Multiple-beam grating interferometry and its general Airy formulae

Abstract

Multiple-beam grating interferometry, a hybrid of the multiple-beam interference and grating interferometry, is introduced and conducted by building a Littrow-type cavity with a diffraction grating. Based on multi-beam interference and grating interferometry, mathematical derivation reveals that the fringes of the multi-beam grating interferometry follow a general form of Airy formulae, while the period of which is additively determined by phases from grating pitches and laser wavelength. Two crucial parameters, peak transmission and finesse describing brightness and sharpness of fringes, are defined and investigated, whose results reveal that fringe shape of multiple-beam grating interferometry is determined by amplitude coefficients of two surfaces forming the cavity and could be explained by multiple beam interference with intensity loss. Consistency of simulation and experiment results are proved and analyzed. Multiple-beam grating interferometry is promising for in-plane and multi-dimensional displacement measurements and might inspire novel enhancement for sensors and instruments based on Fabry-Pérot interferometry.