Multiple-order staircase etalon spectroscopy

Traditional Fabry-Perot (FP) spectroscopy is bandwidth limited to avoid mixing signals from different transmission orders of the interferometer. Unlike Fourier transformation, the extraction of spectra from multiple-order interferograms resulting from multiplexed optical signals is in general an ill-posed problem. Using a Fourier transform approach, we derive a generalized Nyquist limit appropriate to signal recovery from FP interferograms. This result is used to derive a set of design rules giving the usable wavelength range and spectral resolution of FP interferometers or etalon arrays given a set of accessible physical parameters. Numerical simulations verify the utility of these design rules for moderate resolution spectroscopy with bandwidths limited by the detector spectral response. Stable and accurate spectral recovery over more than one octave is accomplished by simple matrix multiplication of the interferogram. In analogy to recently developed single-order micro-etalon arrays (Proc. of SPIE v.8266, no. 82660Q), we introduce Multiple-Order Staircase Etalon Spectroscopy (MOSES), in which micro-arrays of multiple order etalons can be bonded to or co-fabricated with a sensor array. MOSES enables broader bandwidth multispectral and hyperspectral instruments than single-order etalon arrays while keeping a physical footprint insignificantly different from that of the detection array.