration. Requiring only minimal
hardware changes, with respect to a comparable "static" layout, the proposed
technique will not only enable us to explore the stability limits of an optical
resonator with realistic mirrors exhibiting inevitable surface imperfections,
but also the opportunity to measure coating Brownian noise at frequencies as
low as a few hundred Hertz. A detailed optical design of the tunable
interferometer is presented and requirements for the optical elements are
derived from robustness evaluations.
