English: (A,B) Analytical “design curves” for normalized optimal aperture radius (nOAR) and optimal resolution (RES) versus magnification (MAG) over index of refraction (range 1.33–1.91) and ball lens radius (range 40–1200 µm). (C) Comparison of analytical (3D surface) and numerical (plotted as points) results for RES versus index of refraction and ball lens radius. (D) Modulus of the Optical Transfer Function (MTF) over the optimal field of view for a 300 µm sapphire lens with optimal aperture. (E,F) Image of USAF 1951 resolution target taken with 430X ball lens, including an enlarged caption of Group 9, and an intensity profile plot along path denoted by green line in image caption. This demonstrates resolvability for Group 9, Element 4 corresponding to 724 Line Pairs/mm or 1.38 µm resolution. (G,H) Image of USAF 1951 resolution target taken with 140X ball lens, including an enlarged caption of Group 8, and an intensity profile plot along path denoted by green line in image caption. This demonstrates resolvability for Group 8, Element 6 corresponding to 456 Line Pairs/mm or 2.19 µm resolution. The data was taken using GUPPY Pro 503C scientific camera, with 2592×1944 pixels and pixel size 2.2×2.2 µm2.