Reconfigurable freeform optical systems enable greatly enhanced imaging and focusing performance within nonsymmetric, compact, and ergonomic form factors. In this paper, several improvements are presented for the design, test, and data analysis with these systems. Specific improvements include definition of a modal G and C vector basis set based on Chebyshev polynomials for the design and analysis of non-circular optical systems. This framework is then incorporated into a parametric optimization process and tested with the Tomographic Ionized-carbon Mapping Experiment (TIME), a reconfigurable optical system. Beyond design, a reconfigurable deflectometry system enhances metrology to measure a fast, f/1.26 convex optic as well as an Alvarez lens. Further improvements in an infrared deflectometry system show accuracy around λ/10 of the notoriously difficult low-order power. Working together, the mathematical vector polynomial set, the programmatic optical design approach, and various deflectometry-based optical testing technologies enable more flexible and optimal utilization of freeform optical components and design configurations.