A planar microlens with N.A. = 0.54 has been obtained (Δn = 0.27) by stacking two lenses. The maximally obtainable N.A. is then expected to be ~0.7 but it is limited by aberration, which is discussed theoretically using a Luneburg lens model.
© 1984 Optical Society of America
Shigeyoshi Misawa, Masahiro Oikawa, and Kenichi Iga, "Maximum and effective numerical apertures of a planar microlens," Appl. Opt. 23, 1784-1786 (1984)