Analytic-domain ray tracing gives the equation describing the locations and angles of all rays passing through a system as a function of the input ray parameters (field angle and pupil position) and the system design parameters (lens radii of curvature, lens thickness, glass refractive index, distance to the image plane, etc.).
Channeled spectropolarimetry (CHSP) is a technique for obtaining spectrally-resolved polarization data in a snapshot. By making use of the wavelength-dependence of thick retarders, a CHSP encodes the polarization information into modulation frequencies in the spectrum.
Snapshot image slicing spectrometry
Image slicing spectrometry is a method of separating different 2D “slices” of the three-dimensional (x,y,λ) datacube so that they can be detected on a 2D sensor array. The slicing mirror is a precision faceted mirror containing hundreds of facets tilted at various 2D angles, sending the reflected light along different paths. A lenslet array is used to build a different imaging spectrometer for each of the reflected paths, allowing for hundreds of slices to be detected simultaneously. The result is a fast system with extremely high light throughput.
Gas cloud imaging is a technique of measuring the infrared spectral image of a scene, analyzing it for the signature of infrared-absorbing gases, and quantifying the amount of any gases found. With continuous video data, the camera can also estimate the leak rate of the gas.
Thermal infrared imaging polarimetry
Polarimetric imaging in the thermal infrared shows behaviors that are not commonly considered in the visual spectrum, such as the tradeoff between emission and reflection polarization, the generalized Snell law for refraction with absorbing media, the mixed Poynting vector (sometimes producing surface transmittances larger than 2000%), and more.
By processing the video data stream from a single infrared camera to enhance small-amplitude short-time temperature changes, we find that the scene becomes covered with striations that move along with the wind flow according to the speed of wind flow along the imaged surfaces.
A physical model for geometric phase
We show that the origin of geometric phase lies simply in the superposition of two or more waves. While this is quite simple in 1D, the behavior becomes surprisingly complex in 2D, but we show that the geometric phase can easily be calculated using the Jones calculus. Doing so shows that all of the mathematical abstractions that have gone into prior work on geometric phase — using differential geometry, high-dimensional fiber bundles, or the solid angle in an abstract spherical space — are distractions. While they can be used to derive the correct answer, they obscure the underlying wave behavior, and have led to mistakes in the existing theory.
Calculating the statistical properties of Stokes polarization measurements
While the Stokes parameters can often be approximated as Gaussian-distributed random variables to model their noise, the normalized Stokes parameters have a “Gaussian ratio distribution” with unusual properties, such as not having a mean value and having infinite variance. Luckily, these are only formal properties, and we show that it is straightforward to truncate the formal distribution in order to give it well-behaved mean and variance, with negligible effect on the overall distribution model.
Measurements of the rainbow outside the visible spectral range are surprisingly rare. If our eyes could see over this entire range, with enough UV and IR light we would see a rainbow almost 14 degrees in width — seven times wider than the 1.9 degree width that we see in the visible spectrum. In this project. we measured an artificial rainbow with an imaging spectrometer from 354nm to 1650nm wavelengths, and explain the challenges of capturing this data over such a wide spectral range. These include the first-ever images of the rainbow captured in the SWIR spectral range.