Characterization of multi-element lenses. (a) Computational ray-trace model for correction of internal surface curvatures. Blue lines represent simulated chief rays and red lines show the corresponding surface normal at the measured external lens surface (S1). S2 Distorted denotes the internal surface segmented from LCI measurements. Each chief ray is refracted at S1 by the phase index and propagated by its respective distance through the lens thickness, which is calculated by scaling the corresponding optical distance between S1 and S2 Distorted by the group index. The resulting three-dimensional propagated chief ray coordinates are used to remap S2 Distorted to a distortion-corrected internal surface (S2 Corrected). (b) Percent deviation between radius of curvature measured externally and their respective manufacturer specification (Rair:spec). Inset shows a magnified view of the cluster of points between ±100 mm specification curvature. (c) Percent deviation of internally measured radius of curvature, through either 1 or 2 glass elements, relative to the corresponding externally measured curvature (Rglass:air). Data points and error bars represent mean percent deviation and standard deviation, respectively (n = 5). (d) Plots of the measured thicknesses (Tmeas) and (e) corresponding errors relative to the manufacturer specification (Tspec). Manufacturer tolerances were ±1% for radius and ±200 µm for thickness.