Study of cross-talk of parallel Fabry-Perot sensors in path-matching differential interferometry

Cross-talk in multiplexing parallel Fabry-Perot sensors in a path-matching differential interferometry (PMDI) can be limited by corresponding path-matching read-out systems. Nevertheless, improper design in cavity lengths of Fabry-Perots can result in serious cross-talk. This paper presents a spectrum analysis to design the parallel Fabry-Perot sensors quantitatively without cross-talk. The spectrum analysis used to solve the cross-talks in a multiple parallel Fabry-Perot system is proved to be an efficient tool. To the author's knowledge, cross-talk problems were first investigated in a multiple parallel Fabry-Perot system quantitatively and experimentally. In a spectrum analysis, the spectrum transfer function in a broadband light source and a Fabry-Perot cavity are simulated by a Gaussian distribution spectrum and a low-finesse reflectivity, respectively. After integrating the whole spectrum system with respect to the wave number, the cross-talk terms can be removed by assuming zero. It is concluded that the cavity length differences between two Fabry-Perots should be longer than the coherence length of a broadband light source to diminish cross-talk effects. Experimental results for two parallel Fabry-Perots in PMDI are presented and compared with theoretical predictions. This study shows good agreement between experimental results and theoretical predictions, indicating that spectrum analysis can be applied properly to the design of two- or multiple-parameter sensors.