\section{Introduction} \label{sec:introduction}

The optical interferometer is a scientific instrument with many applications, such as in the detection of gravitational waves~\cite{abramovici1992ligo, abbott2016gw150914}, quantum optical experiments~\cite{rempe1992measurement, vahala2003optical, reiserer2015cavity}, and the development of various sensors~\cite{yoshino1982fiber}. 
The operation of optical interferometer requires a good amount of noise isolation to achieve position stability -- for a Fabry-Perot interferometer with finesse $\mathcal{F}$, the mirror spacing needs to be stabilized to a small fraction of $\lambda/2\mathcal{F}$.
Large interferometers such as LIGO, with separate mounting of mirrors, use a combination of passive and active stabilization on stacked pendulum systems~\cite{giaime1996passive, aasi2015advanced}. 
On the other hand, small cavities used in quantum optics experiments are typically operated in a low vibration environment; they are also usually constructed with rigid structures~\cite{notcutt2006contribution, kessler2012sub, gallego2016high}, mounted in a symmetric configuration~\cite{notcutt2005simple, webster2007vibration} with high bandwidth piezos~\cite{briles2010simple, janitz2017high}, or controlled with additional gain filters~\cite{ryou2017active, okada2020extending}.

Some cavity systems~\cite{greuter2014small, nguyen2018operating} may require a relatively large movement (more than $10~\mathrm{\mu m}$) between the two mirrors in three directions. In these systems, mechanical noises can couple easily to the cavity system, due to (a) the number of components necessary to actuate three directional movements, which precludes a rigid structure, and (b) the necessity for piezos with large movement range, which can lower the resonance frequency~\cite{yong2012invited}. 
Large movement ranges with a piezo can be achieved by either using a slip-stick mechanism~\cite{pohl1987dynamic, renner1990vertical} or a flexure-based mechanical amplification~\cite{scire1978piezodriven, yang1996design}.
Stacked translation stages based on slip-stick mechanism have been used to align a microcavity in three directions, with a relatively low mechanical noise~\cite{greuter2014small}. However, it might not be as compact or cost-effective as flexure-based stages which can implement three directional movement with a single stage.
These flexural stages are typically used in scanning probe microscopy (SPM) experiments~\cite{yong2012invited}.
However, they have a relatively low resonance frequency (typically less than 1~kHz), and hence couple easily to acoustic noises. This limits their scanning speed and movement resolution~\cite{scire1978piezodriven, zhu2015novel}, which can be improved with well-designed control systems~\cite{dong2008robust, fleming2009nanopositioning, fleming2009new, ryou2017active}, improved vibration isolation system~\cite{lee2017control, ryaboy2005optical}, counter balancing~\cite{ando2001high, kodera2005active}, mechanical rearrangement~\cite{kim2011design}, symmetrical flexure arrangement~\cite{yong2008design}, or adding a clay damper~\cite{carrasco2008cutting}. 

We propose an alternative method to reduce mechanical noises of the flexural stages in optical interferometer systems by using friction dampers made from thin pieces of aluminum. Such friction-based damping elements are also used to damp resonant stresses in gas-turbine blades~\cite{griffin1980, menq1986influence} and to dissipate earthquake energy from building structures~\cite{popov1995developments, loo2014new}.

First, we give a brief description of the cavity used in our study and describe the method used to characterize the noise. 
Next, we introduce the friction dampers and briefly discuss the advantages of using them. 
We demonstrate that the friction dampers work to reduce the mechanical noises in the stick regime, while also allowing for large movements between the mirrors via the slip motion. 
Furthermore, we quantify the effect of different friction damper masses to the DC gain of the translation stage and the overall mechanical noise. 
Due to the relative ease of application and its compactness, this method can potentially be applied to any position-sensitive systems requiring further noise isolation, particularly in interferometric system with less rigid structures, in atomic-scale microscopy, or in compact systems with no separate vibration isolation.