Birefringence interferometers for ultra-high-speed FT spectrometry and hyperspectral imaging: I. Dynamic model of the resonant photoelastic modulator

We discuss in this paper some of the technical developments that make possible the second generation of photoelastic modulator (PEM) based Fourier transform (FT) spectrometers. These instruments aim to achieve spectral resolutions as high as 10 cm−1 while preserving the speed (typically 6 × 104 to 1.2 × 105 interferograms per second) and spectral range (vacuum UV to near-IR with fused silica optics and near-IR to 12 μm in the mid-IR with ZnSe) characteristic of first-generation instruments.We begin by describing a simple model of the dynamic properties of resonant PEMs driven at high oscillation amplitudes, where thermal effects become significant sources of nonlinear behavior and potential instability. This model provides a wealth of insights into PEM behavior and indeed explains observed instabilities. It also provides simple and effective solutions for designing stable and efficient controllers and drivers for the high-amplitude régime. Furthermore, the model suggests relatively simple ways of adding and implementing new control capabilities such as real-time tuning and the tracking of externally supplied clock signals. We illustrate these new capabilities with a discussion of some of the drivers and controllers developed in our lab.