Relativistic kinematics formulation of the polarization effects of Jones-Mueller matrices.

The polarization of a partially coherent, transverse electric, electromagnetic plane wave is commonly represented by a Stokes vector. The similarity between Stokes vectors and four-momentum vectors in special relativity (SR) is studied in depth. The set of Stokes vectors naturally possesses a Euclidean and a Lorentzian geometry. The latter is used to express the polarization-altering properties of Jones-Mueller matrices in a simple and elegant way. In particular, it is shown that the action of a diattenuator on a Stokes vector can be understood in terms of the addition law for velocities from SR. An important simplification in the resulting mathematical expressions further arises if the degree of polarization of a Stokes vector is represented by a hyperbolic polarization angle. This then allows us to demonstrate that the output hyperbolic polarization angle is related to a diattenuator hyperbolic polarization angle and the input hyperbolic polarization angle by the hyperbolic law of cosines holding in a hyperbolic triangle.

Tunable acousto-optic spectral imager for atmospheric composition measurements in the visible spectral domain.

We describe a new spectral imaging instrument using a TeO(2) acousto-optical tunable filter (AOTF) operating in the visible domain (450-900 nm). It allows for fast (~1 second), monochromatic (FWHM ranges from 0.6 nm at 450 nm to 3.5 nm at 800 nm) picture acquisition with good spatial resolution. This instrument was designed as a breadboard of the visible channel of a new satellite-borne atmospheric limb spectral imager, named the Atmospheric Limb Tracker for the Investigation of the Upcoming Stratosphere (ALTIUS), that is currently being developed. We tested its remote sensing capabilities by observing the dense, turbulent plume exhausted by a waste incinerator stack at two wavelengths sensitive to NO(2). An average value of 6.0±0.4×10(17) molecules cm(-2) has been obtained for the NO(2) slant column density within the plume, close to the stack outlet. Although this result was obtained with a rather low accuracy, it demonstrates the potential of spectral imaging by using AOTFs in remote sensing.