The conventional Zernike polynomial fit of circular aperture interferograms is reviewed and a more quantitative and statistical analysis is added. Some conventional questions such as the required number of polynomials, sampling requirements, and how to determine the optimum references surface are answered. Then, the analysis is applied to the polynomial fit of noncircular aperture interferograms and axicon interferograms. The problems and limitations of using Zernike polynomials are presented. A method of obtaining the surface figure error information from several smaller subaperture interferograms is analyzed. The limitations of the analysis for testing a large flat, a large parabola, or an aspheric surface are presented. The analysis is compared with the local connection method using overlapped wavefront information. Finally, the subaperture interferogram analysis is used to average several interferograms and to analyze lateral shearing interferograms.

Structural organization refers to the particular ordering of scatterers. Probing structural organization by imaging polarized spectral scatter provides insight into the composition of a medium, and can aid in remote sensing, the identification of tissue pathologies, and material characterization and differentiation. The vector nature of polarized light enables it to interact with optical anisotropies within a medium, while the spectral aspect of polarization is sensitive to small-scale structure. However, many polarization studies have limitations, as they provide qualitative image analysis, incomplete anisotropy information, or both. The ability to image the effects of anisotropy and small-scale structure at multiple wavelengths is key for parameterizing structural organization. The Stokes/Mueller formalism is a framework that quantifies a medium's complete spectral polarization response, and allows for the parameterization of structural organization. Additionally, advances in liquid crystal (LC) technology have resulted in new polarimetric devices. These computer-controlled devices impart spectral polarization effects on the millisecond timescale with no mechanically moving hardware, providing the ability for making rapid polarimetric measurements. This dissertation describes a methodology for revealing structural organization by exploiting the Stokes/Mueller formalism and by utilizing measurements from a spectral imaging polarimeter constructed from variable retardance LC devices, such as liquid crystal variable retarders (LCVRs) and a liquid crystal tunable filter (LCTF). The methodology includes developing the system, the Stokes/Mueller model, and all of the procedures, calibrations, and data interpretation. Developing the system also consists of component and system calibration, a system sensitivity and performance analysis, and finally test measurements for system validation. The final validation measurement is made on a mineral sample for inferring structural organization.

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