Snapshot spectropolarimetry

Abstract

Channeled spectropolarimetry is a novel method of measuring the spectral dependence of the polarization state of light. Amplitude modulation is employed to encode all four Stokes component spectra into a single optical power spectrum. The encoding is performed with a simple arrangement of two thick birefringent retarders and a linear analyzer. No moving parts are required, and the system is able to acquire its data in a single detector array integration time. We report the results of an in-depth study of channeled spectropolarimetry. The mathematics of the amplitude modulation analogy are explored, providing a basic design procedure. The system's spectral resolution is described in terms of the space bandwidth product. The technique is then analyzed in the general context of linear operator theory, using both analytic and computational approaches to the singular value decomposition and pseudoinversion of the system's operator. This analysis highlights the importance of the choice of object space in constraining linear reconstructions of data from under-determined systems, and provides the underpinnings of the calibration and reconstruction techniques for a hardware prototype. Calibration of the prototype is approached as experimental estimation of the system's operator. Our basic method of reconstruction involves pseudoinversion of the operator while constraining object space to a truncated Fourier basis. Apodization is helpful in reducing the ringing of reconstructions of spectra which extend beyond the edges of the system's spectral range. Experimental results are presented, including comparisons between measurements taken with the channeled spectropolarimeter and a reference rotating compensator, fixed analyzer instrument. We have used measurements of the effects of stress birefringence on light propagated through material subject to time-varying stress to demonstrate time-resolved snapshot spectropolarimetry. Continuing efforts include the combination of channeled spectropolarimetry with computed tomography imaging spectrometry to realize a snapshot imaging spectropolarimeter.