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.).

**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.

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.

**Quantitative sectioning for structured illumination microscopy**

Structured illumination microscopy has long been used as an alternative to confocal microscopy to obtain sectioned images of thick tissue samples. Although it was long regarded as a nonquantitative visualization method, this work demonstrated how to make it quantitative, and quantitatively compared its results with confocal measurements.

**Calculating the statistical properties of Stokes polarization measurements**

Polarimeters are simple enough devices that the statistical properties of their measurements can be thoroughly understood. Using these statistical properties, system designers can optimize the measurement system for their application.